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Institut international de chimie Solvay (1956). Quelques problèmes de chimie minérale: rapports et discussions : dixième Conseil de la chimie tenu à l'Université de Bruxelles du 22 au 26 mai 1956. Bruxelles: R. Stoops. Disponible à / Available at permalink :

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INSTITUT INTERNATIONAL DE CHIMIE SOLVAY DIXIÈME CONSEIL DE CHIMIE tenu à l’Université de Bruxelles du 22 au 26 mai 1956

QUELQUES PROBLÈMES DE

CHIMIE MINÉRALE RAPPORTS ET DISCUSSIONS publiés par les Secrétaires du Conseil sous les auspices du Comité Scientifique de l’Institut

R. STOOPS Editeur 76-78, COUDENBERQ, BRUXELLES 1956

INSTITUT INTERNATIONAL DE CHIMIE SOLVAY DIXIÈME CONSEIL DE CHIMIE tenu à l’Université de Bruxelles du 22 au 26 mai 1956

QUELQUES PROBLEMES DE

CHIMIE MINÉRALE RAPPORTS ET DISCUSSIONS publiés par les Secrétaires du Conseil sous les auspices du Comité Scientifique de l’Institut

R. STOOPS Editeur 76-78, COUDENBERG, BRUXELLES

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V.

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INTRODUCTION

Institut International de Chimie Solvay EXTRAIT DES STATUTS. Article premier. — Il a été fondé, à Bruxelles, à l’initiative de M. Ernest SOLVAY et pour une période de trente années, à partir du 1®’' mai 1913, un Institut International de Chimie. La durée avait été prorogée jusqu’en 1949. Après le décès de M. Ernest Solvay, survenu le 26 mai 1922, M™ Ernest Solvay et ses enfants ont désiré assurer l’avenir de l’institut pour un temps plus long que celui qui avait été prévu. Dans ce but, une convention a été conclue entre les prénommés et l’Université de Bruxelles; en vertu de cette convention, l’avoir actuel de l’Institut est remis à l’Université en même temps que la somme nécessaire pour qu’à l’échéance prévue de 1949 le capital d’un million primitivement consacré par M. Ernest Solvay à l’Institut International de Chimie se trouve reconstitué. L’Université assumera la gestion de cette somme en se conformant à toutes les dispositions des présents statuts. Art. 2. — Le but de l’Institut est d’encourager des recherches qui soient de nature à étendre et surtout à approfondir la connais­ sance des phénomènes naturels à laquelle M. Ernest Solvay n’a cessé de s’intéresser. L’Institut a principalement en vue les progrès de la Chimie, sans exclure cependant les problèmes appartenant à d’autres branches des sciences naturelles, pour autant, bien entendu, que ces problèmes se rattachent à la Chimie. Art. 3. — L’Institut International de Chimie a son siège social à l’Université Libre de Bruxelles, qui met à la disposition de l’Institut les locaux nécessaires à la tenue des Conseils de Chimie. Art. 4. — L’Institut est régi par une Commission Administrative comprenant cinq membres, belges de préférence, et par un Comité Scientifique international comprenant huit membres ordinaires

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auxquels peut être ajouté un membre extraordinaire ayant les mêmes droits qu’un membre ordinaire.

Art. 9. — Le Fondateur a manifesté le désir qu’avant tout, l’Institut fasse preuve dans tous ses actes d’une parfaite impartialité; qu’il encourage les recherches entreprises dans un véritable esprit scientifique, et d’autant plus que, à valeur égale, ces recherches auront un caractère plus objectif. Il lui a semblé désirable que cette tendance se reflétât dans la composition du Comité Scientifique. Par consé­ quent s’il y avait des savants qui, sans occuper une haute position officielle, pourraient être considérés, en raison de leur talent, comme de dignes représentants de la Science, ils ne devront pas être oubliés par ceux qui désigneront les candidats aux places vacantes.

COMPOSITION DE LA COMMISSION ADMINISTRATIVE

MM. J. BORDET, Professeur honoraire et membre du Conseil d’Administration de l’Université Libre de Bruxelles, Président. E. -J. SOLVAY, Gérant à la Société Solvay et Cie, membre du Conseil d’Administration de l’Université Libre de Bruxelles. P. HEGER-GILBERT, Professeur honoraire à l’Université Libre de Bruxelles. P. ERCULISSE, Professeur à l’Université Libre de Bruxelles. F. -H. van den DUNGEN, Professeur à l’Université Libre de Bruxelles, Secrétaire de la Commission administrative. R. LECLERCQ, Secrétaire de l’Université Libre de Bruxelles

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10® CONSEIL DE CHIMIE 22 au 26 mai 1956 LISTE DES PARTICIPANTS A. Le Comité Scientifique. MM. Paul KARRER, Prof, à TUniversité (Zürich), Président, (Excusé). H.-J. BACKER, Prof à la Rijksuniversiteit (Groningen). Ch. DUFRAISSE Prof au Collège de France (Paris), (Excusé). K. LINDERSTRÔM-LANG Directeur du Carlsberg Laboratorium (Copenhague), (Excusé). P. PASCAL Prof à la Sorbonne (Paris), (Excusé). Sir Robert ROBINSON Prof à l’Université (Oxford), (Excusé). A. R. UBBELHODE Prof à l’Imperial College of Science (Londres). H. WUYTS Prof honoraire à l’Université Libre de Bruxelles, secrétaire honoraire. Jean TIMMERMANS, Prof honoraire à l’Université Libre de Bruxelles, secrétaire. B. Les Membres rapporteurs. MM. Prof R. M. BARRER, Impérial College of Science, Departement of Chemistry, London. Prof. J. BENARD, Faculté des Sciences de Paris. R. COLLONGUES, Chef de Service au Centre d’Etudes de Chimie Métallurgique, Vitry s/Seine. Prof. H. FORESTIER, Directeur de l’Ecole Nationale Supérieure de Chimie, Strasbourg. Prof J. A. HEDVALL, Institut for Silikatkemisk Forskning, Chalmers University, Gôteborg. Dr. Klixbüll JÔRGENSEN, Denmarks Tekniske Hojskole, Copenhague. Dr. R. LINDNER, Institut for Silikatkemisk Forskning, Chalmers University, Gôteborg. Prof. R. S. NYHOLM, University College, Department of Chemistry, London. Dr. Leslie E. ORGEL, The Departement of Theoretical Chemistry, Cambridge, England. Dr. H. M. POWELL, Chemical Crystallography Laboratory, University Muséum, Oxford. Prof W. A. WEYL, Chairman, Division of Minerai Technology, Pennsylvania State University, University Park, PA.

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C.

Les Membres Invités.

MM. J. BJERRUM, Jr., Copenhague.

Dr.

Sc., Denmarks Tekniske H0jskole,

V. CAGLIOTI, Directeur de l’Institut de Chimie Générale et Inorganique, Université (Rome). J. CHATT, Dr. Sc., Akers Research Laboratories, Welwyn Herts. G.

CHAUDRON, Membre de l’Institut (Paris).

L.

D’OR, Professeur à l’Université (Liège).

G. HÂGG, Professeur à l’Université (Uppsala). W. KUHN, Professeur à l’Université (Bâle). W. SCHLENK, Dr. Sc., Ammoniak-Laboratorium der Badischen Anilin und Sodafabrik, Ludwigshafen.

D. M.

Les Membres Secrétaires.

J. TIMMERMANS, Professeur à l’Université Libre de Bruxelles, Secrétaire du Comité Scientifique de l’Institut.

M®ii« L. de BROUCKÈRE, Professeur à l’Université Libre de Bruxelles. MM. R. DEFAY, Professeur à l’Université Libre de Bruxelles. W. DE KEYSER, Professeur à l’Université Libre de Bruxelles. F. BOUILLON, Assistant à la Faculté des Sciences. I. LAFONTAINE, Licencié en Sciences Chimiques.

E.

Auditeurs Invités.

MM. DECROLY, DESCAMPS, ERCULISSE, GOLDFINGER, GUILLISSEN, PRIGOGINE, l’Université Libre de Bruxelles.

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FLAMACHE, Professeurs à

ACTIVITÉS DU DIXIEME CONSEIL Le dixième Conseil de Chimie Solvay s’est tenu à Bruxelles du 22 au 26 mai 1956 dans les locaux de l’Université Libre de Bruxelles. Les travaux ont été ouverts le mardi 22 à 10 heures. En l’absence du Prof. Karrer, souffrant, le Prof. Backer a prononcé une allo­ cution et la présidence du Conseil a été confiée au Prof. Ubbelohde. Le mercredi 23 à 17 h 30, les autorités universitaires ont reçu les membres du Conseil dans le bâtiment central de l’Université. Le vendredi 25, le banquet offert suivant la tradition par la famille Solvay et la Commission Administrative de l’Institut a réuni les membres du Conseil et les autorités universitaires. Au dessert, M. E.-J. Solvay qui présidait a donné la parole à M. De Groote, Président du Conseil d’Administration de l’Université, à M. Timmermans qui a lu une lettre du Prof Karrer et à M. Ubbelohde, Président du Conseil. Le samedi 26 à 12 h 30, le Conseil a terminé ses travaux par uns allocution du Prof. Hedvall. Mmes. Timmermans et Erculisse ont très aimablement guidé les dames qui accompagnaient les membres dans leurs visites de la Ville de Bruxelles et de ses environs.

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Message du Professeur P. Karrer Président du Comité Scientifique de l’Institut

Mesdames et Messieurs^

Des raisons de santé m'ont interdit de prendre part au Dixième Conseil de Chimie Solvay. Je le regrette profondément, mais je ne veux tout de même pas manquer de vous transmettre par la voix de M. le Prof. Timmermans avec mes compliments l'expression de mes remerciements les plus cordiaux. Nos remerciements vont tout par­ ticulièrement à la famille Solvay, au Gouvernement belge et à l'Uni­ versité Libre de Bruxelles qui a fondé l'Institut de Chimie Solvay et l'administre avec compétence. Nous ne manquerons pas d'y associer aussi les organisateurs de ce Dixième Conseil et tout spécialement M. le Prof, van den Dungen, secrétaire-administrateur, M. le Prof. Timmermans, secrétaire du Comité Scientifique et les membres secrétaires du Conseil. En tant que président. J'ai l'honneur d'appartenir au Comité Scientifique depuis 1947 et j'ai toujours trouvé l'appui le plus constant et le plus dévoué auprès des membres de ce Comité. Que mes collègues en soient remerciés une fois de plus. Aujourd'hui, j'ai le plaisir de transmettre cette présidence à mon successeur le Prof. Ubbelohde. Je suis heureux qu'il ait accepté cette charge et lui souhaite la réussite la plus complète à son nouveau poste. Nous sommes persuadés qu'il exercera ses fonctions avec compétence et succès. Depuis la fin de la deuxième guerre mondiale, il y a eu quatre Conseils de Chimie Solvay, en 1947, en 1950, en 1953, et en 1956. Le Septième Conseil de 1947 était consacré aux isotopes, le Huitième aux réactions d'oxydation, le Neuvième aux protéines et le Dixième aux combinaisons non stoechiométriques, aux sels complexes et à la réactivité des solides. Vous voyez combien le domaine scientifique auquel s'intéresse l'Institut International de Chimie Solvay est vaste. Malheureusement la biochimie manque à cet éventail coloré et ce

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sera peut-être la tâche d'un futur Conseil de Chimie Solvay d'y consa­ crer une rencontre, car je n'ai pas besoin de signaler ici l'importance capitale des processus chimiques dans le captivant mystère de la vie. Il est certain que de telles rencontres donnent une impulsion nouvelle à la recherche scientifique et que cette impulsion contribue à la réso­ lution de nombreux problèmes. On doit à Ernest Solvay, le fondateur de l'Institut de Chimie Solvay la maxime suivante : « La vérité sera la science ou elle ne sera pas ». Cette maxime exprime la foi iné­ branlable dans l'idéal de la science, seule capable d'ouvrir aux hommes les portes de la vérité, vérité n'acceptant ni maître, ni histoire mais seulement les résultats expérimentaux. Mais plus la science progresse et nous dévoile des secrets nouveaux et plus nous constatons qu'à elle seule elle ne peut apporter la paix et le bonheur à l'humanité. C'est encore à Ernest Solvay qu'on doit cette deuxième pensée sur la Société : « La Société est condamnée à la Justice sous peine de mort ». Là encore Ernest Solvay apparaît comme un homme sage et avisé, ayant étudié les fondements des communautés humaines et ayant dégagé d'un coup d'œil infaillible l'essentiel de ces fondements. La justice est le fondement de toute société', ce fait est malheureu­ sement trop souvent méconnu pour le plus grand dommage de la paix entre les hommes. A ces considérations sur la vérité et sur la justice on doit ajouter une troisième maxime ayant trait au bonheur et à la paix intérieure des hommes. Elle a été formulée par un ami des enfants et des hommes : Heinrich Pestalozzi : « Rien n'est plus profitable que l'amour voué à son prochain ». Sans l'amour du prochain il manque à la science et à la justice le fondement moral qui anoblit et embellit la vie. Science et justice sont deux formules froides n'apportant aux hommes bonheur et prospérité que revêtues du manteau de l'amour. Nous espérons que la science moderne qui a obtenu de si remarquables succès dans tous les domaines n'oubliera pas ce précepte et comprendra que seule son association avec l'amour du prochain donnera son plein sens à la destinée humaine. Et maintenant. Mesdames et Messieurs, je voudrais terminer ce court exposé en renouvelant une dernière fois mes remerciements les plus sincères à toutes les personnes ici présentes.

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Discours de M. P. De Groote Président du Comité d’Administration de l’Université Libre de Bruxelles

BANQUET DU DIXIEME CONSEIL DE CHIMIE SOLVAY du vendredi 25 mai 1956 au Métropole

Mesdames et Messieurs, Il est de tradition que le Président de /’ Université Libre de Bruxelles prenne la parole au cours du dîner qui accompagne chacune des sessions des Conseils Internationaux Solvay. Je tiens à vous dire tout le prix que l'Université et moi-même, nous accordons à ce privilège qui donne l'occasion de vous exprimer nos sentiments et qui nous permet de remplir à l'égard de votre Institution nos devoirs de très sincère gratitude. Vos travaux se développent sous le signe de l'objectivité et de la concision. Je ne dérogerai pas à cette règle, en ce qui me concerne, et je serai donc bref dans mes propos. Je m'incline, tout d'abord, devant la mémoire d'Ernest Solvay, qui, en créant les Conseil Internationaux, a servi la science de façon particuliè­ rement féconde et distinguée. Le hasard de mes lectures m'a fait connaître, il y a quatre jours à peine, le texte d'une lettre adressée par le Roi Albert à Ernest Solvay. J'en extrais le passage suivant : Je saisis cette circonstance pour vous adresser encore mes félicitations particulièrement chaleureuses à l'occasion de la récente fondation de l'Institut International des Sciences. Vous avez donné là un magni­ fique exemple en consacrant des sommes aussi importantes à l'établis­ sement d'un véritable budget du progrès scientifique. Quant à moi (continue le Roi) je suis flatté d'être associé à une œuvre qui sert le bien de l'humanité et dont le succès est assuré par la valeur incontestée des hommes que vous avez appelés à concourir à la réalisation de votre remarquable initiative. » Cette lettre porte la date du 8 octobre 1912.

Reportées à l'époque de la fondation des Conseils de Chimie et de Physique, les idées maîtresses des conceptions d'Ernest Solvay frappent par leur caractère original et leur parfaite appréciation des besoins ultérieurs des sciences en expension. Elles sont marquées de compréhension de l'homme et d'espoir dans les fonctions dévolues aux élites. Confrontées, à quarante ans de distance, avec la réalité présente, la pensée du fondateur apparaît dans toute sa vigueur, son à-propos et son opportunité durable. Elle porte cette marque particulière du génie créateur qui fait durer les choses. Je prie Monsieur Solvay qui préside ce banquet, de recevoir l'expression de la déférente estime dans laquelle nous tous, nous resterons tenir la mémoire de son illustre grand-père. Je m'adresse maintenant, aux membres du Conseil International de Chimie Solvay qui participent aux travaux de la présente session Vos réunions se placent au niveau scientifique le plus élevé; elles réalisent, marquent ou précisent les étapes des progrès accomplis dans votre spécialité. Tout le monde de la science vous en sait gré et formule le vœu cordial de voir se poursuivre les activités de votre Institution dans la même fécondité, le même esprit et la même conscience. Il attend de vous, et c'est là une marque de confiance et d'égards, de nouveaux apports et de nouveaux enrichissements de notre patri­ moine intellectuel commun. Puis-je souligner que l'Université Libre de Bruxelles, intimement associée à l'organisation des Conseils Solvay, est votre lieu de réunion et votre foyer, qu'elle s'enorgueillit de la chose et que son désir demeure de se mettre à votre disposition pour vous apporter l'aide la plus complète et la plus appropriée. Si votre Conseil entrevoyait des voies nouvelles suivant lesquelles l'Université pourrait développer ou renforcer sa collaboration en vue d'alléger vos devoirs ou d'intensifier votre action, nous ne ménagerons aucun effort, je vous demande d'en être assurés, pour répondre à vos vœux. Messieurs, Vous accomplissez dans la poursuite de vos recherches et dans l'association de leurs résultats, au cours de sessions comme celles des Conseils Solvay, une fonction éminente que comprennent et qu'appré-

dent tous les hommes soudeux de faire prévaloir le bien commun sur les intérêts personnels. Vos activités se classent parmi les multiples manifestations de générosité humaine, parmi les cas de collaboration désintéressée que suscite la vie dans les domaines les plus divers. Mais à l'encontre des efforts visant aux réalisations sociales, politiques et internationales qui se développent à travers les écueils du verbalisme, des appréciations subjectives et de l'appauvrissement des compromis inévitables vos travaux, eux, se situent sur le plan de l'objectif et du concret, se poursuivent dans un climat moins ingrat peut-être, mais combien plus rigoureux, où les opinions se nivellent devant la réalité des faits et où les progrès engagés sont mis généreusement à la disposition de la communauté, sans monopoles ni restrictions. Mais cette tâche qui est la vôtre et que vous accomplissez avec talent, revêt pour une large part sa pleine signification humaine du fait de sa continuité et de sa permanence, au-délà des personnalités particulières des savants qui se succèdent et se relaient. A cet égard puis-je évoquer devant vous un problème qui vous touche directement et qui suscite chez moi de réelles appréhensions pour l'avenir : le problème de l’insuffisance des moyens dont souffrent des universités de plus en plus nombreuses, spécialement en Europe. Vous qui êtes les artisans de la grande œuvre scientifique, vous comprenez mieux que quiconque l'angoisse montante que ressentent beaucoup d’établis­ sements d’enseignement supérieur devant le manque ou la médiocrité des ressources dont ils disposent et devant les difficultés et les res­ trictions qui découlent de cet état de fait. Et cependant, ce sont ces mêmes institutions qui assument la responsabilité d’initier les jeunes hommes de science, appelés à animer les laboratoires, les écoles, les services de l’administration et de l’industrie, dans leurs échelons les plus élevés, ce sont ces mêmes universités qui ont la charge de former ces hommes de science qui, si leur valeur les y destine, feront dans l’aboutissement de leur carrière votre relève en temps opportun. Bien sûr, la recherche scientifique suscite l’intérêt actif et la géné­ rosité des gouvernements et des mécènes, mais la tendance se manifeste de plus en plus de négliger dans ces soutiens, les besoins de base aux­ quels il doit être satisfait pour permettre la formation, par les universités, dans les meilleures conditions et dans le plus grand nombre, des jeunes hommes appelés à remplir des fonctions dans la recherche et l’ensei­

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gnement. Si le toit de l’édifice scientifique reçoit généralement l'attention qu’il mérite, il n’en est pas de même des fondations, et ces fondations risquent s’il n'est pas porté remède à la situation, de se désagréger faute de ressources appropriées. On pourrait croire dès lors que les garanties de disposer d’une pépinière adéquate de cher­ cheurs ne sont plus données. La parcimonie des moyens menace d’engendrer la médiocrité et de saper la fondation formative que les universités ont la charge d’accomplir. Les contacts nationaux et internationaux que l’accomplissement de mes charges me ménage, me portent à juger que le mal que J’évoque est très général et tend à s’étendre. C’est ce qui justifie pour moi l’appel que je vous adresse. Des groupes de savants tels que le vôtre ne doivent pas être des épisodes dans la grande élaboration de la science. Ces groupes doivent se perpétuer. C’est dans vos successeurs que vous vous survivrez et c’est donc dans les garanties de formation de successeurs dignes de vous que vous trouverez les as.<;urances de voir votre œuvre se poursuivre. Je vous demande de nous aider, partout où cela est nécessaire, à mener une action vigoureuse pour combattre le dépérissement ou la stagnation dont sont menacés les établissements d’enseignement supérieur. Je requiers l’appui de toute votre autorité morale dans cette action. La science ne poursuivra ses progrès que si l’armature universitaire qui l’étaie et qui l’alimente en hommes, demeure forte et vivante.

Mesdames et Messieurs, Je voudrais terminer cette intervention en saluant ceux des membres du Conseil que les circonstances ont empêché d’assister, partiellement ou totalement, à la présente session. Je remercie très cordialement M. le Prof. Backer qui, malgré son état déficient, a tenu à se rendre à l’appel du Conseil. Je formule aussi mes vœux de bon rétablissement pour M. Karrer, et mets la circonstance à profit pour vous signaler qu’au cours de sa dernière séance, le Conseil d’Administration de l’Université de Bruxelles a conféré à M. Karrer, le titre de Docteur honoris causa de la Faculté des Sciences.

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Discours de M. le Professeur Ubbelohde Président du Dixième Conseil

Mesdames et Messieurs, Vous venez d'écouter le message du Président du Conseil Scientifique de l'Institut Solvay. Nous regrettons tous que le Prof. Karrer n'ait pas pu être avec nous en personne. Je voudrais seulement ajouter quelques mots au sujet des travaux scientifiques du Dixième Conseil. Ne vous alarmez pas. Je dois toutefois vous avertir que les corps solides ne sont plus du tout aussi inchangeants et aussi impénétrables que l'on pensait anciennement. Surtout à des températures élevées, il y a des migrations très considérables des éléments de structure dans les solides. En utilisant une grande variété de techniques nouvelles, la chimie a fait d'importants progrès dans l'étude des défauts de struc­ tures dans les corps solides et, dans la découverte des réactions chimiques à l'état solide. Ces développements de la chimie sont à la fois de haut intérêt scientifique, et de grande importance industrielle. C'est un plaisir de voir parmi les membres de ce Dixième Conseil de grands pionniers dans ces recherches tels que le Prof. Hedvall et le Prof. Chaudron. Mais tous les membres du Conseil qu'ils soient anciens ou nouveaux chercheurs dans cette nouvelle branche de chimie, ont profité des discussions germinatives qui ont eu lieu. Comme l'a dit une fois Sir Lawrence Bragg, il y a des discussions qui donnent une brûlante envie de retourner immédiatement au laboratoire pour mettre des nouvelles idées à l'épreuve. Je crois pouvoir vous assurer que nos débats donneront un nouvel essor aux recherches dans la chimie des corps solides. Nous avons également discuté les complexes inorganiques qui sont d'intérêt grandissant pour la théorie de la liaison chimique. Très certainement il y a un grand avenir pour l'étude de ces composés dans la chimie et dans la biochimie. Tous les membres du Dixième Conseil apprécient l'organisation très ejficace du congrès-, cette organisation et l'hospitalité plénière, mais sans encombrements, a grandement aidé à soutenir nos discussions. Sans ce soutien, les débats auraient été durs à mener à bonne fin. Nous remercions les fondateurs de l'Institut Solvay, le Comité Administratif, et l'Université Libre de Bruxelles pour le privilège qui nous a été donné de faire partie de ce Dixième Conseil. Je pense pouvoir promettre que ses résultats seront aussi importants et aussi fructueux que ceux des conseils précédents. Encore une fois merci.

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Allocution de M. le Professeur Hedvall à la clôture du Conseil Solvay

Mesdames et Messieurs,

Ayant terminé nos discussions sur la multiplicité des problèmes de l’Etat Solide, nous désirons exprimer notre profonde et respectueuse gratitude à tous ceux qui se sont occupés des préparatifs de ce Dixième Conseil Solvay, qui nous ont permis d’effectuer un travail extrêmement constructif Nous réalisons l’ampleur de l’effort qu’il vous a fallu fournir pour organiser ce Conseil. Nous vous félicitons cordialement d’avoir obtenu ce « produit » d’une qualité extraordinaire de vos actions et réactions, catalysées, nous l’espérons, par des phases liquides dont vous avez eu la bonté de verser pendant nos plantureux déjeuners et dîners. Nous adressons nos remerciements à vous tous, mais nous sommes sûrs que vous n’objecterez pas que nous citions spécialement M. le Prof. Timmermans et M. le Prof. Ubbelohde. Celui-ci a dirigé, en tant que Président de notre assemblée, nos discussions avec une habilité et une capacité extraordinaire, profonde, amicale et circon­ stancielle. Vous tous, vous nous avez donné un « screening » parfait. Nos imperfections se sont transformées en un état à la fois stable et actif, et les forces d’affinité se sont extrêmement renforcées, fait qui, pour sûr, n’est pas un phénomène superficiel.

20

Physical Chemistry of some Non-Stoicheiometric Phases by R. M. BARRER

SUMMARY

A range of non-stoicheiometric phases has been classified and discussed, with particular reference to defect structures in which the defects take the form of included atoms or molécules. Systém­ atisation is possible in terms of the idea of a “ host ” lattice with “ guest ” molécules. Structural features of various host lattices hâve been indicated, including some new data on two remarkable crystalline zeolites, with cavities able to accommodate ~ 29 and ~ 32 water molécules respectively. The interprétation of occlusion or inclusion isotherms has been especially considered. These isotherms may be smooth curves, or they may hâve continuons régions separated by one or more steps. A general thermodynamic criterion for differentiating between continuons and discontinuons isotherms has been given, before proceeding to spécifie statistical thermodynamic interprétations. Particular attention has been paid to continuons occlusion isotherms in zeolites, and their quantitative interprétation. The standard entropy of occlusion for a successful isotherm model will fall in one or other of a sériés of entropy levels according to the degrees of freedom possessed by the occluded molécule. Partial molal entropies of the occluded molécules can be and hâve been employed to interpret the physical State of argon occluded within chabazite, and to obtain information regarding that of paraffins occluded within faujasite. The entropy fonction is shown to be of great usefulness in this direction.

21

1. In 1803 Berthollet published his “ Essai de Statique Chimique In it he expressed the opinion that the composition of a compound depended upon the conditions of its formation. This view drew the strongest opposition from Proust, whose work established the law of constant composition. Indeed for a long while the weight of Chemical evidence grew in favour of Proust. Nevertheless we now know that both Proust and Berthollet were correct, each up to a point. Compounds of variable composition are now the concern of different industries as well as of more academie scientists. With the development of the wave mechanics of the solid State, and by the application of statistical thermodynamics to heterogeneous and homogeneous equilibria between and within phases, much insight has been obtained into the properties of Berthollide com­ pounds. Classifications of Berthollide compounds are more a matter of convenience than of rigorous distinctions. However we may give two categories : (i) those showing small departures from stoicheiometry, (ii) those which may show gross departures from stoicheiometry^ In group (i) are a number of oxides (CU2O, NiO, ZnO, FeO), sulphides (Ag2S, PbS) and halides (NaCl, KCl, NaBr, KBr, AgCl, Agi), the compositions of which vary to a minor extent if concen­ trations of the anionic constituent, or on occasions of the cationic constituent, are maintained about the crystals (i). In this group we may also place a range of phases the non-stoicheiometry of which is associated with the introduction of small amounts of foreign atoms or ions (i). Examples are: NaCl.SCdCl2; AgC1.8CdCl2 ; AgBr.SAg2S; Ni0.SLi20; Gei_§Ga5; Gei_sAss; Al2_sCrs03. The quantity S of added impurity may become considérable in some of these phases. The second category of Berthollide compounds, exhibiting appréciable or large departures from stoicheiometry, is remarkably diverse both in range and in character. The following Systems are typical : (i)

Metallic and metalloid phases : a) Intermetallic alloys.

b) Interstitial phases 0 (H2 in Pd, Pt, Fe, Ni, Ce, Zr, Ti, Th, U; O2 in Zr, Ge, Ti; N2 in Fe; C in some transition metals).

22

c) Interlamellar phases 0 (graphite with alkali metals, Br2, F2, AICI3, FeClj, Cr02Cl2, Cr02F2, CUCI2, BCI3, Z1CI4, M0CI5, WCle, ICI3, etc.). (ii) Covalent Systems : a) pénétrants.

Interlamellar complexes of graphitic oxide (4) with organic

(iii) Ionie Systems : a) TiO, Pts, CrS, FeS, Fe203 (i). h) Layer lattice basic salts (5) (e. g. basic Zn salts with H2O, CH3OH, C2H5OH, C2H4(0H)2, CH3CN, C2H5CN, CH2OH.CHOH.CH2OH). c) Potassium benzene sulphonate (6) with H2S, H2O, NH3 and many organic species. (iv) Polymerised ionic Systems : a) Framework aluminosilicates exhibiting replacements (J) of types NaAl Si; Na ^ K; Al Ga; Si ^ Ge. b) Open Framework aluminosilicates with cavities (8) filled by neutral molécules (NH3, H2O, CO2, S, I2, hydrocarbons, hydro­ carbon dérivatives). c) Open Framework aluminosilicates (®) with cavities filled by ionic species (NaCl, KCl, HgCl2, BaCl2, BaBr2, Na2Sx, Na2C03, Na2S04, Na2Se04, etc.). d) Lamellar aluminosilicates such as montmorillonite (io-iO“) with inter-lamellar guest molécules (H2O, NH3, pyridine, CH3OH, C2H5OH, C2H4(0H)2 and many organic species). (v) Molecular Systems : a) Dianin’s compound (H) (4-p-OH-phenyl-2:2 ;4-trimethyl chroman) forms inclusion complexes with I2, SO2, and a very wide range of organic species. b) Urea and thio-urea form adducts (12) with many hydro­ carbons and organic compounds. c) Amylose, the straight chain fraction of starch forms complexes with I2, and some n-fatty acids and alcohols (i^).

23

d) Quinol forms clathrate compounds CH3OH, C2H2, CO2. e) Water forms clathrate compounds species (CH4, CH3CI, CH2CI2, C2H6).

with A, Kr, Xe, with simple organic

f) Schardinger’s dextrin forms adducts with I2, Br2, octanol, hexanol, trichlorethylene, p-nitrophenol, nitrosophenol and other species. Some molecular complexes appear to be nearly stoicheiometric (e.g. those formed by nickel cyanide ammonia with benzene, pyridine, quinoline, etc.). In any case the above list is not a detailed one. Much attention has been devoted to crystals showing small stoi­ cheiometric defect (1). Crystals may contain Schottky or Frenkel types of flaw; cation vacancies may be balanced electrically by an associated positive hole (e.g. a cation of higher valency); anion vacancies may be neutralised by the presence in them of an électron (F-centre) or pair of électrons (F'-centre); and the aggregation of F-centres may lead to the nucléation of a new phase. These and allied phenomena may govern the behaviour of semi-conductors; absorption and émission spectra of many crystals; and varions catalyses and solid State reactions. Many of the Systems in category two of Berthollide compounds hâve been little investigated from the quantitative aspect at least. This has been remedied more recently in the case of intracrystalline occlusion by zeolites (*“**). Considérable attention of a quantitative kind is moreover now being given to intercalation by clays (lO) and in varions molecular complexes At the same time much remains obscure, and an examination of some features of a few of the Systems in category two is more than opportune, and will be made in the présent paper.

2. The host lattice In many interstitial solid solutions, interlamellar complexes, inclusion complexes of three-dimensional crystalline silicates and molecular adducts it is appropriate to speak of a host lattice. This may be thought of as a continuons lattice within which a second

24

component is dispersed. In the water clathrate complexes (e.g. hydrocarbon hydrates) the water molécules are linked through hydrogen bonds into continuons Systems of cages (15). The three-dimensional structures are based upon a tetrahedral arrangement of hydrogen atoms around each oxygen atom, part of the two fondamental networks being shown in Fig. 1. The cages so enclosed hâve 12 and 14 (Fig. la) and 12 and 16 faces (Fig. \b) and are large enough to contain single guest molécules. Quinol (i"*“20), again by hydrogen bonding, forms two interpenetrating threedimensional networks, in which each oxygen atom is at the centre of three diverging bonds. The interpenetrating networks enclose cavities in which small molécules are located (Fig. 2). Dianin’s compound (H) forms a six-membered ring by hydrogen bonding with other molécules of the same substance, and produces the structural unit formalised in Fig. 3. This unit can be further formalised as an hour glass truncated at each end. The packing of such units to give the crystal now provides substantial cavities which enclose guest molécules of considérable dimensions and of great diversity. Non-stoicheiometric proportions may occur between the numbers of guest molécules and those of the molécules composing the host lattices because the latter may exist even when some of the cavities they enclose are empty. The concept of host lattice and of guest molécules is equally appropriate in the case of urea and thio-urea adducts (12) and of amylose ('3) complexes. Here the host lattice consists of a spiral arrangement of hydrogen-bonded urea or thio-urea molécules, or of coiled amylose chains (Fig. 4). The guest molécules then lie along the axes of these spirals. Stoicheiometry is not found even if ail the space along the axes of these spirals is occupied by the guest molécules, for the number of such molécules required dépends only on their length. This is illustrated in Fig. 5 in which the number of moles of urea binding a mole of hydrocarbon is plotted against the number of C-atoms in the n-paraffin Chain (2i). The simple linear relationship is clearly seen. The paraffins are of necessity extended in their intra-crystalline environ­ ment, because there is no room for other configurations. In thiourea adducts, the thiourea molécules are also linked to form rather wider spirals still, which can occlude some branched chain paraffins

25

(a)

(b)

Figs, la and 16. — The two kinds of cage structure found in water-clathrates, after von Stackelberg (15). Structure (a) is composed of 12 and 14 faced polyhedra; structure (6) of 12 and 16 faced polyhedra. Only the dodecahedra are shown above.

Fig. 2. — A model of the quinol clathrate structure (}*) containing atoms such as argon (after Wells « The Third Dimension in Chemistry », Oxford, 1956).

26

Fig. 3. — Formai représentation, due to Powell and Wetters (*i) of the spaceenclosing unit based on six molécules of Dianin’s compound.

Fig. 4. — The configuration of the amylose complex with iodine. molécules lie along amylose helices [Rundle and Baldwin (13)].

lodine

Fig. 5. — The dépendance of the composition of urea-paraffin adducts upon the Chain length of the parafifin [Cramer (i2), after Schlenk (i^)]. Ordinate ; Moles of urea binding a mole of hydrocarbon. Abscissa : Chain length of hydrocarbon.

27

and aromatics. The configurational restriction is still severe, but may be less marked for some molécules than in urea adducts. When we consider the open framework aluminosilicates such as felspathoids and zeolites the concept of host lattice and guest molé­ cules is particularly clear. A very sturdy anionic framework is often found enclosing cavities joined into continuous channels by common Windows (23). These channels cross other channels and very open frameworks then arise. The channel directions in several species are indicated without structural detail in Fig. 6 (24). (a)

(b)

Fig. 6. — Formai représentation of arrangement of channels in (a) analcite (b) chabazite and (c) cancrinite (normal to the place of the paper), [Barrer and Falconer (24)].

Framework aluminosilicates are based ultimately upon the tetrahedral (Al,Si)04 unit. However structural considérations of nets of tetrahedra can be much simplified for some open frameworks in the following way. The primary building units may be assembled to give secondary polyhedral building units, which can then be stacked in different ways in different co-ordinations. Fig. 7 (25) illustrâtes part of a polyhedron so formed. The complété polyhedron

28

comprises eight rings of six tetrahedra and six rings of four tetrahedra and is a truncated octahedron. This unit has proved of great interest in aluminosilicate structures. We hâve found only three ways of assembling them, and hâve realised each in varions synthèses. The résultant structures provide remarkable frameworks capable of forming non-stoicheiometric phases in great numbers. In each framework every 0-atom is joined to each of two Si-atoms or to one Si- and one Al-atom. In the first structural type the polyhedra are stacked in 8-fold co-ordination, by the sharing of the 8 X six-membered rings of a given central polyhedron with eight other polyhedra, one six-ring between each two polyhedra. The spatial arrangement is shown in Fig. 8, and is found in the following minerais : Felspathoids : Sodalite Nosean Ultramarine

Zeolites : Chabazite Gmelinite (?)

In the felspathoids each polyhedron (or cage) contains amounts of salts (Na2Sa;, NaCl, Na2S04, Na2C03, NaOH, H2O) in somewhat variable proportions. The zeolites contain water. The frameworks are capable of some distortion, so that the crystal symmetries may vary. We hâve synthesised nearly ail the above crystals and a number of variants on them. In the second structural type the same polyhedra are stacked in 6-fold co-ordination, by union of each of their 6 X four membered rings with one such ring in another polyhedron. This union occurs through oxygen bridges as formalised below :

This mode of linking créâtes additional very small cages. However arranging the original polyhedra in this manner also encloses super-

29

Fig. 7. — The structural polyhedron of importance in Figs. 8 and 9 and 10. It is a truncated octahedron with 14 faces.

Fig. 8. — The structural units of Fig. 7 are stacked in 8-fold co-ordination to give a framework of chabazite type (P).

30

Fig. 9. — The structural units of Fig. 7 are stacked in 6-fold co-ordination to give the framework of a synthetic zeolite (26).

Fig. 10. — A third packing of the polyhedra of Fig. 7 to give a very open network characteristic of faujasite (2t).

31

cages. The framework is shown in Fig. 9, and has been realised in a synthetic zeolite without natural counterpart. In the third structural type (27) the polyhedra are stacked in 4-fold co-ordination, by union through oxygen bridges of four of the 8 X six-membered rings of a central polyhedron to one such ring in each of four other polyhedra :

This arrangement of the large polyhedra thus créâtes the additional small cages represented above. The large polyhedra are arranged like the atoms in diamond, and they enclose very large supercages indeed. This framework is shown in Fig. 10, and we hâve synthesised it in the form of faujasite-like crystals. In Table I are given some characteristics of the crystals of the three structural types. The free diameters in column 3 are derived from the volumes of water which may be removed from the watersaturated crystals. It is further assumed that this water occupies the largest cavities only. The interstitial volumes in Column 7 are experimental values; and the numbers of molécules needed to saturate the largest cages (Column 6) are derived assuming only these cages to be filled. In chabazite, only one type of cage occurs; in the other two structures there are independent reasons for assuming only the larger cavities to be available, with the possible exception of water. Interstitial cations occupy positions in the cages, and it must be emphasised that the accessibility of cages to diffusing molécules may be influenced and even dominated by the situation of the cations. The faujasite lattice is thermally stable, yet it is the most open structure yet discovered, within which CHj CHj large molécules like iso-octane (CH3 — C — CH2 — CH) CHj

32

CHj

can

diffuse with the greatest ease (28). These zeolites, and others, provide almost perfect examples of host lattices, with a wide range in openness and accessibility to diffusing molécules. As a final example of crystals acting as host lattices one may turn to an entirely different group of substances. Small non-metallic atoms such as hydrogen, oxygen, carbon and nitrogen may form interstitial solid solutions with a number of transition metals (2). The latter serve as host-lattices. In close-packed hexagonal or cubic crystals there are tetrahedral cavities, sometimes able to accommodate H atoms, and octahedral cavities, able to contain O, N and C atoms in some cases. Rundle (2) has shown that many interstitial carbides, oxides and nitrides hâve rock sait structures (Table II), but the siting of the interstitial atoms causes very little séparation of the métal atoms, which then remain almost in contact and close packed.

TABLE I Properties of open frameworks formed by stacking the cages of Fig. 7.

Unit cell edge AO

Free diameter of largest cage in A®

Type of window joining largest cagesinto channels

l.(Fig.8) Chabazite, Ca-form

9.5

~ 7.3

6-membered rings (eight in number)

n-paraffins (Crosssectional diameter ~4.9 AO)

6-7 ~3

H2O A, N2 or O2

0.46

2. (Fig. 9) Synthetic zeolite, Ca-form

12.27

~11.8

8-membered rings (six in number)

n-paraffins

~29 H2O 12-14 A, N2 or O2

0.46

3.(Fig.lO) Synthetic faujasite, Na-form

24.8

~12

12-member- n-, iso-, and neoed rings (four paraffins and aromin number) atics readily occluded. Largest molécule not determined.

~32 17-19 ~4.5 ~3.5 '—'2.8

0.53

structural type

Largest molécules admitted to dehydrated crystals

Nos. of molécules needed to fill the largest cages

Interstitial volume in cm3 per cm3 of crystal

H2O A, N2 or O2 n-CsHu n-C7H,6 iso-CsHis

33

TABLE II Metal-metal distances in metals and in interstitial phases. Distances between Métal atoms (in AO) Element Métal

Carbide

Sc La Ce Pr Nd Ti Zr Th V Cb

3.20 3.75 3.64 3.64 3.64 2.93 3.19 3.59 2.63 2.85

Ta Cr

2.85 (A2) 2.71 (A2)

3.14 (Bl)

Mo W

2.72 (A2.A3) 2.74 (A2)

2.90 (Hex) 2.91 (Hex)

AI A2 A3 B1 Hex

(Al) (Al) (Al) (A3) (A3) (A3) (A3) (Al) (A2) (A2)

— — — —

3.05 3.32 3.75 3.03 3.16

(Bl) (Bl) (Bl) (Bl) (Bl)



Nitride

3.14 3.73 3.54 3.65 3.64 2.99 3.27 3.68 2.92 3.12

(Bl) (Bl) (Bl) (Bl) (Bl) (Bl) (Bl) (Bl) (Bl) (Bl)

( 2.75 (Hex) f 2.93(?)(B1) 2.86 (Hex) 2.86 (Hex?)

Oxide

— — — —

2.99 (Bl) —

3.71(?)(B1) 2.91 (Bl) 2.96 (Bl) distorted) __

_

= cubic close packed = body centred cubic = hexagonal close packed = sodium chloride = hexagonal

3. Stability of host lattices It is usefui for some considérations of inclusion to recognise three degrees of stability (29) of the host lattices : (i) The host lattice becomes unstable as soon as the concentration of occluded guest molécules (or atoms) falls below a certain value (some complexes of potassium benzene sulphonate; clathrate compounds of quinol; hydrocarbon hydrates). (ii) The host lattice retains some structural features, but changes in others as guest molécules are progressively withdrawn. This is often found in layer lattice intercalation complexes of substances such as montmorillonite, graphite and graphite oxide. Thus Fig. 11 gives the c-spacing of montmorillonite (30) as intercalated water is progressively removed or added. Fig. 12 indi ates the way in which

34

it has been suggested (^i) that graphite bisulphate loses the interlamellar bisulphate ions. MOLECULES OF WATE/t PEA UNÏÏ CEU

Fig. 11. —

The one-dimensional swelling of montmorillonite on hydration (30).

X

»

»

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

K

X

X

X

X

X

X

Fig. 12. — Suggested step-wise mode of loss of sulphate from graphite bi­ sulphate (31).

(iii) The host lattice exists permanently whether intra-crystalline guest molécules are présent or absent. This is the case in some interstitial alloys (2) of, for example, hydrogen in transition metals, or of dilute nitrogen solutions in iron, or oxygen in Zr, and even, it has recently been reported, of Ge(2i“). It is also true of the robust framework zeolites and of the molecular crystal of Dianin’s compound (*i). These examples are merely illustrations drawn from diverse molecular and atomic architectures and involving varions types of bond between host lattice and guest molécule or atom.

35

4. Inclusion isotherms Equilibrium isotherms of amount included vj equilibrium pres­ sures can be measured by methods developed for studying adsorption of gases and vapours for ail Systems where the guest molécules are mobile within the host crystal and are volatile. These criteria are obeyed for many Systems (hydrogen in metals; gases and vapours in zeolites, montmorillonite, graphite). Inclusion isotherms of three kinds hâve been observed : (i) continuons curves (e.g. gases and vapours in zeolites (2*), ammonia, ethylamine or éthanol in potassium benzene sulphonate (®),

Fig. 13. — Typical continuons isotherms for intralamellar complexes of alkyl ammonium montmorillonite (lO).

36

hydrogen above a critical température in some transition metals, hydrocarbons between lamellae of alkyl ammonium montmorillonites (lO) (Fig. 13); (ii) isotherms showing a step (e.g. benzene in potassium benzene sulphonate (*5), methanol or éthanol in montmorillonite (^2) (Fig. 14) and hydrogen below a critical température in some transition metals (33) (Fig. 15); t«)

_

tw

40

1

/

/ /

-20

, NH.dt 325 K \

^•-'^“«3"K

O

I/ r

10 /

rtlativt ^rcMurt 14 2S 42 (e)

M

CH, OH rtiflift irisiitrc 0-2 0-4 0-6 OB (O

1

(CH,), COH «1 323* K

jf

to *^60 ;4o

C.H.OH «t 323’K

^____

“20

L/^ 0-2

'

(V4 0-6 0* rtlitlvt ^rtiiuri 240

PyrHltc II

323* K

0*2 0*4 06 0-8 rilltlvt ^riuurt (1) H,0

y

«I 323*K

/y

,___________________y * 4C 20

/

1 0-2

0-4

rtlfllii

Fig. 14. —

0-6

0’8

0-2

0 4

0-6

0-4

^rtsiurt

Typical isotherms for polar sorbates (32) in montmorillonite. © = adsorption points ; x = desorption points.

(iii) isotherms showing two steps (e.g. water in potassium benzene sulphonate (6) and in montmorillonite (32) (Fig. 14), sulphur in PtS-PtS2 phases (34) and hydrogen in O-Zr (35). When isotherms exhibit steps these are often associated with perceptible and sharp lattice changes. In other Systems however lattices changes are not associated with obvious isotherm discon-

37

Fig. 15. —

Stepwise isotherms for occlusion of hydrogen by zirconium métal (39).

tinuities, and the question arises as to when structural or other changes are associated with isotherm steps and when they are not. A thermodynamic criterion of the condition for stepwise or for continuons isotherms may be given as follows (3^). We consider a System such as "b

B

where A dénotés a mole of the guest molécules and B a comparable amount of the host lattice. A fraction x of the mole of A is gaseous (or dissolved in an inert solvent) and a fraction (1 —x) is included in the host lattice. Suppose the Gibbs free energies, G, of the System for different values of x are plotted as a function of température, T, and lie as in Fig. 16a so that the Crossing points for decreasing x move from left to right. Then the envelope of lowest free energy corresponding to the stable State of the System touches each G — T curve at a single point only. As T rises x decreases continuously giving a continuons isobar (Fig. 16c). On the other hand if the Crossing points of the G — T curves for decreasing values of x move from right to left as in Fig. 16b, the curve of lowest free energy consists of two linear sections meeting

38

Fig. 16o and 166, illustrating the thermodynamic requirement to obtain isobars which are continuous (Fig. 16c) or show a step (Fig.l6(^). Figs 16e and 16/ show the way in which isobars with steps lead to isotherms with steps.

at a critical température Te. In Fig. \6h x changes discontinuously from 0.8 to 0.2 at Te. The isobar is now stepwise (Fig. 16 d). Combinations of both types of behaviour may occur and régions of isobars both continuous and discontinuons then arise. Moreover a sériés of isobars will be obtained at a sequence of pressures P\
39

isotherms and outline models which give continuons régions separated by one or more discontinuities. It is also convenient not to calculate families of G — T curves for different pressures and thence find the isotherms, but instead to dérivé the isotherms directly. Three approaches hâve been developed. The first is that of Lâcher (33), used for the interprétation of isotherms of hydrogen in palladium which show a single step below a critical température, Te. The interstices in the Pd-lattice constitute sorption sites in the Langmuir sense, but distributed through the métal crystals instead of being confined to the surface. If there is no interaction between hydrogen atoms in these interstices then for a fraction 6 occupied

would define the equilibiium, K being a constant which can be evaluated by the statistical thermodynamic method. No isotherm step could then occur. However Lâcher made the additional assumption that when two interstitial hydrogen atoms occupy adjacent

2w

2

sites there is an exothermal interaction, — (the factor —

being

included for convenience and Z being the co-ordination number of a site). The number of pairs of adjacent H-atoms is approxZN2 .0 0(1—0)x imately exactly ZN(^-------- ^ i )' where

? - {> - "“<' - ®)(' N is the number of H-atoms in interstices, and N« is the saturation number of interstices. One may treat the interstitial H-atoms as oscillators and evaluate their partition fonction and hence their Chemical potential. This can be equated at equilibrium to the Chemical potential of gaseous H-atoms in equilibrium with molecular hydrogen. The isotherm équation then is p2 = K -j------- K exp 1 O KV

^

0

2

(approximate treatment)

20

= ^^7r^rëj-(p +7^)

40

5.2

Z treatment)

5.3

where the constants K are evaluated explicitly in the treatment and where p dénotés the pressure of molecular gaseous hydrogen. These équations hâve an interesting property. Provided w < 0 (exothermal interaction of adjacent H-atoms) there is a critical w W température Te = —■ — for eq. 5.2 and — kZln Z — 2 w for eq. 5.3, for which with Z = 6, Te 2.43-t • At températures below Te compositions near 6 = 0.5 are metastable and the solid phase splits into two phases with concentrations of hydrogen symmetrically related to 0 = V2- Above but near Te the isotherms show an inflection but no discontinuity while as w — grows smaller the idéal Langmuir isotherm is more and more K J. nearly approached. Lâcher (33) was able to fit eq. 5.2 successfully to the experimental data of Sieverts (37) and of Gillespie (3*). Lacher’s approach is essentially a treatment of a defect structure, the lattice defects being interstitial hydrogen atoms with the spécial property of interacting with one another. This treatment was taken further by Rees (i). He also started with a host lattice of A and treated ail entering atoms. B, up to the limiting composition AB« as interstitial atoms. The host lattice was supposed to remain unaltered during this process and the spécifie treatment envisaged three phases A, AB and AB2. The occupation of one site per A atom by B atoms was supposed to produce a second kind of site. Thus the physical situation recalls that in the BET adsorption iso­ therm limited to the growth of two layers. However, unlike the BET isotherm interaction energies between pairs of B atoms were considered. The terminology used was N

= no. of A atoms in the crystal;

N“ = no. of sites of the first kind occupied; N* = no. of sites of the second kind occupied; — E“ = energy of a B atom in a site of the first kind, in its lowest quantum State relative to a free B atom in the gas phase;

41

— E*" = the corresponding energy of a B atom in a site of the second kind; 2E“« —^— = interaction energy of a pair of adjacent B atoms in sites of the first kind; 2E'"’ —^— = this energy for sites of the second kind. Interaction between occupied sites of the first and second kind is included in the energy différence E*— E®, so that cross terms E®* need not be considered. The approximate values were used for the number of pairs on sites of the first and second kind respectively : _

z„ (N“)2 2N

N66 =

Z6(N»)2 2N®

The same method of approach as used by Lâcher (22) then gives for the isotherms 1 p2

exp —

= Ka

1

QbjQa

= Kft

1 — 0î>/0®

exp —

2 0a E®® ~Tf 2 (e«>/e®) E**

^T

where K« and K6 were evaluated explicitly and 0® =

5.4

5.5 N® /N;

06 = The résultant isotherm shows two steps, separated by continuously varying compositions (Fig. 17). This treatment has been applied by Martin and Rees (29) to the H2 — Zr System (Fig. 15). However one of the two critical températures must here be assumed low and the critical pressure to fall below the experimental pressure range. An interesting point in the general treatment is that it appears possible to pass from one structure to another which may be of different symmetry without a change of phase, provided one is above the critical température Te. This happens because the disordered parent lattice A with, for example, 33 % of interstitial atoms

42

Fig. 17. — Construction of complété isotherm from component isotherms [Rees (1)].

of B is indistinguishable from the disordered lattice of AB of dif­ ferent symmetry containing 50 % vacant B sites. Above the critical températures of the two phase régions there is no phase change in passing from A to AB to AB2. Also if T > T“, T*, the two critical températures, then the disorder is such that no distinction arises between the two kinds of B-atom site. Another point made is that if one introduces holes into the lattice of A atoms by removing A atoms from the interior to the surface of the crystal of A then the number of interstices suitable for occupancy by B atoms may be reduced. If the number of such Schottky defects in the A lattice is large, and since their number will normally increase as température rises, it could follow that the saturation content of B atoms in the A crystal decreases as the température rises. This argument has also been used in a discussion of the H2 — Zr System. The most difficult part of the above treatment perhaps lies in envisaging how the introduction of a B-atom into an “a” type site créâtes a “b” type site not previously there. There is a third treatment of isotherms exhibiting discontinuities, however, which is very general, and which was developed by Anderson (34). He was concerned with the conditions for co-existence of holes and of interstitial defects in the lattice of one of the component ions or atoms of a two component System. As is always necessary for

43

discontinuous isotherms he again postulated an exothermic inter­ action between defects of the same kind. If N* and dénoté respectively the numbers of holes vacated by atoms A and of interstitial A atoms in the crystal AB bathed in the diatomic gaseous species, A2, then the number of pairs of holes and of interstitial atoms in juxtaposition are approximately

Thus, if

ali 2E‘

2E**

2Nb

2Nb

and are the interaction energies per pair, Za Zi then the total interaction energies are respectively

Nb



^ E«

Nb

Here Zi and Z* are the co-ordination numbers of interstitial A-atoms and of holes in the A-atom lattice. The usual statistical thermodynamic procedure then leads to the two équations Qh = K'a

= K'i

1 — e* e*

1



6‘

exp

exp

26* E** kT

20< E« kT

5.6

5.7

where the constants K'a, K'j are evaluated specifically in the dériv­ ation. If P 0 dénotés the pressure of A2 molécules at which the stoicheiometric composition AB exists in the crystal, then when Nb>N^ (AV/2 Vpo/

= Ka -

0*

0*

1

exp

20* E**

5.8

and when Ng < 0« \po/

1—

20< E«

5.9

where Ka and Kf are also evaluated specifically. Below critical _E*ft —E" températures TJ and T' , defined by T* = ^ and ^^ these isotherms each show a two phase région, just as in the case

44

of Lacher’s and Rees’s treatments. For any température T < T* , the limits of the homogeneous composition ranges are given by the pressures for 6* = 0.5 = 6'. Then Kft exp

. (P\l2\V2 kT ’ \ po /

K«exp—

5.10

Three cases may be visualised : <2) P\j2> Po\ P\i2 < Po- The stoicheiometric composition AB is stable, and the composition varies continuously on both sides of this composition before the upper and low'er two phase régions appear (Fig. 18a). b) Pij2 Pi/2In this case the stoicheiometric composition AB falls in the two phase région (Fig. 18è)

Fig. 18. — Isotherms illustrating possible behaviour of a System in the neighbourhood of a stoicheiometric composition AB [Rees (i)].

c) P\i2 < Pu2- No homogeneous range occurs in the neighbourhood of the stoicheiometric composition AB, and the two two-phase régions overlap (Fig. 18c). No crystal AB can exist. This situation is not physically possible, and in constructing isotherms the limiting condition must be = Pi/2> giving a curve with only one step. This treatment has been applied to the System Pt — PtS — PtS2 (^4). While Anderson has in this case considered non-stoicheiometry in terms of interstitial S and of S-vacancies, in some non-stoicheiom-

45

etric phases other defects are involved. For example S-TiO(NaCl-type) varies continuously in composition from TiO 135 to TiO g.eo. the variation being due to anion vacancies trapping électrons and to Ti++-cation vacancies trapping positive holes (Ti4+ ions). Even stoicheiometric TiO has 15 % unoccupied sites in each lattice (Table III). TABLE III Disorder in 8-TiO.

Composition

Ti sites occupied /o

TiO 1.33 TiO 1.25 TiO 1.12 TiO i.oo TiO 0.69

74 77 81 85 96

0

sites occupied %

98 96 91 85 66

There is a strong élément of similarity in the three treatments of Lâcher, Rees and Anderson for in ail these approaches the décisive factor in introducting steps into isotherms is the interaction between like defects, which may in turn be of several types.

6. Hystérésis If isotherms show discontinuities there is often marked hystérésis associated with a sorption-desorption cycle. Such behaviour has been established in hydrogen-transition métal alloys (H2—Pd, H2—U), in H2O, NH3, CH3OH, C2H30H-montmorillonite inclusion complexes (^2), in Br2-graphite (^o), or in H2O, CgHg, thiophen, toluene, xylene, naphthalene-potassium benzene sulphonate phases (^) (Fig. 19). The hystérésis phenomena hâve been attributed to the need to nucleate a second phase of host crystal and guest molécules on or in a parent phase. Suppose AG is the molar free energy for the reactions P^gas P^gas

46

^so/id ^n^soiid

^p^solid ^p+t^solid

Fig. 19. — Sorption isotherms for some aromatic hydrocarbons. a, benzene, b, scanning loop for benzene at 31.4 °C, c, toluene, d, o-xylene, e, O, #, o-xylene, 30.5 °C; A, x, p-xylene, 30.5 °C; □, m-xylene, 30.5 “C. /, naphthalene. [Barrer, Drake and Whittam (*)].

However, when a germ-nucleus of the new phase richer in A forms on or in a matrix of the parent phase poorer in A then two additional free energy terms are involved, each of which is positive in sign. These are associated with surface free energy (Ag^,) and with strain (Ags). Thus if the germ-nucleus comprising say i units ApB forms on or in the matrix of B the actual free energy formation of the germ is AG Agi = i-------- -1- Ag^ -t- Ag* No

6.1

47

At the true thermodynamic equilibrium point, AG = 0, but from 6.1, Agi is seen to be positive and so the germ-nucleus will not grow. However as the pressure of A grows, and the true thermodynamic equilibrium point is passed, AG becomes increasingly négative and reaction may set in. The further condition for this may be seen as follows. One may suppose that Ag^ = constant X area of germ-nucleus = Ai2/3, and that Agj = constant X volume of germ-nucleus = Bi. Thus . AG Agi = / 6.2 -t- Ai^'^ + Bi No If we plot Agi against i. Agi is at first positive, but as i increases it reaches a maximum value and thereafter decreases. Any germnucleus reaching this critical size will then develop spontaneously. At the maximum

^(AgO di

= 0 and so from eq. 6.2

Im ~ —

8A3

6.3

Through fluctuations there will be at first a steady State population of germ-nuclei of different sizes, but at pressures near the true thermodynamic equilibrium the number passing through the critical size im is negligible. As the pressure of A increases however the “ current ” of germ-nuclei exceeding the critical size rises very swiftly indeed, so that a threshold pressure is often found, below which the new phase does not appear and above which reaction is nearly complété. On the desorption branch exactly the same kind of considérations delay the formation of crystallites of say B in or on a matrix of ApB. Evidently then these considérations provide a very reasonable explanation of hystérésis, which may be made more realistic still when it is recalled that Ag, and Ag„ may dépend on the shape of

48

the germ-nuclei and their situation in the crystal (6). This means a spectrum of values of A and B, and the summation of groups of rectangular hystérésis loops which, as seen in Fig. 20, average to a sloping hystérésis loop such as is commonly observed.

Fig. 20a, 20b and 20c. — The addition of the group of isotherms of 20a showing rectangular hystérésis loops gives the résultant isotherms in dx

Fig. 20b. Fig. 20c then shows the curves of—^ against p for sorption dp and desorption branches («).

7. Non-stoicheiometric phases giving continuous isotherms We return now to consider continuous isotherms. The possibility of having non-interacting or only slightly interacting defects, the number of which varies according to the environment of the phase, is realised in a variety of Systems. If the empty host lattice is regarded as the parent structure, this lattice with the interstices partially filled with guest molécules or atoms is a defect structure. The equilibrium content of such molécules is normally determined by their concentration in the ambient atmosphère of gas or vapour. Some of these phases are non-stoicheiometric even when ail available interstices or cavities are filled, e.g. those formed by occlusion in

49

zeolites, or in certain alkyl ammonium ion exchanged forms of montmorillonite. These host lattices are stable in the complété absence of guest molécules. In other Systems the host lattice tolérâtes only a limited range of vacant cavities and if the content of guest molécules falls below this limit the host lattice décomposés, or at least becomes metastable (29). Examples include the quinol clathrate compounds and the hydro­ carbon hydrates. Van der Waals (4i) has discussed the true equilibrium occlusion isotherm in such Systems with particular reference to the clathrate compounds, and has concluded that it should resemble the Langmuir isotherm. While van der Waals has outlined a possible method of measuring occlusion equilibrium within a given quinol clathrate this type of System offers some spécial experimental difficulties. These arise because the guest molécules are locked into the cavities of the host lattice at the moment of formation and so from then on cannot establish any fresh equilibrium vapour pressure. The only way guest molécules can escape is through the décomposition of the complex. It may be that the stoicheiometric hydrates such as CUSO4.5H2O also tolerate a small number of defects in the form of vacant water positions, and that this defect structure permits diffusion of water molécules. Experiments on such aspects of stoicheiometric hydrates do not appear to hâve been made. If water can diffuse then these hydrates could be thought of as zeolitic structures in which only a minute range of guest molécule concentrations is possible without nucléation of a new phase.

8. Formulation of continuons inclusion isotherms We may formulate possible isotherms for Systems in which the whole eourse of the isotherm may be realised. From this viewpoint the occlusion of gases and vapours by certain of the robust framework zeolites, such as those described in Section 2, is of most significance, because the frameworks of the host lattices are virtually unchanged by the inclusion process, and because the high intracrystalline mobility of guest molécules enables réversible equilibria to be established readily and measured accurately.

50

If we regard the crystal framework as inert, and consider the transfer of a mole of gaseous sorbate from the gas phase where its activity is Ug to an infinité amount of the zeolitic solution where its activity is the free energy of transfer is AA = —RT In

+ RT /« — = —RT /« K + RT In — 8.1 \Pe)g

Og

dg

In this expression (ae)^, i,Oe)g are respectively the activities of occluded and of gaseous sorbate and K is the equilibrium constant. If a^= üg = 1, then AA = AA<> = — RT In K, where AA^ is the standard free energy of sorption, and K = ,——. i^e)g

In an equilibrium System, AA = 0, and so \Lg = where p, dénotés the Chemical potential. For the gaseous sorbate V-9 _ , kl

P kl

In

(27imkl)H2

InJil)

Â3

8.2

for molécules of mass m at a pressure p. JÇT) is the partition fonction for rotations, vibrations and electronic States of the molécule. The Chemical potential, pz’ *he intracrystalline molécules can only be defined if a model for the sorbed State is available. The whole intracrystalline volume Vi may for example be regarded as composed of N« equal sites each able to accommodate one sorbate molécule, and that the situation corresponds to localised sorption as in Langmuir’s isotherm. Then (33-i9)

kl

= /„

_____L'

" Ll — 0

8.3

a(T).

where 0 is the fraction of sites occupied and a(T) dénotés the partition fonction for a sorbed molécule including its degrees of freedom relative to its intracrystalline environment. The equilibrium con­ dition then gives 6

where

Ml - 0)

= Kl ; AAO

K, = kl

RT In

p{\ — 0)

{2nmkl)i/2 j(l) a{l) hi

0

8.4

8.5

51

We may test this relation by evaluating RT/«

p{\ - 0)

0

AAO,

and

plotting this quantity against 0. In this way it was shown (42) that Langmuir’s isotherm is only an approximate description of the equilibria between occluded n — C4H10, CaHg, C2H6 and H2 in chabazite for 0 < 0 < 0.30. Isotherms of C2H6 and of O2 in “ active analcite ” are in better agreement with the above model. The departures from the localised model may be due to the trend in sorption beat, AH, with 0, so that ail the sites are not homogeneous. Zeolites normally show the most marked change in AH with 0 when the values of 0 are not very great (42-43). We may accordingly re-examine the concept of localised sorption for large values of 0, when the trend in AH will be small and when the caging action of the molécules upon one another within the crystal framework further supports the idea of localisation. Table IV (28) gives p{\ - 0) for high densities of n-butane occluded by values of faujasite from which it is apparent that the concept of localised sorption while not quantitatively exact is a reasonable qualitative description of the situation for 0.89 < 0 < 0.98. We hâve observed similar qualitative agreement for other paraffins in faujasite in similar high concentration régions. TABLE IV Sorption of «-C4H10 in faujasite at 50“ C. P(\ - 0) 0

0

0.74 0.84 0.87s 0.894 0.90s 0.91s 0.94s 0.952 0.97o 0.984

0.21 0.43 0.59 0.70 0.84 0.92 0.93 1.20 1.06 0.73

At the same time localised sorption may not be true in the strict Langmuir sense of sorption on a constant number of fixed sites.

52

In faujasite n-paraffins and other sorbates behave like liquids near saturation of the sorption volume Vi (28). The number of molécules required to saturate this volume decreases as the molecular volume increases. The coefficient of thermal expansion of sorbed fluid is parallel with this coefficient for the liquid sorbate, and the amounts of a given sorbate required to fill Vj at different tempér­ atures are proportional to the densities of the liquid sorbates at the same températures. Attention has already been drawn to the large interstitial volume in faujasite, and to the exceptionally wide cavities (~ lôA^ free diameter) and the wide interconnecting Windows leading from any one cavity to each of four others (Table I). In faujasite, the synthetic zeolite of Table I, and chabazite we hâve three crystals with decreasing size of cavity and inter-connecting Windows. Ail three crystals however are open enough for the idea of localised sites in the strict Langmuir sense to be less easy to visualise. However this idea becomes physically very definite in the case of the interstitial hydrogen alloys of transition metals. A development of localised sorption, in which interaction occurs between adjacent pairs of occluded atoms or molécules, has already been referred to (eqs. 5.2 and 5.3). When sorption occurs without dissociation eq. 5.3 takes the form (44) ^2

p(l _ 6)

+ 1 _ 2q)

In the cavities found in chabazite three argon atoms may occur 2w (Table I), and so Z = 2. The interaction energy~ —240 cals per Avogadro number of interactions. Careful measurements of the beat of occlusion are able to demonstrate the reality of such inter-molecular potentials for simple gases in chabazite (Fig. 21). In faujasite and in the synthetic zeolite referred to in Table I, Z will exceed two, and the contribution due to self-potential of the occluded molécules may become greater. Other models also require careful examination for inclusion within such open structures as the zeolites. In these the occluded molécules are assumed to hâve translational degrees of freedom. One, two, or possibly, in exceptional structures such as faujasite, even three translational degrees of freedom might be envisaged, with the appropriate molecular co-length, co-area or co-volume

53

»\oiii/|mi| uoiidjot P 4D3H

Volume sorbed mi S.T.P. g’'

Fig. 21. —

Heats of sorption or argon in natural chabazite at 90 “K. Isosteric —

beat, 9st = Hg — Hs; run 9, 0; run 9d, •; run 96, <) ; run 9c, (>; intégral molar beat, (Hg — Hs), A .

[Garden, Kington and Laing (>8)].

Fig. 22. — Argon in natural cbabazite at 90.19 “K. Isotberm constants. Curve 1, mobile model; curve 2, mobile model witb interactions; curve 3, localized model; curve 4, localized model witb interactions (>*).

54

of the sorbate, corresponding to the Volmer équation of State. The isotherm then takes the form ("*5) K3

6 ~ p{\ — 6)

0 1 — 6

8.7

Finally, the interaction potential between sorbate molécules may be allowed for, by using an équation of State for the occluded sorbate which is a one, two or three dimensional analogue of van der Waals équation. In this case (“*6)

where a is a constant, and is a measure of the interaction potential. A careful examination of ail these forms of isotherm équation has been made by Kington et al for oxygen, argon and nitrogen at liquid air températures (i^). They used chabazite as sorbent, outgassed at 300 °C. The test was made by evaluating isotherms extremely carefully, making due correction for thermo-molecular pressures. From the experimental data the equilibrium constants were obtained. 2w Thus for argon, ~ = — 240 cals per Avogadro number of inter­ actions, Z = 2, and the saturation sorption was taken as 130 cm^ at N.T.P. per g. of chabazite. Finally, in the isotherm 8.8 a was taken as 1.0, corresponding approximately only to the above value 2vv of —. The values of Kj, K2, K3 and K4 are shown as fonctions of 0 in Fig. 22 (47). Quite clearly équation 8.7 gives easily the best représentation over a substantial range in 0, followed by eq. 88. The models corresponding to localised sorption (eqs. 8.4 and 8.6.) give an unsatisfactory description of the occlusion of argon. The foregoing probe into the State of the occluded guest molécules is a powerful one, which involves, however, the free energy relations of occlusion only. It is not possible on the basis of these relations to distinguish, for example, between the one, two or three translational degrees of freedom implied in the isotherm équations 8.7 and 8.8. A more délicate procedure which permits this requires the évaluation of the entropy of the occluded molécules and the spécifie interprétation of this in terms of conligurational and thermal entropy contributions. This method will be developed subsequently. We may first give spécifie évaluations of the equilibrium constants K.

55

9. Spécifie évaluations of equilibrium constants The equilibrium constant may be represented, whatever the degrees of freedom possessed by the included molécules, by the expression already given (Section 8, eq. 8.5). We now consider the values which may be taken by the partition fonction a(T). First the term exp — x/RT may be factorised from a(T), where x is the least energy required to remove a mole of sorbate from an infinité amount of zeolite + sorbate into the gas phase. Then K

9.1

Ja{l)

where y'a(T) is the partition fonction of the occluded molécule, for ail its internai degrees of freedom and for its degrees of freedom relative to its intracrystalline environment. One then obtains the results given in Table V (*), assuming that ail internai degrees of freedom of the guest molécule are unchanged by its inclusion. In Table V, T, V and R dénoté respectively a translational, a vibrational and a rotational degree of freedom. N's, N"s and N"'« in column 2 dénoté respectively the numbers of molécules required to fill completely 1 cm^, 1 cm^ or 1 cm of intracrystalline volume, area or length. V and v are vibration frequency or mean vibration frequency respectively. Ij, I2, I3 dénoté the three principal moments of inertia of the occluded molécule and S is its symmetry number. The values of x may be related to AH, the isosteric beat of sorption» obtained from the Clapeyron équation (^înp_\ = —9 2 V ST )a RT2 where the subscript “a” dénotés a constant amount occluded and — AH is the beat of desorption. We then hâve for the models (i) to (vii) inclusive of Table V (i) AH = -— X — RT (ii) AH = -— X — 1/2RT (iii) AH = -— X (iv) AH = -— X + 1/2RT (V) AH = -— X + RT (vi) AH = -— X + 3/2RT (vii) AH = -— X + 2RT (*) In the expressions in column 2 of this table, if p is expressed in cm of Hg, /t in the first termappearing throughout has the value 1.03 X

56

IO-20.

TABLE V Values of equilibrium constants for different degrees of freedom of sorbate.

Degrees of freedom of occluded molécule relative to its environment

(i)

3T, 3 R

(ii)

V, 2T, 3 R

(üi) 2V, T, 3 R

Equilibrium constants, K

Relevant isotherms

0 0 - pO - 6) “P I - 9

Tr TF 8 “P or 8 \ \ kT l "FF kj • 1F777 N"' ■ F---2Trw • — -, exp ^-/ RT s

K4

-

6 0 p^, _ e, “P (, _ e

K

~

^ Pii - 0)

(iv) 3V, 3 R

(v)

4V, 2R

1 /^Ty/2 1 / kT y/2 kT ■ \2nm) -4 V

^ or

(vi) 5V, R

(vii) 6V

1 / kT y/2 1 kT 1 kT ■ \2nm) -5 8ti:3 ’ (Ii 12)^'^ 1 r kT ^y3/2 1 ^kT '^ili 1 , itT (271m) -6 (87:2) (I1I2I3)

^

^ S , 1/2

P

0 / 2-20 y p(l — 0) V|3 + 1 — 20/

“'O

Moreover, the standard entropy of sorption AS^ is given by S S/«K RT, and therefore for the ASO = -^(RT /« K) = R /« K oT ST seven models takes the value R

(H) S

,ii,)

as«

=

r;„[^.^.|L._1]

(,v) AS0=R/„[T(^)>«1] + 1/2 R V R

3/2 R (fih) 1

8 -

2R

V“ dll2l3/'^ “ Contained in the expressions for ASO is a requirement of a spread of entropy levels which should serve to characterise the (V, T, R) State of the occluded molécules (^^). The spread in entropy over the seven models was about 16 e.u. (*) for a molécule of molecular weight lôwith v = 6x10*2 sec~> and 1], I2 and I3 each equal to 10“29 e.g.s. units. An alternative method of investigating the degrees of freedom of occluded molécules has been developed by Kington and his co-workers (•*) and is outlined below. 10. Entropies of occluded molécules The isosteric beat of sorption, AH, may be determined either by direct calorimetry or from the change in equilibrium pressure ^S In p\ AH The isosteric beat of sorpwith température RT2. ST /a tion is however given by AH = H. — H,

10.1

(*) In the original paper the terms Nj were omitted from (i), (ii) and (iii). This was corrected later.

58

where Hs is the partial molal enthalpy of occluded molécules and H g is the intégral molal enthalpy of these molécules in the gas phase. From AH one may obtain an entropy of occlusion of the guest molécules :

AS =

= S,10.2

where and S* are the molal entropy of the guest molécules in the gas phase and their partial molal entropy in the host crystals respectively. Sÿ is the entropy at the pressure p.

Referred to the

entropy So^ at a standard pressure, /?+, Si, = Sog + R In P^lp

10.3

Accordingly by combining (*) 10.1, 10.2 and 10.3

S« = Sog + R^ !p +

.p ■

10.4

The standard pressure, ;?+, for a gas is normally taken to be 1 atm. Fig. 23 shows the partial molal entropy, S«, of argon occluded in a natural Ca-rich chabazite at 90.19 °K, as a function of 0. The entropy decreases steadily with increasing 6 over a wide range in the values of 0. We now express Ss as the sum of two terms :

Ss = Sc -f-

10.5

where Sc is the partial molal configurational entropy of the intracrystalline guest molécules which hâve undergone localised occlusion and S^h is their differential thermal entropy. In the case of guest molécules possessing one or two translational degrees of freedom in their intracrystalline environment.

and

Sfi — jSj + S-pj,

10.6

Sg = 2^T

10.7

^Th

(*) Should correction for non-ideality of the gas be required we subtract a _ 27 R term a.p from the above expression for Sj, where approximately, a = ° . Pc 32rc1^ and Te are respectively the critical température and pressure.

59

a\ O TABLE VI

Isotherm équation

Entropies Sc, iSt, 2St

eq. 8.4 . Kj -

eq 86- K, eq. 8.Ô . K2

eq. 8.7 : K, -

Sc-Rln^^ ~7 ü ® / _ 0) 0

K \

0

exp

and eq. 8.8 : K4 =

S

2 - 20 y ^ 1 _ 20 ;

0

2(1-0) y w (P-1 + 20) (,p + 1 _ 20; + T P

5 _ P 7, ri2^mkTŸ'" (1 _ 0)-.

.

0

\ 0

exp

/

0

^

n0)

1

)

C _ P r27rm^T (1 _ 0)-, r ^^"L/72N"S 0 J + ^L^

0 -1 1-0J

Fig. 23. — Comparison of experimentally observed differential entropy Ss of argon in natural chabazite with differential translational entropy of mobile models with one and two degrees of translational freedom. Curve 1, exper­ imental Ss; curve 2 ,287 ; curve 3, iSt ; curve 4, Ss— iSx (is).

where

and 2^r

the differential entropies of molécules posses-

sing one or two translational degrees of freedom respectively, and Sj^, Sjf, are the residual differential thermal entropies of these molécules. In Table VI are given Sc, iSy and 28^ relevant to the appropriate isotherms 8.4, 8.6, 8.7 and 8.8. Now the test already carried out in which Kl, K2, Kj and K4 were computed from experimental data and plotted as a function of the amount of argon occluded (Fig. 22) has already shown that isotherm équation 8.7 is the appropriate one. Ail that is now to be settled is whether the occluded argon atoms possess one or two translational degrees of freedom. Fig. 23, in addition to the experimentally determined relation between S* and 0 (curve 1), also shows iSj and 28^ calculated from the formulae in Table VI, as function of 6 (respectively curves 3 and 2).

If we subtract iS^ and 287 from Ss we should, according

to eqs. 10.6 and 10.7 obtain Sj^ and the residual differential thermal entropies. These must be positive quantities, and in the range in 0 for which the sorption model is valid they should be constants independent of 6. In fact, when 287 is substracted from Sg the différ­ ence is a négative quantity so that the occluded argon cannot possess two translational degrees of freedom. On the other hand when

61

]Sj is subtracted from S* the différence is a positive quantity and is nearly constant at about 4 e.u. up to about 100 cm^ at S.T.P./g of occluded argon (curve 4). Argon therefore possesses one translational degree of freedom within the chabazite crystals. The quantity S* — is the vibrational entropy of argon relative to its intracrystalline environment. Since the atom possesses one translational degree of freedom, it must hâve two vibrational degrees of freedom : Sjj, = 2Sy ~ 4 e.u. For simple harmonie oscillations and for each vibrational degree of freedom

iSv = R Ke“ — l)-i — lti{\ — e-“)]

10.8

hV where u = —. Up to about 0 = 0.77, v ranges from 1.5 to K1 2.2 X 10*2 sec~i, which are physically reasonable values. The failure of the isotherm équation 8.7 above 0 = 0.77 was tentatively ascribed to a transition from mobile to localised sorption, due to caging action of the molécules of the denser intracrystalline argon fluid upon each other, as was also suggested for dense intracrystalline hydrocarbon fluids in faujasite. In this région of dense intracrystalline fluid, where Langmuir’s isotherm has been found to be reasonably valid (Table IV), partial molal entropies of paraffins hâve been obtained in faujasite (28). Table VII records such entropies, at 298°, and for 0 = 0.90 or 0.95.

TABLE VII Some entropies in faujasite at 298" K.

Paraffin

n-C4Hio iso-C4Hio n-CsHu iso-CsHia neo-CsHi2 n-CsHn n-CyHis iso-CsHig

62

0

0.9 0.9 0.95 0.95 0.95 0.95 0.95 0.95

si

S, (e.u.)

Sth (e.u.)

(e.u.)

32.2 27.6 33.4 29.7 31.5 39.1 44.6 44.5

38.6 32.0 39.3 34.6 37.4 45.0 50.5 50.4

53.9 51.3 63.5 63.1 53.7 70.5 77.9 79.7

Si — Sxh (e.u.)

15.3 19.3 24.2 28.5 16.3 24.5 27.4

29.3

(1-0) From the values of S« one may subtract Sc = R/n —^— , the differential configurational entropy, which is •— 4.4 and — 5.9 e.u. at 6 = 0.9 and 0.95 respectively.

of Column 4.

This gives the thermal entropies In Column 5 are given the molar entropies of the

liquid paraffins, and in the last column is recorded (Si — Sjj,), a quantity of particular interest.

Si = iSc + iS^-h where iSc and

the molal configurational and thermal entropies of the liquid. According to Slater (^8) the value of iSc should be small (-~0.33 e.u. in a typical case). Thus the thermal entropy of the liquid exceeds that of the occluded molécules by a substantial amount (*). This indicates that at 0 = 0.9 or 0.95 molecular freedom is much restricted. This is reasonable in view of the rigid anionic framework closely surrounding each small cluster of hydrocarbon molécules (cf. next section).

11. Inclusion of long-chain molécules Occlusion of n-paraffins up to n-heptane has been followed in chabazite ('t^) and up to n-octane in faujasite (28), while it has been noted that a synrhetic zeolite occludes tetradecane (^f). Very longchain molécules, through segmentai rotation, may assume many configurations in the gas phase which would not be possible in the confinement of the intracrystalline channels and cavities. Accordingly, losses in entropy can be expected in addition to any considered in the previous section. No fully quantitative treatment of the configurational restraints is possible, but the order of magnitude of the entropy changes associated with them may be estimated (86). We assume long flexible chain molécules closely sheathed by intra­ crystalline channels, and so restricted to stretched out configurations. We may let = the greatest possible distance between the terminal carbon atoms of the paraffin chain in gas phase or in zeolite. = the smallest possible distance between these atoms in the gas phase. = the smallest possible distance between these atoms for the molécule in its intracrystalline environment. (•) In a range of 9 values over which Langmuir’s isotherm is valid, as is assumed in calculating Sc and is demonstrated for «-C4H10 in Table IV, Sjh is equal to Sth.

63

In general < '"z < ''max- When P (/•) dénotés the probability of finding a given r, one bas the following relations

P(r) dr = 1

P(r) dr = R /«

= R /n

P(r) dr

11.1

rr„ P(a) dr

where AS^^n dénotés the entropy change associated with restrictions in configurations. The values of P(r) within the zeolite will for longer chains differ from P(r) in the gas phase, because for a give r^ some configurations possible in the gas may still be unrealisable in the zeolite. This however will merely increase —• Evidently eq. 11.1 will give only a lower limit to the magnitude of — AS^o^. Values of P(r) for n-hydrocarbons are known for chains with 3-, 4- and 5-links and also approximately for chains with 10-, 20-, 40- and 80-link chains (^O). The intégrations of eq. 11.1 were carried out and the results are given in Fig. 24a, where the change in conActual range in r figurational entropy is plotted against p = 100 77—^------------------- ^— Maximum range in r for 3, 4, 5, 10, 20 and 30 link chains. In Fig. lAb, the complementary relation between — ASj,on and chain length is shown for typical values of p. It is seen that — AS^.^^ may assume very large values indeed if the value of p is small. (i) curves of — AS^on chains ;

In particular : p cross at p ~ 20 % for 3, 4 and 5 link

(ii) as chains grow longer — AS^on becomes rapidly greater for smaller values of p. When the chain is a long one configurational restraints thus substantially diminish the free energy of occlusion; (iii) — ASj.(,n, for given p and for longer chains, becomes a nearly linear function of chain length.

64

According to this approach, in terms of Langmuir’s isotherm. f* f

A

------------- = K p(l-0)

,

max

P(A dr, where K will be given by models such

as (vii) or (vi) of Table V. AS(.o„ will also play a considérable part in determining the free energy of formation of adducts of paraffins with urea or thio-urea where the hydrocarbons are stretched along the axes of spirals formed by hydrogen bonded urea or thio-urea molécules.

Amylose chains also form spirals along the axes of

which lie included molécules such as iodine, fatty acids, and n-alcohols.

Fig. 24. — Calculated entropy effects for configurational restrictions of long Chain molécules, such as might be found in zeolites or in urea-hydrocarbon adducts (36).

65

12. Concluding remarks In this review no discussion has, for reasons of space, been given of the energetics of formation of Berthollide compounds of the host lattice-guest molécule type, although some extremely interesting Work has been carried out in this direction. Similarly no examination has been made of the bond types formed, although here also con­ sidérable understanding has now been reached. Instead attention has been drawn to the generality of the statistical thermodynamic approach in interpreting equilibria between gases and vapours which act as guest molécules within host lattices. Our investigation of spécifie isotherm models indicates that even for continuons inclusion isotherms one physical model is not normally able to describe the entire course from 0 < 6 < 1. Host crystals range from those which can accommodate only one atom per cavity (H2 — Pd, Zr, Ti), those providing isolated cavities capable of containing one sizeable molécule (quinol clathrate compounds), and those which provide long cylindrical channels (urea adducts) to those in which big cages are interconnected by wide Windows to give an intersecting network of channels (some zeolites). Individual cages may in the extreme case of faujasite be able to contain 32 water, 18 argon or 2.8 iso-octane molécules, and so become of remarkable dimensions. In interpreting some of the properties of the guest molécules in their intracrystalline environment there is great advantage in the measurement and interprétation of the entropy fonction for these molécules. This approach has accordingly been particularly developed with a view to demonstrating its potentialities. REFERENCES (1) e.g. « Chemistry

State », (Butterworths), (1955), edited by W. E. Garner; A. L. G. Rees, «Chemistry of the Defect Solid State », (Methuen), (1954). (2) . e.g. R. E. Rundle, Acta. Cryst. (1948), 1, 180. J. R. Lâcher, Proc. Rov. Soc. (1937), A 161, 525. T. R. P. Gibb and H. W. Kruschwitz, J. A. C. S. (1950), 72, 5365. T. R. P. Gibb, J. J. MeSharry and R. W. Bragdon, ibid., (Ï95Ï). 73,1751. R. K. Edwards, P. Levesque and D. Cubicotti, ibid. (1955), 77, 1307. B. M. Abraham and H. E. Flotow, ibid. (1955), 77, 1446. D. P. Smith, Phil. Mag. (1948), 39, 477. M. Hoch and H. L. Johnston, J. Chem. Phys. (1954), 22, 1376. (3) G. Hennig, J. Chem. Phys. (1952), 20, 1438. A. Herold, Compt. Rend. (1954), 239, 591. R. C. Croit, Nature (1953), 172, 725; Jour. App. Chem. (1952), 2, 557. R. C. Croft and R. G. Thomas, Nature (1951), 168, 32. H. Thiele, Z. Elektrochem. (1934), 40, 26. H. A. Frenzel and U. Hoffman, Z. Elektrochem. (1934), 40, 511. O. RufF, Angew. Chemie (1933), 46, 739.

66

of Solid

(“) J. C. Rinz and D. MacEwen, Nature (1955), 176, 1222. (5) e.g. W. Feitknecht and H. Burki, Experientla (1949), 5, 154. W. Feitknecht and H. Weidmann, Heh. Chim. Acta (1943), 26, 1560, 1564, 1911. D. MacEwen, Trans. Far. Soc. (1948), 44, 349. W. Feitknecht and H. Burki, Chimia (1949). 3 146; W. Feitknecht and F. Blatter ibid. (1954), 8, 261. (S) R. M. Barrer, J. DrakeandT. V. Whittam, Froc. 5oc. (1953), A 219, 32. W. Lange and G. Lewin, Ber. (1930), B 63, 2156. W. Lange and G. von Kreuger, Zeit. anorg. Chem. (1933), 216, 49. C) e.g. A. N. Winchell, Amer. Min. (1925), 10, 88. J.R. Goldsmith, Jour. ofGeol. (1950), 58, 518; Min. Mag. (1952), 29, 952. R. M. Barrer and J. W. Baynham, J. C. S., in press. R. M. Barrer and D. Sammon, ibid. (1955), 2838. R. M. Barrer, J. W. Baynham and N. McCallum, ibid. (1953), 4035. (*) e.g. R. M. Barrer, Ann. Reps. Chem. Soc. (1944), 41, 31; Quarterly Rev. (1949), 3, 293; J. Chim. Phys. (1950), 47, 82; Far. Soc. Discussion {l949), 7, 135; R. M. Barrer and D. W. Brook, Trans. Far. Soc. (1953), 49, 940. (9) R. M. Barrer and E.A. White, J. C. S. (1952), 1561. R. M. Barrer, L. Hinds and E. A. White, ibid. (1953), 1466. R. M. Barrer, Int. Symposium on the Reactivity of Solids, Gothenburg (1952), Part I, p. 373. ('<>) e.g. R. Greene-Kelly, Trans. Far. Soc. (1955), 51, 412. J. W. Jordan, J. Phys. Chem. (1949), 53, 294; J. W. Jordan, B. J. Hook and C. M. Finlayson, ibid. (1950),54, 1196. J. E. Gieseking, Soit Sci. (1939), 47, 1. (>0a) R. M. Barrer and D. M. McLeod, Trans. Far. Soc. (1955), 51, 1290. (>■) W. Baker and J. F. McOmie, Chem, and Ind. (1955), 256. H. M. Powell and B. D. Wetters, Chem, and Ind. (1955), 256. (*^) F. Cramer, « Einschlussverbindung », (Springer), (1954), p. 11 et seq. B. Angla, Ann. Chim. (1949),12, 639. W.J. Zimmerschied, R.A. Dinerstein, A.W. Weitkamp and R.F. Marschener Ind. Fng. Chem. (1950), 42, 1300; M. F. Bengen, Z. angew. Chemie (1951), 63, 207; W. Schlenk Jr„ Liebig’s Ann. (1949), 565, 204; (1951), 573, 142; E. V. Truter, Research (1953), 6, 320; R. J. Meakins, Trans. Far. Soc. (1955), 51, 953. (13) R. E. Rundle, J. A. C .S. (1947), 69, 1769. F. F. Mikus, R. M. Nixon and R. E. Rundle, ibid. (1946), 68, 1115. R.E. Rundle and R. R. Baldwin, ibid. (1943), 65, 554. R. E. Rundle and F. C. Edwards, ibid. (1943), 65, 2200. R. S. Stein and R. E. Rundle, J. Chem. Phys. (1948), 16, 195. (1-») H. M. Powell, Nature (1951), 168, 11. H. M. Powell, J. Chem. Soc. (1950), 298, 300, 468. H. M. Powell, Fndeavour (1950), 9, 154. (•5) e.g. M. von Stackelberg and H. Muller, Naturwiss. (1949), 36, 327; (1951), 38, 457; (1952), 39, 20. M. von Stackelberg and W. Jahns, Zeit. Flektrochem. (1954), 58, 162. (16) e.g. F. Cramer, ref. 12, p. 49 et seq. (17) K. A. Hofmann and H. Arnoldi, Ber. (1906), 39, 359. H. M. Powell and J. Rainer, Nature (1949), 163, 566. J. Leicester and J. K. Bradley, Chem, and Ind. (1955), 1449. (1*) e.g. R. M. Barrer and A. B. Robins, 7>rwi. Fac. .Soc. (1953), 49, 807 and 929 R. M. Barrer and L. V. Rees, ibid. (1954), 50, 852 and 989. R. M. Barrer and D. W. Brook, ibid. (1953), 49, 941 and 1049. L. A. Garden, G. L. Kington and W. Laing, ibid. (1955), 51, 1558. L. A. Garden and G. L. Kington, Proc. Roy. Soc. (1956), A 234, 24. L. A. Garden, G. L. Kington and W. Laing, Proc. Roy. Soc. (1956), A 234, 35.

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(>9) J. H. van der Waals, Far. Soc. Discussion (1953), 15, 261 ; Trans. Far. Soc. (1956), 52, 184. (20) A. F. Wells, « The Third Dimension in Chemistry », O. U.P. (1956), Fig. 99. (2>) F. Cramer, ref. 12, p. 13; W. Schlenk Jr., Liebig's Ann .(1949), 565, 204. (22) . W. Milligan and Fl. Weiser, J. Phys. Chem. (1937), 41, 1029. R. M. Barrer, Proc. Roy. Soc. (1938), A 167, 392. (23) J. Wyart, Bull. Soc. Franc. Min. (1933), 56, 81. W. H. Taylor, Z. Krist. (1930), 74, 1. W. H. Taylor, Proc. Roy. Soc. (1934), A 145, 80. W. H. Taylor, C. A. Meek and W. W. Jackson, Z. Krist. (1933), 84, 373. G. L. Kington and W. Laing, Trans. Far. Soc. (1955), 51, 287. (24) R. M. Barrer and J. Falconer, Proc. Roy. Soc., inpress. (25) W. L. Bragg, « Atomic Structure of Minerais », O. U. P.(1937). (26) R. M. Barrer and W. Meier, in préparation. (27) R. M. Barrer

and

F. W. Bultitude, in préparation.

(28) R. M. Barrer

and

J. W. Sutherland, in préparation.

(29) R. M. Barrer, « Conférence on Co-ordination Compounds », Amsterdam (1955); Nature (1955), 176, 745. (30) G. Nagelschmidt, Zeit. f. Krist. (1936), A 93, 481. (31) H. A. Frenzel and U. Hoffmann, ref. 3. (3ifl) M. Hoch and H. L. Johnston, J. Chem. Phys., (1954), 22, 1376 (32) R. M. Barrer and D. M. McLeod, Trans. Far. Soc.(1954),50,980. (33) e.g. J. R. Lâcher, ref. 2. See also refs. 37 and 38. (34) A. L. G. Rees, ref. 1 ; J. S. Anderson, Proc. Roy. Soc. (1946), A 185, 69. (35) R. K. Edwards and P. Levesque, J. A. C. S. (1955), 77, 1312. (36) R. M. Barrer, Trans. Far. Soc. (1944), 40, 374. (37) A. Sieverts and H. Bruning, Zeit. phys. Chem. (1932), A 163, 409. A. Sieverts and G. Zapf, ibid. (1935), A 174, 359. (38) L. J. Gillespie and F. P. Hall, J. A. C. S. (1926), 48, 1207. (39) S. L. H. Martin and A. L. G. Rees, Trans. Far. Soc (1954), 50, 343. (40) J. Wertz, W. Weltner and H. B. Whitehurst, « Interaction of bromine with graphite », OANAR Report (1951). (41) R. H. Fowler and E. A. Guggenheim, « Statistical Thermodynamics », C. U. P. (1939), p. 426. (42) R. M. Barrer and D. Ibbitson, Trans. Far. Soc. (1944), 40, 194. (43) R. M. Barrer, ref. 22; R. M. Barrer and D. W. Riley, /. C. S. (1948), 133; R. M. Barrer and D. W. Riley, Trans. Far. Soc. (1950), 46, 853; L. A. Garden, G. L. Kington and W. Laing, ibid. (1955), 51, 1558. (44) . Ref. 42, p. 441. (45) M. Volmer, Z. phys. Chem. (1925), 115, 253; D. H. Everett, Trans. Far. Soc. (1950), 46, 942. (46) R. M. Barrer and A. B. Robins, Trans. Far. Soc. (1951), 47, 773. D. H. Everett, ref. 45. (47) L. A. Garden, G. L. Kington and W. Laing, Proc. Roy. Soc. (1956), A234, 35. (48) J. C. Slater, «Introduction to Chemical Physics», McGraw Hill, (1939), p. 263. (49) Linde Air Products Co., « Technical Information on Hydrocarbon Purific­ ation ». (50) L. R. G. Treloar, Proc. Phys. Soc. (1943), 55, 23.

68

Discussion M. Hedvall. — Je crois qu’il est nécessaire de définir plus exactement la notion stœchiométrie. Nous en avons — pour ains’ dire — deux conceptions : la forme classique basée seulement sur les facteurs analytiques et d’affinité dans les composés hétérogènes; la forme plus moderne où les structures des solides sont d’une importance fondamentale. M. Barrer. — In the gaseous State stoicheiometry in the classical sense is appropriate : when atoms combine they do so in simple proportions by numbers. Perhaps this idea is at its best with the électron pair bond. Even for covalent species however, when two species are both présent as complexes in the solid State, Dr. Powell’s report draws attention to circumstances when compositions determined analytically may deviate from simple stoicheiometric ratios between the associated species. In ionic lattices the idea of stoicheiometric proportions (eq Na : Cl = 1 : 1 in rock sait) may still hâve its uses, provided it is realised that in general departures from stoicheiometry may be encountered (even in NaCl). On the other hand, in the equilibrium State, departures from electrical neutrality throughout the crystal are not found, however gross the stoicheiometric defect. Equally, a stoicheiometric proportion between atoms does not always mean absence of lattice defects. It is believed for example that S TiO (of NaCl structure) has 15 % vacancies, both anion and cation sites, at the stoicheiometric composition. On the whole, I think the concept of electrical neutrality should replace the old idea of stoicheiometry in ionic crystals. M. Powell. — My remarks on the word « stoicheiometric » were made in relation only to « organic non-stoicheiometric compounds » which at first seems not a rational term. They do not seem relevant to the présent question.

69

M. Defay. — J’ai été vivement intéressé, dans la communication du professeur Barrer, par le rôle joué par les surfaces intérieures du « host-lattice ». Je voudrais poser deux questions à ce sujet : Première question. — Les isothermes d’équilibre d’occlusion ou d’inclusion d’un gaz dans un solide sont à tous les points de vue si semblables à des isothermes d’adsorption que leur allure ne semble pas permettre de distinguer ces deux phénomènes. Je suppose qu’il serait possible de les distinguer en vérifiant si la quantité de gaz fixée par le solide est indépendante de la surface externe du solide et donc de son degré de pulvérisation. Est-ce ainsi que l’on procède ou bien existe-t-il un autre mode de discrimination? Seconde question. — L’explication du phénomène d’hystérèse par le retard de nucléation me paraît parfaitement valable. Il existe cependant dans les phénomènes d’adsorption des vapeurs par les corps poreux, une autre explication qui est également satisfaisante : c’est celle de la condensation capillaire dans des pores ayant un orifice étranglé. Dans ce cas, comme l’a suggéré Kraemer, si l’on considère un pore en forme de bouteille, l’hystérèse est due à ce que pendant la phase de sorption, la condensation commence dans la partie large de la bouteille, tandis que pendant la phase de désorption, la vaporisation doit commencer par le goulot de la bouteille. Je voudrais demander au professeur Barrer s’il existe un moyen expérimental de savoir si l’on a affaire, soit à un phénomène de nucléation, soit à un phénomène de condensation capillaire. M. Barrer. — In answer to professeur Defay’s first question, I would say that it is in general not easy to distinguish between sorption on external surfaces and sorption within a substance. However, no difficulty présents itself in the case of the zeolitic crystals used by me. These are well crystallised, of ~ 10~2 mm or even larger diameter as grown by hydrothermal technics, or as ground from natural crystals. They give excellent X-ray powder photographs. The estimated external surfaces (measured in some cases by the permeability method of Kozeny-Carman) are of the

70

order of 1 m^/g.

The équivalent of the intra-crystalline sorption,

when expressed as the monolayer value, v„,, of the Brunauer Emmelt Teller treatment may range from ca. 500 to ca. 1 000 m^/g for different crystals. Accordingly in these cases virtually ail the « surface » is intracrystalline. The amount of sorbed gas is indeed independent of the size of particules provided grinding is not carried to such an extent as to increase external surface beyond a few percent of the « internai surface ». As regards the second question, it is perfectly possible to explain hystérésis in ternis of capillary condensation in capillaries of suitable shape, as shown by Cohan, and by MacBain and Kraemer.

For

capillary condensation of liquids, I do not think one need postulate difficulties of nucléation as a cause of hystérésis, because an adsorbed monolayer, or a multilayer, film précédés formation of the more bulky capillary condensate, and the process may be thought to proceed smoothly through mono and multi-layer sorption stages. In solids it is easy to demonstrate nucléation and growth of a new phase by X-ray or optical technics, but for liquid condensâtes in capillary Systems, the use of such methods is not likely to help. M. Ubbelohde. — The extreme cases of capillary condensation of a liquid and sorption of a gas can be clearly distinguished provided the range of molecular forces is short compared with the diameter of the « capillaries ». This question may be easy to satisfy in the case of molecular forces of short range such as the ordinary van der Waals interactions. There are however forces of longer range, for example between polynuclear aromatic molécules where the van der Waals interactions fall off less steeply than the sixth power, or in ionic fluids. The range of effective forces between the walls of the capillary and the molécules may also extend beyond one molecular layer and may likewise become comparable with the capillary diameter. In such cases, the concept of a liquid must be used with care. Any surface tension effective in capillaries can be very different from the surface tension of the bulk liquid. M. Barrer. — Molecular forces may indeed be of considérable range.

The dispersion or London energy of interaction falls off

71

for a molécule interaction with a solid plane surface, according to the inverse cube of the distance from the molécule to the surface (this is seen by integrating, throughout the volume of the substrate, the expression for the interaction energy between an isolated surface atom and the molécule). I always regard the molécules occluded within the crystals of even the most open structure zeolites such as fanjasite as being subject to a powerful interaction with their environment. Clusters of molécules within a cage are then under the influence not only of this interaction, but also of the selfpotential which they develop by interacting with each other. Such clusters may then be subject to interactions different in magnitude from those which a similar cluster would undergo in the interior of its own liquid. Also one must not forget the intracrystalline calories and framework charges. I tend to regard the zeolitic water as being in a State in some measure akin to that which would characterise water in a concentrated electrolyte solution, although of course there will also be very significant différences. M. Kuhn. — How far are the hystérésis effects a phenomenon which is due to the limitation of time which the System is allowed to take for reaching equilibrium? From the point of view of thermodynamics one might expect that the amount of material adsorbed or condensed at the surface will, if the vapour pressure is given, be entirely definite. No hystérésis would then occur provided the System is given enough time to reach equilibrium.

M. Barrer. — Hystérésis both in sorption processes and in processes involving nucléation of new species on or in a matrix of a parent phase may be entirely reproducible and independent of time (provided an adéquate interval is allowed per point). This is fully understandable in terms of current treatments of hystérésis based for example upon domain theory. Very recent treatments of this type are contained in the papers of Everett and of Enderky published in the Faraday Society Transactions. An example of time-independent sorption hystérésis is provided by argon sorbed by « Nycer » porous glass (Barrer and Barrie, Proc. Roy. Soc., 1952); an example of time-independent hystérésis involving nuclé­ ation of a new phase is provided by the formation and dissociation

72

of the benzene-potassium benzene sulphonate complex (Barrer, Drake and Whittam, Proc. Roy. Soc., 1953, A 219,32). In other cases, points determined on the hystérésis loop may be independent of time, but the shape of the loop may dépend upon the previous history of the sample, e.g. the number of hystérésis cycles around which the System has been taken. This may mean change in the relative number of nuclei for which A and B in my eq. 6.2 hâve one pair of values as compared with the number for which A and B hâve another pair of values. This is reflected in a change of the sizes of the component rectangular loops of figure 20a, and hence in a change in the shape of the résultant loop of my figure 20 b.

This change in emphasis can arise if the parent

crystallites progressively break up, as a resuit of the strains of nucléation, when the System is taken round successive hystérésis cycles. The proportion of edges to surfaces may then change, and nucléation of course is not likely to occur equally easily, at ail crystallographic sites. This is one physical reason for a range of values of A and B (of fig. 20 a). This type of behaviour was observed in the p-dioxane-potassium benzene sulphonate System (Barrer, Drake and Whittam, loc. cit.). Finally however we corne to time-dependent hystérésis effects, such as professor Kuhn refers to. These arise for example in the sorption of pénétrants in polymers, if the polymer possesses considér­ able internai stiffness and viscosity. These effects, in which the hystérésis loop in a sorption-desorption cycle dépends upon the time scale of the experiments, we ascribe to slow visco-elastic relaxations within the polymer which modify its sorptive properties slowly. The visco-elastic processes are set up by sorption of pénétrant and swelling of polymer or by desorption and deswelling. Examples include the sorption of methanol, acetone or benzene by cellulose ether (Barrer and Barrie, in press). M. Bénard. — 1. M. Barrer a attiré notre attention sur la distinc­ tion à faire entre le « host lattice » et les « guest molécules ». Cette distinction est parfaitement claire dans le cas des systèmes qu’il a étudiés personnellement, parce qu’il existe dans ces systèmes, une différence fondamentale entre le type de liaison qui assure la stabi­ lité du réseau fondamental, et celui qui fixe les molécules étrangères

73

dans ses intervalles. Mais il est bon de remarquer que dans bien des cas la distinction est beaucoup plus difficile à faire; en parti­ culier, on peut assister dans certaines séries d’hydrates à un accrois­ sement des forces de liaison entre le réseau et les molécules d’eau. A ce moment les possibilités d’écarts à la stoechiométrie diminuent et on arrive aux hydrates définis, dans lesquels le nombre des molé­ cules d’eau qui peuvent être acceptées par le réseau est invariable. Comme corollaire, on constate que dans ces cas, il n’existe plus à proprement parler de « host lattice », puisque le type de structure caractéristique de l’hydrate ne peut exister lorsque l’eau a été éliminée. 2. Les tentatives de Lâcher, d’Anderson et de Rees, pour retrouver par la thermodynamique statistique les résultats expérimentaux que l’on possède sur l’étendue des domaines monophasés et diphasés dans les systèmes non stœchiométriques sont extrêmement inté­ ressantes car elles constituent les premières tentatives effectuées pour obtenir des données quantitatives sur ce problème. Je pense cepen­ dant qu’à l’heure actuelle, il est impossible d’affirmer qu’il existe un accord satisfaisant entre la théorie et l’expérience, car les exemples cités (zirconium-hydrogène et soufre-platine) sont encore trop mal connus. Je pense par contre qu’il serait intéressant de suivre dès maintenant, une démarche inverse et d’utiliser certains résultats expérimentaux relatifs à des systèmes aujourd’hui bien connus, pour déterminer à l’aide de ces théories, les valeurs des énergies d’interaction des défauts. M. Barrer. — The concept of host lattice and guest molécules is not to be used in ail cases of association between a solid and a volatile component. Pr. Bénard refers to the so-called « stoicheiometric hydrates » eg. CUSO4.5 H2O, N1S04.7 H2O. One could only speak of a CUSO4 host lattice in such a System if the water-content were not in fact invariable. If, for example a definite small amount of water could be withdrawn without nucléation of a new phase, then vacant water positions would appear, and the idea of a host lattice could be acceptable. Whether there is a small non-stoicheiometric range of compositions of such crystallohydrates is not yet known, though we hâve some experiments in progress designed to test this point. As regards Pr. Bénard’s comment on the application of statistical

74

mechanics to some stepwise isotherms (eg. H2 — Pd below the critical température) I would be surprised indeed if anything approaching perfection in the treatments were yet achieved. The models used are the simplest possible ones, and their approximations, introduced for the purpose of retaining this simplicity, are well known to the authors and to others of us who hâve been interested in these problems. The degree of success achieved, combined with the simplicity, is indeed most encouraging provided one does not press the treatments too far in the quantitative sense. This proviso applies to Pr. Bénard’s suggestion of using the théories in the converse sense to calculate defect interactions, though one should note that such calculations hâve been made. M. Hedvall. — I am very glad to hear that Professor Barrer has so clearly pointed out the importance of the influence of ail sorts of imperfections and surface properties, for the reactivity. I hâve been ail my life working in close contact with Chemical industries and also from their view points, it is rather pressing, — for instance in powder metallurgy, powder ceramics and catalytically working factories — to know much more about these factors. *

Professor Backer asked me to tell the history of the Aristotelian dogma corpora non agunt nisi liquida. I was telling Professor Backer yesterday that the start of my work in this field was that I — still at that time, fifty years ago, a schoolboy — never believed in this dogma. One did not know very much about the build of crystals at that time, however it was possible to say that vibrations only did not imply any sort of transport, which of course is necessary for ail reactions. But if one could trap a solid and combine it with another solid reactant just during a transition State it might be possible to get real powder reactions. That was true and the systematical work started on this line. Before that, some testing experiments were carried out by Spring in this country. Corning back to Professor Backer’s question, a good friend of mine, Professor Düring of Gôteborg, finally found what Aristoteles had said — of course he did not speak latin.

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When lecturing once at the university of Athen, I told my Greek colleagues that the right form of the dogma was : « Ta hygra meikta malista ton somaton » i.e. in modem Chemical language : It is in the first line the fluid substances that can react, a form which is much milder than the latin one. It was the first time my Greek colleagues heard the original form! M. Chatt. — If I may refer back to the first part of Professor Bénard’s question regarding the stoicheiometry of hydrated alumi­ nium sulphate, some twelve years ago Professor H. Bassett told me that in his study of the System SO3 — AI2O3 — H2O he found that in ail his samples of hydrated aluminium sulphate, there was a slight deficiency of 804“. This was true even when crystallisation took place from strongly acid solutions. He also analysed a large number of samples of naturally occuring aluminium sulphate and found a similar defi­ ciency of 804“. He never found the exact stoicheiometric ratio of AI2O3 to 8O3. M. Barrer. — This is an interesting observation, which suggests that there is incipient hydrolysis in the solid, to give some basic sait. Presumably, there is a concomitant requirement of some defect structure in the lattice. It would, in connection with Pr. Bénard’s remark and my reply to it, be interesting to know whether there were also non-stoicheiometric proportions of molecular water in the crystal. One difhculty in establishing such non-stoicheiometric proportions for water would be that water might be adsorbed as well as incorporated within the crystal lattice. However, since large crystals are no doubt readily grown, the external surface could be reduced to a negligible value as far as absorption of water is concerned. M. Ubbelohde. — Are there any exact measurements on the proportion of defect sites that can be formed by removal of water from sait hydrates? The formation of such defects can hardly require large energies and the usual calculations of independent lattice defects indicate that a considérable variation in the proportion of « water holes » should be attainable without collapse of the hydrate structure.

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We hâve started to look for shrinkages of the lattice without collapse by précision X-ray measurements in certain organic acid hydrates, but hâve found it difficult so far to maintain equilibrium concentrations of water molécules in the crystal lattice.

M. Barrer. — No previous measurements are known to me. However we are attempting to investigate the possible occurrence of « water holes » in so-called stoicheiometric hydrates. The deuterated crystals, e. g. CUSO4.5 D2O, are suspended by a silica spring in a light water vapour atmosphère, constantly renewed, and the attempt is being made to measure exchange and diffusion of H2O and D2O by weighing the crystal strength by the extension of the calibrated spring. The first runs, conducted at room tempér­ ature, hâve so far not shown interchange. At the same time this does not disproove the existence of « water holes » whose mobility may be very small at room température. These experiments will be suitably extended.

M. Kuhn. — The diffusion in ionic crystals is, according to the concepts of Schottky, Frenkel and others, mostly considered to be due to imperfections of the crystal lattice, i.e. either to particles placed in interstitial positions or to holes in the crystal lattice. It seems that in some instances at least, the diffusion might as well be ascribed to an exchange reaction between neighbouring molé­ cules or atoms in the normal crystal lattice. This last conception seems especially to be an appropriate description in the case of the diffusion of ice, i.e. of i*0 and of D in ice. We hâve together with M. Thürkauf (1) recently determined the diffusion coefficient at about — 1° C. The diffusion coefficient was found to be about 10“10 cm2 sec.“i, i.e. about 10~5 times the diffusion coefficient in liquid water. It is possible from this value of the diffusion coefficient to calculate the mean time t, needed for neighbouring molécules to exchange. It is thus found, that t = 5.10 6 sec.; this means that a given water molécule in ice is changing position with one of its neighbours 2.10^ times during one second.

(1) Diss. Basel 1956.

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It seems that in a case like this, the ability to diffuse might be described as a normal property of the normal constituents of the crystal lattice and not so much as a property of well defined defects of long life in the crystal lattice. There is certainly a continuons transition between the two modes of description. They coincide if the life-time of the crystal deficiencies assumed in the SchottkyFrenkel theory becomes of the order of magnitude of the mean time needed by one exchange reaction. The concept of the crystal deficiency theory will therefore only be essentially different from the concept in those cases where there is a definite life-time of a crystal deficiency is of an than the mean time required for an molécules.

of direct exchange reaction reason to believe that the order of magnitude longer exchange of neighbouring

M. Barrer. — In some crystals there is convincing evidence of defects of definite kinds and of long life, and their mobility can be measured or estimated. The processes of diffusion may then logically be ascribed to this mobility. In other media, the diffusion mechanisms hâve not been so clearly established. In metals for example while the bulk of the evidence points to vacancy diffusion, other possibilities hâve not been rigourously excluded, for example the ring mechanism of Zener :

O O--0 1 t 1

O

O

©--©

(f

©

©

©

©

1

O

©

The atoms 1, 2, 3 and 4 in the above diagram can move in unison in the directions of the arrows to give place changes with the minimum of disturbance of the surrounding lattice. The direct interchange of atoms 5 and 6 as indicated would create a greater disturbance in the lattice. As I hâve said, much thought and experiment has been devoted to deciding between vacancy and other mechanisms in metals and the body of the evidence favours vacancy diffusion.

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When we corne to diffusion of liquids in one another, or diffusion of molécules dissolved in rubber, then I believe the place exchange mechanism cornes into its own. Such structures are much looser and more irregular than are crystals and opportunities for inter­ change of molécules must be frequent. Incidently, for small clearing forces, I would expect a close corrélation of molecular events resulting in unit acts of viscous flow and those resulting in unit acts of self diffusion.

M. Lindner. — I wonder if Professor Barrer would tell us something about the kinelics of the processes discussed by him. If the diffusion of the gas would need a sufficient activation energy, one might obtain information concerning an eventual real lattice diffusion of the gas atoms within the solid, as sometimes postulated in connection with the « émanation » technique; but obviously struc­ tures of that kind hâve not been investigated by Professor Barrer.

M. Barrer. — We hâve studied the diffusion of gases such as H2, Ne, A, N2, O2 and other species into lattices of the zeolites, levynite, mordenite, sodium and calcium rich chabazites, and some synthetic zeolites. We hâve in some cases measured diffusion coeffi­ cients, and found these to dépend, in a straight forward way, upon the cross-sections of the diffusing molécules, which hâve to squeeze through « Windows », or restrictions, in the channel System. Energy barriers of several K cals up to 10 to 12 K cals were encountered in such diffusions. Moreover the diffusions were sensitive in what was quite often a complex way to the number and dimensions of the cations distributed through the aluminosilicate frameworks. One must suppose that sometimes cations are placed like sentinels before the « Windows » leading from one cage to another in what are otherwise very open structures indeed; that when so placed, they can block these Windows and slow down diffusion or prevent it altogether. Ca-rich chabazites behave as though there were no sentinels or only a few, guarding the way through Windows, while Na-rich chabazite behaves as a guarded structure. One then finds a virtually free diffusion of O2, N2, A, C2H6, etc., into Ca-rich chabazite, but a very much more restricted access into the lattice of Na-rich chabazite.

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M. Ubbelohde. — The Professer Kuhn is of very to measure separately the and the diffusion of the

case of diffusion in ice referred to by considérable interest, since it is possible proton or deuteron diffusion mechanism, molécule containing the oxygen atom.

Are the two rates different? I would also like to ask whether proton defect sites can be deliberately included by freezing acide molécules such as HCl into the lattice as it has been reported on the basis of experiments (in Germany)? We hâve carried ont ion migration experiments in varions hydrated organic acids containing hydrogen bonds, with the object of correlating migration kinetics with the presence of short hydrogen bonds in the crystals. The results show a general corrélation between cooperative Systems of hydrogen bonds, and ease of migration, though it is too early to establish detailed conclusions.

M. Kuhn. — The question whether the mobility of D and that of 1*0 in ice would be identical or not was given particular care. It was not sure at ail whether a différence should be expected or not. The question could be solved without ambiguity from the concentration différences chosen and from the transport of the different kinds of atoms determined by the mass spectrometer after the diffusion had taken place. It was found that the diffusion coefficient was the same for D and for within the limit of accuracy of the experiment, say about 10 %. This means that the diffusion in ice is occurring by an exchange of water molécules and not, or nearly not, by an exchange of H and D through hydrogen bridges and not essentially by transport of ions.

M. Lindner. — I should like to ask a question concerning the experimental details of your procedure for measuring the selfdiffusion of hydrogen and oxygen in ice.

I assume the time function is established and I may suggest a simultaneous measurement of (ionic) conductivity for further élucidation of the transport process. A direct place exchange of water molécules looks not too probable at first sight (as remarked already by Professor Barrer).

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M. Kuhn. — In order to measure the self diffusion of

and D

in ice, we hâve prepared ice cylinders diflfering in their contents of H2 160, H2 180 and OH2, OHD. They were brought into contact with each other, either directly or with an air gap of about 10^2 cm. A calculation shows that an air gap of said magnitude is, as far as the résistance to migration of H2O, etc., is concerned, équivalent to less than lO”"! mm of ice. Furthermore the results obtained in the case of direct contact and by the air gap method coincided.

The cylinders were separated

after being in contact with each other for 20, 30 days and then analysed with respect to H, D, i^O and 1*0 in a mass spectrometer. As a resuit of these experiments it was found that the diffusion coefficients of 1*0 and D coincided within the limits of the exper­ imental error of a few percent. This indicates that the diffusion in ice is taking place by migration of water molécules, and not or not essentially by a migration of hydrogen ions.

M. Ubbelohde. — Has Dr. Linder observed actual examples of migration in molecular crystals?

M. Lindner. — We did not State a transport of molécules in a molecular lattice, but rather got evidence that in some cases of solid State reactions involving ionic compounds of higher orders as e.g. silicates, both ions of one component as e.g. Pb2+ + 02are transported in the same direction, which nowadays is considered being an ionic transport rather than a molecular one.

M. Timmermans. — Je voudrais faire une remarque élémentaire sur les conflits de la stœchiométrie classique et sa forme contem­ poraine. C’est que nos idées classiques sur la nature chimique intime des substances résultent surtout de l’étude des gaz et ne doivent pas nécessairement s’appliquer en tout cas aux solides; elles ne sont strictement valables que dans le domaine pour lequel elles sont vérifiées et dans les limites de la précision des expériences à diffé­ rentes époques. Les vues antinomiques de Proust et de Berthollet, qui ont si longtemps paru exclusives l’une de l’autre, tendent à faire place

aujourd’hui, comme si souvent dans l’histoire des sciences, à une synthèse plus générale où chacune d’elles trouve sa place comme un aspect particulier des mêmes phénomènes; pour beaucoup d’entre nous, il faut faire un grand effort d’imagination pour s’adapter à ces théories nouvelles et c’est là ce qui fait notamment l’intérêt des discussions d’aujourd’hui.

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Composés d’insertion des métaux de transition par Jacques BÉNARD

LA NOTION DE COMPOSÉ D’INSERTION ET LA CONCEPTION DE HÂGG Le terme composé d'insertion a été fréquemment utilisé pour désigner des catégories de composés très diverses : hydrures, car­ bures, zéolithes, clathrates, hydrates de gaz, etc. Le caractère commun généralement attribué à ces corps est la parenté de leur structure cristalline par rapport à un édifice primitif plus simple d’où ils semblent pouvoir se déduire par l’introduction d’atomes ou de groupes d’atomes dans certains vides de dimensions appréciables. Nous nous bornerons à étudier ici les composés d’insertion pour lesquels l’édifice primitif est celui d’un métal de transition, c’està-dire possédant une sous-couche électronique d incomplète, et les particules insérées sont soit l’hydrogène, soit un élément électro­ négatif de la première période brève du tableau périodique ; bore, carbone, azote, et éventuellement oxygène. Cette délimitation qui peut paraître à première vue arbitraire trouve sa justification dans le fait que la plupart des composés ainsi obtenus possèdent une physionomie particulière, non seulement du point de vue de la structure cristallographique mais encore du point de vue des pro­ priétés physiques. Bon nombre de carbures, borures et nitrures des métaux de transition possèdent en effet, une conductibilité électrique de caractère métallique élevée, associée à une dureté et à une infu­ sibilité exceptionnelles. Ces propriétés dont l’intérêt technique est considérable ont fait l’objet de nombreuses recherches qui trouvent leur origine dans l’œuvre magistrale élaborée il y a plus d’un demi siècle par Moissan et ses collaborateurs. Quant aux phases résultant

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de l’insertion d’atomes d’hydrogène dans un réseau métallique, bien que leurs propriétés physiques paraissent assez différentes de celles des composés précédents, leur étude est instructive car elle permet de mieux comprendre par comparaison, ce qui donne à ces derniers leur physionomie particulière. 11 ne saurait être question de décrire dans le présent rapport toutes les phases qui rentrent dans le cadre que nous venons de fixer. Cette description a d’ailleurs été faite au moins partiellement dans des monographies récentes auxquelles on pourra utilement se reporter (b 2, 3, 4, 5, 6). Nous nous proposons plutôt d’examiner quelles sont, à la lumière des recherches accomplies au cours de ces dernières années, les réponses qui peuvent être données à un certain nombre de questions générales concernant la constitution et les propriétés de ces phases, et en particulier les suivantes : 1° Existe-t-il comme pourrait le laisser penser ce terme, une parenté étroite entre la structure des composés interstitiels et celle du métal d’où ils dérivent? 2° L’ensemble des propriétés physiques des composés intersti­ tiels est-il suffisamment caractéristique pour qu’il soit possible de leur attribuer un mode de liaison particulier? 3° La variation de composition en phase homogène est-elle un caractère général des composés interstitiels? Le problème de la constitution des composés interstitiels des • métaux de transition a été abordé dans son ensemble, il y a plus de vingt ans, par Hâgg Ç). Si des modes d’interprétation nouveaux ont été introduits depuis quelques années, il n’en reste pas moins que les idées de cet auteur peuvent constituer encore maintenant un bon point de départ pour l’étude de ces composés . L’étude de nombreux hydrures, nitrures et carbures des métaux de transition au moyen des rayons X, semble montrer d’après Hâgg que la structure des composés interstitiels dépend avant tout du rapport du rayon atomique de l’élément léger à celui du métal. r élément léger Si le rapport R =-------------^—;------- est inférieur à 0,59 la strucr métal ture est généralement simple avec disposition compacte des atomes métalliques (cubique à faces centrées ou hexagonale compacte, plus rarement cubique centré) et répartition des atomes de l’élément

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léger dans les interstices laissés libres entre les atonies métalliques. Lorsque le rapport R dépasse la valeur critique 0,59 les composés formés possèdent des structures complexes. Tels sont les carbures de chrome, manganèse, fer, cobalt, nickel et la plupart des borures. A vrai dire, la signification générale de cette règle est singulièrement amoindrie si Ton remarque que le passage du rapport critique ne peut être observé que pour les carbures, tous les hydrures, oxydes et nitrures conduisant à des rapports inférieurs à 0,59. Le cas des borures doit être mis à part, car il est apparu postérieurement aux premiers travaux de Hâgg que la structure de ces composés était plus complexe qu’il n’était prévu initialement (8) et ne pouvait par conséquent être incluse sans aménagements dans une systé­ matique qui a pour objet de couvrir l’ensemble des composés inter­ stitiels des métaux de transition. Outre cette limite supérieure, essentiellement empirique du rap­ port R, au-delà de laquelle les structures simples ne sont plus obser­ vées, Hâgg fut amené à postuler l’existence d’une limite inférieure au-dessous de laquelle ces structures deviennent également instables. L’instabilité apparaîtrait lorsque l’atome inséré possède des dimen­ sions insuffisantes pour entrer simultanément en contact avec tous les atomes métalliques entourant une position interstitielle. La vérification du bien-fondé de cette dernière conclusion ne peut être tentée que dans le cas des hydrures et pour certains oxydes inter­ stitiels, qui seuls conduisent à des rapports inférieurs à cette seconde valeur critique. Nous examinerons maintenant comment se situent les données expérimentales actuellement à notre disposition par rapport à cette conception.

CARACTERES GÉNÉRAUX DES HYDRURES DES MÉTAUX DE TRANSITION Au voisinage de la température ordinaire il existe dans un certain nombre de systèmes métal-hydrogène : 1° Une phase possédant la structure du métal pur et qui a été fréquemment considérée comme une solution solide d’hydrogène dans le métal (phase a) ;

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1° Une ou plusieurs phases correspondant à des teneurs en hydro­ gène supérieures et dont les structures sont généralement différentes de celles du métal pur. Les phases contiguës peuvent coexister deux à deux en équilibre à une température et sous une pression donnée, en formant des systèmes invariants à température donnée qui se signalent par des paliers sur les isothermes d’absorption. Les limites des domaines d’existence de ces phases, signalées par les extrémités de ces paliers, varient en fonction de la température et de la pression. Il en résulte que de façon générale, il est illusoire d’attribuer, comme on l’a fait trop souvent, une signification particulière à la concentration limite observée pour une phase donnée, dans des conditions de tempé­ rature et de pression particulières. Seules présentent dans une certaine mesure une signification les concentrations caractéristiques vers lesquelles tendent parfois les limites des phases lorsque les variables physiques se modifient d’une façon continue. Il s’en faut de beaucoup, cependant, qu’une telle tendance se manifeste d’une manière nette dans tous les cas. Parmi les valeurs particulières de la concentration en hydrogène qui répondent à ce critère, la mieux marquée paraît être celle qui correspond aux compositions TiH2, ZrH2, HfH2, vers lesquelles tend la phase solide lorsqu’on accroît la pression de l’hydrogène au-dessus du titane (lo, n), du zirconium (12. 13), ou du hafnium (i^). Les phases correspondantes se présentent donc, non comme des composés définis mais comme des limites supérieures de domaines homogènes. Les phases limites TiH et Pd2H apparaissent également dans les diagrammes titane-hydrogène (H) et palladium-hydro­ gène (15. 16, 17). Enfin une limite extrêmement bien marquée est celle qui correspond à la formule UH3 dans le système uraniumhydrogène (18. 19). Dans plusieurs systèmes l’étendue des domaines diphasés observés à la température ordinaire se rétrécit au point de disparaître lorsque la température et la pression d’hydrogène s’accroissent simulta­ nément. On peut de cette façon réaliser aux pressions et températures élevées, des variations importantes de concentration en phase homo­ gène dans les systèmes palladium-hydrogène, titane-hydrogène, zirconium-hydrogène. La fig. 1 indique à titre d’exemple la forme des isothermes d’absorption dans le système palladium-hydrogène.

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d’après Gillespie et Hall, qui montre la réunion progressive des domaines a et [î; la fig. 2 montre, d’après McQuillan, ce même phénomène pour les phases « et p du système titane-hydrogène. On notera, par contre, que la phase y de ce dernier système reste distincte dans tout le domaine de température et de pression exploré.

Quelles sont les structures attribuées à ces phases? Seul de tous les systèmes étudiés ici le système palladium-hydrogène ne comporte qu’un seul type de structure; les atomes de palladium conservent, en effet, quelle que soit la concentration en hydrogène, la disposition cubique à faces centrées qu’ils possèdent dans le métal pur (20). L’état diphasé observé aux températures et pressions

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peu élevées correspond à la coexistence de deux phases, présentant le même réseau métallique cubique à faces centrées des atomes de palladium, et qui ne diffèrent que par leur paramètre; cette dif­ férence tend d’ailleurs à s’atténuer lorsque la température et la pres­ sion augmentent simultanément, en accord avec les données indi­ quées plus haut.

Pour les autres systèmes, la disposition présentée par les atomes métalliques dans le métal pur n’est conservée que dans les solutions solides primaires, dont l’extension est parfois très faible à la tempé­ rature ordinaire. Les phases plus riches en hydrogène possèdent encore des struc­ tures simples, mais qui sont généralement différentes de celle du

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métal pur. Tel est le cas de la phase y du système titane-hydrogène dans laquelle les atomes de titane ont un arrangement cubique à faces centrées alors que le titane métallique est hexagonal compact (6 < 900 oC) ou cubique centré (900 °C < 0). Dans les systèmes zirconium-hydrogène et hafnium-hydrogène les phases proches de la formule ZrH2 et HfH2 ont un arrangement quadratique à faces centrées, alors que le métal est dans le premier cas hexagonal compact (6 < 862 °C) ou cubique centré (862 «C < 0) et dans le second cas

hexagonal compact. La phase p du système tantale-hydrogène est hexagonale compacte alors que le métal est cubique centré. L'affirmation selon laquelle les atomes métalliques posséderaient dans les hydrures des métaux de transition des configurations analogues à celle qu'ils possèdent dans ces métaux à l'état pur n'a donc pas, comme on le croit souvent, une valeur générale. La fréquence des structures compactes ou quasi-compactes observées dans la plupart de ces composés, qui a contribué à accréditer cette opinion, résulte en réalité de la grande différence

des dimensions du

métal de l’hydrogène, qui permet aux atomes métalliques de réaliser des configurations simples analogues à celles qu’ils ont tendance à adopter en l’absence d’atomes étrangers. Il est hors de doute que c’est l’impossibilité de localiser directement les atomes d’hydrogène par les rayons X qui a conduit inconsciem­ ment les chercheurs à minimiser le rôle joué par ces atomes dans l’édification des phases hydrogénées.

LOCALISATION DES ATOMES D’HYDROGENE Deux types de positions peuvent être envisagés pour des atomes d’hydrogène placés en insertion dans un assemblage quasi-compact d’atomes métalliques tel qu’on en rencontre dans bon nombre d’hydrures interstitiels ; positions hexacoordinées (sites octaédriques) et positions tétracoordinées (sites tétraédriques) (figure 3). Si l’on admet à la suite de Hâgg C?) que la phase d’insertion n’est stable que si tous les atomes antagonistes sont en contact, on doit conclure que les atomes d’hydrogène occupent toujours des positions tétracoor­ dinées. En effet un raisonnement élémentaire montre que le contact entre l’atome inséré et les atomes métalliques contigus ne peut être assuré que si le rapport R du rayon de l’atome léger à celui de l’atome lourd est supérieur à la valeur critique 0,41. Si l’on prend

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pour dimension de l’atome d’hydrogène la valeur rjj — 0,30 Â adoptée initialement par Hâgg les rapports caractéristiques de tous les hydrures des métaux de transition se situent entre les valeurs extrêmes 0,16 < R < 0,24, toujours inférieures à la valeur critique.

En fait il ne semble pas possible de tirer de ces considérations des conclusions certaines quant à la position des atomes d’hydrogène dans le réseau métallique. En effet, les valeurs du rapport R sont subordonnées au choix d’une valeur pour le rayon atomique de l’hydrogène, choix qui présente encore un certain caractère arbi­ traire. Cet inconvénient serait d’ailleurs minime si l’on pouvait considérer cette valeur comme immuable dans tous les termes d’une série de composés homologues, mais il est certain que cette valeur se modifie en même temps que la nature des liaisons dans chaque série. Tout au plus semble-t-il donc possible de prévoir d’après ces raisonnements que dans les hydrures caractérisés par les rapports R les plus élevés, les atomes d’hydrogène ont tendance à occuper les positions tétracoordinées, tandis que pour les rapports les plus faibles l’hydrogène est dans les positions hexacoordinées. On a d’autre part cherché à préciser la position des atomes d’hydro­ gène en se basant sur l’examen des compositions limites atteintes par les phases hydrogénées lorsqu’on fait varier la température et

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la pression. On pouvait espérer en particulier que les limites de phases observées correspondaient à l’occupation complète de différentes catégories de sites cristallographiques, ce qui aurait permis d’iden­ tifier ces sites par les valeurs des concentrations limites. Malheu­ reusement il est fréquent que les limites caractéristiques observées ne peuvent être expliquées par l’occupation complète d’une catégorie déterminée de sites. C’est ainsi que si, dans la phase ZrH cubique à faces centrées, on localise à la suite de Hâgg Ç) et de Pauling et Ewing (21) les atomes d’hydrogène dans les sites tétracoordinés, on est conduit à admettre qu’à la saturation la moitié seulement de ces sites peuvent être occupés. De même quelles que soient les positions que l’on assigne aux atomes d’hydrogène dans TiH cubique centré, on doit envisager à la saturation une occupation qui n’est que partielle de ces positions. L’accord est meilleur dans les phases type TiH2 cubiques à faces centrées, ou dérivées de ce système cristallin comme ZrH2 quadratique à faces centrées ; on peut en effet considérer que dans ces cas, la saturation correspond à l’occupation de la totalité des sites tétraédriques disponibles. Il n’en est pas moins vrai que dans l’ensemble, la considération des limites de phases ne permet pas, dans l’état actuel de nos connais­ sances, de localiser les atomes d’hydrogène. Le fait que des limites varient d’une façon considérable en fonction de la température et de la pression montre d’ailleurs très clairement qu’elles dépendent de nombreux facteurs autres que les facteurs géométriques. Il n’est même pas évident que les atomes soient localisés pour chaque phase dans une catégorie de sites déterminée et on pourrait envisager dans certains cas l’existence d’une répartition désordonnée des atomes d’hydrogène entre plusieurs catégories de sites. La tendance des phases differentes à se confondre, qui se manifeste dans certains systèmes lorsqu’on augmente la température et la pression corres­ pondrait ainsi à la disparition de la localisation des atomes d’hydro­ gène et la réalisation progressive d’un état idéalement désordonné. Il ne faut pas oublier enfin que le problème de la localisation des atomes d’hydrogène va se trouver d’ici peu entièrement renouvelé lorsque la diffraction des neutrons aüra apporté un nombre suffisant de données. Nous citerons pour mémoire le très récent travail de Zachariasen et alii (22) qui ont déterminé par cette méthode la posi­ tion des atomes d’hydrogène dans les phases du système cériumhydrogène.

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NATURE DE LA LIAISON DANS LES HYDRURES DES MÉTAUX DE TRANSITION Le problème de la nature de la liaison dans les hydrures des métaux de transition ne semble pas encore avoir été traité dans son ensemble. Il paraît toutefois établi que l’hypothèse d’une dissolution de nature essentiellement physique doit être rejetée. A l’encontre de celle-ci plusieurs faits doivent être pris en considération: 1° L'action de l'hydrogène sur ceux des métaux de transition qui absorbent ce gaz en quantité notable s'accompagne le plus souvent d'un dégagement de chaleur important, dont l’ordre de grandeur (30 à 40 K/cal par mole H2) ne diffère pas essentiellement de celui qui est mis en jeu dans la formation des hydrures ioniques. Seules font exception les phases hydrogénées du palladium, dont la cha­ leur de formation est beaucoup plus faible, de l’ordre de 10 K cal par mole d’hydrogène. 2° Le paramagnétisme des métaux de transition qui résulte de la présence d'électrons solitaires, dans l'état métallique, décroît lorsque la teneur en hydrogène augmente. Ceci prouve que les électrons apportés par l’hydrogène sont au moins en partie transférés dans le niveau d incomplet du métal. Dans le cas du palladium, le para­ magnétisme disparaît totalement à la composition PdHo g pour laquelle la totalité des niveaux d du métal se trouverait par consé­ quent occupé (23). 3° Le transfert de l'électron de l'hydrogène au métal est confirmé par les expériences de diffusion de l'hydrogène dans les phases palladiumhydrogène sous l'influence d'un champ électrique (24. 25). Ces expé­ riences supposent en effet une ionisation électropositive au moins partielle des atomes d’hydrogène en insertion. 4° Les variations parfois importantes des distances métal-métal lorsqu'on passe du métal pur aux phases hydrogénées ne peuvent s'expliquer que par un changement important dans la nature des forces de liaison. Le changement du type de liaison se manifeste d’ailleurs dans chaque système, en fonction de la teneur en hydrogène, par l’altération progressive des propriétés physiques du métal. Alors que dans les phases primaires et même dans certaines phases inter­ médiaires déjà riches en hydrogène, l’atténuation du caractère

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métallique est relativement discrète et ne se traduit guère que par la diminution de la conductibilité électrique et l’apparition de la fragilité, les phases les plus riches en hydrogène comme ZrH2 et TiH2 perdent totalement le caractère métallique et s’apparentent par leur physionomie générale aux hydrures salins. Se basant sur le fait que dans le système palladium-hydrogène le caractère métallique persiste aux concentrations en hydrogène les plus élevées, Ubbelohde (26) a traité le problème de la liaison dans ces phases en les assimilant à des alliages dans lesquels l’hydrogène jouerait le rôle d’un métal. Cette conception paraît cadrer d’une manière assez satisfaisante avec les propriétés de ce système, mais il ne semble pas possible de l’étendre à l’ensemble des hydrures des éléments, de transition, car le système palladium-hydrogène constitue un cas à bien des égards exceptionnel. Une intéressante suggestion de Rundle (22), reprise récemment par Pauling et Ewing (2i) a été faite pour interpréter la structure de l'hydrure d'uranium dont la composition limite correspond à la formule UH3. Bien que ce composé se situe par certains de ses caractères à la frontière des hydrures interstitiels et des hydrures salins, l’étude de sa constitution est instructive parce qu’elle souligne certaines particularités qui n’apparaissent qu’à l’état d’ébauche dans les hydrures interstitiels des métaux de transition des deux premières longues périodes. En effet UH3 bien que conducteur de l’élec­ tricité, ne possède qu’un très petit nombre de liaisons métalliques comme il est facile de le constater en comparant les distance U — U dans sa structure aux distances correspondantes dans l’uranium métal. Cette structure comporte par contre un certain nombre de distances U — U qui sont trop grandes pour être des distances U — U normales et trop petites pour correspondre à l’insertion pure et simple d’un atome H entre deux atomes métalliques sans apparition d’une liaison nouvelle. Ces distances témoigneraient selon Rundle de l’existence d’une liaison U — H ^— U résultant du partage par moitié de l’orbitale s de l’atome d’hydrogène entre deux atomes d’uranium voisins et diamétralement opposés. L’exis­ tence de ces ponts hydrogène à liaison fractionnaire serait compa­ tible avec l’existence des caractères métalliques et en particulier de la conductibilité électrique. Le caractère orienté de ces liaisons, comparables à cet égard à des liaisons de covalence, expliquerait d’autre part la grande fragilité du composé. Il est difficile de savoir

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dans quelle mesure leur présence peut être escomptée dans d’autres hydrures des métaux de transition. Seule une étude comparée appro­ fondie des distances métal-métal dans ces hydrures et des mêmes distances dans le métal pur permettrait d’en décider. Il ne saurait être question de rechercher un type unique d’inter­ prétation pour définir l’ensemble des phases métal-hydrogène qui viennent d’être citées. Ces phases possèdent en effet une extrême diversité de propriétés, correspondant à des modes de liaisons manifestement différents et doivent s’intégrer dans une série évolutive. A l’une des .extrémités de cette série se situe le palladium dans lequel la dissolution de l’hydrogène bien que couvrant un large domaine de concentration, n’altère que partiellement les caractères métal­ liques et ne modifie pas la configuration des atomes lourds. A l’autre extrémité un hydrure ionique comme CaH2 auquel les caractères métalliques font totalement défaut et où la configuration des ions Ca2+ n’a aucun rapport avec celle des atomes dans le métal. Jalon­ nant la transition on pourrait d’une façon très approximative établir le classement suivant : Pda — Pdp — Taa — Tia et (3 — Zr e et Ti y — UH3 — CaH2 Cette évolution s’accompagne d’un accroissement de la chaleur de formation, d’une diminution de la conductibilité et de la dis­ parition des variations de composition en phase homogène. Il paraît nécessaire d’admettre de plus que le caractère de la liaison se modifie non seulement lorsqu’on passe d’une phase à une autre mais encore au sein d’une même phase en fonction de la concentration de l’hydrogène. Ceci permet d’expliquer en particulier que des phases présentant à basse température et sous la pression atmosphérique des structures et par conséquent des modes de liaison probablement différents, puissent arriver à se confondre en une phase unique de composition variable à plus haute température. On ne peut manquer de rapprocher la situation attribuée à UH3 dans ce classement, à la limite des hydrures à caractère métallique et des hydrures à caractère ionique, de la présence dans ce composé des ponts métal-hydrogène postulés par Rundle. Dans les phases hydrogénées métalliques type palladium-hydrogène, il paraît établi en effet que les électrons Ij de l’hydrogène, viennent remplir au

94

moins partiellement les niveaux 4d du métal. L’opération peut être assimilée sous une forme schématique à un transfert d’électrons de l’hydrogène au métal. Dans les hydrures ioniques type LiH ou CaH2, c’est le métal qui cède irréversiblement un électron à l’hydro­ gène pour compléter le niveau 1j, opération inverse de la précédente et qui conduit à la formation d’un anion H~. Il n’est pas impos­ sible de concevoir des couples métal-hydrogène intermédiaires dans lesquels la tendance de l’hydrogène à compléter son niveau 1j équi­ librerait sensiblement la tendance du métal à compléter un ou plusieurs niveaux sous-jacents incomplets. Cette situation pourrait être favo­ rable à l’apparition des ponts hydrogène et trouverait son illustration dans la structure de UH3. Bien qu’on ne possède encore que peu de renseignements sur la structure de l’hydrure de thorium et des hydrures des lanthanides, on a tout lieu de penser que ces composés présentent des caractères analogues.

CARACTERES GÉNÉRAUX DES CARBURES, NITRURES ET OXYDES DES MÉTAUX DE TRANSITION La plupart des carbures, nitrures et oxydes des éléments de tran­ sition possèdent un réseau métallique simple. Les seules exceptions sont constituées par les carbures de chrome, manganèse, fer, cobalt et nickel dont les structures sont complexes et pour lesquels le rapport du rayon atomique de l’élément léger à celui de l’élément lourd est supérieur à 0,59. En comparaison de la structure des hydrures, celle de ces phases apparaît comme beaucoup moins variée et se limite à un très petit nombre de configurations. Les phases répondant à la formule générale Me X constituent en particulier un ensemble extrêmement homogène dans lequel le métal de transition et l’élément léger alternent dans un réseau cubique type chlorure de sodium (fig. 4). Chaque sorte d’atome possède six voisins disposés aux sommets d’un octaèdre dont il occupe le centre. Ces phases sont traditionnel­ lement citées comme exemples de composés interstitiels des métaux de transition. La liste en est donnée dans le tableau avec indication des structures et des distances métal-métal. Les phases Me2X, qui ne se rencontrent que parmi les carbures et les nitrures, sont le plus souvent hexagonales compactes, à l’exception des composés W2N et M02N qui sont cubiques à faces centrées. Les phases Me4X enfin, qui sont peu nombreuses (Mn4N, Fe4N), possèdent également une

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répartition des atomes métalliques sur les nœuds d’un réseau cubique à faces centrées. La haute symétrie et la compacité de l’arrangement des atomes métalliques dans ces composés permettent-elles de les considérer comme résultant simplement de l’insertion d’atomes de carbone, d’azote ou d’oxygène dans les interstices de l’édifice cristallin du métal pur? L’examen du tableau montre que contrairement à une opinion communément admise, la configuration des atomes métal­ liques dans les composés d’insertion étudiés ici est le plus souvent différente de celle qu’ils adoptent dans le métal. La formation de ces composés entraîne donc une réorganisation complète de l’édifice du métal.

L’union des métaux de transition au carbone et à l’azote ne provoque pas seulement un changement de la structure; elle s’accom­ pagne en outre de l'apparition de propriétés physiques entièrement nouvelles. Tous possèdent une dureté élevée comparable à celle du diamant, dureté qui s’accompagne le plus souvent d’une grande fragilité. Leur infusibilité est également remarquable et les points de fusion, toujours supérieurs à 2.000°, atteignent fréquemment 3.000°. Il est remarquable de constater qu’en dépit de ces changements, certains caractères de l’état métallique subsistent, en particulier l’opacité, l’éclat métallique et une conductivité électronique appré­ ciable avec un coefficient de température négatif.

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Structures comparées de quelques carbures, nitrures et oxydes interstitiels des métaux de transition (lorsque aucune indication contraire n’est mentionnée les indications fournies se rapportent au composé MeX).

MÉTAUX

Maille

'-J

Distance Me-MeA

Maille

OXYDES

NITRURES

CARBURES

Distance Expansion Me-MeA Me-MeA

Maille

Distance Expansion Me-MeA Me-MeA

Maille

Ti

hex. c.

2,92

cub. fc.

3,04

0,12

cub. fc.

2,27

0,65

cub. fc.

Zr

hex. c.

3,12

cub. fc.

3,30

0,18

cub. fc.

3,21

0,09

cub. fc.

Hf

cub. c. hex. c.

3,16

cub. fc.

3,27

0,11

cub. fc.

Th

cub. fc.

3,60

cub. fc.

3,76

0,16

cub fc.

3,66

0,06

cub. fc.

V

cub. c.

2,60

cub. fc.

2,93

0,33

cub. fc.

2,90

0,30

cub. fc.

Nb

cub. c.

2,86

cub. fc.

3,14

0,28

cub. fc.

3,10

0,24

cub. fc. déformé

Ta

cub. c.

2,86

cub. fc.

3,13

0,27

hex. (Ta2N)

3,05

0,19

cub. fc.

Mo

cub. c. hex. c.

2,72

hex.

2,90

0,18

hex.

2,86

0,14

W

cub. c.

2,72

hex.

2,90

0,18

cub. fc. (WîN)

U

cub. c. orth. rh.

2,76

cub. fc.

3,48

0,72

cub. fc.

3,44

0,68

Cr

cub. c.

2,50

cub. fc.

cub. fc.

2,92

0,42

Distance Expansion Me-MeA Me-MeA

2,99

0,07

2,91

0,31

3,13

0,27

cub. fc.

cub. fc.

Le problème de la localisation des atomes légers dans la structure se pose, dans le cas des carbures, nitrures et oxydes, d’une façon beaucoup plus simple que dans celui des hydrures. L’encombrement des atomes de carbone, d’azote et d’oxygène est en effet, quel que soit l’état dans lequel ils se trouvent dans ces composés, nettement supérieur à celui de l’atome d’hydrogène. Il en résulte que pour ces atomes la position la plus probable est celle des sites hexacoordinés, dont la totalité se trouve occupée dans les composés MeX, et dont une partie seulement est occupée dans les composés Mc2X (la moitié) et Me4X (le quart). C’est sans doute l’une des raisons pour lesquelles les structures des carbures et nitrures et oxydes interstitiels des métaux de transition sont généralement plus simples que celles de leurs hydrures.

NATURE DES LIAISONS DANS LES CARBURES, NITRURES ET OXYDES DES MÉTAUX DE TRANSITION Différentes tentatives ont été faites, pour interpréter l’ensemble des propriétés des composés d’insertion des éléments de transition d’après la nature des liaisons mises en jeu. La difficulté majeure à laquelle on se heurte est d’arriver à justifier dans ces composés la coexistence de caractères considérés comme spécifiques de types de liaison entièrement différents. Le problème est en effet compliqué dans le cas des carbures et des nitrures par l’apparition de la dureté et de l’infusibilité qui caractérisent habituellement les composés (ou éléments) possédant un réseau tridimensionnel de liaisons covalentes, tandis que la conductivité électrique et l’opacité jointes à l’éclat métallique témoignent d’un mode de liaison comparable à celui des métaux. Umanski a repris en 1943 (28) la conception que Ubbelohde avait utilisée pour interpréter les propriétés du système palladiumhydrogène et l’a étendue aux carbures et nitrures interstitiels. Le carbone et l’azote dont les potentiels d’ionisation ne sont pas extrê­ mement différents de celui de l’hydrogène céderaient comme celui-ci une partie de leurs électrons au métal auquel ils se trouvent associés en formant des phases à caractère métallique. Cette conception trouve un appui dans les expériences de Seith et Kubachewski (29)

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qui ont montré qu’à 1.000° le carbone dissous dans le fer migre vers la cathode sous l’influence d’un champ électrique. Il est vrai que dans le système fer-azote, Seith et Dauer (30) avaient cru observer dans des conditions analogues une migration vers l’anode, mais ce résultat s’est trouvé infirmé par Prosvirin (^i) qui a observé un transport électrolytique simultané du carbone et de l’azote vers la cathode dans les carbo-nitrures de fer. La première difficulté à surmonter dans cette théorie est d’expli­ quer la réorganisation complète de la structure du métal à la suite de son union avec le carbone et l’azote. Comment comprendre en effet que l’introduction d’atomes supplémentaires de dimensions minimes puisse entraîner une perturbation importante de la structure, si la nature des liaisons ne se trouve pas entièrement modifiée du fait de cette introduction? L’explication fournie par Umanski repose sur l’intervention des pressions internes élevées résultant de l’introduction des atomes étrangers, pressions dont l’existence serait prouvée par l’expansion des distances métal-métal, lorsqu’on passe du métal à la phase d’insertion, et qui provoquerait une véritable transformation allo­ tropique du métal. Cette explication à laquelle Ubbelohde avait déjà fait appel dans le cas des hydrures, semble présenter dans le cas présent un caractère exclusivement formel. Une autre difficulté est d’expliquer par cette théorie l’apparition de l’extrême dureté et de l’infusibilité. D’après Umanski la dureté élevée des composés d’insertion résulterait d’un mécanisme de blocage des plans de glissement du métal par les atomes interstitiels, analogue à celui qui fut invoqué à peu près à la même époque pour expliquer le phénomène de durcissement structural dans les alliages. Il ne fournit semble-t-il aucune explication de l’infusibilité. On peut être surpris enfin de voir un échange électronique s’effec­ tuer dans le sens prévu par cette théorie, entre deux catégories d’éléments dont les électronégativités sont telles que l’on escompterait plutôt un échange en sens inverse, à savoir un transfert électronique du métal à l’élément léger. Toutefois il n’est pas impossible que la présence des niveaux électroniques sous-jacents vacants dans les métaux vienne infirmer les prévisions que l’on peut faire en se basant sur la comparaison des électronégativités, lorsque ces dernières ont des ordres de grandeur voisins.

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Rundle a développé en 1948 (3^) une interprétation issue en partie des idées de Pauling (33). Cette interprétation au lieu de mettre l’accent comme les précédentes sur l’aspect métallique des liaisons, donne une importance plus grande à l’aspect covalent de celles-ci. Rundle fonde son raisonnement sur la remarque faite plus haut que dans la plupart des carbures, nitrures ou oxydes interstitiels répondant à la formule Me X, les atomes légers possèdent six voi­ sins métal équidistants, échangeant avec ceux-ci six liaisons orien­ tées suivant les sommets d’un octaèdre. La permanence de cette structure en dépit des variations nombreuses de valence et d’affinité que présentent les métaux de transition, jointe aux caractères phy­ siques dont il a été question plus haut, tendrait à prouver, selon cet auteur, que ces liaisons ont des orientations imposées par leur nature même et possèdent par conséquent un certain caractère covalent. Il ne peut s’agir d’une liaison de covalence classique puisque les éléments légers : carbone, azote, oxygène, appartiennent à la première série brève du tableau périodique et ne peuvent mettre en jeu de ce fait que quatre orbitales alors que dans l’hypothèse de Rundle ils contractent six liaisons équivalentes. Le problème est donc de trouver une combinaison stable de trois ou quatre orbitales qui puissent se répartir uniformément entre six liaisons. Parmi les solutions possibles on peut mentionner l’intervention des trois orbitales 2 px, 2 py, 2 pz orientées suivant les arêtes d’un trièdre trirectangle et assurant par symétrie les six liaisons octaédriques équivalentes, mais ce n’est pas la seule possibilité qui puisse être envisagée. Quelle que soit la solution adoptée, cette interprétation suppose le partage par résonance de chaque doublet électronique entre plusieurs orbitales du métal. Ce partage s’accompagnerait d’une mobilité particulière des électrons et par suite de l’apparition de la conductibilité électrique; il n’irait pas cependant jusqu’à entraîner la délocalisation des liaisons comme cela est le cas dans les édifices métalliques typiques, de sorte que les propriétés physiques liées au caractère orienté des liaisons se trouveraient sauvegardées. Rappelons que la notion de liaison covalente fractionnaire a été introduite par le même auteur pour expliquer l’existence d’une liaison uranium-hydrogène-uranium dans l’hydrure d’uranium. Elle semble trouver toutefois un champ d’application plus vaste dans les carbures, nitrures et oxydes que dans les hydrures, chez lesquels la permanence du caractère métallique est beaucoup plus grande par

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suite du caractère électropositif plus marqué de l’hydrogène. Cette conception a été étendue récemment par Krebs

à un certain

nombre de composés ioniques présentant simultanément le caractère métallique.

TRANSITION CARBURES

DE ET

LA

LIAISON

NITRURES

DANS

LES

METALLIQUES

Pour mieux prendre conscience de la valeur des arguments invoqués à l’appui des théories que nous venons de passer en revue il est intéressant d’étudier par comparaison les carbures et nitrures métal­ liques dans lesquels les liaisons sont nettement différentes. La transition des carbures interstitiels typiques cubiques à faces centrées (représentés par exemple par le monocarbure de titane) vers les carbures ioniques, ne semble se manifester dans aucun monocarbure. Par contre, plusieurs dicarbures des métaux de tran­ sition (LaC2, ThC2, UC2) témoignent déjà d’une évolution vers l’état ionique; celle-ci se marque par un accroissement de l’activité chimique et par l’apparition d’une structure à basse symétrie mono­ clinique (35). Dans ces composés les atomes de carbone se trouvent associés par paires dans les intervalles du réseau des atomes métal­ liques. . Avec les dicarbures des métaux très électropositifs du type Ca C2, on a affaire à des composés franchement ioniques, comportant des ions C2~ et facilement décomposables par l’eau avec formation de carbures d’hydrogène à deux atomes de carbone, parmi lesquels domine l’acétylène. L’association des atomes de carbone par paires dans ces composés est due au fait que si les atomes de carbone demeuraient isolés, la coordinence qui leur serait imposée deviendrait incompatible avec le diamètre élevé des ions métalliques qui sont appelés à les entourer. C’est également la raison pour laquelle, en dépit de leur électropositivité élevée, des métaux comme le sodium ou le potassium donnent des carbures du type Na2C2 et non pas du type Na4C (36. 37). Ceci constitue un bon exemple des restrictions que les facteurs d’ordre géométrique peuvent, dans ces composés, apporter à la réalisation des possibilités offertes par la constitution électronique des éléments en présence.

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Si nous examinons d’autre part la transition des carbures inter­ stitiels vers des formes de liaison spécifiquement métalliques, nous sommes amenés à constater qu’un bon exemple de système présen­ tant ce mode intermédiaire de liaison est constitué par la solution solide de carbone dans la structure cubique à faces centrées du fer (austénite). Cette dissolution entraîne une dilatation progressive du volume de la maille (^8) sans apporter de changement radical aux propriétés du métal pur sous l’état y. La diminution progressive de la conductibilité électrique et l’altération de quelques autres propriétés en fonction de la teneur en carbone prouve cependant que l’introduction de cet élément en insertion modifie l’état élec­ tronique du métal. Si l’on se réfère aux résultats expérimentaux signalés plus haut concernant le transport du carbone dans le fer à l’état solide sous l’influence d’un champ électrique (29), il apparaît que dans cette phase la liaison résulte d’un transfert électronique du carbone vers le métal, ce qui, joint à l’absence des caractères de dureté exceptionnelle et d’infusibilité, conduit à la considérer comme authentiquement métallique. Les mêmes observations pourraient être faites au sujet de la solution solide d’azote dans le fer y. Par contre le système fer-azote possède en outre une phase distincte, répondant sensiblement à la formule Fe4N, et qui se rapproche beaucoup par ses caractères des composés interstitiels typiques (^9. 40). Il existe donc parmi les carbures et dans une certaine mesure parmi les nitrures, une filiation qui fait apparaître les composés interstitiels typiques du carbone et de l'azote avec les métaux de transition, comme des termes de passage entre des phases purement ioniques dans les­ quelles l'élément léger joue le rôle d'un anion et des phases essentiel­ lement métalliques. Il semble ainsi possible de concilier dans une certaine mesure les différentes théories qui se proposent d’expliquer les caractères des composés d’insertion typiques, à l’exclusion toutefois de celles qui voudraient assimiler l’union de l’élément léger au métal de transition à une sorte de coexistence uniquement régie par les lois de la géométrie. Il est hors de doute que la conception de Ubbelohde-Umanski représente d’une manière satisfaisante les caractères du système palladium-hydrogène à partir duquel elle a été édifiée. Elle correspond également assez bien aux solutions solides primaires non seulement de l’hydrogène mais encore du

102

carbone, transition,

de

l’azote

et

de

l’oxygène

dans lesquelles l’élément léger

dans

les

semble

métaux

de

effectivement

adopter un état pseudo-métallique, et qui conservent l’essentiel des propriétés physiques du métal. Cette conception s’écarte par contre manifestement de la réalité lorsqu’elle prétend égale­ ment expliquer la constitution des carbures et nitrures d’inser­ tion, infusibles et de grande dureté, dont le type est le earbure de titane. Elle est en effet incapable de rendre compte de l’apparition des structures et des propriétés entièrement nouvelles qui carac­ térisent ce genre de composés. Pour les composés de ce type la conception de Rundle mérite à son tour d’être prise en considération, car elle permet de justifier la coexistence des caractères covalents typiques qui s’y manifestent avec évidence et des caractères métalliques qui ne sont qu’en appa­ rence hérités du métal d’origine. C’est en particulier à la formation d’un réseau tridimensionnel de liaisons quasi-covalentes que sont dues la dureté et l’infusibilité exceptionnelles de ces phases au même titre que dans le diamant et dans le carbure de silicium. Il apparaît ainsi que les composés d’insertion typiques des métaux de transition doivent leur physionomie, bien moins à des relations d’ordre géométrique entre les atomes comme on l’avait pensé jadis, qu’à des particularités étroitement liées à la structure élec­ tronique à savoir : 1° Une faible différence d’électronégativité entre les partenaires, exeluant la formation d’une liaison ionique et tendant à favoriser la liaison de covalence ; 2° L’existence dans le métal d’un nombre d’orbitales supérieur à celui des doublets disponibles, entraînant ipso facto le caractère métallique. Ces considérations ne doivent pas inciter cependant à négliger les méthodes d’approche géométriques du problème, qui fournissent à toutes les théories la base concrète qui leur est indispensable. Les données de structure sont en effet susceptibles de donner des indications précieuses sur la nature des liaisons, et la voie indiquée par Hâgg, il y a plus de vingt ans, conserve aujourd’hui encore toute sa valeur.

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VARIATIONS DE COMPOSITION DANS LES COMPOSÉS D’INSERTION Nous examinerons tout d’abord à ce point de vue les hydrures. Les phases figurant dans les systèmes métal-hydrogène possèdent dans bon nombre de cas des domaines extrêmement étendus de variation de la concentration en phase homogène. Ces domaines s’accroissent lorsque la température et la pression d’hydrogène augmentent et il est difficile, comme il a été dit plus haut, d’attribuer une signi­ fication particulière aux concentrations limites observées par exemple à la température ordinaire. On peut tenter de justifier cette extension des domaines monophasés par le petit rayon de l’atome d’hydrogène mais cette explication est insuffisante puisqu’un métal comme le nickel, dont la structure est pourtant identique à celle du palladium ne fixe pas d’hydrogène dans le réseau cristallin Tout au plus peut-on affirmer que les facteurs géométriques ne viennent pas, dans les systèmes métal de transition-hydrogène, restreindre les variations de concentration autorisées par les données électroniques. En ce qui concerne ces dernières, qui demeurent donc primordiales, on pourrait faire observer en se basant sur l’exemple du système palladium-hydrogène, que l’étendue

maximum

du

domaine

de

concentration est fixée par le taux de remplissage des niveaux d vacants du métal par les électrons provenant de l’hydrogène. Dans l’état actuel de nos connaissances cette interprétation ne peut malheu­ reusement pas être poussée très loin et nous en sommes réduits aux conjectures pour la plupart des autres systèmes. Par une voie entièrement différente. Lâcher (“*2) et Anderson (‘•3)* puis Rees (44) ont tenté de retrouver a priori les valeurs des limites de phases en rattachant le passage des états monophasés aux états diphasés, à l’énergie d’interaction des atomes d’hydrogène dispersés dans le réseau du métal. Cette méthode, comme nous l’avons dit plus haut, a donné des résultats conformes à l’expérience dans les systèmes palladium-hydrogène (42), platine-soufre (43) et zirconiumhydrogène (45), mais ne semble pas avoir pu être étendue à d’autres systèmes. Ces larges variations de concentration ne s’observent que dans les phases hydrogénées qui conservent un caractère métal­ lique marqué. L’apparition des premiers indices de liaison ionique s’accompagne d’une diminution brusque de l’étendue des domaines d’homogénéité comme c’est le cas pour l’hydrure d’uranium (i*’ 3^).

104

Les variations de concentration des carbures des métaux de tran­ sition sont, à quelques exceptions près, beaucoup moins importantes que celles des hydrures. En ce qui concerne les solutions solides primaires tout d’abord, il est remarquable de constater qu’elles sont extrêmement réduites, sinon absentes, pour tous les métaux donnant des carbures interstitiels typiques (Zr, V, Mo, W, etc.). Seul le titane dissout le carbone jusqu’à atteindre la formule Ti Co_o5 Le fer, qui ne donne pas de carbure interstitiel typique, donne naissance dans l’état y à la solution solide primaire austénitique dont la concentration peut atteindre 1,8 % à 1.100<>, ce qui correspond à la formule Fe Cq os- L’existence des formes martensitiques instables dans lesquelles le carbone est placé dans les lacunes d’un réseau quadratique, et la solubilité pratiquement négligeable du carbone dans la ferrite témoignent d’une manière évidente de l’influence de la structure sur la solubilité. Néanmoins le facteur géométrique n’est certainement pas le seul à intervenir puisque, pour ne citer que cet exemple, le nickel dont la structure est la même que celle du fer y et les dimensions très voisines ne dissout à la même température que 0,3 % C (47). En ce qui concerne les carbures interstitiels proprement dits, les variations de composition sont particulièrement importantes pour le monocarbure de titane (de Ti Cq j8 à Ti C) (46) et le monocarbure de vanadium (de VCq^j à VC, J (48). Les composés similaires du zirconium, du hafnium, du molybdène et du tungstène par contre ne présentent pas d’écarts à la stoechiométrie. Pour ce qui est des carbures de thorium et d’uranium, on a signalé (49. so) un passage continu de Th C à ThC2 et de UC à UC2 aux températures élevées, sans que des précisions aient été données semble-t-il sur la façon dont la structure s’accommode de ces variations de concentration. Les nitrures interstitiels typiques présentent des caractères simi­ laires du point de vue des écarts à la stoechiométrie. La composition du nitrure de titane, de même structure cubique à faces centrées que le carbure, varie de Ti N0 42 à Ti N,,05. Le nitrure de vanadium présente des écarts moindres, quant aux autres nitrures les rensei­ gnements sont trop imprécis pour qu’il puisse en être fait état. Les données concernant les oxydes interstitiels sont encore peu nombreuses. Le cas du monoxyde de titane est remarquable car ce composé présente des variations de composition depuis

105

Ti Og jg jusqu’à Ti 0,33 sans autre changement de structure qu’une variation linéaire de l’arête de la maille en fonction du rapport du titane à l’oxygène. En se basant sur la mesure des densités, Ehrlich (5i) a cru pouvoir affirmer qu’à la composition stoechiométrique Ti O le réseau comportait un nombre égal de sites vacants de chaque espèce, évalué à 15 % du nombre total des sites. Dans les phases riches en titane, le nombre des lacunes oxygène serait supérieur à celui des lacunes titane et inversement dans les phases riches en oxygène. Dans le cas du monoxyde de vanadium (52) la composition varierait de VOq s à VO, 2 • Les données concernant ZrO, HfO, NbO, et VO ne permettent pas de conclure quant à l’étendue des variations de composition. De l’ensemble des renseignements que l’on possède sur les écarts à la stoechiométrie des composés interstitiels typiques il résulte qu’il existe une analogie évidente à cet égard entre les carbures, nitrures et oxydes. Deux métaux : le titane, et à un degré moindre le vanadium présentent, quel que soit l’élément léger qui leur est associé, des variations de composition importantes de part et d’autre de la composition stoechiométrique du monoxyde. Etant donné le petit nombre des données expérimentales, il n’est pas certain qu’ils soient les seuls à posséder ce caractère. Toutefois, il ne semble pas possible d’affirmer, comme on l’a fait parfois, que l’existence de domaines importants de variations de concentration en phase homo­ gène soit un caractère général propre aux composés d’insertion typiques. Si certains d’entre eux présentent effectivement des variations considérables, ils paraissent plutôt constituer des exceptions parmi l’ensemble des composés de ce type. Cette remarque ne concerne ni les systèmes métal-hydrogène dans lesquels les variations impor­ tantes de concentration sont de règle, ni les solutions solides primaires résultant de l’insertion d’atomes légers dans le réseau d’un métal.

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BIBLIOGRAPHIE

(>) H.J. Goldschmidt, J. Iran Steel Inst., 160 (1948), p. 345. (2) D.P. Smith, « Hydrogen in metals », Univ. Chicago Press, Chicago (1948)* (3) W. Klemm, Naturwiss, 37 (1950), p. 172.

(“•) P. Schwartzkopf et Kieffer, « Refractory hard metals », Mc Millan, New York (1953). (5) D.T. Hurd, « An introduction to the chemistry of the hydrides », J. Wiley & Sons, inc., New York (1952). (®) E. Wiberg, Angew. Chem., 65 (1953), p. 16. (J) G. Hâgg, Z. Phys. Chem., B 6 (1930), p. 221; Z. Phys. Chem., B 11 (1931), p. 433; Z. Phys. Chem., B 12 (1931), p. 33.

(8) R. Kiessling, Acta Chem. Scand., 4 (1950), p. 209. (9) G. Hâgg et Kiessling, J. Inst. Metals, 81 (1952), p. 57. (10) R. Gibb et Kruschwitz, J. A. C. S., 72 (1950), p. 5365.

(11) A. Mc Quillan, Proc. Roy. Soc., 204 (1950), p. 309. (12) Mrs. M.N.A. Hall, Martin et Rees, Trans. Farad. Soc., 41(1945), (13) E.

p. 306.

Gulbransen et Andrew, /. Electrochem. Soc., 101 (1954), p. 474.

(14) S.S. Sidhu et Mc Guire, /. Applied Physics, 23 (1952), p. 1257. (15) L. Gillespie & Hall, J. A. C. S., 48 (1926), p. 1207. (16) L. Gillespie & Galstaun, J. A. C. S., 58 (1936), p. 2565.

(17) E.A. Owen, Phil. Mag., 35 (1944), p. 50; E.A. Owen & Williams, Proc. Phil. Soc. (Londres), 56 (1944), p. 52. (18) J. Burke & Smith, J. A. C. S., 69 (1947), p. 2500.

(19) T. Gibb, Mc Sharry & Kruschwitz, J. A. C. S., 74 (1952), p. 6203. (20) A. Michel, J. Bénard & G. Chaudron, Bull. Soc. Chim. France, 12 (1945), p. 336. (21) L. Pauling & Ewing, J. A. C. S., 70 (1948), p. 1660.

(22) C.E. Holley, Mulford, Ellinger, Koehler & Zachariasen, J. Phys. Chem., 59 (1955), p. 1226. (23) N.F. Mott, Proc. Roy. Soc., A 153 (1935), p. 699. (24) A. Coehn & Specht, Z. Physik, 62 (1930), p. 1. (25) B. Duhm, Z. Physik, 94 (1935), p. 434; Z. Phys, 95 (1935), p. 801 (26) A.R. Ubbelohde, Proc. Roy. Soc., A 159 (1937), p. 295. (27) R.E. Rundle, J. A. C. S., 69 (1947), p. 1719. (28) J.S. Umanski, Ann. Sect. anal. Phys.-chim., Inst. chim. gen. (U.S.S.R.), 16

n» 1, (1943), p. 127. (29) W. Seith & Kubachewski, Z. Elektrochem., 41 (1935), p. 551.

(30) W. Seith & Daur, Z. Elektrochem., 44 (1938), p. 256. (31) V.I. Prosvirin, Vestnik Metallprom., 17, n” 12 (1937), p. 102. (32) R.E. Rundle, Acta Cryst., 1 (1948), p. 180. (33) L. Pauling, « Nature of Chemical Bond », Ithaca (N. Y.) (1945), p. 419. (34) H. Krebs, Naturwiss., 40 (1953), p. 525.

(35) E.B. Hunt & Rundle, J. A. C. S., 73 (1951), p. 4777. (36) V. Stackelberg, Z. Physical Chem., B Tl (1934), p. 53.

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(37) H. J. Emeleus & Anderson, « Modem Aspects of inorganic chemistry » Routledge, Londres (1954), p. 477. (38) C.S. Roberts, Journal of Metals, 5, n» 2 (1953), p. 203. (39) V.G. Paranjpe, Cohen, Bever & Floe, Journal of Metals, 188, n° 2 (1950)

p. 261 (Transactions). (40) K.H. Jack, Acta Cryst., 3 (1950), p. 392; Acta Cryst., 5 (1952), p. 404. (41) M. Baker, Jenkins & Rideal, Trans. Farad. Soc., 51 (1955), p. 1592. (42) Lâcher, Proc. Roy. Soc., A 161 (1937), p. 525. (43) J.S. Anderson, Proc. Roy. Soc., A 185 (1946), p. 69. (44) A.L.G. Rees, Trans. Farad. Soc., 50 (1954), p. 335.

(45) S. Martin & Rees, Trans. Farad. Soc., 50 (1954), p. 343. (46) p. Ehrlich, Z. anorg. Chem., 259 (1949), p. 1. (47) R.H. Schaefer (non publié). (48) E. Maurer, Ddring & Pulewka, Arch. Eisenhüttenwesen, 13 (1939), p. 337. (49) H.A. Wilhem, Chiotti, Snow & Daane, J. Chem. Soc., cinquième partie

(1949), p. 318. (50) H.A. Wilhem & Chiotti, Trans. A.S.M., 42 (1950), p. 1295. (51) P. Ehrlich, Z. Elektrochem., 45 (1939), p. 362. (52) N. Schônberg, Acta Chem. Scand.. 8 (1954), p. 221.

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Composés ioniques non stoechiométriques par Jacques BÉNARD

L’existence de composés minéraux susceptibles de présenter dans l’état solide des variations de la composition sans que le système cessât de demeurer monophasé a été signalée depuis longtemps. L’exemple le plus anciennement connu est celui des silicates naturels dans lesquels la proportion des différentes catégories d’atomes métal­ liques peut varier considérablement dans une même famille cristalline. Ce n’est qu’à une époque relativement récente que furent signalées dans certains composés ioniques binaires des variations du rapport métal --------------- . Plusieurs groupes de chercheurs s’efforcèrent de préciser non métal l’étendue des domaines d’homogénéité de ces phases, parmi lesquels on peut citer principalement Schenck et ses collaborateurs en Alle­ magne, Jette et Foote aux Etats-Unis, Haraldsen et ses collaborateurs en Norvège, Hâgg et ses collaborateurs en Suède, Chaudron et ses collaborateurs en France. On s’aperçut ainsi peu à peu que les premiers exemples sur lesquels on s’était appuyé pour édifier ces théories, loin de constituer des exceptions comme on l’avait pensé tout d’abord, n’étaient en fait que des manifestations exceptionnel­ lement marquées, d’une propriété générale des composés ioniques solides. Grâce au perfectionnement des méthodes expérimentales d’investigation, un nombre sans cesse croissant de composés non stoechiométriques est maintenant signalé chaque année. (*) * Nous conviendrons d’appeler composé non stoechiométrique (Berthollide) tout composé dans lequel on peut faire varier de façon continue le rapport cation -----:----- sans changement de phase. anion D’après cette convention, le domaine de stabilité d’un composé non stoechio­ métrique peut inclure ou ne pas inclure le rapport stoechiométrique simple par lequel il est habituellement désigné.

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Parallèlement à cette accumulation de données expérimentales le développement des études sur les imperfections des édifices cristallins vint apporter à cet ensemble la justification théorique qui lui faisait défaut. Généralisant, en effet, la conception introduite initialement par Frenkel et par Schottky pour expliquer la formation des défauts dans les composés stoechiométriques, plusieurs auteurs parmi les­ quels il faut citer surtout Wagner et Hâgg proposèrent différents mécanismes permettant de justifier les variations de composition observées dans les phases non stoechiométriques. Bien que ces interprétations comportent maintenant encore bien des aspects obscurs, elles constituent à l’heure actuelle un outil de travail extrê­ mement précieux. Il est à noter que la physique a fait de son côté très largement appel à l’existence de défauts de ce genre pour justifier l’apparition de certaines propriétés dans les solides. L’abondance des défauts indiquée par ces propriétés étant toutefois très inférieure à celle qui correspondrait au seuil de sensibilité des méthodes de l’analyse chimique, il est le plus souvent impossible de contrôler directement la réalité des variations de composition postulées. Afin d’établir une ligne de démarcation entre ces deux ordres de recherches, nous nous limiterons ici à l’étude des composés non stoechiométriques dans lesquels les variations de composition peuvent être contrôlées par l’analyse chimique. Il ne saurait être question de passer en revue, même brièvement, dans le cadre de ce rapport, tous les travaux qui ont été effectués depuis quelques années dans ce domaine. On trouvera dans une excel­ lente mise au point due à Anderson (i), la plupart des références des publications antérieures à 1947; seules seront reprises ici celles d’entre elles qui offrent un intérêt pour l’interprétation générale des phéno­ mènes en discussion. Notre bibliographie sera par contre plus explicite en ce qui concerne les publications postérieures à 1947. Nous avons rassemblé sous forme d’un tableau les composés binaires non stoechiométriques pour lesquels les variations de composition semblent les mieux établies. Ce tableau ne prétend pas être complet; n’y figurent pas en particulier les systèmes encore très controversés ou trop complexes pour s’accommoder de cette représentation sché­ matique (système uranium-oxygène par exemple). On ne manquera pas de remarquer enfin que, bien que cette étude ne concerne en

110

principe que des composés ioniques, le tableau comporte bon nombre de corps dans lesquels la liaison est sans aucun doute partiellement covalente ou métallique.

METHODES DE DÉTERMINATION DE L’ÉTENDUE DES DOMAINES La détermination de l’étendue du domaine de variation de la concentration d’une phase non stoechiométrique peut se faire par des méthodes variées. La valeur des renseignements obtenus dépend dans une large mesure de la nature de la phase examinée. Lorsque la variation de concentration s’accompagne d’une varia­ tion importante des paramètres cristallins, la méthode la plus sensible est la détermination des paramètres limites aux deux extrémités du domaine, au moyen de la diffraction des rayons X. Si l’on a déterminé au préalable la courbe de variation des paramètres en fonction de la concentration, on obtient immédiatement les valeurs des concen­ trations limites correspondantes. On est limité dans cette voie par la sensibilité des méthodes de mesure ; pour les phases de symétrie cubique présentant un état de cristallisation optimum, la précision relative la meilleure que l’on puisse obtenir est semble-t-il voisine de 1/10.000 en employant la méthode en retour. On ne peut espérer obtenir des résultats sérieux en se fondant sur la non évidence d’une seconde phase pour conclure qu’un échan­ tillon est situé dans le domaine monophasé. La sensibilité des méthodes d’identification au moyen de microscope ou des rayons X ne dépasse pas en effet quelques unités pour cent. Seule la méthode magnétique peut assurer une grande sensibilité (*5o) lorsque la seconde phase dont la présence est escomptée est ferromagnétique. On a beaucoup utilisé la méthode basée sur l’étude des équilibres de réduction. Considérons par exemple le sulfure de nickel NiS, qui a fait l’objet d’un travail récent (i8). Ce sulfure coexiste en équi­ libre à 600° soit avec le sulfure Ni3S2 (côté pauvre en soufre) soit avec le sulfure NiS2 (côté riche en soufre). L’étude du domaine de variation de composition de cette phase peut se faire en partant d’un mélange NiS2 -f NiS en équilibre avec une atmosphère H2S/H2 à cette température. Si l’on soustrait périodiquement de l’hydrogène

111

sulfuré de la phase gazeuse, en mesurant après chaque soustraction la valeur du rapport /7H2S/PH2 après rétablissement de l’équilibre, on obtient une courbe présentant la forme indiquée schématiquement

Figure 1.

Equilibres de NiS avec les mélanges H2-*-H2S d’après Rosenqvist.

dans la figure 1. La portion oblique correspond au domaine de variation continue de la composition de NiS dans lequel le système est monovariant à température et à pression données. Les limites de ce domaine correspondent aux abcisses des points anguleux de la courbe dont les valeurs sont en principe faciles à déterminer si l’on connaît la composition initiale du système et les quantités d’hydrogène sulfuré soustraites. Avec un composé rigoureusement stoechiométrique le passage d’un palier à l’autre s’effectuerait au contraire par une discontinuité verticale. Le danger de ce procédé réside dans le fait que la lenteur de la diffusion dans la masse solide tend à arrondir les courbes aux environs des points angu­ leux et peut laisser croire à une étendue du domaine monophasé plus grande qu’elle n’est réellement. En fait, il est très difficile de conclure par cette méthode à l’existence de domaines monophasés dont l’étendue est inférieure à 1 %. Pour ces derniers, la seule solution est de suivre les variations d’une grandeur physique liée à la concentration : point de Curie pour les ferromagnétiques, conductibilité électrique, etc. La sensibilité des variations de la conductibilité électrique est parfois considérable et a conduit à présumer de l’existence des variations de composition inappréciable par les méthodes chimiques classiques; elle offre toutefois l’incon­ vénient de ne pouvoir être rattachée directement à l’échelle des

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concentrations; de plus, comme toutes les méthodes très sensibles, elle peut être troublée par des facteurs secondaires difficiles à apprécier (impuretés, état de cristallisation, etc.)A côté des méthodes qui se proposent de déceler l’étendue des variations de composition, il faut mentionner celles qui permettent d’identifier la nature des défauts de réseau qui en sont responsables. La densité tout d’abord qui, jointe à la mesure des paramètres cristal­ lins, permet lorsqu’elle est mesurée avec précision de décider si la variation de la concentration est due à une soustraction d’atomes ou à une insertion d’atomes supplémentaires dans le réseau. Il convient toutefois de n’user qu’avec circonspection de l’argument densité, lorsqu’il s’agit de conclure comme l’ont fait certains auteurs à la présence d’une certaine proportion de défauts dans un composé rigoureusement stoechiométrique, en comparant les valeurs des densités déterminées expérimentalement à celles que l’on peut calculer à partir des dimensions de la maille cristalline. En ce qui concerne la polarité des défauts, la conductibilité électrique, le pouvoir thermo­ électrique, et surtout l’effet Hall donnent des informations intéres­ santes. Plus récemment ont été mises à profit les méthodes magné­ tiques et la spectroscopie d’absorption pour l’étude des états électro­ niques des ions en présence.

DONNÉES GÉNÉRALES SUR LES DÉFAUTS DE RÉSEAU Les interprétations, auxquelles on fait actuellement appel pour expliquer les variations de composition des phases ioniques non stoe­ chiométriques, ont trouvé leur origine dans la théorie des défauts dans les composés stoechiométriques, qui fut édifiée jadis par Frenkel (49), Wagner et Schottky (50-5i). Cette théorie a été maintes fois décrite depuis et il ne saurait être question de l’analyser ici dans tous ses détails. Nous retiendrons seulement pour clarifier la discussion qui va suivre qu’elle postule l’existence de deux sortes de défauts: 1“ Un ion occupant initialement un site cristallographique normal peut venir occuper une position interstitielle normalement inoccupée dans le réseau idéal, en faisant apparaître une lacune réticulaire; 2° Un ion occupant initialement un site cristallographique nor­ mal peut venir occuper une position réticulaire normale, à la surface du solide, en faisant apparaître une lacune réticulaire comme dans le cas précédent.

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Alors que le premier type de défaut ne peut en aucun cas entraîner un changement de composition, le second type de défaut ne répond à cette condition que s’il affecte en nombre égal les cations et les anions. L’existence de ces deux catégories de défauts dans des composés qui doivent être considérés, d’après les critères de la chimie classique, comme des composés strictement stoechiométriques, est demeurée pendant de nombreuses années hypothétique. Le développement des recherches sur la conductibilité ionique des halogénures alcalins et la comparaison des résultats ainsi obtenus avec ceux de l’autodiffusion des éléments marqués dans ces composés (53-54) a conduit à en confirmer l’existence. L’argument essentiel réside en effet dans l’impossibilité où l’on se trouverait d’expliquer, dans l’hypothèse d’un réseau complet, les énergies d’activation de diffusion relativement peu élevées que l’on mesure. Bien que l’idée jadis émise par Smekal selon laquelle les migrations ioniques s’opéreraient grâce à la présence des défauts mosaïques des cristaux, ait bénéficié depuis quelques années d’un regain d’actualité à 1a suite du succès de la théorie des dislocations, rien n’indique qu’un changement des conceptions fonda­ mentales soit à la veille de se produire dans ce domaine. Si l’on considère d’autre part qu’à une température donnée un cristal stoechiométrique en équilibre avec une atmosphère de composition déterminée comporte un certain nombre de défauts de chaque sorte, on peut admettre qu’il existe à l’intérieur du solide un équilibre entre les différentes catégories de défauts. Comme les énergies de formation des différentes catégories de défauts sont inégales, l’une d’elles prédomine généralement dans un édifice cristallin déterminé à une température donnée. Les défauts de Schottky se forment de préférence dans les solides dans lesquels les ions antagonistes ont des dimensions voisines et l’énergie de Van der Waals peu élevée. Ces deux conditions se trouvent réalisées dans un certain nombre d’halogénures alealins. Les défauts de Frenkel sont au contraire plus fréquents dans les solides présentant une grande disparité dans les dimensions des ions et mettant en jeu une énergie de Van der Waals importante. Différentes tentatives ont été faites pour calculer a priori les énergies de formation des défauts dans un réseau idéal (55-56-57). On a pu atteindre ainsi des ordres de grandeur dans le cas de formation des lacunes au sein d’un réseau simple.

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mais il n’existe aucune méthode qui permette d’évaluer l’énergie de formation des défauts interstitiels. A la lumière de ce qui précède la conception que l’on peut se faire des causes des variations progressives de la composition chimique d’un composé ionique binaire non stoechiométrique AB peut donc se ramener aux quatre mécanismes suivants : 1° Insertion d’atomes A supplémentaires dans le réseau de AB supposé complet; 2° Soustraction d’atomes B non compensée par celle d’un nombre égal d’atomes A; 3° Insertion d’atomes B supplémentaires; 4° Soustraction d’atomes A non compensée par celle d’un nombre égal d’atomes B. Il convient de noter que les possibilités d’insertion et de soustrac­ tion posent des problèmes entièrement différents suivant qu’il s’agit de cations ou d’anions. Ce point marque la différence essentielle qui distingue les composés non stoechiométriques ioniques des com­ posés intermétalliques dans lesquels les deux types d’atomes possèdent des électronégativités voisines et peuvent, de ce fait, être aisément permutés. On remarquera en particulier que nous avons éliminé a priori dans le cas présent la cause de variation de composition qui correspondrait à une substitution de A à B ou de B à A, une telle opération étant irréalisable dans un composé à liaison ionique marquée.

CONSTITUTION ELECTRONIQUE DES COMPOSÉS IONIQUES NON STOECHIOMÉTRIQUES Les différents mécanismes qui viennent d’être envisagés comportent un certain nombre de conséquences d’ordre électronique, géométrique et thermodynamique. Nous examinerons tout d’abord l’aspect électronique du problème. Considérons en premier lieu le cas le plus fréquent d'une soustraction de cations dans le réseau cristallin. Cette soustraction se traduit du point de vue de la composition chimique, par un accroissement de la teneur en l’élément non métallique au delà de la composition

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théorique qui correspond à l’occupation complète de tous les noeuds du réseau. Afin que soit maintenue la neutralité électrostatique de l’édifice, il est nécessaire qu’un certain nombre d’entre les ions restants modifient leur charge en conséquence. Ce résultat pourrait être atteint en principe aussi bien par une diminution de la charge négative des anions que par un accroissement de la charge positive des cations. La première solution n’est pas à envisager dans les halogénures, oxydes et sulfures métalliques parmi lesquels se rangent la plupart des com­ posés non stoechiométriques. Reste la seconde qui est effectivement observée dans la plupart des oxydes des métaux de transition dans lesquels le métal ne se trouve pas à l’état de valence électropositive maximum. L’un des exemples les plus connus est celui de l’oxyde FeO dont le domaine de composition peut s’étendre jusqu’à FeOi,i9 à la température de 1.000“ Jette et Foote (15*) furent les premiers à suggérer que pour chaque ion Fe^+ soustrait du réseau cristallin de FeO, deux ions Fe^+ devaient apparaître. Un peu plus tard cette hypothèse fut utilisée par Hâgg pour expliquer la formation de Fe203y par soustraction d’ions Fe2+ dans le réseau de Fe304 avec passage simultané d’un nombre double d’ions Fe2+ à l’état de Fe3+ (16). Depuis lors, nombreux sont les exemples qui ont été cités de composés qui seraient le siège d’un équilibre ionique analogue. Dans tous ces cas l’écart à la stoechiométrie ne se manifeste, comme il est normal de le prévoir, que dans le sens correspondant à un excès du constituant non métallique. On pourrait citer à l’encontre de cette règle le cas des monoxydes de certains métaux à valence élevée parmi lesquels TiO, ZrO, VO, qui peuvent comporter des variations de composition correspondant à un excès de métal; nous verrons plus loin cependant qu’il s’agit de composés dans lesquels les confi­ gurations électroniques sont entièrement différentes de celles que l’on rencontre dans les oxydes supérieurs correspondants (Ti02, Zr02, VO2). La même remarque vaudrait pour de nombreux soussulfures des métaux de transition, parmi lesquels on peut citer la phase non stoechiométrique Ni3S2. Le fait que la réalisation de ce type de défaut soit subordonnée à l’existence d’un état stable de valence supérieure du cation consti­ tue, sur le plan des propriétés chimiques usuelles, l’expression d’une condition plus générale à savoir la possibilité pour celui-ci d’atteindre un état d’ionisation supérieur en ne mettant en jeu qu’une énergie minime. Cette condition est réalisée pour la plupart des éléments

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de transition dont les énergies d’ionisation successives ne sont pas extrêmement différentes. De ce point de vue il n’est nullement néces­ saire que l’état d’ionisation impliqué dans la phase non stoechio­ métrique corresponde à un état de valence du métal apparaissant dans l’une de ses combinaisons stables. C’est ainsi que l’enrichissement en oxygène de la phase NiO entraîne l’apparition d’ions Ni3+ aux­ quels ne correspond semble-t-il aucun composé ionique connu. On a supposé qu’un enrichissement en constituant non métallique pouvait encore se produire, à une échelle il est vrai beaucoup plus réduite, dans des composés comportant des cations qui ne possèdent pas la même aptitude à changer de valence. Tels sont les halogénures alcalins qui semblent pouvoir tolérer dans le réseau un très léger excès d’halogène. Il ne semble pas à vrai dire que la variation de composition correspondante ait pu être déterminée dans ce cas et seules les variations des propriétés physiques sont là pour en témoi­ gner (58). Ceci nous amène à poser la question de savoir dans quelle mesure il existe une relation entre l’énergie qu’il faut mettre en jeu pour changer l’état d’ionisation des cations et l’étendue des domaines de variation de composition dans les composés non stoechiométriques à lacunes cationiques. L’exemple des halogénures alcalins, dans lesquels une énergie d’ionisation élevée se trouve associée à un domaine de variation de composition extrêmement faible, serait en faveur d’une telle relation mais, hormis ces cas extrêmes, il ne semble pas possible d’en confirmer l’existence. Le changement de l’état d’ionisation du cation constitue en effet une condition nécessaire mais non suffisante à l’existence d’une variation de composition selon le processus examiné ici, et d’autres facteurs parmi lesquels les interactions de défauts et les facteurs d’ordre géométrique doivent être pris en considération. Bien que l’étude des propriétés physiques ne puisse être appro­ fondie ici, il est intéressant de noter au passage que les composés non stoechiométriques à lacunes cationiques sont des semi-conduc­ teurs du type P, dans lesquels la conductibilité est assurée par les trous positifs et croît avec la pression partielle de Télément non métal­ lique en équilibre avec le solide. Des études très complètes ont été faites d’autre part concernant l’incidence d’un excès d’halogène sur les spectres d’absorption des halogénures alcalins; des bandes apparaissent en particulier, dans le proche ultra-violet.

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L'existence des écarts à la stoechiométrie par suite de la soustraction des anions a été reconnue plus tardivement que l'existence des écarts dus à la soustraction des cations. Du point de vue de l’équilibre électrostatique, la soustraction des anions exige en principe le passage d’un certain nombre de eations restants à un état inférieur de valence électropositive. Il y a lieu de prévoir que ce mécanisme doit appa­ raître en particulier dans les composés qui correspondent à la valenee ionique la plus élevée d’un métal possédant plusieurs états de valence. Tel est le cas des dioxydes des métaux tétravalents : Ti02, Mn02, Ce02, entre autres, qui peuvent perdre une partie de leur oxygène lorsqu’ils sont portés sous vide aux températures élevées ou traités en atmosphère réductrice. Ainsi le dioxyde de titane stoechiométrique qui est blanc lorsqu’il est chauffé aux températures moyennes en atmosphère fortement oxydante, perd de l’oxygène lorsqu’il est chauffé en atmosphère réductrice. La variation de composition qui en résulte conduit à la valeur limite TiOi,9 (3); elle s’aeeompagne d’un aceroissement considérable de la conduetibilité électrique et d’un changement de teinte (passage au bleu-noir). Dans le cas du dioxyde de manganèse (14) la perte d’oxygène conduit à la com­ position limite MnOi,g; dans le cas du dioxyde de cérium (32-33) jusqu’à la valeur limite CeOi,5. Dans tous ces exemples on admet que la perte d’oxygène entraîne l’apparition de sites inoccupés dans le réseau des anions, un eertain nombre d’ions tétravalents passant à l’état trivalent. Les oxydes supérieurs des métaux de transition dont la valence maximum n’excède pas III semblent beaucoup moins sujets aux variations de composition par perte d’anions. Par exemple, le ses­ quioxyde de fer sous sa forme stable rhomboédrique présente des variations de composition qui exercent une certaine influence sur les propriétés physiques, et en particulier sur les propriétés magné­ tiques, mais qui sont difficilement appréciables par les méthodes chimiques. La présence d’un excès de constituant métallique explicable par la présence d’un réseau anionique lacunaire ne se limite pas exclu­ sivement aux composés de métaux de transition. Le cas de l’oxyde de baryum est instructif à cet égard. Chauffé à 1.000° dans la vapeur de baryum cet oxyde acquiert une teinte bleue (3i). L’étude de la diffusion thermique de cette coloration conduit à un coefficient de diffusion très différent de celui de baryum dans BaO (39), ce qui

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laisse à penser qu’elle n’est pas due à la diffusion d’ions baryum. Les défauts résultant du traitement dans la vapeur de baryum seraient donc vraisemblablement des lacunes d’oxygène. La détermination de l’excès de baryum par la voie chimique conduit à 0,04 % Ba dans les oxydes traités à 1.100°. Il n’est pas surprenant que l’étendue du domaine de variation de la composition observée ici soit très inférieure à celle que l’on peut observer dans les composés des métaux qui se prêtent à un changement facile de valence. Le méca­ nisme de compensation électrostatique ne saurait être en effet ici le même puisque le baryum ne possède qu’une seule valence ionique stable. Il faut donc admettre qu’en présence de vapeur de baryum à haute température certains ions O^- du réseau cristallin intérieur se portent vers la surface. Chaque fois qu’un atome de baryum supplémentaire issu de la phase vapeur s’agrège à la surface de l’oxyde après ionisation, un ion oxygène de l’intérieur du réseau migre à la surface en faisant apparaître une lacune anionique dans laquelle les deux électrons provenant de l’ionisation de l’atome de baryum sont captés. C’est à la présence de ces électrons dans les lacunes anioniques que serait due l’apparition d’une bande d’absorp­ tion dans le visible. Cette conception due à Sproull, Bever et Libowitz (^t) montre que la diminution de charge électropositive des cations restants n’est pas la seule voie par laquelle un composé ionique peut tolérer un accroissement de la teneur en métal. La différence entre les deux processus réside essentiellement dans le fait que dans l’un (cations à valence variable) les électrons provenant de l’ionisation des atomes métalliques supplémentaires sont captés par certains cations, tandis que dans l’autre (cations à valence fixe) les électrons viennent se fixer dans les lacunes du réseau anionique. Bien que dans ce dernier cas la présence des électrons dans les lacunes assure à celles-ci une relative stabilité, les variations de composition qui en résultent sont toujours de faible amplitude. Ce mécanisme est identique à celui qui est admis pour expliquer les colorations prises par certains halogénures alcalins chauffés dans la vapeur du métal correspondant (60-61-62)_ Par exemple, le chlorure de potassium chauffé vers 5(X)° dans la vapeur de potassium devient violet par suite de la formation de lacunes anioniques occupées par les électrons (centres F) provenant de l’ionisation d’atomes de potassium supplémentaires fixés à la surface. Les variations de composition correspondantes sont toutefois

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trop faibles pour être perceptibles par l’analyse chimique, aussi ne nous étendrons-nous pas sur cette question si importante à d’autres égards. La formation des lacunes ioniques occupées par des électrons, qui provoque l’apparition des bandes d’absorption dans le visible fait également apparaître des propriétés électriques entièrement différentes de celles du composé stoechiométrique. Si l’extraction des électrons des lacunes a lieu spontanément à température peu élevée, le solide est semi-conducteur avec un coefficient de température positif. Un grand nombre de phases non stoechiométriques, isolantes à la tempé­ rature ordinaire, acquièrent par ce mécanisme une conductibilité électronique appréciable lorsque la température s’élève, alors que les phases stoechiométriques correspondantes demeurent d’excellents isolants dans les mêmes conditions. L’extraction des électrons des lacunes anioniques peut également se produire par absorption d’éner­ gie lumineuse et le composé non stoechiométrique manifeste alors la propriété de photo-conductivité. Les variations de composition résultant de l'insertion d'ions supplé­ mentaires dans les intervalles d'un réseau cristallin sont beaucoup moins fréquentes que celles qui résultent de la soutraction de certains ions. Si l’on s’astreint à ne considérer comme nous l’avons fait jusqu’ici que les combinaisons binaires dans lesquelles la liaison possède un certain caractère ionique, c’est-à-dire si on élimine d’une part les hydrures, borures, carbures et nitrures des métaux de transition et d’autre part les composés d’insertion moléculaires, le nombre des composés non stoechiométriques interstitiels s’avère singulièrement réduit. L’insertion des unions autres que ceux qui viennent d’être cités est en effet peu probable si l’on tient compte du volume relati­ vement élevé de la plupart d’entre eux. Seules ont été en fait observées quelques insertions de cations, n’entraînant d’ailleurs que des varia­ tions de concentration très minimes. Un bon exemple en est donné par l’oxyde de zinc, qui est suscep­ tible de dissoudre une petite quantité de zinc; on admet généralement que le zinc en excès se trouve en position interstitielle dans le réseau hexagonal de ZnO. Cette hypothèse, préférée à celle qui consisterait à attribuer la présence d’un excès de zinc à des lacunes d’oxygène, est fondée à la fois sur les études de structure (30-63) et sur les études

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de diffusion du zinc radioactif dans l’oxyde

Les écarts à la

stoechiométrie entraînent l’apparition dans l’oxyde d’une conduc­ tibilité électronique élevée de type n, qui témoigne de l’état au moins partiellement ionisé des atomes de zinc en insertion. Les variations de la conductibilité électrique en fonction de la température et de la pression partielle d’oxygène qui règne au-dessus de l’oxyde ont fait l’objet de très nombreuses études mais il ne semble pas que l’étendue du domaine de variation de la concentration ait été déter­ minée avec certitude. L’existence de phases analogues semble avoir été également démontrée dans le cas de l’oxyde de cadmium et de l’oxyde d’argent par des études de structure. Dans le cas de l’oxyde de cadmium la proportion des ions Cd2+ s’élèverait à 0,5 % de la masse de l’oxyde. La variation de composition serait plus impor­ tante dans le cas de l’oxyde d’argent et égale à 4 % à 200“. La première remarque suggérée par l’étude de ces résultats est la faible étendue des variations de composition qui en résultent. Ceci est dû vraisemblablement aux énergies de répulsion élevée qui se manifestent dans le réseau à la suite de l’introduction des atomes interstitiels; dès que le nombre de défauts atteint une valeur même peu élevée, ceux-ci tendent à s’associer pour reconstituer la phase métallique après avoir récupéré les électrons cédés au moins partiel­ lement à l’oxyde. La seconde remarque, corollaire de la précédente, concerne le fait que les trois exemples cités ici, qui sont véritablement les seuls à propos desquels on puisse parler avec quelque certitude d’insertion, se rapportent à des combinaisons dans lesquelles le cation (Zn2+, Cd2+, Ag+) a la structure électronique à 18 électrons externes. On sait que ces ions sont extrêmement favorables au dévelop­ pement des forces de polarisation. L’insertion des ions supplémentaires serait donc rendue possible par la déformation des ions contigus. Du point de vue de la chimie descriptive, l’existence de ces phases résoud d’une manière semble-t-il définitive la question des sousoxydes de zinc, cadmium et argent dont on avait jadis admis l’exis­ tence. Les changements de teinte que l’on observe lorsque les oxydes normaux se trouvent en présence d’un excès de métal et qui avaient contribué pour une grande part à affirmer cette existence résultent simplement du déplacement des bandes d’absorption propres à l’oxyde stoechiométrique vers le visible par suite de l’introduction des défauts de réseau.

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Avant de passer à l’étude géométrique de ces problèmes, il est nécessaire de faire remarquer que de nombreux écarts à la stoechiométrie ont été signalés dans la littérature sur la foi d’arguments indirects, parmi lesquels la variation de la conductibilité en présence d’un excès de l’un ou l’autre des éléments constitutifs est le plus souvent invoquée. Nous n’en ferons pas état ici pour rester fidèle à la règle que nous nous sommes imposée dans ce rapport de ne tenir compte que des systèmes dans lesquels l’existence d’une variation de composition a été démontrée par voie chimique. Il est hors de doute cependant que ces composés sont pour la plupart le siège de processus similaires à ceux que nous venons d’étudier. Seule la faible importance des variations de composition n’a pas permis encore de la confirmer et il serait souhaitable que des efforts soient faits pour mettre au point des méthodes microanalytiques appropriées à la résolution de ce genre de problème.

INCIDENCE DES VARIATIONS DE COMPOSITION SUR LA STRUCTURE L’existence de variations de la composition chimique dans les composés ioniques ne soulève pas seulement des problèmes d’équilibre électronique. Les différents processus que nous avons envisagés pour expliquer ces variations de composition supposent en effet des réorganisations dans la nature et les positions des ions qui doivent être discutées du point de vue de la structure. Cette discussion se fonde actuellement sur deux ordres de renseignements ; les résultats de l’analyse de structure par les rayons X et les mesures de densité. Nous examinerons tout d’abord l’incidence des processus de formation de laeunes ou d’insertion sur les constantes cristallines. La présence d’un excès de l’un des constituants dans un composé ionique se traduit suivant les eas par un accroissement ou par une diminution du volume de la maille cristalline. On a toujours admis, jusqu’à maintenant, que l’accroissement du volume de la maille constituait une preuve de la position interstitielle des atomes en excès, tandis que la diminution du volume correspondait à la formation de lacunes. Il paraît certain que l’introduetion d’atomes plus ou moins ionisés dans des interstices dont les dimensions sont insuffisantes pour leur faire place sans déformer les atomes contigus, entraine

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un accroissement des forces de répulsion qui doit provoquer un accroissement du volume de la maille cristalline. On trouvera dans la figure 2 la variation de la maille de l’oxyde de cadmium en fonction de la quantité de cadmium en excès dans le réseau. Les solutions interstitielles à caractère métallique ont aussi un volume de maille croissant en fonction de la teneur en élément supplémentaire, mais l’étendue des domaines homogènes est généralement plus grande dans ces systèmes. Dans le cas des variations de composition par formation de lacunes, la diminution du volume de la maille est parfois importante (fig. 2). Il a été jusqu’à maintenant impossible d’établir une corrélation entre

Figure 2.

Variation du volume de la maille en fonction de la composition : CdO d’après Faivre NiS d’après M. Laffitte et Bénard

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les variations du volume de la maille et les rayons des ions soustraits, car de nombreux facteurs influent sur cette variation : énergie de réseau du composé à l’état stoechiométrique, changement de dimen­ sion des ions ayant été amenés à changer de valence, polarisation des ions. L’incidence des variations de la composition des composés non stoechiométriques sur leur densité dépend elle aussi de la nautre du processus mis en jeu. Si la variation du rapport du nombre des unions à celui des cations n’entraînait aucune variation du volume de la maille, toute insertion s’accompagnerait d’une augmentation de la densité et toute soustraction d’une diminution de celle-ci. Mais les paramètres cristallins varient, de sorte qu’il faut tenir compte de cette variation pour décider de la nature des défauts du réseau d’après l’étude de la variation de la densité. En fait les insertions s’accompa­ gnent toujours d’un accroissement de la densité, accroissement d’ail­ leurs minime si l’on tient compte de la faible étendue des domaines correspondants, tandis que la formation des lacunes peut entraîner suivant les cas une diminution ou un accroissement de la densité. La comparaison des variations de la densité mesurée et des variations calculées dans l’une ou l’autre hypothèse fournit donc en principe un critère de la nature des défauts de réseau responsables de la variation de composition. Ce critère a été fréquemment utilisé, mais pas toujours semble-t-il avec toute la prudence désirable. On sait, en effet, combien l’obtention de chiffres de densité ayant une réelle signification est difficile, et combien leur interprétation peut donner lieu à des erreurs. La technique de mesure semble autoriser une précision correspondant à quelques unités de la troisième décimale sous réserve de prendre les précautions d’usage : élimination préalable des gaz adsorbés et remplissage sous vide du vase pycnométrique en particulier. Mais les valeurs ainsi obtenues sont fonction de la température à laquelle a été préparé le solide, la densité étant d’autant plus élevée que la température de préparation est elle-même plus élevée. Il en résulte que les valeurs de densité ainsi obtenues sont très souvent inférieures, dans le cas du composé strictement stoechio­ métrique, à la densité calculée. On a reproduit dans la figure 3 quelques courbes de variations de la densité en fonction de la composition qui ont permis de décider de la nature des défauts dans des cas aujourd’hui classiques. On voit d’après ces exemples que si les valeurs absolues de la densité n’ont pas toujours une signification

124

Figure 3. Variation de la densité en fonction de la composition; FezOjy d’après Hâgg; FeSe d’après Hâgg et Kindstrdm; NiS d’après M. Laffitte et Bénard

indiscutable, le sens de la variation de la densité en fonction de la composition est généralement significatif si les échantillons comparés ont été préparés à la même température. En fait tous les cas dans lesquels l’argument densité a été décisif sont des cas de formation de lacunes qui sont les seuls à donner lieu à des variations de concen­ tration relativement importantes et par conséquent à des variations de densité également importantes. L’existence fréquente des écarts de densité par défaut dans les composés stoechiométriques eux-mêmes pose un problème qui méri­ terait d’être discuté. Ces écarts sont souvent dus, lorsque le solide a été préparé à une température relativement peu élevée par rapport à sa température de fusion, à des imperfections de cristallisation. Ces imperfections disparaissent parfois lorsque la température augmente, mais il y a des cas où la densité théorique n’est jamais atteinte. De là a attribuer l’écart de densité du composé stoechiométrique à la présence d’une proportion déterminée de lacunes ioniques des deux espèces il n’y a qu’un pas qui a été franchi par différents auteurs. L’exemple le plus caractéristique a été fourni par Ehrlich (}) à propos de l’oxyde TiO dans lequel il y aurait à la composition stoechio­ métrique 15 % environ de lacunes de chaque sorte, et des interpré­ tations analogues ont été produites pour les oxydes similaires comme VO. Il y a Heu de noter toutefois que ces composés possèdent un type de liaison particulier, fort éloigné de la liaison ionique et l’on ne connaît en fait aucun exemple de composé purement ionique possédant un nombre aussi grand de lacunes symétriques.

ECARTS A LA STOECHIOMÉTRIE PAR SUBSTITUTION D’IONS DE VALENCE DIFFERENTE Nous avons vu que la variation de composition dans une phase non stoechiométrique binaire s’accompagnait le plus souvent d’un changement de valence de certains cations restants. Il a été reconnu qu’inversement le remplacement progressif des ions du réseau normal par des ions étrangers possédant une valence fixe différente de celle des ions auxquels il se substituent, provoquait l’apparition d’écarts à la stoechiométrie grâce à la stabilisation d’un certain nombre de défauts de réseau. Nous nous bornerons à citer ici quelques cas typiques qui illustrent les différentes possibilités offertes par ces substitutions.

126

Zintl, Croatto et Hund ont montré par de nombreux travaux l’extraordinaire aptitude des réseaux cristallins du type fluorure de calcium à subir une variation du nombre des cations lorsqu’on remplace les cations du composé stoechiométrique par des cations de valence différente. Deux sortes de variations sont à envisager : a) Lorsque les cations du réseau stoechiométrique normal sont remplacés par des ions de valence inférieure, la compensation des charges à lieu par la formation d’un certain nombre de lacunes dans le réseau anionique. Tel est le cas des phases mixtes qui se forment dans les systèmes Zr02-Ca0 (66), Zr02-Y203 (67), UO2-Y2O3 (68), Ce02-La203 (69), Th02-La203 (70). On aura une idée de l’étendue des variations de composition qui peuvent être réalisées de cette façon en examinant le dernier cité de ces systèmes qui présente un domaine homogène jusqu’à la composition ThLa03,5 correspondant au remplacement de la moitié des ions Th*+ de Th02 par des ions La^+, et à l’absence d’un ion O^- sur quatre initialement contenus dans Th02. b) Lorsque les cations du réseau stoechiométrique normal sont remplacés par des ions de valence supérieure, la compensation des charges a lieu par insertion d’un certain nombre d’anions supplé­ mentaires dans les positions disponibles (4 par maille élémentaire) du réseau. Tel est le cas du système Cap2-YF3 dans lequel chaque substitution de Y8+ à Ca2+ entraîne l’insertion d’un ion F~ supplé­ mentaire (71). Le même processus entre en jeu dans le système

CaF2-LaF3. Ces opérations sont rendues possibles grâce à la similitude des ions échangés, qui permet l’introduction massive des cations étrangers sans apporter de perturbation notable dans la structure. Mais il est hors de doute que la nature du réseau type du fluorure de calcium est pour beaucoup dans cette possibilité de variation du nombre des sites anioniques occupés dans un domaine aussi étendu. Rien ne permet semble-t-il d’expliquer actuellement cette aptitude tout à fait exceptionnelle parmi les composés ioniques. Tout au plus peut elle être comparée par son ampleur à celle que l’on rencontre dans les phases possédant la structure de l’arséniure de nickel (à l’exception de NiAs lui-même) ou au passage de Fe304 à Fe203y dans la structure spinelle.

127

Wagner, Hauffe et leurs collaborateurs (72-73-74-75-76-77) ont pos­ tulé l’existence de phases non stoechiométriques résultant de substitu­ tions d’ions divalents dans les halogénures des métaux monovalents. Par exemple la substitution d’un ion Cd2+ à Ag+ dans le bromure d’argent entraîne la formation d’une lacune Ag+; celle de Sr2+ à K+ dans le chlorure de potassium entraîne la formation d’une lacune K+. L’étendue des phases homogènes non stoechiométriques ainsi obtenues serait assez grande puisque d’après Teltow (28) AgBr dissoudrait à 350° 25 mol % CdBr2, 10 mol % PbBr2 et 1 mol % ZnBr2- L’existence de phases mixtes dont la formation résulterait de ce processus a été admise sur la foi des variations de la conduc­ tibilité électrique dans de nombreux autres systèmes. On peut citer dans le même ordre d’idées les phases mixtes intermédiaires entre les ferrites substituées Fe2^+ (Fe2+, Me2+04) de structure type spinelle et les oxydes mixtes correspondants dérivés du sesquioxyde y de fer (79) les phases mixtes entre Fe2Co04 et Fe203y (80) et celles entre FeO et FeLi02 (*')• H convient de rappeler enfin que Verwey (82) a été le premier à préconiser la mise à profit des substitutions pour stabiliser dans un édifice ionique une certaine proportion de défauts et obtenir ainsi des propriétés physiques déterminées.

DÉTERMINATION A PRIORI DE L’ÉTENDUE DES DOMAINES Les bilans d’échanges électroniques qui ont été décrits dans les paragraphes précédents définissent des conditions nécessaires à la réalisation des variations de composition dans les phases non stoechio­ métriques, mais ne constituent qu’un des aspects de la question. Il est facile de se rendre compte en effet que le nombre maximum de défauts tolérés par un édifice peut accuser des différences considé­ rables d’un système à l’autre sans qu’il soit toujours possible de relier ces différences aux énergies d’ionisation des cations figurant dans cet édifice. Tout au plus est-il possible d’énoncer la proposition suivante : les variations de composition des combinaisons ioniques sont généralement favorisées par : 1° Le passage facile des cations d’un état d’ionisation à un autre 2° La polarisabilité élevée des anions, elle-même reliée à leur grand diamètre

128

3° L’existence de certaines structures parmi lesquelles on peut citer celle de l’arséniure de nickel et celle du fluorure de calcium. Pour ces raisons les chercheurs se sont orientés simultanément vers une étude globale de l’équilibre des défauts, ne préjugeant en aucune façon de la nature des forces, d’origines multiples qui concourent à l’établissement de cet équilibre et en déterminent les limites. L’idée centrale est due à Wagner-Schottky (5i), qui se sont placés dans le cas de solides présentant un nombre de défauts suffisamment petit pour qu’il soit possible de négliger leurs interactions; elle réside dans l’existence d’une relation entre la présence de défauts dans les solides répondant à la composition stoechiométrique (défauts intrinsèques) et l’aptitude de ces derniers à présenter des variations de composition en phase homogène. Il est admis au départ que tout composé ionique solide, stoechiométrique ou non, comporte un certain nombre de défauts qui coexistent en équilibre. La proportion des différents types de défauts qui participent à cet équilibre est fonc­ tion de la température et de la composition de l’atmosphère. Le caractère endothermique de la formation des défauts entraîne en l’absence de toute autre cause de variation de leur nombre un accrois­ sement de celui-ci lorsque la température s’élève. A une température donnée, une variation de la pression partielle du constituant volatil dans l’atmosphère peut provoquer dans certains cas une variation du rapport du nombre des défauts des différentes catégories, c’est-à-dire une variation continue de la composition. L’énergie libre du solide varie de ce fait et passe généralement par un minimum pour une valeur particulière de la composition qui correspond à un état de stabilité maximum. L’énergie mise en jeu dans la formation des défauts étant la même, que ces défauts entraînent ou non une variation de la composition, on conçoit que l’existence de nombreux défauts dans un édifice à rapport stoechiométrique simple soit favorable à l’apparition de variations de composition importantes lorsque les conditions du milieu s’y prêtent. Inver­ sement un édifice dans lequel la répartition des ions est quasi-idéale à la composition stoechiométrique ne doit présenter que des variations de composition insignifiantes. Le calcul, conduit d’après cette idée, permet d’établir la relation qui existe à une température donnée entre la pression partielle p„ du constituant volatil dans l’atmosphère en équilibre avec le solide, (rapportée à la pression partielle po en

129

équilibre avec le solide de composition théorique) et les écarts à la composition stoechiométrique exprimés par le nombre « de défauts non compensés. La phase dont la composition est la plus influencée par les variations de pression est celle dont l’état de désordre S est le plus grand à l’état stoechiométrique (fig. 4).

Figure 4

Relation entre les variations de composition et la pression par­ tielle pn du constituant volatil, pour différents états de désordres intrinsèques S (d’après Anderson).

L’établissement a priori de ces courbes se heurte à de grandes difficultés. 11 faudrait en effet connaître au préalable les énergies de formation des lacunes de différents types ainsi que la proportion des défauts intrinsèques de la phase stoechiométrique. Or ni l’une ni l’autre de ces grandeurs ne peut être appréciée d’une façon certaine dans l’état actuel de nos connaissances. Par contre, de telles relations devraient permettre, si elles étaient vérifiées, de déterminer la proportion des défauts dans les phases stoechio­ métriques d’après le tracé expérimental des courbes de variation de la composition en fonction de pjp^ qui n’offre aucune difficulté Dans tout ce qui précède les défauts responsables des variations de composition sont supposés en nombre suffisamment petit pour que leurs interactions soient négligeables. Cette hypothèse étant dans bon nombre de cas en contradiction avec les faits, différents auteurs parmi lesquels il faut citer dans l’ordre chronologique : Lâcher (*3), Anderson (*•♦) et Rees (*5), se sont efforcés de transposer

130

le mode de raisonnement précédent en faisant intervenir les inter­ actions entre défauts dans le cadre de la mécanique statistique. Bien que la plupart des exemples envisagés par ces auteurs concernent des phases métal-hydrogène totalement dénuées de caractère ionique, nous croyons nécessaire de mentionner ces tentatives car elles semblent a priori pouvoir s’appliquer à tous les systèmes non stoechiométriques. D’après ces auteurs, il est théoriquement possible en introduisant un certain nombre d’hypothèses sur la nature des interactions entre les différents types de défauts, de déterminer les valeurs des concentractions limites au-delà desquelles se produit une ségrégation des défauts avec apparition d’une nouvelle phase. Un excellent accord entre la théorie et les données expérimentales a été obtenu de cette façon par Lâcher pour les phases palladium-hydrogène, par Anderson pour les phases platine-soufre et par Rees pour les phases zirconiumhydrogène. En ce qui concerne le dernier de ces systèmes, il paraît toutefois prématuré de considérer l’accord comme définitif, car l’étude expérimentale laisse encore place à bien des incertitudes. Pour séduisantes que soient ces méthodes d’approche, il ne semble pas cependant qu’elles aient apporté jusqu’à maintenant beaucoup de résultats positifs. Le petit nombre des systèmes dans lesquels leur application a été tentée laisse planer un doute sur leur généralité. Elles n’en constituent pas moins des tentatives intéressantes qui pour­ ront être reprises lorsque nous posséderons plus d’informations sur les caractères thermodynamiques des défauts réticulaires. Nous avons attiré l’attention il y a un instant sur l’existence d’un minimum sur les courbes de variation de l’énergie libre d’une phase homogène présentant des variations de composition, en fonction de la composition. Il est logique d’admettre que le plus souvent la position de ce minimum dans l’échelle des concentrations doit correspondre à un rapport stoechiométrique simple puisque c’est pour ce rapport que chaque ion d’une espèce est entouré du nombre maximum d’ions de l’espèce antagoniste. Mais il convient de noter que l’étendue des domaines d’homogénéité de la phase à une tempé­ rature déterminée ne dépend pas exclusivement de la forme de la courbe d’énergie libre de cette phase. En effet, si une courbe d’énergie libre à minimum très accusé correspond nécessairement à un domaine étroit, une courbe à minimum très arrondi ne corres­ pond pas nécessairement à un domaine large. La largeur du domaine

131

est en effet déterminée dans ce second cas par la différence entre l’énergie libre du minimum de la phase considérée et celles des minima des phases adjacentes. On peut comprendre ainsi que dans certains cas le rapport stoechiométrique simple soit exclu du domaine de concentration à l’intérieur duquel la phase peut être observée dans un état stable.

132

133

134 Métal

Mn

Composé

MnO

NaCl

(14)

Mn203

cubique 112O3

(14)

Sn02 orthorhombique

(14)

a, b)

NaCl

F6304

spinelle

(16)

spinelle

(16)

(15

(17) (18)

FeSe

1-NiAs 2-monoclinique

Fei_xTe

Ni As

FeTei.ii FeTe2

Co

PbO marcassite

MeX,

H 1 1,13

■ m 1,33 1,4 1,5 1,6

1,8

1 3.5

2

(14)

FeO FC2037

^deXj

(14)

tétragonal

Mn207

MeX

Me Réf.

Mnj04

MnOz

Fe

Type de structure

(19) (20) (21) (21)

1 0

1 0

I 0

■IB 1,19

1

___ l

NiAs

(18)

CoTe

NiAs

(22)

CoTB2

Cdl2

(22)

1,14

1 1,11

■ 1.4 1,5

■ 1,95

2,10

H

1 0

0

^■■Bl l 1,15 1,33

(21)

CoS

1.33 1,5

1,04 1,15

1 0

1

2

>600 «C

Métal

Ni

Composé

NiO NijSz NiS NiS2 NiSe NiSc2 NiTe NiTc2 Ni As

Zr

Nb

Mo

Type de structure

NaCi rhomboédrique NiAs pyrite NiAs Cdh NiAs Cdl2 hexagonal

ZrS ZrS2

AgZr Cd(OH>2

Nbi-xS Nbi+xS NbS2

WC NiAs CdCl2

M0O2 M04O11

135

M0O3

monoclinique orthorhombique orthorhombique

Me

MeX

tIeXa

MeX,

Réf.

(23)

1

1

0,988 1

0

(18) (18) (24) 0 (22) (22) (22) (22) (25) (26)

(6) (®) (22)

1

0

1



0 = 600*C

■ 1 1,06

2

1

2

1

1 0

2 2

1

1

0

(®) (6) («)

0,577 0,794

1 1

1

2

H 0

0,9

1

2

1,2

(28) (29)

1 (28) (29) (28) (29)

0

1

1,97

2,08

■ 2,65 2,75 2,95 3

136 Métal

Composé

Type de structure

Me

Ag

Ag2Û

CU20

(30)

Cd

CdO

NaCl

(30)

Ba

BaO

NaCl

(31)

Ce203

cubique

Ce

Ta

Ce02

1 0

1

0

(32) (33)

1

(32) (33)

0

1

06283

Th3P4

CeS2

Th3P4

(34)

0

(35)

H ■ 0 0,25

Ta40

TaS2

orthorhombique orthorhombique Cd(OH)2

WS2

clinique M0S2

MeX,

1

1 1,006

0,99977 I

1,5 1,33

2

1,5

2

2,5

(35) (S)

(36) (37)

WO3

yIeX2

1 0,48 0,5

1 0

(34)

Ta02

w

cubique

MeX

Réf.

1 0

2

1,6

B 2,82 2,95

1 0

(38) (39)

1 0

■ 1,95 2

Métal

Tl

Composé

Type de structure

Me

(44)

TI4S3

0

PbO (rouge)

pseudo tétragonal

(41) (42) (43)

Pb304

tétragonal

(42) (43) (44) (45)

Pb02

tétragonal

(42)

Th

ThvSia

hexagonal

(46)

NP

NP3Û8

U3O8

(47)

PU2O3

cubique faces centrées

(48)

Pb

MeX

MeXî

MeXj

Réf.

■ 0,66 0,75

1 0

1 1,02

1,315

1,33

1,57

1,87 2

■ 1,71 1,76

1 0

1

■ 2,61 2,67

0

1 0

1,5

1,75

137

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(33) M. Bruno, Rie. Sci., 20 (1950), p. 645. (34) W.H. Zachariasen, Acta Cryst., 2 (1949), p. 57. (35) M. Schônberg, Acta Chem. Scand., 8 (1954), p. 240. (36) O. Glemser & H. Sauer, Z. anorg. Chem., 252 (1943), p. 144.

138

(37) G. Hâgg & A. Magneli, Arkiv Kem. Min. Geol., 19 A (1945), n° 2, p. 14. (38) O. Glemser, S. Hubert & O. Konig Z. anorg. Chem., 257 (1948), p. 241. (39) P. Ehrlich, Z. anorg. Chem., 257 (1948), p. 247.

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16 (1949), p. 124. (93) R. Faivre, Arch. orig. Centre Docum. C.N.R.S. (1950), n” 308, p. 96. (99) G.L. Clark & R. Rowan, J. amer. Chem. Soc., 63 (1941), p. 1305. (95) P. Laffitte & C. Holtermann, C. R. Acad. Sci, 204 (1937), p. 1813.

(96) W.H. Zachariasen, Acta Cryst., 2 (1949), p. 288. (97) J.J. Katz & D.M. Green, J. amer. Chem. Soc., 71 (1949), p. 2106.

(98) R.C.L. Mooney & W.H. Zachariasen, Natl. Nuclear Energy Ser., Div. IV, 14 B; « Transuranium Eléments Pt. II » (1949), p. 1442. (99) J. Frenkel, Z. Phys., 35 (1926), p. 652. (50) C. Wagner, Phys. Chem. Ionie Cryst., SI (1953), p. 741. (51) W. Schottky, Z. phys. Chem., 29 B (1935), p. 335; C. Wagner & W. Schottky, Z. phys. Chem., 11 B (1930), p. 163. (52) W. Lehfeldt, Z. phys., 85 (1933), p. 717. (53) D. Mapother, H. Crook & R. Maurer, J. Chem. Phys., 18 (1950), p. 1231. (59) J.F. Laurent & J. Bénard, C. R. Acad. Sci., 241 (1955), p. 1204. (55) W. Jost, Trans. Farad. Soc., 34 (1938), p. 860. (56) N.F. Mott & J. Littleton, Trans. Farad. Soc., 34 (1938), p. 485. (57) R. Hutner, E. Rittner & F.K. du Pré, J. Chem. Phys., 17 (1949), p. 198; J. Chem. Phys., 17 (1949), p. 204; J. Chem. Phys., 18 (1950), p. 379. (58) K. Hauffe, Ergebnisse der Exakten Naturwiss., XXV (1951), p. 193. (59) R.W. Redington, Phys. Rev., 87 (1952), p. 1066. (60) R. Pohl, Z. Phys., 39 (1938), p. 36. (61) I. Estermann, Lievo & Stern, Phys. Rev., 75 (1949), p. 627. (62) G. Dienes, J. Chem. Phys., 16 (1948), p. 620. (63) T. Gray & Rodgers, Bristol (travail non publié). (69)

p.H. jr Miller, Phys. Rev., 60 (1941), p. 890.

(65) W. Moore & E. Secco (rapport communiqué personnellement).

(66) F. Hund, Z. phys. Chem., 199 (1952), p. 142. (67) F. Hund, Z. Elektrochem. angew. phys. Chem., 55 (1951), p. 363.

(68) J. Anderson, I. Ferguson & L. Roberts, J. inorg. and nuclear Chemistry, 1 (1955), p. 340. (69) E. Zintl & V. Croatto, Z. anorg. Chem., 242 (1939), p. 79. (70) F. Hund & W. Dürrwàchter, Z. anorg. Chem., 265 (1951), p. 67. (71) E. Zintl & Udgard, Z. anorg. Chem., 240 (1939), p. 150. (72) C. Wagner, /. Chem. Phys., 18 (1950), p. 62. (73) K. Hauffe, Ann. Phys. (6), 8 (1950), p. 201. (79)

K. Hauffe & A. Vierk, Z. Phys. Chem., 196 (1950), p. 160.

(75) K. Hauffe & J. Block, Z. Phys. Chem., 196 (1950), p. 438; Z. Phys. Chem.,

198 (1951), p. 232.

139

(7IS) K. Hauffe & H. Grunewald, Z. phys. Chem., 198 (1951), p. 248. {J^) K. Hauffe & Ch. Gensch, Z. phys. Chem., 195 (1950), p. 116. (78) J.

Teltow, Ann. Physik (6), 5 (1949),

p.

63.

(79) J. Bénard & G. Chaudron, C. R. Acad. Sci., 207 (1938), p. 1410. (80) J. Robin, Ann. Chimie, douzième série, 10 (1955), p. 389; C. R. Acad. Sci., 234 (1952), p. 956. (81) R. Collongues, C. R. Acad. Sci., 231 (1950), p. 143. (82) E. Verwey & F. Romeyn, Chem. Weekblad, 44 (1948), p. 705; E. Verwey, Bull. Soc. Chim. (1949), p. D 122; E. Verwey, « Oxidic Semiconductors », Butterworths Scientific Publications Ltd., London (1951), p. 151. (83) J.R. Lâcher, Proc. Roy. Soc., A 161 (1937), p. 525. (8‘t) J. Anderson, Proc. Roy. Soc., A 185 (1946), p. 69. (85) A. Rees, Trans. Farad. Soc., 50 (1954), p. 335.

140

Discussion M.

Timmermans. — Je voudrais soulever une question préjudi­

cielle. Comment distinguer entre les composés non stoechiométriques et des systèmes à cristaux mixtes et où séparer le domaine de ces composés non stoechiométriques de celui des systèmes chimiques en voie d’évolution? M. Bénard. — A l’origine, la notion de cristaux mixtes reposait essentiellement sur la possibilité que présentent deux phases distinctes de former des phases de compositions intermédiaires et variables, dont la structure est identique à celle des phases consti­ tutives. La plupart des exemples cités étaient en fait des solutions solides de substitution dans lesquelles la variation de composition résultait du remplacement de certains ions du réseau par des ions de même charge. Depuis quelques années, de nombreux exemples de phases à composition variable ont été étudiés, dans lesquels la variation de composition résulte d’opérations plus complexes parmi lesquelles on peut citer en particulier les substitutions d’ions de valence différente (Li+ substitué à Ni2+ dans NiO). Dans l’état actuel de nos connaissances, il paraît sage de réserver le terme de cristaux mixtes aux phases à composition variable dans lesquelles la variation de composition résulte de la substitution isomorphique d’ions ou de radicaux équivalents, sous réserve que les composés extrêmes soient connus. Nous appellerons, au contraire, composés non stoechiométriques, les phases dans lesquelles on peut provoquer des variations de composition autres que celles qui peu­ vent résulter d’une simple substitution isomorphique. A cette caté­ gorie appartiennent en particulier les composés ioniques binaires, dans lesquels on provoque une variation progressive du rapport du nombre des anions à celui des cations. Le terme de solution solide me paraît devoir être employé seule­ ment dans un sens extrêmement général, lorsqu’il n’est pas néces­ saire de préciser l’origine des variations de la composition. 141

Pour ce qui est de la distinction à établir avec les systèmes en voie d’évolution, les composés non stoechiométriques étudiés ici correspondent en principe, à des états d’équilibre. A chaque compo­ sition particulière de la phase solide non stoechiométrique, il doit être possible de faire correspondre une atmosphère particulière qui soit en équilibre avec elle. Il est évident que dans bien des cas les études ont été faites sur des systèmes hors d’équilibre en raison de la lenteur des transformations dans le solide.

M. Hâgg. — It may be appropriate to mention that cases hâve been found recently, where phases, which hâve since long been considered to hâve extended homogeneity ranges, are represented by a sériés of discrète phases with fixed compositions and closely related structures. In the System V — O, Anderson has found a sériés of phases with compositions VO,; where x— 1.67, 1.75, 1.80, 1.84, 1.86, 1.87. Ail these phases hâve been previously considered to belong to an extended VO2 phase. It is possible that they hâve hâve the general formule Vn02„_i (« = 3-8) and that their structure is related to the idéal VO2 structure in principally the same way as the structures of the phases Me„03n_| found by Magnéli in the System Mo — W — O, are related to the Re03 structure (the molybdenum oxides M08O23 and M09O26 are members of this sériés). Unpublished experiments show that an analogous sequence of phases exists in the System TiO at oxygen contents closely below the composition Ti02. The appearance of these phenomena seems to be connected with the pronounced tendencies of the central atoms to coordinate six oxygen atoms independent of charge variations.

M. Bénard. — Les observations rapportées par le Professeur Hâgg sont extrêmement intéressantes et soulèvent un problème très général. Il est hors de doute que certains systèmes non stoechiométriques manifestent une tendance très marquée à se résoudre en phases distinctes dont les compositions sont apparemment très voisines. Aux exemples cités par l’auteur, j’ajouterai celui du système uranium-oxygène, dans lequel un certain nombre de phases distinctes ont été signalées entre l’oxyde UO2 et l’oxyde UO3. La question se pose toutefois de savoir s’il s’agit de véritables combinaisons

142

définies excluant la possibilité d’existence de phases intermédiaires et excluant par conséquent l’idée même d’une continuité possible dans l’échelle des compositions, ou au contraire de compositions particulières dans la série des phases homogènes, compositions dont la stabilité serait légèrement supérieure à celle des phases de compo­ sition voisine. Nous avons en effet eu l’occasion fréquente d’observer avec le Dccleur Robin que dans des séries de spinelles mixtes (Fc2Co04 — C02C0O4) certaines compositions apparaissent de pré­ férence au cours de la formation de ces phases, sans que soit exclue l’existence d’une parfaite continuité, réalisable seulement à la suite de traitements thermiques prolongés. Dans l’état solide, la coexistence, même à des températures très élevées, de deux phases de même structure et de composition légèrement différente, est parfois insuf­ fisante pour conclure définitivement à la présence d’une zone de non miscibilité entre ces phases. On peut, en effet, imaginer que dans une série de phases homogènes, certaines compositions puissent donner lieu à des phénomènes d’ordonnancement qui conféreraient aux phases correspondantes un léger supplément de stabilité ren­ dant leur formation plus probable que celle des phases intermédiaires. Il s’agirait là, en fait, de la manifestation discrète d’une tendance à la formation d’un composé défini, mais n’excluant pas pour autant l’existence d’une continuité dans l’ensemble du système. Dans le cas où la variation d’énergie libre résultant de l’ordonnancement devien­ drait suffisamment importante, la probabilité d’existence des phases de composition voisine deviendrait très faible et l’on se trouverait placé dans le cas d’un véritable composé défini. M. Ubbelohde. — Has Professor Hâgg any théories of the bond différences to account for the gaps in composition between oxides such as Mog023 ^tid M09O26? For example, it could be that functionally one molybdenum atom in eight in the unit cell of Mog023 behaved as Mo*'^ and the remaining seven as Mo'^*, but this would hâve to be apparent in the crystal structure. Alternatively are there Brillouin zone eflfects in the electronic energy of the crystals that would account for the gaps?

Do the electronic conductivities

of these oxides show gaps in activation energy or in mobility to correspond with gaps in the range of crystal compositions? I am assuming that the electrical conductivities obey semi-conductor équations of the type a = Gq exp. (— E/KT) where a is the conductivity and E the activation energy.

143

M. Hagg. — The occurrence of definite formulae has geometrical causes. If the phases hâve to be built of blocks of Re03 structure, joined in principally the same way, the formula dépends on the thickness of these blocks. This thickness can only vary in steps, difîering in magnitude by one MeOg octahedron at a time. The oxides in question contain métal atoms of different charge but the charge seems to be distributed evenly over ail métal atoms. The existence of « résonance » is indicated by the dark blue colour of the oxides.

M. Collongues. — Je voudrais faire une remarque sur la répar­ tition des lacunes dans les composés non stoechiométriques très lacunaires. Cette remarque rejoint d’ailleurs celle du Professeur Hagg sur l’existence simultanée de deux composés non stoechiométriques de même structure. Dans un travail récent, Bertaut, à Grenoble, a mis en évidence l’existence d’un ordre dans la répartition des lacunes du sulfure de fer FeS (1). L’établissement de cet ordre traduit la tendance des lacunes à se placer le plus loin possible les unes des autres. Il semble exister une température de transition entre des états ordonnés et désordonnés de FeS, mais l’accord sur cette température est assez médiocre. D’autre part, on sait que le sesquioxyde de fer cubique Fe203y s’obtient par oxydation de la magnétite Fe304, par formation de lacunes et passage d’ions Fe++ à l’état Fe+++. Le diagramme des rayons X de ce sesquioxyde est, en première approximation, iden­ tique à celui de la magnétite, à une petite variation de paramètres près(ap,j04 = 8,378 A; Ope^OjY = 8,322Â). Mais en utilisant des méthodes de rayons X extrêmement fines, nous avons mis en évidence sur le diagramme l’apparition de nom­ breuses raies supplémentaires de faible intensité (2). Ces raies s’in­ terprètent très bien comme les interférences d’un réseau cubique simple de même maille que la magnétite. Ce phénomène conduit à penser que la répartition des lacunes dans la structure du sesquioxyde est ordonnée. Bien entendu, la détermination complète de la struc(1) E. Bertaut, Acta Cryst., 6, 557 (1953). (2) R. Collongues, Thèse, Paris (1954).

144

ture exigerait la préparation de monocristaux, ce qui, étant donné l’instabilité du composé, paraît fort délicat. Je voudrais demander à M. Bénard s’il a rencontré dans son travail beaucoup de composés lacunaires présentant un ordre dans la répartition des lacunes? S’agit-il là d’une règle générale? D’autre part, je pense que lorsque deux phases de même structure et de compositions légèrement différentes coexistent, il n’est pas impossible que ces deux phases correspondent à des états d’ordre différents dans la répartition de leurs ions ou de leurs lacunes. On sait en effet aujourd’hui que la transformation ordre-désordre peut provoquer dans une phase des variations de composition. M. Bénard. — Les remarques du Docteur Collongues concernant l’existence d’un ordonnancement des ions dans certaines phases non stoechiométriques viennent à l’appui de l’explication que je propo­ sais il y a un instant. La question se pose seulement de savoir s’il est possible d’envisager dans des systèmes tels que ceux actuellement étudiés par le Professeur Hâgg, la possibilité d’existence d’états ordonnés successifs correspondant à des différences de composition aussi faibles que celles qui nous sont décrites. Arrivé en ce point de la discussion, je constate qu’en fait il n’existe aucune incompa­ tibilité entre l’interprétation du Professeur Hâgg et celle que je proposais il y a un instant. La seule différence réside dans le fait que dans l’une des hypothèses, on exclut la possibilité d’existence des phases correspondant aux compositions intermédiaires, tandis que dans l’autre on admet seulement que ces phases ont une moindre tendance à se former. 11 doit être possible en fait, de trouver des cas illustrant ces deux interprétations. En ce qui concerne l’existence des phénomènes d’ordonnancement dans les réseaux lacunaires, les exemples bien étudiés sont très rares. Leur analyse suppose, en effet, une détermination très précise des variations des intensités des raies de diffraction des rayons-X, déter­ mination encore très difficile dans l’état actuel de la technique.

M. Chaudron. — De nombreuses phases peuvent donner lieu au phénomène ordre ±5; désordre. On peut penser que dans un certain nombre de cas, ces transformations sont accompagnées par un chan­ gement de composition. Des expériences récentes de Collongues et

145

de Behar au laboratoire de Vitry (1) et (2) montrent l’importance désordre dans le domaine des ferrites. de la transformation ordre La méthode micrographique a été précieuse pour l’étude des ferrites de lithium et de cuivre.

M. Barrer. — I would like to comment upon the significance of experiments made upon the electrolyte migration of hydrogen in palladium, by Duhm. At first he obtained a value of the effective positive charge on hydrogen of 1/500 that on a proton and later he corrected the charge to 1/25 of that value. However, the effective charge, relative to that on the other atomic nuclei, may not be established by migration experiments. The small hydrogen is so much more mobile than the large métal nuclei which compose the lattice of the host crystal. Perhaps if the mobility of the métal nuclei was equal to that of the hydrogen it would be found that most of the cationic transport was provided by the métal. I doubt therefore whether the relative effective positive charges on H and on métal can be established by migration experiments. The photo-electric work function of a clean tungsten surface and of tungsten with a chemisorbed hydrogen layer has established a dipolar surface W — H bond in which hydrogen is négative with respect to tungsten. Experiments of this kind may give an insight into the relative tendency of hydrogen within the métal and the métal atoms themselves to contribute to the free électron pool of the crystal. These remarks regarding the relative charges on the guest atom and the métal atom may apply also to the C — Fe System where C also migrâtes to the cathode. Arguments based on electronegativity of the two éléments would suggest that carbon nuclei would be less positive than Fe-nuclei, assuming both éléments to contribute to the free électron pool of the métal.

M. Ubbelohde. — Has it now been verified that the migration of hydrogen in palladium under the influence of an electric fleld is a true lattice effect ? It has been suggested in cases where the hydrogen is introduced into the métal by cathodic treatment, that a very thin (1) R. Collongues, Comptes rendus, 241, 1577 (1955). (2) 1. Behar, Comptes rendus, 242, 2465 (1956).

146

film of electrolyte remain on the surface and in cracks of the métal and accounts for the proton migration observed under the influence of an electric field. M. Bénard. — Je suis tout à fait d’accord avec le Professeur Barrer en ce qui concerne la prudence avec laquelle il faut interpréter les résultats de conductibilité électrique pour conclure à l’état d’ioni­ sation de l’hydrogène dans les métaux. Je n’ai pas cru devoir passer sous silence ces mesures, mais je concède que leur interprétation peut donner lieu à des controverses. On peut déplorer de ne pas disposer à cet égard de plus de résultats expérimentaux récents. En ce qui concerne l’évaluation du potentiel d’extraction des électrons, celui-ci pourrait en effet fournir des renseignements sur la nature des interactions hydrogène-métal. Ces renseignements risquent cependant d’être très qualitatifs, car, si mes souvenirs sont exacts, les valeurs des potentiels d’extraction annoncées par les différents auteurs sont assez dispersées. En outre, cette méthode fournit des renseignements sur l’émission des électrons par la sur­ face, mais il n’est nullement certain que l’état électronique de la liaison chimisorptive telle qu’elle existe dans la couche superficielle soit identique à celui de la liaison métal-hydrogène en profondeur. M. Orgel. — Are the experiments on electrodiflfusion carried out in such a way that they definitely measure the charge on the hydrogen atom at its equilibrium position rather than at the tran­ sition State for the diffusion process? M. Chaudron. — Je rappellerai des expériences faites dans mon laboratoire sur le système Pd-hydrogène, il y a maintenant une dizaine d’années (1) et (2). L’extraction de l’hydrogène en insertion, dans le cas de la solu­ tion solide p, est très facile. Au contraire, avec la solution a, la fixation est très forte. Pour constater l’existence de l’hydrogène après les traitements de déga­ zage, nous fûmes obligés d’utiliser la mesure du paramagnétisme. Il y a là des faits qui montrent l’évolution du mode de liaison de l’hydrogène dans le Pd. (1) G. Chaudron, A. Michel et J. Bénard, Comptes rendus, 218, 913 (1944). (2) J. Bénard et Ph. Albert, Colloque d'absorption cinétique hétérogène, Lyon (1949), p. 207.

147

M. Hâgg. — Professer Bénard has counted oxygen among the non-metals, which may form phases analogous to the metallic carbides and nitrides. It is well known that, for instance, the phase TiO is very similar to the phases TiC and TiN and that these three phases can form solid solutions. But there are also analogies between certain complex carbides, nitrides and oxides. N. Karlsson-Schônberg has found that the ternary carbides, having the idéal formula Me'3 Me"3C (of which the high speed steel Carbide Fe3W3C is best known) possess both nitride and oxide analogues. In the oxides. Me' may be any of the metals Cr — Cu but Me" must hâve a place not too far to the right in the transition métal sériés. It seems to be a condition that the oxides which are similar to metallic carbides and nitrides, should contain transition métal atoms having a fairly uncompleted d shell. I should also like to point out the existence of metallic « suboxides» like Cr30, M03O, W3O, of which the last one has been considered for many years to be a modification of tungsten (p — W).

M. Bénard. — L’existence de sous-oxydes à caractère métallique signalés par le Professeur Hâgg vient enrichir la série des composés «d’insertion », dans lesquels l’oxygène jouerait un rôle analogue à celui du carbone et de l’azote, et qui ne comportait jusqu’à main­ tenant qu’un très petit nombre de termes. Il serait intéressant de savoir si ces oxydes pseudo-métalliques possèdent les mêmes carac­ tères de dureté et d’infusibilité que les carbures et nitrures corres­ pondants.

M. Hedvall. — Nous avons effectué, il y a environ vingt ans, quelques expériences connexes qui présentent peut-être un intérêt du point de vue de la catalyse. Nous avons étudié l’influence des variations de la composition chimique de quelques préparations de HgS et de CdS avec ou sans excès de soufre. On a constaté que l’influence de ces variations sur la capacité d’adsorption des différents substrats est notable, ce qui est évident aujourd’hui.

148

Ce phénomène est important en catalyse du point de vue de l’interaction du catalyseur et de la couche adsorbée. Il se présente certainement pour les oxydes des métaux lourds, qui sont souvent utilisés comme catalyseurs. Vous avez mentionné dans votre premier rapport que vous avez obtenu une couleur bleue en chauffant à 1.000° le BaO, dans la vapeur de Ba. Peut-être y a-t-il intérêt à mentionner que l’on obtient une couleur grise en chauffant le même oxyde dans H, à la même température. Connaissez-vous l’explication de cette couleur. A mon avis, il ne s’agit pas d’une réduction même superficielle; ce sont plutôt les distorsions du réseau qui sont en cause.

M. Bénard. — Il est exact que des teintes très variées peuvent être obtenues avec l’oxyde de baryum porté à haute température dans des atmosphères réductrices. Il semble que ces variations de teinte soient dues à des états de ségrégation variables des défauts réticulaires, les interactions de ces défauts provoquant des déplace­ ments du maximum d’absorption dans le visible. L’origine de ces phénomènes resterait cependant toujours la même, à savoir la pré­ sence de lacunes anioniques occupées par des électrons. J’ajouterai que les expériences que j’ai citées à ce propos n’ont pas été faites dans mon laboratoire.

M. Forestier. — Comment explique-t-on la conductibilité des carbures et nitrures des métaux lourds?

M. Bénard. — L’interprétation la plus récente de la conductibilité électrique des monocarbures et mononitrures des métaux lourds a été donnée par Rundle; elle repose sur l’idée qu’il existe dans tous ces composés une liaison d’un type particulier que j’ai tenté de décrire dans le rapport. Cette liaison tente de concilier dans une certaine mesure le caractère orienté des liaisons covalentes classiques et le partage des orbitales de l’atome léger entre plusieurs liaisons contractées par cet atome avec ses voisins. On peut considérer que cette conception justifie la conductibilité électrique de ces composés, dans la mesure même où l’on est 4isposé à admettre que la théorie de Pauling explique la conductibilité dans l’état métallique.

149

Il est hors de doute que la conductibilité électrique élevée de ces composés a été pour beaucoup dans leur assimilation trop hâtive aux phases métalliques typiques. Actuellement, le nombre des con­ ducteurs électroniques non métalliques que l’on connaît est extrê­ mement élevé, et une telle assimilation ne se justifie plus. M. Forestier. — W3O peut-il être considéré comme un composé défini, ayant une conductibilité de type analogue à celui des car­ bures de métaux lourds? M. Hâgg. — The structure of W3O présents a spécial difficulty in that the X-ray data can only be interpreted if some of the métal and oxygen atoms are assumed to be distributed at random over structurally équivalent positions. Under those circumstances it is too early to say anything about the bonds in this phase.

150

Les composés non stoechiométriques à caractère métallique. Phases intermétalliques par Robert COLLONGUES

Le chimiste minéral qui a étudié les composés non stoechiomé­ triques par suite de leur grand intérêt scientifique et de leurs nom­ breuses applications pratiques, ne peut pas ignorer le domaine des phases intermétalliques. Dans ce domaine, le composé défini est assez rare et la phase intermédiaire apparaît le plus souvent sous des aspects extrêmement variés. On peut se demander les raisons de cette multiplicité des phases et de la diversité de leurs propriétés. C’est à cette question que nous voulons répondre et, pour cela, nous avons analysé quelques uns des travaux les plus récents. Nous citerons tout particulièrement l’application des théories de HumeRothery à l’étude systématique des diagrammes d’équilibre (HumeRothery et Raynor) et les nombreuses déterminations de structures dues surtout à Bradley, Westgren, Taylor, Laves et Hâgg.

CARACTERES GENERAUX DES PHASES INTERMEDIAIRES Formation des phases intermédiaires Considérons

deux

éléments

quelconques

de

la

classification

périodique, le cuivre et l’aluminium par exemple, et préparons par fusion des alliages contenant des quantités croissantes d’aluminium. Lorsque l’addition d’aluminium est de faible importance, le dia­ gramme de Debye-Scherrer du cuivre reste sensiblement inaltéré : on note seulement un léger déplacement des raies. Quelques atomes d’aluminium ont remplacé les atomes de cuivre dans le réseau de

151

■f*

Al a tomes %

Al poids %

Fig. 1

Diagramme Cu-Al dans la région riche en cuivre.

•c

«F 2000

IBOO

1600

1400

1200 1000

600

Fig 2

152

Diagramme d’équilibre Cu-Al.

ce métal d’une manière désordonnée. On obtient ainsi la solution solide primaire a (fig. 1). Or, les dimensions des deux atomes sont e

O

différentes = 1,28 A; = 1,43 A). L’introduction d’un nombre croissant d’atomes d’aluminium va donc provoquer une dilatation homothétique croissante du réseau du cuivre. Pour une teneur en atomes d’aluminium supérieure à 20 %, il existe un autre arran­ gement des deux sortes d’atomes plus stable que l’arrangement initial cubique à faces centrées. Un nouveau réseau se forme alors : c’est la phase intermédiaire [3 cubique centrée. Cette structure sera stable tant que la teneur en atomes d’aluminium ne dépassera pas 30 %. Pour des teneurs supérieures, la deuxième phase intermé­ diaire y apparaît : elle est cubique mais sa structure est complexe (type laiton y). Nous rencontrons ainsi sur le diagramme d’équi­ libre (1) (fig. 2) toute une série de phases intermédiaires (p, y. S, £, 7), 0) de structures différentes. Chaque structure représente l’arrangement le plus stable des deux sortes d’atomes dans un cer­ tain intervalle de composition et pour une certaine température.

Structure des phases intermédiaires Les structures des phases intermédiaires peuvent être ordonnées ou désordonnées. Dans l’exemple choisi, la composition moyenne de la phase p correspond à Cu,:» Al (20,3 à 30,8 % Al). Or, cette phase est cubique centrée (type chlorure de césium). La maille contenant deux atomes, il est impossible de répartir d’une manière ordonnée, dans une telle structure deux sortes d’atomes différents

1 dans un rapport autre que y. La phase p est donc nécessairement désordonnée (2).

Au contraire, la phase S du système nickel-aluminium est ordonnée. Sa structure est également cubique centrée (type chlorure de cérium) et sa composition moyenne corrspond à Ni Al (39, 9 à 54,75 %A1) (^) (fig. 3). Les atomes de nickel sont répartis aux sommets d’un cube dont le centre est occupé par un atome d’aluminium. Bradley (4) a mis en évidence l’apparition, sur le diagramme de Debye-Scherrer des raies de surstructure caractéristiques de cette répartition ordonnée.

153

•c

T

Ni atomes %

-> Ni poids %

Fig. 3

Diagramme d’équilibre Al-Ni.

Conditions de formation d’une phase intermédiaire La possibilité d’existence d’une ou plusieurs phases intermédiaires entre deux éléments A et B sera déterminée avant tout par les dimen/•a = —) ''b Nous avons représenté sur le diagramme (fig. 4 a) l’étendue du sions relatives des deux atomes (facteur de dimension

domaine d’homogénéité de toutes les phases intermédiaires formées entre l’argent et un autre métal On constate que la forma­ tion d’une phase ne sera possible que si les deux éléments ont des dimensions suffisamment voisines. Les deux valeurs extrêmes(*) (*) Pour établir ce diagramme, nous avons utilisé, le plus souvent possible, les valeurs des rayons atomiques déterminées expérimentalement dans les phases intermédiaires elles-mêmes. Les valeurs données dans les tables sont, en effet, généralement mesurées dans les éléments. Or, on sait (®) que la valeur du rayon atomique varie suivant l’état de coordination de l’atome. D’autre part, comme nous le verrons, les atomes peuvent être partiellement ionisés dans la structure de la phase intermédiaire.

154

'In iii

'Ag

^Ag

^Ga

du rapport des rayons atomiques sont : — = 1,055; — = 1,15. Cette valeur (1,15) constitue une valeur limite pour beaucoup de phases intermédiaires. 11 est, du reste, important de signaler qu’on aboutirait aux mêmes conclusions et à la même valeur limite pour les solutions solides primaires a (5). Si le facteur de dimension est élevé, il apparaîtra à la place de la phase intermédiaire, un composé défini.

BaSrCaf^hMh VCrFèCoNi

(D m Na Cl ^ Zn Oou ZnS 'm. Ni As

Fig. 4

a) Etendues des domaines d’homogénéité des phases intermédiaires

formées entre l’argent et des métaux de rayons atomiques croissant. b) Structures des phases ou composés AB formés entre des métaux

d’électronégativité croissante et les éléments du groupe VI B.

L’électro-affinité des deux éléments interviendra également pour déterminer la structure de la phase et le mode de liaison des atomes (liaison ionique, covalente ou métallique). Nous avons indiqué sur le diagramme (fig. 4 b) les structures des phases ou des composés de formule générale AB formés entre des métaux d’électronégativité

155

différente et les éléments du groupe VI B. On constate que les struc­ tures formées sont par ordre d’affinité décroissante type NaCl

type ZnO ou ZnS ^ type NiAs

Lorsque les liaisons sont du type métallique, la structure dépendra, comme nous le verrons, de la concentration électronique, c’està-dire du nombre d’électrons associé à chaque atome de la phase intermédiaire. Il est intéressant de noter que la structure de la phase intermé­ diaire peut parfois être déterminée par un seul de ces facteurs. Les composés de Laves (J), de formule générale AB2, constituent des exemples, tout à fait remarquables de structures déterminées par le ''a facteur de dimension : le rapport —est voisin de 1,3 pour tous ces composés. Le rôle de l’électro-affinité des éléments dans la formation de ces composés semble tout à fait négligeable. On notera d’ailleurs qu’un même métal peut, suivant les dimensions de son partenaire, jouer le rôle de métal A ou de métal B ; par exemple, le magnésium dans MgCu2 et CaMg2, le bismuth dans BiAu2 et KBi2, l’argent dans AgBe2 et CaAg2. D’autre part, il est impor­ tant de remarquer que ces composés, dans lesquels la structure géométrique est capitale, ne peuvent s’expliquer par une concentra­ tion électronique globale.

Formule des phases intermédiaires Les diagrammes Al-Cu et Al-Ni présentent, comme nous l’avons indiqué, un certain nombre de phases intermédiaires. Leur domaine d’existence peut être très étendu : par exemple, la composition de la phase p du système Al-Cu varie de 20,3 à 30,8 % d’aluminium. L’importance de ces variations a conduit certains auteurs à mettre en doute la signification d’une formule An,B„ attribuée à de telles phases. Glazunov (8) propose de distinguer deux types de phases inter­ médiaires ; 1° les solutions solides dérivant d’un composé défini A„,B„. La courbe représentant les variations, en fonction de la composition, d’une propriété quelconque de la phase, la température de fusion

156

par exemple, présente alors un point singulier pour la composition A„,Bn. C’est le cas des phases p et des systèmes Al-Cu et Al-Ni dont le solidus et le liquidas présentent un maximum pour les composi­ tions exactes CU3AI et NiAl. 2° les berthollides. Les courbes représentant les variations des propriétés en fonction de la composition ne possèdent pas de point singulier à l’intérieur du domaine d’homogénéité. C’est le cas des phases 0 du système Al-Cu (®) et p du système Cr-Al par exemple. L’étude aux rayons X a cependant montré que la structure de cette dernière phase dérivait d’un manière évidente de celle du composé Cr2Al (10) (fig. 5), quelques atomes de chrome étant remplacés par des atomes d’aluminium.

(b)

©Cr Fig. 5

QAL

Structure du composé Cr2Al.

Mais la composition stoechiométrique ne fait pas nécessairement partie du domaine d’homogénéité de la phase. Trois cas peuvent se présenter (fig. 6) : 1° La composition stoechiométrique est à l’intérieur du domaine d’homogénéité de la phase. Nous citerons comme exemples : les phases p des systèmes Cu-Al (CU3AI) (fig. 6 a); Ag-Mg (AgMg); la phase S du système Al-Ni (AlNi); les phases y des systèmes Cu-Cd (CusCds), Cu-Zn (Cu5Zn2i); les phases s des systèmes Ag-Al (AgsAl3), Ag-Zn (AgZu3). 2° La composition stoechiométrique limite le domaine d’homo­ généité. Nous citerons comme exemples : les phases p des systèmes

157

abc Fig. 6

Diverses positions possibles de la composition stoechiométrique par rapport au domaine d’homogénéité d’une phase intermédiaire.

Cu$ zng. Aqs ZHg

Cus Cd«

Aus {«)

Fig. 7

158

Cil, Aq,Au

(i)

Structures de Cuj Zn, et Cus Cd«. Les voisins de l’atome # sont différents dans les deux structures.

Cu-In (CU3I11) (fig. 6 b), Be-Cu (BeCu); de la phase y du système Cu-Al (CU9AI4) ainsi que de plusieurs phases non métalliques, par exemple FeO (H), NiS (12), etc. 3° La composition stoechiométrique est nettement extérieure au domaine d’homogénéité. Nous citerons comme exemples : la phase e du système Cu-Zn (CuZn3) (fig. 6 c), la phase y du système Au-Zn (AusZng), ainsi que plusieurs phases non métalliques, par exemple FeSe (13), FeS (14), etc... Lipson et Wilson (13) pensent que ces différentes formes de dia­ grammes résultent des diverses positions relatives possibles des courbes d’énergie libre de la phase considérée et des phases voisines (fig. 6). On peut supposer que la courbe d’énergie libre d’une phase p présente un minimum pour un rapport atomique simple des consti­ tuants. Si l’ordonnée de ce minimum est inférieure à celles des minima des phases voisines, la composition stoechiométrique A„,B„ est à l’intérieur du domaine d’homogénéité de la phase p. Si l’ordonnée du minimum de la phase p est comprise entre celles des minima des phases voisines, la composition stoechiométrique est à l’extérieur du domaine d’homogénéité de la phase p. Il résulte de cette remarque que les propriétés d’une phase intermédiaire dépendent dans une large mesure des propriétés des phases voisines. Il importe de remarquer que l’analogie de formule n’implique nullement une analogie de structure. Par exemple, les phases Cu5Cd0 et CusZng possèdent des formules identiques et la même maille cristalline. Mais les analyses très précises de la structure effectuées par Bradley et ses collaborateurs (i^> i’^) ont montré que les répar­ titions des atomes à l’intérieur de la maille étaient différentes dans les deux cas. Les cinquante-deux positions possibles de la maille peuvent être divisées en quatre groupes de positions équivalentes contenant respectivement 8, 8, 12 et 24 atomes. Dans les deux phases considérées, les répartitions sont les suivantes : III

IV

I

II

(8 atomes)

(8 atomes)

CugZng

Cu

Zn

Cu

CUgCdg

Cu

Cu

32 Cd + 4 Cu

groupes

(12 atomes) (24 atomes) Zn

159

Les atomes de cadmium de la phase CusCdg ont donc des voisins différents des voisins du zinc de la phase CusZng (18) (fig. 7).

ETUDE DES DIVERS TYPES DE PHASES INTERMEDIAIRES La formation d’une phase dérivant d’un composé réel ou hypothétique (c’est-à-dire placé en dehors du domaine d’homo­ généité de la phase) peut s’effectuer de plusieurs manières : 1° remplacement d’un certain nombre d’atomes de l’élément A par des atomes de l’élément B. On obtiendra ainsi une phase de substitution de formule A^_g B„^j.; 2° élimination d’un certain nombre d’atomes de l’élément A, le réseau des atomes B restant inaltéré ou encore addition d’atomes de l’élément B dans les intervalles de la structure, le réseau A restant inaltéré. On obtiendra ainsi suivant les cas une phase lacunaire de formule A„_j. B„ ou une phase « interstitielle » de formule A,„ B„_,_g. L’utilisation simultanée des mesures précises du paramètre cris­ tallin et de la densité permet, en général, de distinguer entre ces diverses possibilités. Le premier processus ne pourra bien entendu intervenir que si les caractéristiques des deux atomes (en particulier rayon atomique et électro-négativité) sont très voisines (par exemple Ni-Zn). Au contraire, lorsque les deux éléments seront nettement différents (Ni-Se par exemple), toute substitution de l’un à l’autre sera impos­ sible et, seule, la formation de lacunes pourra provoquer une variation de composition de la phase. Dans le cas intermédiaire (Ni-Al par exemple), les deux processus pourront se rencontrer dans la même phase.

Phases intermédiaires de substitution Les phases intermédiaires de substitution se rencontrent presque uniquement dans les alliages formés : 1° soit entre deux métaux de transition; 2° soit entre un métal de transition et un élément des groupes

II B, III B, IV B;

160

3° soit entre un élément du groupe I B et un élément des groupes II B, III B, IV B. Dès 1926, Hume-Rothery (>9) mettait en évidence l’existence d’une importante caractéristique commune aux alliages de cette dernière catégorie : pour toutes les phases p de ces alliages, la concentration électronique (rapport du nombre d’électrons de valence au nombre d’atomes) est égale à 3/2; pour toutes les phases y, elle est égale 21 7 à — et pour toutes les phases e à — . Ekman (20) montrait ensuite que les alliages de la seconde catégorie pouvaient satisfaire aux règles de Hume-Rothery à condition d’attribuer une valence nulle à l’élément de transition. Nous signalerons quelques problèmes particulièrement intéres­ sants qui se posent à propos de ces phases. Nous étudierons ensuite les principales phases intermédiaires des alliages formés entre deux métaux de transition : elles sont du type phase a. Nous montrerons enfin qu’il convient de considérer les surstruc­ tures comme des phases intermédiaires d’un type particulier.

Phases obéissant aux régies de Hume-Rothery Les principales propriétés de ces phases ont été décrites en détail dans des ouvrages classiques de Hume-Rothery (2i. 22, 23). Les règles de Hume-Rothery ont fait l’objet des études théoriques de Jones (24. 25)^ Dehlinger (26) et Slater (22. 28). Elles ont été remar­ quablement vérifiées par les déterminations de structures de Westgren (i®, 30, 3i)^ puis de Bradley (lo. I6, 17, 32, 33). Nous pensons qu’il convient d’insister sur les points suivants : 1° La valence apparente des éléments de transition. On sait que la troisième couche quantique des éléments de transition de la pre­ mière longue période est incomplète. La structure électronique du nickel, par exemple, est la suivante : n

1

2

3

4

Ni

2

2 6

2 6 8

2

161

D’après Ekman, cet élément présent dans une phase aura ten­ dance à capter les électrons de son partenaire pour compléter sa troisième couche quantique. Il pourra ainsi fournir deux électrons de valence à la structure de la phase, mais il recevra également deux électrons de son partenaire. Sa valence apparente sera alors nulle. La phase intermédiaire sera donc dans ce cas partiellement ionisée. On constate en effet que sa formation s’accompagne d’une très nette contraction, les distances interatomiques observées étant inférieures à la somme des rayons atomiques Le fer et le cobalt devraient dans ces conditions posséder une valence négative, mais il est possible que l’élément de transition ne puisse recevoir qu’un nombre limité d’électrons de l’élément allié. Dans un travail récent (^5) Douglas a mis en évidence l’absorption des électrons de valence par le métal de transition dans les phases C02AI9, MnAlg, MnSi3Al9 : l’analyse de la structure montre que l’atome de cobalt possède une valence apparente négative voisine de — 2. Dans sa théorie générale (36. 37) Pauling distingue des éléments « hyperélectroniques » (donneurs d’électrons), indifférents, et « hypoélectroniques » (accepteurs d’électrons). Les métaux de transition appartiennent à cette dernière catégorie. Chacun d’entre eux pourra capter un certain nombre d’électrons : au maximum 4,66 pour le chrome, 3,66 pour le manganèse, etc. Il est remarquable de constater que la valence maximum du cobalt déduite de la théorie de Pauling est — 1,71 voisine de la valeur expérimentale. 2° Il est intéressant de comparer la forme et l’étendue du domaine d’homogénéité des différentes phases p des alliages d’or, d’argent et de cuivre obéissant aux règles de Hume-Rothery (38) (fig. 8). Dans les alliages d’or, on remarque l’existence de nombreux points de fusion congruente et de plusieurs structures ordonnées. Au contraire, dans les alliages de cuivre, les structures ordonnées sont très rares et il apparaît de nombreux points eutectoïdes. Les alliages d’argent ont des caractères intermédiaires. Il semble que ces phé­ nomènes doivent être attribués aux différences d’électronégativité entre les éléments alliés qui sont beaucoup plus élevées dans les alliages d’or que dans les alliages de cuivre. Le rôle du facteur de dimension apparaît aussi très nettement. En général, l’étendue du domaine d’homogénéité diminue lorsque

162

—In

Au

A u —Cd A u -S n A u — Zn A u "A l

Gi

• Au

Fig. 8

Différentes formes des domaines d’homogénéité des phases obéissant aux règles de Hume-Rothery (en abscisses le facteur de dimension

100 Nota. — L’étendue du domaine d’homogénéité des phases AgMg et AuMg n’est pas anormale ; si l’on calcule le facteur de dimension à partir des rayons atomiques mesurés dans la phase elle-même, on trouve un facteur voisin de 3. Ces phases étendues devraient donc se trouver dans la partie centrale du diagramme.

163

le facteur de dimension augmente. Nous noterons, d’ailleurs, que l’étendue du domaine d’homogénéité des phases Au Mg et Ag Mg n’est nullement anormale à condition de définir le facteur de dimen­ sion comme le rapport des rayons atomiques des éléments déterminés dans la phase elle-même et non comme le rapport des rayons ato­ miques déterminés dans les éléments. La distance Ag-Mg mesurée O dans la phase est en effet 2,92 A, très voisine de la distance mesurée dans Ag-Cd (2,93 A), alors que la distance calculée (r^g + r^jg ) e

est 3,04 A. Il en est de même pour la phase Au Mg Phases

.

g

Les phases a et les surstructures se rencontrent souvent dans les mêmes systèmes et parfois pour la même composition. D’autre part, leurs conditions de formation sont assez voisines. C’est pour­ quoi dans certains alliages la formation de la phase g a été assimilée à une transformation ordre-désordre. Plusieurs arguments s’opposent à cette conception : 1° La complexité quasi générale de la structure des phases a, qui n’a aucun rapport avec la structure de la phase mère.

1 2° le fait que la composition stoechiométrique (en général y)

est parfois en dehors du domaine d’homogénéité de la phase n; ce phénomène serait difficilement compréhensible si la phase g dérivait simplement de la phase mère par une transformation ordredésordre. Dans un travail récent, Pomey (39) a pu étudier séparément les deux phénomènes dans l’alliage Fe-Cr. Il a trouvé pour les deux phases des domaines d’homogénéité très différents (43 à 50% Cr pour la phase a, 40 à 78 % Cr pour la phase ordonnée). De plus, la transformation a désordonné -> a ordonné se produit dans une zone de température (500-600°) nettement inférieure à la zone de température correspondant à la transformation a désordonné ->■

g

(825° environ). Enfin, Pomey a mis directement en évidence la trans­ formation a ordonné -> g montrant ainsi que seule la structure g est stable à la température ordinaire. On sait aujourd’hui que les phases g se forment dans de nombreux alliages binaires ou ternaires : Mn-V (“*0), Mn-Cr, Mn-Mo, Mn-Ti,

164

Fe-Cr, Fe-V (4i), Fe-Mo, Fe-W (42), Co- V(40), Co-Cr (43), Co-Mo, Co-W, Ni-V (44). En général, le domaine d’homogénéité entoure la

1 composition —, mais quelques exceptions ont été signalées : Co-Mo (59-61 % Mo), Co-Cr (56-61 % Cr), Ni-V (55-61 % V), Mn-Cr et Mn-V à 75 % Mn. Toutes ces phases n ont la même structure qua­ dratique avec 30 atomes par maille. Un certain nombre de structures (phases Ç, p, ) se rattachent aux phases cr. Dans toutes ces phases, le facteur fondamental est le facteur de dimension : le rapport des rayons atomiques ne doit pas dépasser 1,08. Certains auteurs ont pensé qu’il était possible de considérer toutes les phases cr comme des phases ayant la même concentration électronique. Il semble fort délicat de prendre position sur un tel problème en raison de l’incertitude sur la valence des éléments de transition. Il est seulement intéressant de noter le déplacement du domaine d’homogénéité des phases ct en fonction de la position des éléments dans la classification périodique. Ce déplacement indique que le facteur concentration électronique doit jouer un rôle important dans la formation de ces phases. Mn (Fe,Co,Ni) %

Cr Mn

25

50

'////////////

Co

Fe

100

m//m////i//

Fe

V Mn

75

'/////. /m/m/m/m 7////,

Co Ni

7///m////m/////i

Surstructures Lorsqu’une phase ordonnée se sépare de la solution solide primaire, doit-on la considérer comme une phase distincte ayant sa place dans le diagramme d’équilibre? En général, les théoriciens n’ont pas envisagé la transformation ordre-désordre comme un véritable changement de phase dans lequel une structure subit une transfor­

165

mation discontinue (^s. 46). Dans la transformation ordre-désordre, la répartition des atomes semble varier de façon continue en fonction de la température. Or, un groupe très important de travaux récents (en particulier, ceux de Newkirk et Smoluchowski sur le système Co-Pt) (47) a conduit à réviser cette conception. Ces auteurs ont mis en évidence sur le diagramme d’équilibre l’existence d’une région biphasée entre les domaines ordonné et désordonné (fig. 9). L’examen microgra-

Fig. 9

Diagramme d’équilibre Co — Pt montrant l’existence d’un domaine à deux phases (ordonnée + désordonnée).

phique montre la phase ordonnée précipitée à l’intérieur de la matrice désordonnée sous forme d’une structure de Widmanstâtten. Les deux phases coexistant à l’équilibre ont des compositions légèrement différentes. De même, dans l’exemple classique des surstructures CU3AU la

166

coexistence des deux phases a été mise en évidence (‘♦S). De plus, dans ce cas, l’existence d’une différence de composition entre la phase ordonnée et la phase désordonnée a été nettement démontrée : l’augmentation de la teneur en cuivre de la phase désordonnée provoque une augmentation du paramètre, l’établissement de l’ordre provoque une diminution. Le problème est loin d’être résolu. Nous pensons cependant que l’existence d’un domaine biphasé est aujourd’hui bien établie. Ce domaine peut, dans certains cas, être très étroit. Mais, c’est seule­ ment à la composition stoechiométrique que la transformation peut être considérée comme un simple ré-arrangement atomique.

PHASES LACUNAIRES OU INTERSTITIELLES Exemple d’un travail type C’est Bradley et Taylor qui, les premiers, mirent en évidence l’existence d’une phase lacunaire dans un système intermétallique : la phase Ni-Al. A la composition stoechiométrique, cette phase a la structure cubique centrée du chlorure de césium. Lorsque la teneur en nickel est supérieure à 50 %, quelques atomes d’aluminium sont remplacés par des atomes de nickel. Ceux-ci sont plus lourds et plus petits que les atomes d’aluminium : la densité augmente et le paramètre cristallin diminue (fig. 10). La limite de solubilité correspond à 61 atomes % de nickel. Inversement, quand on enrichit la phase Ni-Al en aluminium, on devrait s’attendre à une diminution de la densité et à une augmentation du paramètre. Or, on constate bien une diminution de la densité (beaucoup plus rapide d’ailleurs que celle résultant d’une simple substitution), mais aussi une dimi­ nution très rapide du paramètre. L’étude comparée des variations des densités mesurée et calculée conduit à supposer l’élimination d’atomes de nickel de leurs positions dans le réseau. L’accroissement de la teneur en aluminium de la phase se produit donc en réalité par extraction d’atomes de nickel avec formation de lacunes. La phase la plus pauvre en nickel (42,25 atomes % ) contient 8 % de lacunes dans le réseau. Cette hypothèse est confirmée directement par la mesure des intensités des raies du diagramme de rayons X. Une autre confir-

167

densité

Fig. 10

Variations du paramètre (a) et de la densité (b) de la phase Ni-Al en fonction de la composition.

Fig. 11

Intervalles octaédriques (a) et tétraédriques (h) dans la structure Ni-As.

168

mation moins directe est l’étude de la diffusion dans la phase Ni-Al. La valeur élevée trouvée pour la vitesse de diffusion de 60Co ne peut s’expliquer que par l’existence de nœuds réticulaires non occupés (50). A la suite de ce travail original, un grand nombre d’alliages d’aluminium binaires ou ternaires ont été étudiés. Des phases lacu­ naires ont été signalées dans les systèmes Co-Al (5i), Fe-Ni-Al (52), Cu-Ni-Al (55), Fe-Cu-Al (54). Le composé U AI4 dériverait du composé U AI3 par formation de lacunes dans le réseau des atomes d’uranium (55). Il est cependant difficile dans ce cas de préciser si la variation de composition s’effectue bien par ce processus ou par substitution d’atomes d’aluminium à des atomes d’uranium. Les structures du type laiton y contiennent aussi dans leur réseau un certain nombre de lacunes (56. 57, 58)_ Nous citerons les exemples du laiton y, des phases NiGa4 (59), Ni2gln72, Pdln3 (60. 6I). Cer­ tains auteurs ont insisté sur le caractère hétéropolaire de ces struc­ tures et envisagé la possibilité d’existence de molécules Ni2Ga3 et Niln (59). Phases lacunaires de type NiAs Mais c’est surtout dans les phases de type NiAs formées entre un métal de transition et un élément des groupes IV B, V B et VI B que de nombreuses phases lacunaires d’étendue importante ont été mises en évidence. Les atomes B forment un réseau hexagonal compact (fig. 11) délimitant des intervalles tétraédriques et octaé­ driques. Dans la structure du composé stoechiométrique, les inter­ valles octaédriques sont seuls occupés par des atomes A (*5). Mais un certain nombre d’atomes peuvent manquer provoquant ainsi la formation de lacunes. Le réseau B demeure inaltéré. Dans les cas extrêmes, la moitié des intervalles octaédriques peut être inoccupée : par exemple, dans les alliages Co-Se, Ni-Te, V-Se, Ti-Se, Ti-Te, on atteint à la limite et de façon continue les composés CoSc2, NiTc2, VSc2 (62. 63)^ TiSc2, TiTc2 (64. 65). Inversement, la variation de composition peut être produite par insertion d’atomes A dans les intervalles tétraédriques normalement inoccupés de la structure. Ainsi, la phase NiSb peut contenir jusqu’à 54,4 % atomes de nickel. On peut dans certains cas atteindre la composition A2B (Ni2ln). 169

—► At

% Se,

Al,

Ge, G»

Fig. 12

—* Al % Po. ft. Pb

Phases lacunaires de type Ni As.

La composition stoechiométrique peut ne pas faire partie du domaine d’homogénéité

: c’est le cas par exemple pour FeSe,

FeS, FeSb (52 à 58% atomes Fe) (13. 14).

170

L’examen de l’ensemble de ces phases (fig.l2) révèle un certain nombre de phénomènes dont le plus curieux est certainement le déplacement du domaine d’homogénéité vers les fortes teneurs en élément A, lorsque le caractère métalloïdique de l’élément B dimi­ nue (fig. 13).

Fig. 13

Nijin

NiSb NiTe

J'

'i'

NlTcj

Variation de la position du domaine d’homogénéité d’une phase lacunaire (type Ni-As) en fonction de l’élément B. Se

Te

As

Sb

Bi

Sn

In

Ni %

33,4-50

• 33,4-50

50

45-54

52-58

54-62

62-66,6

Co%

33,4-50

33,4-50

50

51-57

56-60

Fe %

43-47

< 50

50

52-58

55

Un autre phénomène très intéressant est la variation du rapport —des axes de la maille hexagonale en fonction de l’électronégativité de 1 element A. ou de 1 element B. On remarque que le rapport — a c décroît lorsque l’électronégativité de l’élément B diminue (— = 1,55 pour NiS; — = 1,23 pour Niln) (fig. 14 à). Hume-Rothery (23)

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a

Fig. 14

Variation du rapport - des axes de la maille hexagonale des phases de type Ni-As formées par : A) Le nickel avec des éléments d’électonégativité décroissante ; B) Le tellure et l’étain avec des éléments d’électronégativité croissante.

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pense que ce phénomène résulte d’une variation continue du mode de liaison des atomes dans la structure. D’autre part, dans les phases c de type A Te, le rapport — diminue rapidement lorsque l’électroC . c négativité de l’élément A diminue (— = 1,66 pour TiTe; — = 1,36 a a pour NiTe) (fig. 14 b). Au contraire, dans les phases de type ASn, c le rapport — est sensiblement indépendant de l’électronégativité du métal A. Les liaisons sont toujours, dans ce cas, de type métallique.

Autres exemples de phases lacunaires Earley(66)a montré que le composé Cu3Se2 qui existe à l’état naturel, et qui peut aussi être préparé par fusion des constituants, était en réalité le composé limite d’une phase lacunaire Cu4_xSe2. La phase RhSe2 est une phase mixte lacunaire et de substitution Enfin, des phases lacunaires se rencontrent dans certains alliages ternaires. Les phases LiZnAs, LiMgP, LiZnP ont une structure de type CaF2 dans laquelle les atomes de lithium occupent les inter­ valles octaédriques. Certains d’entre eux peuvent manquer : il apparaît ainsi une phase lacunaire de formule Lii_g ZnAs (6*). Ces phases nous paraissent occuper une position extrêmement importante : elles constituent vraiment les structures de transition entre les phases intermétalliques et les composés non stoechiomé­ triques de la chimie minérale.

MODES DE LIAISON DANS LES PHASES INTERMEDIAIRES Nous traiterons très succinctement ce problème important, mais nous nous proposons de développer ultérieurement notre étude. Nous avons déjà montré qu’il pouvait exister, dans une série homologue de phases, une variation continue du mode de liaison entre atomes et nous avons cité l’exemple des phases lacunaires de type NiAs. On rencontre un phénomène analogue dans la série des composés Mg2Si, Mg2Ge, Mg2Sn, Mg2Pd, qui possèdent tous une structure cubique, anti-isomorphe de la structure de la fluorine. Le

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composé Mg2Sn est un semi-conducteur : sa conductibilité croît exponentiellement en fonction de la température. Le composé Mg2Pd est un conducteur métallique : sa résistivité croît linéairement en fonc­ tion de la température. De plus, à la température ordinaire, la résis­ tivité Mg2Sn est environ deux cents fois supérieure à la résistivité de Mg2Pd (6®). Ce phénomène indique nettement une différence notable entre les modes de liaison des atomes dans ces deux composés. Mais on peut aussi rencontrer différents modes de liaison à l’inté­ rieur d’une même phase. Nous avons signalé l’ionisation partielle des atomes dans les phases obéissant aux règles de Hume-Rothery, le caractère hétéropolaire des structures du laiton y, des phases NiGa4, Ni2gln72, etc. Nous citerons maintenant quelques exemples particulièrement frappants. Il nous paraît tout d’abord intéressant d’établir un parallèle entre deux composés, l’un intermétallique PrGa2; l’autre bien connu en chimie minérale : le sous-fluorure d’argent Ag2p. Le composé Pr Ga2 a une structure hexagonale, constituée de couches d’atomes se succédant dans l’ordre suivant : Pr - Ga - Ga - Pr - Ga ...(™). L’étude aux rayons X a montré que la distance entre atomes de gallium était nettement inférieure au diamètre atomique de cet élément. La distance entre atomes de praséodyme est, au contraire, supérieure au diamètre atomique. Il semble nécessaire, pour expliquer une telle structure, d’admettre l’existence entre les atomes de gallium de liaisons plus fortes que les liaisons métalliques (liaisons de cova­ lence par exemple). Ce composé possède d’ailleurs un point de fusion très élevé 1470° (tfca = 30°; tfp^ = 940°) et sa stabilité chimique est notable. Le sous-fluorure d’argent Ag2p possède une structure du même type constituée de couches successives : Ag - Ag - P - Ag - Ag ("^i). La mesure des distances interatomiques montre que les liaisons entre atomes d’argent et de fluor sont du type ionique pur, alors que les liaisons entre atomes d’argent sont de type métallique. Les cristaux de ce corps possèdent en effet l’éclat métallique et sont fortement conducteurs. Ces deux composés PrGa2 et Agp2, en apparence si différents, possèdent un important caractère commun : leurs liaisons sont de type mixte. Il en résulte qu’ils possèdent à la fois les propriétés caractéristiques des composés minéraux et les propriétés de l’état métallique.

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Nous signalerons enfin un exemple plus curieux encore que l’on rencontre dans le système Mg-Al

La phase de composition

voisine de Mg3Al2 possède la structure du manganèse a, avec 58 atomes par maille répartis en trois groupes de 24, 24 et 10 atomes. Sa véritable formule doit donc être Mgi7Ali2 avec 2 (Mgi7Ali2) par maille. La mesure des distances interatomiques montre qu’en réalité les atomes d’aluminium sont groupés en doublets dans les­ quels la distance entre deux atomes est nettement inférieure au diamètre de l’atome d’aluminium. Les deux atomes doivent donc être liés sous forme de groupements diatomiques par des liaisons homopolaires; les deux électrons supplémentaires nécessaires seraient fournis par l’ionisation des atomes de magnésium. Nous avons ainsi dans chaque maille : 12 « groupements » [AI2]

, 24 ions Mg+

et 10 atomes de magnésium. La formule de la phase peut donc s’écrire [AI2]

12 Mg+24 Mgio.

Une bonne confirmation de cette structure est fournie par la mesure des distances entre un atome d’aluminium et les 34 atomes de magnésium de la maille : 24 d’entre elles (correspondant aux 24 ions Mg+) sont nettement inférieures aux 10 autres (correspon­ dant aux 10 atomes de magnésium). Dans cette structure inter­ viennent donc des liaisons ioniques, homopolaires et métalliques.

CONCLUSION L’ensemble des travaux que nous avons analysés permet de souligner l’intervention de plusieurs facteurs dans la formation des phases intermédiaires : le facteur de dimension, la concentration électronique et l’électro-affinité. La liaison des atomes dans ces phases nous apparaît, d’autre part, comme une synthèse de modes de liaison de caractères très différents. On comprend alors la multiplicité des phases possibles dans un système et l’étendue souvent importante de leur domaine d’homo­ généité, par suite de mécanismes variés de formation et de liaison. Au contraire, dans les parties de la chimie où prédomine très lar­ gement le caractère ionique des liaisons, les possibilités de formation et de structure d’une phase étendue sont nettement réduites. On expliquerait ainsi en première approximation le caractère stoechio­

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métrique des composés ioniques. De toute manière, les transposi­ tions d’idées d’un domaine à l’autre nous paraissent devoir être très précieuses pour le chercheur. Je tiens à remercier très sincèrement Monsieur le Professeur Chaudron, Membre de l’Institut, Directeur de notre Laboratoire, pour l’intérêt constant qu’il a porté à ce travail et les conseils qu’il m’a prodigués au cours de nos conversations au Centre d’Etudes de Chimie Métallurgique.

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Discussion M. Ubbelohde. — It seems rather important to define more precisely what is meant by « phase » in describing changes such as order-disorder in crystals. The classical phase rule is based on the possibility of describing the free energy G of, say, a simple substance entirely in terms of the variables P, V, T ; G = / (P, V, T). At constant pressure, the curve relating G with T is infinitely thin. Modem theory of solids indicates that whilst this may still be a permissible approximation ordinarily, an important réservation is necessary near a transition between two structures. If these structures are quite independent and one solid is formed in extenso from the other, the classical phase rule indicates a point of inter­ section of the infinitely thin G, T curves. From this, ail the classical thermodynamic relationships, such as Clausius Clapeyron can be readily deduced. But examination e.g. by précision X-ray methods shows that for many transformations ® ->■ (D in solids, provided the change of structure is small, régions of ® and (g) coexist over a narrow interval of températures in the same matrix. Suppose we start with structure ® and approach the transfor­ mation température ® -> ©. Régions of (D begin to appear within the matrix of ®. They are obviously in some State of strain, and in the matrix, the séparation surface between ® and @ may involve appréciable internai surface energy. As a resuit, the free energy of (D appearing in (D can no longer be represented by the classical équation for an extensive phase G2 = /a (P, V, T) (A) but two additional parameters to allow for strain energy Ç21 and surface energy 7)21 must be added G2' =/2 (P, V, T, Ç21, ^21) (A') In the same way, starting with structure @ and approaching the

transformation température, régions of ® begin to appear in the matrix of (D so that for its free energy, we must write instead of

Gi =/i (P, V, T) (B) Gl' =/l (P, V, T, ^12, 7)12) (B)' Intersection of the thickened surfaces A' + B' will no longer be at a transformation point, but over a smeared narrow région. explains the following :

This

A. Hystérésis occurs since the intersection of G'2 with Gj does not follow the same path as the intersection of G'i with G2 (the unprimed free energies refer to the values for structures undistorted by inclusions of the other). B. There is a kind of rough contact or overlap over a narrow range of températures, between the Gi and G2. This appears to be the real structural explanation of many so called phase transfor­ mations of the « second order ». In reality these are examples of the coexistence of two structures in a common matrix over a narrow range of thermodynamic variables tj and Varions structural tests proving coexistence hâve been reviewed for a variety of A point transitions, in a paper by me, shortly due to appear in the British Journal of Applied Physics, entitled : « Crystallography and the Phase Rule ». These lambda point transitions ail involve only small différences of structures between ® and (D such as « rotation » or « nonrotation » of NH4+ in a crystal lattice, positional order-disorder, etc. In conséquence régions of © begin to form in ® but the mechanical strains do not exceed the breaking strength, so that the « hybrid » crystal lattice with régions of ®) in a matrix of (J) retains its crystal axes. We hâve actually followed certain apparently single crystals through a température cycle ®

® to test

how far the crystal axes persist, but it would take too long to describe these in detail. The two main points to note are : (a) instead of referring to « equilibrium between two phases » it is more correct in such cases to refer to « coexistence of two structures over a narrow région of températures and pressures ». Such transformations would theoretically be of the first order if

179

the two phases were présent in extenso.

But because © can

only be formed within the matrix of ®, and vice versa, the extra parameters and ^ automatically smear the transition point into a transition région. (b) Generally speaking the free energy of small régions of ® formed in a matrix of ® will not be the same as that of © as matrix, containing small inclusions of ®. This inevitably brings hystérésis into play, since what is nominally the same structure © has a somewhat different free energy according to whether it has just been formed within ® as small régions, or whether it starts as the extensive matrix and merely contains small inclusions of ®. M. Collongues. — Les remarques de M. Ubbelohde nous con­ duisent à préciser le mécanisme de la transformation ordre-désordre. Dans un travail récent (1) Kuczynski a étudié la transformation de l’alliage Au — Cu. Il a mis en évidence l’existence entre 350 et 400° d’une période d’induction de la transformation d’autant plus longue que la tempé­ rature est plus élevée. D’autre part, il a pu établir pour cette trans­ formation un diagramme TTT analogue à celui des réactions eutectoides par exemple. L’ensemble de ces résultats semble montrer que la transformation ordre-désordre s’effectue par un mécanisme de germination et de croissance. Or, dans un tel processus, il est impossible de négliger les variations d’énergie libre provoquées d’une part par la création d’un interface entre les phases 1 et 2 (paramètre d’autre part par la création de tensions dans la matrice au cours de la précipitation (paramètre ^2i)M. Timmermans. — Les vues de M. Ubbelhode confirment ce que nous savons des conditions où la loi des phases est d’application rigoureuse. Si une autre forme d’énergie intervient d’une manière notable, il faut introduire un paramètre supplémentaire; comme c’est le cas par exemple dans l’interprétation de l’opalescence critique dans les phénomènes critiques. Pour compléter l’exposé de M. Collongues, je voudrais rappeler que l’existence d’un composé défini de base dans une série de cristaux mixtes ne doit pas nécessairement conduire à un maximum de la température de fusion pour la concentration stoechiométrique (1) Kuczynski, Hochman et Doyama, J. Applied Physics., 26, 871 (1955).

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correspondante, mais peut produire un maximum à une concen­ tration voisine, comme c’est le cas pour les maximums de tempé­ rature d’ébulition dans les solutions eau + acide nitrique (exemple classique de Proscoe et Dittmer.)

M. Collongues. — Il semble en effet que la température de fusion ne soit pas une grandeur physique très bien choisie pour caractériser le composé stoechiométrique dont dérive une phase. La température de fusion étant, par définition, la température d’équilibre entre les phases solide et liquide, sa variation ne dépend pas uniquement de la composition de la phase solide. Nous pouvons considérer les courbes d’énergie libre de la phase intermédiaire choisie et de la phase liquide et supposer, comme nous l’avons fait jusqu’ici, que la courbe d’énergie libre de la phase intermédiaire présente un mini­ mum pour la composition stoechiométrique A^B„.

Pour que la température de fusion Tf soit maximum à la compo­ sition A^Bq, il est nécessaire que les deux courbes d’énergie libre à la température Tf soient tangentes en leur point minimum. Ce n’est évidemment pas le cas général. Il n’existe donc aucune raison théorique pour que la composition correspondant au maximum de la température de fusion coïncide avec la composition stoechio­ métrique. L’expérience montre cependant que ces deux compositions sont en général extrêmement voisines, phénomène que l’on peut

181

attribuer à la forme des courbes d’énergie libre (très ouverte pour la phase liquide, beaucoup plus fermée pour la phase solide). La conductibilité électrique serait peut-être une grandeur physique permettant de mieux caractériser l’existence d’un composé défini à l’intérieur du domaine d’une phase.

M. Weyl. — It might interest here that in silicate Systems similar phenomena can be observed. Si02 forms immiscible Systems with CaO, MgO and other oxides. With Na20, K2O, etc., no immiscibility is observed. Li20 behaves as an intermediate and is usally described as having a « tendency towards immiscibility ». By adding a solid to such a system (Pt or Pd in colloidal subdivision) we were able to actually separate fused lithium silicate into two liquids.

M. Kuhn. — It has been proved recently that in the simple case of water the freezing point is not exclusively a function of tempér­ ature but also of the magnitude of the crystals which are mechanically possible in the System (1). It was observed that an aqueous gel containing 96 % of water and 4 % of a high polymer (polyacrylic acid and polyvinylalcohol) which has been allowed to swell to saturation in pure water and having exactly the same vapour pressure as water has a freezing point of e.g. — 0.9 or — 2.0° C instead of 0° C. The différence is due to the fact that the presence of the gel lattice prevents ice crystals to reach linear dimensions greater than the dimensions of the meshes of the network of the gel. Micro crystals hâve a lower melting point than macro crystals, due to the interfacial tension between liquid water and ice. This means that the activity of the ice phase and thereby the melting point dépends not exclusively on the température but on the linear exten­ sion of the ice phase too. Similar effects obviously exist in the case of phase transformation in solids where restrictions in the extension of phases may last for considérable lengths of time. In ail these cases the free energy of a phase and, with it, the transformation point, must be considered to be, among other things, a function of the linear extension of the new phase. (1) W. Kuhn

182

U.

H. Majer, Z. physikal Chem., 3, 330 (1955).

M. Bénard. — 1. Je crois qu’une des raisons pour lesquelles les changements de composition qui accompagnent les transformations ordre-désordre ont été antérieurement négligés, est que les cher­ cheurs se sont placés de préférence, pour des raisons de commodité expérimentale, aux teneurs pour lesquelles la transformation ordredésordre se produit aux températures les plus élevées. Or ces teneurs sont précisément celles pour lesquelles la transformation a lieu sans changement de composition. J’ajouterai cependant qu’il ne me paraît pas indispensable d’admettre que toutes les transformations ordre-désordre se produisent suivant le processus de nucléation et croissance. Ce processus ne doit apparaître en réalité que lorsque la différence d’énergie libre massique entre les domaines ordonnés et les domaines désordonnés est suffisamment grande pour compenser l’énergie nécessaire à la création d’un interface entre ces deux types de domaines. Cette condition sera d’autant mieux réalisée, semble-t-il, qu’il existe une plus grande différence d’électronégativité entre les deux espèces d’atomes en présence, dans le réseau. Je crois qu’il est possible de pousser le raffinement plus loin encore que l’a fait le Professeur Ubbelohde. En effet, je crois qu’on est amené à envisager l’existence dans un certain domaine de tempé­ rature, non seulement d’équilibres entre deux états extrêmes, l’un ordonné, l’autre désordonné, mais entre une infinité d’états inter­ médiaires caractérisés par des états d’ordre intermédiaires. Ceci est à rapprocher de l’aspect structural de la transformation a p du cobalt dans laquelle les états extrêmes sont caractérisés par une succession de couches d’atomes en position A, B et C, suivant les séquences AB AB AB AB et ABC ABC ABC, correspondant à deux états d’ordre différents, mais où il existe en fait des états inter­ médiaires correspondant à la coexistence des deux types de séquences précédentes dans des domaines extrêmement petits. M. Chaudron. — C’est un fait de grande importance et bien connu que les traitements thermiques peuvent modifier la structure des phases métalliques. La phase métallique la plus importante par ses applications est sans aucun doute la phase austénite que l’on trouve dans le diagramme fer-carbone et qui est une solution solide de carbone dans le fer y. Cette austénite possède un point eutectoide à 720“ pour une compo­ sition voisine de 0,8 % de carbone. L’ensemble des traitements thermiques peut-être représenté dans un diagramme

TTT (dia­

183

gramme de Bain). On peut également, à partir de la phase FeO, qui a son point eutectoïde à 570° : 4 FeO ^ Fe304 + Fe, établir un diagramme tout à fait semblable. Nous avons pu, avec M. Collongues, mettre en évidence une transformation de type martensitique par trempe de FeO à basse température (1). On peut donc par traitement thermique obtenir une nouvelle phase comme dans le cas des alliages. La transformation ordre-désordre doit également nous montrer l’intérêt pour le chimiste de tenir compte des traitements thermiques dans les domaines pourtant assez éloignés de l’état métallique.

M. Forestier. — Doit-on considérer comme applicable d’une manière générale le point de vue actuel sur le rapprochement entre la transformation du deuxième ordre et du premier ordre dans les cas examinés ici? Cette question vaut aussi bien pour les alliages que pour les composés ioniques.

M. CoUongues. — L’intervention du mécanisme de germination et croissance dans la transformation ordre-désordre a été démontrée d’une manière rigoureuse dans les alliages cobalt-platine (CoPt) et or-cuivre (CU3AU). Pour la phase CuAu, Borelius (1) considérait que la transformation s’effectuait d’une manière discontinue au voisinage de la température de transition et d’une manière continue à basse température. Mais récemment, Kuczynski (2) a mis en évidence l’intervention du processus de germination même à basse température. Au contraire, l’existence d’un mécanisme continu de transformation semble bien démontrée pour l’alliage cuivre-zinc (CuZn) (3). Mais il ne semble pas possible de prévoir a priori le type de transformation suivant la différence d’électronégativité des deux éléments, qui est considérable pour l’alliage CuZn. La première transformation ordre-désordre signalée dans un composé partiellement ionique est celle de l’iodure double d’argent et de mercure Ag2Hgl4 (4). Nous avons étudié plus spécialement les transformations des ferrites, en particulier celles des ferrites de lithium FeLi02 et FesLiOs. La différence des numéros atomiques (1) R. Collongues, Thèse, Paris (1954).

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du fer et du lithium est en effet suffisamment élevée pour que la mise en évidence des raies de surstructure soit possible. Dans les deux cas, nous avons mis en évidence la précipitation de l’une des phases (ordonnée ou désordonnée) à l’intérieur de l’autre. 1° La phase FeLi02 est cubique à haute température. Les ions Fe+++ et Li+ sont répartis d’une manière désordonnée dans les positions cationiques d’un réseau de type NaCl. Au-dessous de 670°, ce ferrite subit une transformation qui conduit à l’établisse­ ment d’un ordre dans la répartition des cations. Les raies de sur­ structure apparaissent et la maille devient quadratique. L’étude aux rayons X révèle la coexistence des deux phases ordonnée et désordon­ née et l’on observe au microscope la précipitation de la phase ordonnée à l’intérieur de la matrice désordonnée sous forme d’une structure de Widmanstâtten (5). 2° Le ferrite FesLiOg subit lui aussi une transformation ordredésordre à 710° avec apparition de raies de surstructure, mais sans modification des dimensions de la maille cristalline. L’étude aux rayons X ne permet donc pas de révéler le mécanisme de la trans­ formation. Mais on observe au microscope la croissance sous forme de dendrites de la phase désordonnée à l’intérieur de la matrice ordonnée (6). Nous pensons que ce processus discontinu de transformation se rencontre également dans d’autres ferrites, comme le ferrite de cuivre. M. Barrer. — I hâve some observations bearing on the comments by Professor Ubbelohde upon the spécial free energy terms which arise when a new phase is nucleated on or in a matrix of a parent phase. In my review I hâve indicaded how hystérésis can resuit from these extra free energy terms. However I would like to illustrate this by reference to some ion exchange experiments made with analcite NaAlSi20gH20. This species can give a variety of exchanges such as Na K; K:^±: Rb; Na:^±Tl, etc., which we hâve studied (1) (2) (3) (4) (5) (6)

Borelius, J. Inst. Metals, 74, 17 (1948). Kuczynski, Hochman et Doyama, J. Applied Physics., 26, 871 (1955). Beck et Smith, Trans AIME, 194, 1079 (1952). Ketelaar, Z. Phys. Chem., 26 B, 327 (1934). R. Collongues, Comptes rendus, 241, 1577 (1955). I. Behar, Comptes rendus, 242, 2465 (1956).

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rather fully.

Some times one end member of exchanges (e.g. the

pure form, KAlSi20(5) is not miscible over the whole composition range in the other form (e.g. the pure Rb form). We hâve demonstrated the appearance of a two phase région by optical and X-ray methods. One form (e.g. Rb rich) grows on or in a matrix of the other form (e.g. K rich) at a critical concentration Rb in the parent crystals. A very striking hystérésis loop OABCD was found in this case (fig. 1). The loop was also scanned (path XCYDX and paths X XiYiX;

X X2Y2X).

Another resuit of the nucléation process I hâve referred to is indicated in figure 2, which is représentative of several of the exchanges studied in analcite.

186

Starting with a solution saturated with respect to each exchanging sait (e.g. KCl and RbCl) and exposing to this solution crystals of pure Rb and K analcite respectively different end points appeared. By using solutions mutually saturated with respect to each exchanging ion A+ and B+ the concentrations of these ions in solution are held constant during the exchange. The explanation follows at once from considération of a typical hystérésis loop. Suppose PP represents constant concentration of A+ in the electrolyte, where PP intersects the loop as shown. Then starting from the 100 % A+ form the end point is clearly Xj and starting from 100 % B+ form the end point is obviously X2. Reaction will never proceed past these two points in the electrolyte of com­ position represented by PP.

M. Defay. — Le Professeur Ubbelohde a attiré l’attention sur le fait que la thermodynamique des milieux solides doit tenir compte de deux facteurs qui ne jouent pas dans celle des phases ordinaires et qui sont : l’énergie superficielle des microphases et leur état de tension. M. Ubbelohde n’emploie pas le mot « équilibre » pour les états stationnaires décrits par cette méthode. Il me semble que l’on peut parfaitement envisager ces problèmes comme problèmes d’équilibre, mais ce sont des états d’équilibre qui ne peuvent se décrire avec les seules variables T, V et concentrations; il faut au minimum adjoindre une variable liée à la dimension des microphases. Même lorsque le système présente le phénomène d’hystérèse, chacun des points de la courbe de montée comme chacun des points de la courbe de descente représente un véritable état d’équilibre. Cela se voit

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très bien dans l’hystérèse de condensation capillaire, où chaque point de la courbe d’hystérèse représente un état d’équilibre avec des pores de rayons déterminés. L’exemple d’hystérèse des courbes de sorption d’un élément dans un solide, donné par le Professeur Barrer, est extrêmement instructif. L’explication la plus vraisemblable est celle des retards de nucléation, proposée par l’auteur dans son rapport. Mais étant donné que tout germe tend en général à croître indéfiniment dès qu’il a dépassé sa dimension critique, les courbes d’hystérèse ne seront chacune de vraies courbes d’équilibre que si quelque chose dans le réseau s’oppose à l’accroissement du germe. Dans la théorie du « host lattice », la dimension et l’environnement des cavités de diverses sortes déterminent cette limite. Elles jouent ainsi un rôle analogue à celui des rayons des pores dans la condensation capillaire, où ces rayons sont nombreux, différents mais fixes. Je vois quelque difficulté à appliquer cette pensée à la nucléation ordre-désordre, car je ne vois pas, à première vue, ce qui va empêcher un germe de s’accroître indéfiniment et d’envahir toute la phase. M. Ubbelohde. — Nuclei of small size hâve their free energy modified by the surface energy term, according to the well known Kelvin équation. But if they are free nuclei without any mechanical constraints they will hâve a true equilibrium point with another phase, determined by their dimensions. In the smeared transitions in solids the nuclei or « régions » of (D are formed within the matrix of ®, and this sets up a System of mechanical strains as well as introducing surface energy terms. If any process could be devised in which solid © could be formed from solid ®, as an extensive phase, one would expect the smeared transition to be replaced by a true first order transformation.

In the immédiate neighbourhood of a transformation, mechanical strains of the kind described must hâve a relaxation time large compared with the time of experiment, since most examples of hystérésis are not suppressed by taking longer over the observations. The State of strain is « frozen in ». On passing beyond the trans­ formation région, the différences between ® and © become larger, so that relaxation of the transformation occurs and the change ® ^ © or © ^ ® is completed.

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There is nothing novel about thermodynamic equilibria which are frozen in with respect to certain changes, whilst other changes set up true equilibrium. For example in a mixture of H2 + O2, at room température true equilibrium is rapidly set up with respect to température, and with respect to mixing of the molécules by diffusion. On the other hand equilibrium with respect to the bond rearran­ gement : 2H 2 + O2 -> 2 H2O is frozen in at room température because of the large activation energy required.

In the sommation of States which déterminés the free energy, the factors referring to such frozen-in fluctuations retain an arbitrary value depending on the past history of the System, and are not minimised. Thus varions mixtures of H2, O2 and H2O can be discussed at room températures. M. Bénard. — Un aspect particulièrement intéressant du problème des combinaisons intermétalliques paraît être la transition pro­ gressive de phases dans lesquelles la liaison est manifestement métal­ lique à des phases dans lesquelles la liaison est sinon entièrement ionique, du moins largement polaire. Cette transition se manifeste dans des séries dans lesquelles le rapport stoechiométrique varie en donnant des phases successives de structures différentes. Un bon exemple est donné par le système nickel-soufre dans lequel la phase Ni3S2 présente un caractère métallique très accusé, tandis que la phase NiS2 présente un caractère salin, la phase NiS possédant des caractères intermédiaires. La transition se manifeste également lorsque dans une même série on remplace le soufre par les homogues supérieurs : sélénium et tellure. Je serais heureux de savoir si l’évolution des propriétés physiques dans ces différentes séries s’accompagne d’une diminution systématique de l’étendue des domaines homogènes lorsqu’on passe des phases type métal­ lique aux phases type ionique. A priori, on pourrait en effet s’attendre à observer une telle variation au moins dans le second cas, puisque les possibilités d’échange entre les positions des deux types d’atomes constitutifs diminuent lorsque la différence d’électronégativité entre ces atomes s’accroît, entraînant de ce fait une réduction de la largeur de la courbe d’énergie libre de la phase en fonction de la compo­ sition. Il est évident cependant que les caractéristiques des phases adjacentes peuvent modifier l’étendue réelle du domaine d’homo­ généité et masquer au moins partiellement cet effet.

189

M. Collongues. — Il ne semble pas possible d’étabbr une relation entre l’étendue des phases intermédiaires et la différence d’électro­ négativité des deux éléments. En effet, dans les phases de substi­ tution, le facteur électroaffinité n’a qu’une importance secondaire vis à vis du facteur de dimension et du facteur concentration élec­ tronique. On peut cependant noter que l’étendue des domaines d’homogénéité des phases y obéissant aux règles de Hume-Rothery est en général plus faible que l’étendue des phases p. Or les liaisons dans les phases p sont essentiellement métalliques; les phases y au contraire sont fortement ionisées. Dans les phases lacunaires, il est impossible de prévoir la variation de l’étendue du domaine d’homogénéité en fonction de la différence d’électronégativité des deux éléments, puisqu’il ne se produit pas d’échange entre les positions des deux types d’atomes. Dans le cas des phases de type NiAs, il est même assez curieux de constater que les domaines d’homogénéité semblent d’autant plus étendus que les différences d’électronégativité sont plus grandes (fig. 12 et 13) : Co — Te Co — Sb Co — Sn 16 %

7 %

3 %

Ni — Te

Ni — Sb

Ni — Sn

Ni — In

16 %

7 %

7 %

4 %

M. Kuhn. — Quelles sont les méthodes par lesquelles le nombre d’électrons libres dans les métaux peut être déterminé. M. D’Or. — Je crois que l’une des données qui renseignent le mieux de façon quantitative sur la densité en électrons « libres » dans un métal est la chaleur spécifique mesurée à de basses tempé­ ratures où la composante de réseau est devenue pratiquement nulle. Ceci se limite cependant au cas des métaux à structure électronique sous-jacente saturée; dans le cas des métaux de transition à couches d non saturées, la relation entre la composante électronique de la chaleur spécifique et la densité en électrons libres est en effet complexe. M. Ubbelohde. — The fact that a métal such as palladium becomes diamagnetic for a given proportion of hydrogen atoms in solid solution does seem to imply that the d bond has been filled at this concentration.

190

The number of électrons added is not immediately

relevant for the number of vacancies in pure palladium, since the overlap of hypothetical atomic orbitals is likely to change as the interatomic distance expands in the crystal as hydrogen is added. There is reason to believe that for some of the transitional metals the d bond is quite sensitive to interatomic séparations. Certain anomalous thermal expansions of alloys of transitional metals may arise in this way. The high solubility for hydrogen of certain alloys of palladium and silver likewise suggests that the model of électron transfer from the added hydrogen atoms to a fixed number df vacancies in a ê? bond in palladium is too simple to account for ail the experimental findings.

M. Chaudron. — Il est possible d’expliquer la stabilisation de certains composés non stoechiométriques par l’application de la théorie lacunaire de Hâgg. Le sesquioxyde de fer cubique pur est instable vers 200° et même à plus basse température. Au contraire, par addition de sodium ce corps peut être obtenu au-delà de TOO^. On peut écrire successivement : 3 Fe2+

2 Fe3+ -|- □

et

2 Fe2+ ^ Fe3+ + Na+

Ce problème a été repris récemment par M. Michel, de l’Univer­ sité de Lille (1) : des ions tétravalents tels que Ti‘*+ qui se substi­ tuent dans la magnétite suivant le schéma :

2 Fe3+^ Ti4+ + Fe2+ provoquent une augmentation du nombre des lacunes et on observe une diminution de la stabilité. Dans le cas du protoxyde de fer, ce sont précisément les compo­ sitions de la phase FeO les plus riches en lacunes qui sont les plus instables. Je pense qu’il serait intéressant de créer sur certains composés, des défauts (lacunes) par bombardement. L’étude de ces composés artificiels serait d’un grand intérêt, mais elle présenterait certainement des difficultés techniques, dues probablement à une trop grande instabilité de ces composés. Enfin, il conviendrait de remarquer que la non-stoechiométrie établit une sorte de continuité

191

entre les composés classiques de la chimie minérale. On ne peut plus dire que la chimie minérale est une chimie de prototypes; en effet, les solutions solides et la non-stoechiométrie sous ses multi­ ples aspects donnent lieu à de nombreuses phases dont les propriétés peuvent varier d’une manière très importante.

(1) A. Michel, Comptes rendus (1956). (2) G. Chaudron et J. Bénard, Premier colloque des réactions dans l'état solide, Paris (1948), p. 88.

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Non-Stoicheiometric Organic Compounds by H. M. POWELL

GENERAL CONSIDERATIONS After the great success of Dalton’s atomic theory which involved the idea of intégral combining powers of atoms, chemists came to think that if éléments combined they did so according to a simple plan. Any pure compound consisted of molécules containing defini te and unalterable numbers of atoms of the éléments involved. If ail atoms of any one of the éléments, A, B, C... are identical, the composition of a compound composed of molécules of formula Ap Bg Cr... where p, q, r... are integers, is constant. The weights of the éléments that can unité to form one of the possible compounds that corne from varying A, B, C... and the integers p, q, r... are simply related to the weights in other compounds. At first the intégral values of p, q, r... were based on the compositions determined by analysis and any substance that did not obey the rule was suspected of being impure. Electronic théories of valency which hâve followed théories of atomic structure explain the intégral values of p, q, r... by identifying Chemical combination with the interaction of électrons which, in some sense at least, are regarded as entities and are ascribed in whole numbers to each atom. The definite compositions of molécules are explained if it is supposed that each atom involved in the formation of a Chemical union must contribute a whole number of électrons for the process. When slightly modified to allow for isotopic variation in the éléments these requirements of composition still hold for molécules or other complexes of finite groups of atoms such as may exist in the vapour and liquid States or in solutions. They also apply to many crystalline substances, but could no longer be maintained as unbreakable rules when crystal structures were examined by X-ray methods. Almost the first resuit of X-ray structure détermination, which naturally was carried out on substances of the simplest Chemical

193

formulae, was to abolish the molécule for some compounds.

After

the atom or ion the next larger distinguishable entity in the structure was not the supposed molécule of a few atoms in the correct ratio to explain the composition, but the crystal as a whole or some other indefinitely extended complex.

Integers p, q, r... may still arise

from electronic requirements, but there are other possibilities. If one of the éléments involved displays more than one valency, its compounds which exist in the form of finite molécules will obey the rules and hâve the compositions predicted from Dalton’s laws. A substance of composition intermediate between two of those predicted from the law of multiple proportions may be described as a mixture of two or more molecular species capable, in principle, of séparation into molécules of different weights. But when the molécule does not exist such a description has no meaning. In many crystalline inorganic compounds no molécules are found. Instead the structures are composed of ions or atoms linked in varions ways. Ideally the crystal is composed of a number of interpenetrating lattices ail of the same dimensions. Ideally also the lattice points of each of these are occupied by a set of identical atoms. The crystal as a whole is made up of a finite number of these lattices, and thus it has a simple formula in accordance with Dalton’s laws. Departures from these laws in crystalline compounds are commonly described therefore in terms of lattice defects. Many types of lattice defect are known and not ail will affect the composition.

The simple

ratios between the numbers of atoms of the varions éléments that compose the crystal may arise from requirements such as the need for over-all electrical neutrality or for the formation of some definite number of electron-pair bonds.

These requirements détermine the

relative numbers of the interpenetrating lattices. If a defect occurs, for example, by the ommission of an atom from one of these lattices, it may be balanced by some other defect, e.g. by an atom in an interstitial position or at the surface, or by the omission of an atom of another kind. It is particularly when a crystal is in part composed of atoms of an element which can hâve more than one valency that the combining ratio of the atoms may vary. If some of the positions that formally are attributed to a set of identical atoms ail in the same valency State are in fact occupied by atoms of the same element

194

in a different valency State the number of combining atoms required in the complementary interpenetrating lattices is no longer that required by the simple formula.

Vacant spaces may be left in the

first lattice to compensate for those occupied by atoms in higher valency States, and the number of atoms in one or more of the inter­ penetrating lattices may vary according to the fraction of the pos­ sible positions occupied. In this way non-stoicheiometric compounds resuit; their existence has a simple structural explanation and the ranges of their compositions can be explained. Some lattice defects do not affect the combining ratios of the atoms. For example crystalline silver cyanide consists of indefinitely extended chains of Ag-CN-Ag-CN-Ag in parallel array (i).

The

disorder which consists of irregular displacements of the chains in the direction of their lengths has no effect on Chemical composition. The thermal oscillation or rotation of atoms or groups of atoms similarly has no effect. A great many organic compounds can exist as single molécules identifiable in the gaseous, liquid or solid States or in solutions as entities separated from the surrounding matter by distances which are large in comparison with the normal distance of sépar­ ation of atoms that are joined by a Chemical bond. If différences such as those due to isotopy and thermal motion are disregarded, a pure substance of this kind must consist of a set of identical molécules. The ratios of the constituent atoms are determined by the intégral valencies of the combining éléments. This is a property of the free molécules and is unaffected by crystallisation. Even if the crystal has more complex aggregates, e.g. by hydrogen bonding of molécules, or there are lattice defects involving whole molécules, the combining proportions of the éléments are unaltered. It seems therefore that only when organic crystals contain two or more kinds of molécules can non-stoicheiometry arise. A molecular crystal grows by using intermolecular attractions which add molécules to a regular stack. It is easy to see why this can proceed readily when ail the molécules are identical. The chance that a mixture of two sorts of molécules will find some way of buil­ ding a regular lattice pattern which contains them both in ordered array must be small, or substances could not be obtained pure from such mixtures, but particular pairs will form molecular compounds

195

of this kind. A few substances seem especially given to this behaviour and any one of these may appear as a constituent common to a large number of related molecular compounds.

Frequently, though

not necessarily, there is a common structural basis in such a sériés. Enough intermolecular compounds are now known to make pro­ fitable a considération of them as a whole with particular reference to their compositions. By analogy with inorganic structures it might be supposed that when analysis reveals a simple ratio of the molecular components the compound should be described as stoicheiometric, and non-stoicheiometric when it is otherwise. The case turns out to be more complex than this but provisionally the Word “ stoicheiometric ” may be understood in this sense. Some groups of molecular compounds dépend on the similar Chemical characteristics of their components. Thus of the large number of intermolecular compounds formed by aromatic polynitro compounds with other molécules (2) many hâve in common the three nitro groups in one molécule and an aromatic System in the other. The formation of such compounds is affected by Chemical factors such as the different electron-donating powers of different substituents, and in many of them there may be a strong localised interaction between particular parts of each molécule. These inter­ actions require a spécial set of interatomic distances between the molécules. The set of contacts of each atom with other atoms in neighbouring molécules is part of the whole complex structural pattern. Lattice defects which could alter the ratio of the components are unlikely. Whole molécules might be missing but the proportion of spaces vacant is likely to be very small since large empty spaces would thus be formed. As will appear, organic crystals sometimes hâve large empty spaces but there are spécial reasons for it. In other sériés there is no Chemical similarity of a group of molé­ cules that show similar behaviour in molecular coumpound formation. Thus J3-quinol clathrates (^) of idéal formula 3 C6H4(OH)2.M are formed where M is SO2, H2S, HCN, CH3OH, H.CO2H, C2H2, N2, O2, CO2, A, Kr, and others. The binding, in some cases at least, is very weak and any similarities of the participating molécules are geometrical rather than Chemical.

Departure from the idéal

formula is common in this sériés. It is convenient for the présent purpose to divide the structures of intermolecular compounds into two main classes.

196

In the first

class the component molécules M and N are intricately related so that the next larger distinguishable unit after the single molécule is some group composed of both M and N molécules in the same ratio as they occur in the crystal as a whole. For example the molécule may be arranged according to a pattern resembling the co-ordination structures of simple inorganic compounds in which after two individual atoms or ions a and b the next larger distinguishable group is the whole crystal of composition an bm, n and m intégral, each a being surrounded by a group of A’s and each b being surrounded by a group of a’s with co-ordination numbers determined by com­ position of the compound and other factors such as the dimensions of the particles. Alternatively the structural sub-unit of the same composition as the whole crystal may extend indefinitely in two dimensions or in one. Spécial interactions between particular atoms or groups of atoms in one molécule M, with some atom or groups in the component N are likely to give structures of this first class. In the second class structural sub-units may be distinguished which contain the component molécules in proportions different from those of the molecular compound as a whole, a spécial and common case being that in which a sub-unit of the structure is composed entirely of molécules of one kind. These sub-units could consist of a group containing a finite group of molécules ail of the same kind or of indefinitely extended groups in 1, 2 or 3 dimensions, to give chains, sheets or 3-dimensional frame-works. In the first class, compositions are determined by the particular interactions of one molécule with those of the other kind. It is not impossible for there to be lattice defects, for example by ommission of a complété molécule, but such defects are not likely to be numerous and the composition should not départ greatly from the idéal. Some kinds of lattice defects such as the displacement of a whole layer or chain component of such a structure would hâve no efîect on the composition since these components of the struc­ tures hâve the composition of the crystal as a whole. In the second class, possibilities for non-stoicheiometric compounds arise in varions ways. The structural part of the crystal composed entirely of molécules M may not be able to exist without its companion of composition N, though in some instances it does, but the fitting together of M with N may be governed by geometrical factors. If there is no strong localised bonding between the two different

197

kinds of molécule, these geometrical factors may lead to simple proportions of M and N, but often they do not. The compositions of some intermolecular compounds of the second class will now be considered.

CHAIN AND LAVER STRUCTURES Among crystalline intermolecular compounds already known to contain a complex made up of molécules of one component only several structural types may be distinguished. The complex may bave a form that could be packed by itself to fill the space satisfactorily, and the molecular compound may be looked upon as built up of complexes containing molécules of the one kind together with other components which lie in between the complexes. These other components may be single molécules, finite groups of molé­ cules, or may themselves also take on the geometrical character of an indefinitely extended complex. It there is no strong localised interaction between the two kinds of molécules, the composition of the molecular compound may be determined by geometrical conditions which hâve to be satisfied when the varions components are fitted together into a structure. For example, suppose that one component forms a chain-like complex consisting of a stack of molécules regularly repeated along a lattice direction. Let the crystalline molecular compound consist of these chains arranged parallel, with regular lattice spacings between their long axes, together with molécules of the other component in positions between the Chain complexes. These molécules between the chain complexes can fit some regular plan of répétition parallel to the chain lengths and might themselves constitute a second form of chain component. In the absence of strong localised bonding which will fix molécules of one kind in definite positions relative to the molécules of the first type of chain complex, there may be no simple relationship between the repeat lengths along the two kinds of chain. The ratio of one component to the other in the structure would then be determined by these repeat lengths, which in turn are related to the lengths of the molécules concerned and the intermolecular séparations in the direction of the chain. An idealised form of structure of this sort can be imagined as composed of two arrays of cylinders which represent the packing dimensions

198

of molécules.

Imagine cylinders end-to-end in chain-like forms

arranged parallel in a square pattern. Let a second and different set of cylinders be placed at the centres of the squares in the first. There is a definite 1 : 1 ratio of chains of the two kinds. If the cylin­ ders of the two kinds are of unequal cross sections but of equal lengths they also hâve a definite 1 : 1 ratio, but if the two kinds are of known unequal lengths there will be a known relation between the number of cylinders of the one kind to those of the other, but this need not be a simple whole number ratio. If, for example, the cylinders of one kind had a length 1 and those of the other had a length ^/2, the composition, although definite, could not be expressed as a ratio. In practice any analytical resuit will be expressible as a ratio of sufficiently large numbers and to describe a compound as non-stoicheiometric simply because these numbers are large may be considered arbitrary. Without any essential change in the character of such a structure it might hâve a simple whole number ratio of the components. If a sériés of cylinders of different lengths can be imagined, e.g. because they represent members of homologous sériés, there will be some packi'ng lengths which bear a simple ratio to the packing length of the other molécule. In this type of structure with parallel chain components, and its analogue with parallel layer components, the molécules therefore fill space satisfactorily and non-stoicheiometry may arise as described from incompatibility of the repeat distances in the one- or two-dimensional lattice patterns of the sub-units. A further possible cause would be the failure of the chain or layer components to repeat in a regular manner, i.e. the chain or layer expected for regularity of the lattice might be sometimes replaced by the “ wrong ” component. Known structures of this possible form are not numerous.

The

molecular compounds formed by hexamethylbenzene with the picryl halides may include examples ('*). These compounds, although formally similar to the general class of molecular compounds between aromatic polynitro-compounds and other aromatic substances, hâve a structural characteristic which is not common among them. Both components occur in the compound as layers. That of the hexa­ methylbenzene differs only slighly from a layer in the structure of the normal anorthic form of the pure substance; it is almost identical

199

with the layers in the less stable orthorhombic form (5). The other component, picryl chloride, bromide, or iodide, forms a layer which does not, however, bear any simple resemblance to the structures, so far as they are known, of the pure picryl halides. The molecular compound consists of alternate layers and has, at least approximately, the 1 : 1 ratio. The molecular compounds with the chloride and bromide hâve orthorhombic pseudo unit cells roughly 14 x 9 x 15.3A. There are, however, for the chloride faint continuons streaks in intermediate positions between the reciprocal lattice rows corresponding to this cell, and for the bromide more intense streaks and smudges which in certain positions hâve the appearance of fuzzy spots cor­ responding to a cell with thee b dimension three times enlarged to approximately 27 A. The direction of the streaks corresponds to an irregularity of spacing along a (14 A), i.e. perpendicular to the layers. In the iodide the irregular streaks and smudges are replaced by Sharp spots which require the three times entarged b spacing, but there is still some disorder since in place of the streaks there are discontinuons lines that break up into spots suggesting an enlargement of a. It is évident that these two layer components hâve a disordered sequence and possibly they do not make a good fit. It might be argued that if one of the three halides could form a layer structure to match that of the hexamethylbenzene then the other two, because of their slightly dififerent dimensions, could not. This is, however, conferring too fixed a character on the hexamethyl­ benzene layer.

This clearly can alter since there are two crystalline

modifications and molécules which are linked by van der Waals forces will to some extent adapt their packing to fit the shapes of their partners in molecular compound formation. In agreement with this the dimensions of the three cells difîer slightly, and most of the observations might be explained as due to an irregularity in the sequence of layers that may fit in several only slightly different positions. However, the compound with picryl iodide has been found to vary in other ways, the enlargement along the a dimension varying from crystal to crystal, although no deliberate variation of the con­ ditions of formation has been made. From the existence of several distinct though related diffraction patterns there must be a number of molecular arrangements which may or may not hâve the same molecular ratio. The disorder effects which relate to the sequence

200

of layers seem most likely to be caused through the identity of the hexamethylbenzene with the layer in the less stable orthorhombic form of this substance. One event that seems almost certain to occur is the déposition of a wrong layer, i.e. a hexamethylbenzene layer in place of the expected picryl halide layer. This must cause a departure from the simple molecular ratio. Disorder may be made apparent to X-rays with a comparatively small number of faults. This, combined with the difficulty of more than one crystal type being produced, makes a considérable analytical difficulty and the case has not been established as firmly as may be desired.

INCLUSION STRUCTURES More numerous are the molecular compounds in which one struc­ tural component consists entirely of one kind of molécule but the form is such that it does not by itself fill space to the extent normally required for formation of a crystal. In addition to the unfilled small spaces that are left even by the closest packing of atoms or molécules there are comparatively large spaces available for the other com­ ponent of the molecular compound. The type may be described as inclusion compounds, and there is not necessarily any strong localised interaction of the enclosing and included molécules. The binding, apart from some spécial cases, arises from the combination of a large number of van der Waals interactions. Whether the mole­ cular compound has a simple molecular ratio is determined in part by geometrical considérations. To be enclosed by another structure a molécule must hâve size and shape suited to the enclosure, and it is convenient to divide the enclosures into those which may be considered as closed and those which are open. Of the two forms considered, one has a closed molecular cage limited in ail directions and into which the second molécule must fit. The other has endless channels running through the structure so that although included molécules may be limited as to what may be called their cross sections, they are not geometrically restricted with regard to length. Since the molecular dimensions used to discuss these matters correspond to equilibrium values and do not hâve the invariability of the geo­ metrical forms used to represent them, this division into two kinds, although practical, is an approximation only.

A space which is

201

effectively closed for a large molécule may be open and continuons with its neighbours for a smaller molécule. A characteristic of structures with closed cavities is that there must be a fixed ratio of cavities to surrounding molécules. In the simples! case of a single enclosed molécule which occupies most of the available space in a cavity, the idéal formula is simple. Thus in the p-quinol clathrates where three molécules of quinol (Q) are required to form a single small cavity able to contain a single atom or small molécule (M), the idéal formula is 3Q.M. It is found when M is methanol or methyl cyanide, the molecular compound being formed by crystallisation of quinol from the solvent which in these cases itself provides the included molécules. A similar definite ratio of water molécules to others is found in the gas hydrates (6). Departures from these idéal stoicheiometric formulae, however, may arise in at least two ways. The cavities are assumed to be subject to very little variation in size and shape for structural reasons. In the case of the quinol clathrates, for example, there is a hydrogenbonding System which, although it does not forbid ail variation, imposes severe limitations. This means that when only two components are présent, the only alternative to a single atom or molécule in the cavity is a vacant space. Whether or not ail the possible cavities are filled dépends on the conditions of formation and in practice clathrates of a wide range of composition 3Q.xM, x having values between 0 and 1, can be made. A second case is that a closed cavity may be large enough to contain more than one molécule. This is the case with Dianin’s compound Ç). There are a set of idéal limiting formulae of fixed numbers of enclosed to enclosing molécules. This is illustrated in Table I.

The idéal formula dépends on the size of the included

molécule, and the actual composition can départ from these only through a deficiency of included material. Me

Me

I

II

\/\

OH

Dianin’s compound

202

TABLE I

6 : 1

2:1*

Bromobenzene

Methanol

1 ; 3-Dibromopropane 3 : 1

m-Dichlorobenzene

Acetic acid

o-Dichlorobenzene

Carbon tetrachloride

Ethylene dibromide

Methyl iodide

lodobenzene

Nitromethane

Tetrachlorethylene

Sulphur dioxide

Argon

* Ratio of Dianin’s compound to included molécule.

The idéal compositions are explained by the sizes of included molécules which are such that one, two, or three molécules may be included in each cavity. Adducts of carbon disulphide, chloroform, and iodine show deficiencies compared with the 3:1 formula ; those of /7-bromanisole and 2-bromopyridine are déficient compared to the 6 : 1 type. The argon compound shown in the table as having the 6 : 1 ratio should, in view of the relatively small size of the argon atom, be regarded as déficient with respect to the 2 : 1 type. The deficiencies might be supposed to arise in the same way as in a singly occupied cavity through chance events when a cavity is closed, but there are différences. It is known that molécules in such cages hâve some freedom of movement (*). In this way they may occupy more than their normal space and thus a single one might hâve an efîect in keeping out a second. A further factor which may apply to enantiomorphous pairs of molécules is mentioned later. Best known of channel inclusion compounds are the adducts of urea and thio-urea (®). In these the space available for the other substance is without limit in one dimension. Possible compositions dépend on whether the channels act as though uniform or nonuniform along their lengths.

When there are no influences strong

203

enough to attach included molécules to particular positions in the channels the molecular ratio is given by formulae such as : U

12 [1.256 («—!) + 4] 2 X 11.01

= 0.6848 (n — 1) + 2.181

U = number of urea molécules, H = number of normal CnH2»+2 molécules (lO). The numerator, the effective length of hydrocarbon molécule, is divided by the constant length of the urea pattern parallel to the channel, and allowance is made for the number of urea molécules and channels per unit cell. These idéal compositions fit well with those found. In adducts of thiourea with ww' dicyclohexylalkanes there are noticeable periodic différences in intensity of interaction of the chan­ nel walls and included molécules. The included molécules do not follow one another at distances determined solely by their lengths. With molécules fixed in a less indiscriminate way, and sometimes repeating with periods related to those of the thiourea channels themselves, simple ratios of the component molécules arise. The same ratio may be found for three successive members of the sériés. For each included molécule there may be as much or more channel space as its packing length requires. There cannot be less, and steady increase in the molecular length according to the number of CH2 groups eventually alters the proportion of components through intermediate values until a new simple ratio is reached. It is certain that defects occur in cage compounds. They differ from some defects in inorganic non-stoicheiometric compounds in that the omission of an enclosed molécule does not require a compensating change in some other part of the structure. For some channel structures the agreement of compositions with formulae based on calculated lengths of included molécules shows that in these sériés effectively ail the available space is filled. It may be that since the channels are open there is a greater chance of filling them. There is no difhculty corresponding to the closing of an empty cavity, in a clathrate, which will then never be filled, but the possibility of deficiencies in channel structures should not be overlooked.

It is perhaps more difficult to detect than to under-

stand such a deficiency.

204

ANALYSIS Whether a given compound is stoicheiometric or not is determined by some form of analysis.

Equilibrium diagrams may not

always be easily obtained, and some organic intermolecular compounds présent other difficulties. When enclosing structures are formed a relatively large amount of material is required for each space available for enclosed molécules. If both components are organic compounds some of the possible analytical quantities may be insensitive to change in the molecular ratio. Thus the compound formed by tri-o-thymotide with butanol would hâve C = 74.4 %, H = 7.25 % for 2 C33H36O6.C4H9OH and C = 74.1 %, H = 7.39 % for 2 C33H36O6.I ^C4H90H.

Différences finer than these must

be measured to establish non-stoicheiometric compositions.

In

such cases it is better to analyse for the included component which amounts to 6.55 % in the 2 : 1 and 8.53 % in the 2:1^ formula, but a direct method, such as heating the material to find the loss of weight, may not be accurate. The enclosed material may be released only at a température far above its normal boiling point

C—O

c=o

Tri-o-thymotide

and even then it is not easy to know that ail the included material has been driven off.

To beat under vacuum is sometimes to risk

possible losses due to volatilisation of enclosing component. In any case ail losses due to whatever cause, such as décomposition, will appear to represent weight of the substance being estimated. When suitable atoms or groups are présent in the included sub­ stance, détermination of halogen, active hydrogen, and the like, may therefore give more reliable estimâtes of the molecular ratios. Estimation of the acid in urea adducts of aliphatic compounds provides a good example. There is, however, in ail Chemical methods.

205

a difficulty concerning the material analysed. Frequently the included component is also the solvent used in its préparation. How a sample may be dried to render it suitable for analysis without loss of included material is uncertain. In these circumstances a direct détermination of the weight of material in the crystal unit cell has much to commend it. Unit cell dimensions may be measured fairly readily to an accuracy of one part in several thousands and a comparable accuracy in density is obtained without difficulty. The case may be illustrated by D. Lawton’s measurements on the adducts of tri-o-thymotide C33H36O6. Several sériés of inclusion compounds are formed by this substance. The compounds in some sériés are stoicheiometric, and hâve a close resemblance to clathrates. The lower members of the «-alcohols apparently fit one molécule per cavity. Thus the adduct with «-butanol has space group P3i2 and a = 13.617 ± 0.002, c = 30.603 ± 0.002 A. From the density (by a density column method) 1.146 g./c.c. the weight of the unit cell not accounted for by its six molécules of tri-o-thymotide, is 225 in molecular weight units. Three molécules of butanol require the value 222 showing that the molecular compounds fits a 2 : 1 ratio very closely. One structural characteristic of channel structures may be used to reveal something about their composition in another method which dépends on X-ray diffraction effects. If the molécules included in the channels can equally well occupy any position with respect to the repeat pattern of the surrounding structure and, in any one channel, follow each other at a regular distance determined by their packing lengths, they will produce an X-ray diffraction effect. In photographs this sometimes consists of streaks which, by suitable experimental procedure may be shown parallel to the layer Unes of the main sharp pattern of spots due to the lattice of the enclosing structure. Effects of this kind hâve been observed with urea and thiourea adducts (H), the blue iodine adducts (12) and other sub­ stances. These streaks which resemble the effects of a one-dimensional lattice may be used to détermine the repeat distance of the material in the channels. The length of the channels being parallel to the rotation axis of the crystal, and the number of them in a unit cell being known, the ratio of the two kinds of molécule is obtained simply by dividing one lattice constant into the other and allowing for the known number of enclosing molécules per

206

TABLE II Tri-o-thymotide channel structures, containing alkyl halides. Hexagonal c-spacing from sharp layer Unes = 29.04 A.

Spacing from streaks parallel to layer Unes (c-axis rotation)

29.04 divided by spacing of column 2

Number of molécules of alkyl halide to 6-tri-o-thymotide (by Chemical analysis)

n-Heptyl iodide

12.72 A

2.26

2.1

n-Octyl

iodide

14.5

2

2.0

n-Cetyl

iodide

24

1.21

1.3

24

1.21

1.1

Included molécule

«-Cetyl bromide

unit cell. Table II gives some compositions calculated in this way. The third column shows the maximum permissible number of included molécules for every six tri-o-thymotide molécules, there being one channel per unit cell containing six tri-o-thymotide molécules. In this method there is no direct détermination of the quantity of included material. That it is correct to divide the lattice constant by the figure calculated from the positions of the continuons streaks is made very probable by a comparison of the observed lengths with the probable dimensions of the included molécules. Thus the distances parallel to the c-axis between the centres of the terminal atoms of heptyl iodide, octyl iodide, and cetyl iodide, estimated from known bond lengths, and with the assumption that the molécule has the normal planar zigzag form, are 9.21, 10.46 and 20.5 A. To obtain the repeat distance allowance must be made for the packing space required by the terminal groups. In the absence of detailed knowledge of the structure this could be guessed as not much more than 4 A. It is simpler perhaps to take the spacings calculated from the continuons streaks and to subtract from each the appropriate value, 9.21 etc., when the remainder should represent the end packing efîects. The values obtained are 3.51, 4.04, and 3.5 A for the compounds in the order given. The approximate constancy and the actual magnitude are in agreement with the assumptions made above. It thus appears that the repeat distance in thé channel is correctly known but it is by no means certain that the whole of

207

each channel is filled. The spread and diffuseness of the streaks in the direction perpendicular to the layer lines may be affected by other factors as well but in principle could be related to the regularity of the packing of molécules along the channels and the occurrence of vacant spaces. It is scarcely practicable to pursue this and the compositions estimated by the method above must therefore be regarded as giving for the included molécule a maximum value that in practice may not be attained. In connection with these continuons streaks a distinction must be drawn between disorder and non-stoicheiometry. When the streaks lie at some arbitrary distance between the layer lines there is no simple ratio of the components if the space provided in the structure is filled as far as is possible with included molécules. However, the mere presence of the one-dimensional layer line streak does not mean that the compound is non-stoicheiometric. Thus in the case of octyl iodide-tri-o-thymotide continuons streaks coincide with the 2nd, 4th and 8th sharp layer lines for rotation about the c axis. This requires a simple ratio (1: 3) of octyl iodide to tri-o-thymotide molécules. When the repeat distance of the included material is the same as, or is simply related to, that of the tri-othymotide, disorder streaks may still arise because although the included material is regularly spaced along each channel it may be irregularly displaced relative to the tri-o-thymotide. The intermediate streaks may also occupy spécial positions between the layer lines, corresponding to enlargement of the unit cell in the direction of the channels to some simple multiple. This, with maximum filling by included molécules, also gives a simple ratio of included to enclosing molécules. Measurement of the lattice constants of the surrounding struc­ ture and of the repeat distance for the enclosed material gives an idéal formula in the same way as complété structure détermination for cage structures. In cage structures this idéal formula has a simple ratio of enclosing molécules to spaces; ideally these compounds should be stoicheiometric ; vacant space defects may make them non-stoicheiometric. In channel structures the idéal formula, corresponding to ail the possible space filled, may be stoicheiometric or not. If it is stoicheiometric vacant space defects will make the compound non-stoicheiometric. If it is non-stoicheiometric vacant space defects in the structure can alter the ratio of the components

208

by lowering the proportion of included molécules.

Thus from the

layer streaks the ratio heptyl iodide to tri-o-thymotide in the completely filled form is calculated as 2.26 : 6. Vacant spaces would diminish this and it is possible that a value 2 : 6 could be obtained in this way. Thus a particular specimen of a channel-structure inclusion compound which ideally is non-stoicheiometric might through imperfections analyse as though it were stoicheiometric. This shows that no single way of investigating these compounds is by itself satisfactory. examined.

Both composition and structure must be

For the better examination of compositions it may be

that analysis should be made more accurate.

Possibly suitable

isotopes should be used for this purpose.

OPTICALLY NON-STOICHEIOMETRIC COMPOUNDS It was stated that non-stoicheiometric organic compounds will arise only when the compound can be regarded as formed from two or more molecular components,

détectable

by

analytical

methods which give their relative proportions. A form of nonstoicheiometry, however, can occur in what might be regarded as pure single substances. A very large number of synthetic organic compounds do not consist simply of identical molécules. They exist in two molecular forms which are the non-superposable mirror images of each other. Sometimes, although it has been comparatively rarely observed, the substance on crystallisation séparâtes spontaneously into two non-superposable mirror image crystalline forms which are identical in nearly ail their physical properties but are distinguishable by their shapes and some physical properties such as behaviour to polarised light. They can be separated by hand and in the examples so far discovered this séparation constitutes a complété optical resolution of the molécules. It is known of a good many other substances that they crystallise as racemates, the crystal structure having symmetry éléments which require the presence of equal numbers of the left and right mirror image forms. These racemates are so common as perhaps to be regarded as pure Chemical substances, although it could be said that they are crystal­ line molecular compounds. Whether they are described in this way or not it remains that the lattice contains two different kinds of molécule.

Any inequality in the number of right and left mirror

209

image forms is in principle measurable since such a mixture can hâve an optical rotation varying between zéro for the racemate to the full rotation given by either of the pure antipodes. Disorders in crystalline structures which contain both mirror image forms could lead to non-stoicheiometric compounds in the optical sense, though they will not affect the atomic ratios. In this case disorders consisting of a vacant space could lead to optical activity in one of several ways. An ordinary racemic structure has space group positions in equal quantities for left and right mirror images. Vacant spaces would be expected to be of about equal frequency in the left and the right forms so that only a very small departure from the racemic mixture is likely. But other forms of crystal structure for optically active compounds are imaginable. In certain crystal structures molécules are found to occupy more than one space group position. For example 3 : 4 : 5 : 6 dibenzphenanthrene has space group A 2/a(i3). Its unit cell contains 12 molécules; 8 of these occupy general positions in the space group which are crystallographically équivalent. The other 4 occupy a

different set of space group positions. The group of 8 équivalent molécules do not use their possible symmetry in forming the struc­ ture, but each molécule of the group of 4 équivalents must show a two-fold symmetry axis. The compound op’dichlorodiphenyltrichloroethane ('4) shows in exaggerated form what may be fairly common behaviour with molécules of sufficient complexity. Its anorthic unit cell contains 20 molécules. This unit cell being formally primitive these twenty require at least 10 crystallographically distinct sets of point positions each containing two molécules. Such complex arrangements of molécules to form a crystalline pattern are presumably due to difficulties in packing of awkward shapes. They are, therefore, in a general way more probable with unsymmetrical molécules which include those that are not superposable on their mirror images. When molécules ail of the same Chemical constitution occupy several different sets of équivalent point positions in the space group, the relative numbers of molécules in the different groups cannot affect the composition except in the optical sense. Let a molécule be imagined in any general position of a non-enantiomorphous space group. If it is a dissymétrie molécule its enantiomorph will occupy an équivalent position in accordance with the symmetry. No matter

210

what other different sets, either of the general or the spécial positions may also be occupied, the same considération applies to each and the crystal as a whole is racemic.

The racemate is optically a stoi-

cheiometric compound of 1 : 1 formula.

Although this is the only

kind known other optically stoicheiometric compounds are ima­ ginable. Let a molécule occupy a general position in an enantiomorphous space group. This molécule may hâve crystallographically équivalent molécules which are related to it by rotation- or screw-axes of symmetry.

If it is dissymétrie these équivalents are ail of the

same optical form. other

molécules

Suppose the structure as a whole contains

occupying

sets

of équivalent

positions.

Each

set consists of molécules ail of the same optical kind, but there is no reason why ail the different sets should hâve the same optical form. It is thus possible to imagine structures which contain the left- and the right-handed forms in varions definite ratios. There could be a single set of équivalent molécules ail of the one hand. Two forms of the structure will exist each being a mirror image of the other and containing one enantiomorphous form of the molécule. This is the kind of structure already known in crystals of resolved optically active substances. But in an enantiomorphous space group one set of équivalent positions could be occupied by the left-handed form of molécule and a crystallographically different set of the same number of équivalent positions could be occupied by the right-handed form of molécule. This structure would not be identical with its mirror image and there could exist both kinds of crystal. Each would display structural enantiomorphism but on dissolving either kind of crystal a racemic solution would be obtained. Defects in such a structure might lead to an optically non-stoicheiometric compound. Since the left- and right-handed molécules occupy structurally different positions a defect may be more likely to occur in one than in the other. There is not the same probability as in a racemic crystal that if, for example, molécules are missing from lattice positions, they will consist of equal numbers of left and right. Similar considérations apply to other conceivable optically stoi­ cheiometric compounds. If two or more sets of équivalent positions are occupied by molécules, each set having only those of one enan­ tiomorphous kind, the crystal has an over-all composition D«Lm where n and m are integers which need not be the same. There might be for example in space group P62 three équivalent L molécules

211

in a spécial position requiring a two-fold symmetry axis in the molécule and a different set of six équivalent molécules, ail D, in a general position. The unit cell would thus contain three L and six D molécules, the over-all composition being given by n = 2, w = 1. Two forms of crystal, the mirror images of each other, would exist, one corresponding to D„Lm the other to D^Ln.

On

dissolution these substances would show equal but opposite rot­ ations of the plane of polarisation of light, and might be mistaken for dextro and laevo forms, unless some other means were available to show that the rotation is a definite fraction, in this case 1/3, of that of the completely resolved form. The idéal structures of such fractionally resolved materials are optically stoicheiometric. As in the preceding case departures from the strict stoicheiometric would occur if defects are more frequent for molécules in one set of positions than another. Such effects if they exist at ail will be on a small scale and are not likely to be detected optically. A defect which has not so far been considered is that in which some of the positions in an optically stoicheiometric structure are occupied by molécules of the wrong hand. This is ordinarily unlikely because in a well packed structure the wrong hand of molécule will not fit easily into the space left by omission of its enantiomorph. The case, however, is different when the optically active molécule is a component of an inclusion compound. The spaces in cage or channel structures are not so closely adapted to contain one particular molécule as is the space left by removal of a single molécule from the crystal structure of a pure substance. As ail the known examples show, the enclosed molécule may be varied in shape. While the cavities, as revealed by lattice constant measurement, may remain unchanged the included molécule may be altered, e.g. propanol may be replaced by methanol in a closed cavity of a tri-othymotide clathrate structure. From this it is certain that in the case of the smaller molécule there must be free space in the cavity. It has been found that both the straight-chain aliphatic compounds and those with a hydrogen atom replaced by another atom or small group to form a slightly branched System may enter the same channel in some Systems. Since there is room for the side group the unbranched molécule, which can sometimes be shown to be in its normal extended form, must fit rather loosely. For some purposes it has been convenient to regard the channels of inclusion structures

212

as uniform hollow cylinders. These if they could contain one of two enantiomorphs could equally well contain the other; both forms may be regarded as fitting loosely, at least in the direction of the channel length.

The proportion of left and right molécules

that entered would be expected to be the same as that in the material used to préparé the inclusion compound. The form of the spaces in inclusion compounds must, however, for this purpose be considered more closely.

In enantiomorphous

space groups they will not be superposable on their mirror images. In non-enantiomorphous space groups they will be superposable or they may occur in mirror image pairs. The opposite extreme to the uniform cylinder which does not discriminate between left and right included forms is a space that can contain only one of these and rigorously excludes the other. It seems most likely to occur in clathrates where the cavity of defined shape may require the enclosed molécule to lie in a particular orient­ ation.

In a channel which is not regarded as a uniform cylinder

but as a sériés of enantiomorphous but connected cavities there may be more freedom to displace the enclosed molécules and thus to find positions in which either right or left forms may be placed. The channel being imagined as composed of cavities ail of the same enantiomorphous kind it may be geometrically possible to enclose both forms although there is a greater probability of fitting in one enantiomorph rather than the other. Compositions in terms of enantiomorphous forms in molecular compounds can be of several kinds. An optically stoicheiometric form may resuit when there is a cage which is highly sélective through close fitting to the enclosed molécule or molécules. This is illustrated by the adduct of tri-o-thymotide with secondary butyl bromide (15). From the racemic solvent any one crystal of the trigonal adduct has the composition 2 C33H360g.C4H9Br, ail the butyl bromide being of one hand only, and similarly ail the tri-o-thymotide being of one enantiomorphous form.

The materials used to préparé this

are both racemates but the yield can be obtained ail in one form. Spontaneous optical resolution occurs and the rapid racémisation of the tri-o-thymotide in solution makes it possible through deliberate or accidentai seeding to crystallise out one form only. Optically stoicheiometric compounds also resuit when the enclosing structure

213

is centrosymmetric as in the adducts of Dianin’s compound. Equal amounts of left and right forms of molécule are enclosed. The solutions of the molecular compounds give no optical rotation. Irrespeetive of the ratio of enclosed moleeules to molécules of the Dianin’s compound itself, there is a 1 : 1 ratio of the enclosed dextro and laevo forms. Optically non-stoicheiometric forms may resuit when, as described above, there is a greater chance of fitting one enantiomorph rather than the other. Examples are cyclodextrin adducts (1*5) and urea adducts ('‘^). The cavities in both these structures are not identical with their mirror images and when a racemic solvent is used to make adducts it is found that a partial optical resolution occurs. In the case of the cyclodextrins ail the cavities are of one enantiomorphous form and it is found that the included solvent contains unequal amounts of left and right forms. A spécial effect may be foreseen for cage structures where more than one molécule may be enclosed in a single cage. If, for example, Dianin’s compound is crystallised from a racemic solvent, it may be expected that some of the cavities, which are centro-symmetic, will hâve a dextro and some a laevo enclosed molécule, or if the molécules are sufficiently small there may be cavities with one dextro and one laevo each. If the compound were formed from a dextro solvent the optical composition is necessarily simple, namely ail dextro, but a curious effect on the composition may be expected in certain cases.

Suppose that the dimensions are sueh that one

dextro and one laevo molécule can be fitted into a cage. Onee the cavity contains a dextro molécule the remaining space is the wrong mirror image form for a second dextro molécule which is the only form available. If this dextro form is as rigorously excluded as the wrong form of secondary butyl bromide in the spaces of the tri-o-thymotide adducts, this would mean that the molecular com­ pound formed from the dextro solvent could include only half as much material as that obtained with racemic solvent.

Partially

resolved solvent should give molecular compounds of intermediate compositions, although it is not obvions that the included material should hâve the same optical composition as the starting solvent. There is, however, here a possibility that the ratio of molécules included to enclosing molécules may be linked with the optical composition of the solvent employed.

214

DESCRIPTION OF MOLECULAR COMPOUNDS It remains to consider how molecular compounds may be described.

One method would be to abandon attempts to understand

or interpret compositions which could then be given as empirical. But variable or possibly misleading compositions can be understood if considered in relation to crystal structure. Many of the apparent complexities of minerai composition are simplified when attention is concentrated on the number and arrangement of the oxygen atoms which occupy much of the unit cell. Other inorganic com­ pounds may be understood in terms of the packing of their halogen or other atoms; metallurgists clarify complex equilibrium diagrams by distinguishing phases which may include some which hâve ranges of inhomogeneity. A similar outlook on intermolecular compounds seems necessary. A formula for such a compound should be based on crystal structure. It might be related to the répétition, if regular, of either component but a choice will usually be simple. For example structural constants common to a sériés of molecular compounds formed by one substance like urea will be preferred to any quantity applicable only to a particular included component. From the structure as a whole an idéal formula is derived, based on some intégral number of molécules of one component. The idéal formula may be described as rational when it requires a simple ratio of the components and irrational when it does not. This description does not by itself State whether the material examined is, on analysis, stoicheiometric. A particular structure may if necessary be further qualified as déficient, the deficiency being in the component on which the idéal formula is not based. As to the resulting composition it is perhaps better to consider constancy or variability rather than stoicheiometric character in the sense originally understood. An irrational molecular compound may be non-stoicheiometric but of such constancy of composition and properties that it may, for analytical purposes, be best compared to an ordinary pure Chemical substance.

A rational but déficient molecular compound is in

general non-stoicheiometric and may hâve a range of composition and variable properties analogous to those of inorganic non-stoi­ cheiometric compounds. An irrational and déficient molecular compound varies in the same way but might by accident analyse as stoicheiometric.

215

It may be appropriate to add whether the compound is disordered or not. Thus there are two closely related but distinguishable adducts of tri-o-thymotide and n-octyl iodide.

That listed in Table II as

having streaks coincident with sharp layer lines may be described as a rational non-deficient channel inclusion structure with dis­ placement disorder in the channels. The other has the same channel structure but instead of streaks there are enhanced sharp spots on the corresponding layers. It is rational, non-deficient, and without displacement disorder. Both would be inadequately described as stoicheiometric of formula 3C33H36O6.C3H15I.

REFERENCES (1) West C.D., Zeit. Krist., 88 A, 173 (1934). (2) Pfeiffer P., Organische Molekülverbindungen, 2 Aufl. (1927); Briegleb G., Zwischenmolekulare Kràfte und Molekülstruktur (1937). (3) Palin D.E. and Powell H. M., J. Chem. Soc., 815 (1948). (4) Powell H.M. and Huse G., ibid., 435 (1943). (5) Watanabe T., Saito Y. and Chihara H., Scientific Papers from the Osaka University, n" 2, (1949). (6) V. Stackelberg M., Naturwissenschaften, 36, 327, 359 (1949); Claussen W.F., J. Chem. Phys., 19, 259, 662, 1425, (1951); Millier H.R. and v. Stackelberg M., Naturwissenschaften, 39, 20 (1952); V. Stackelberg M., and Millier H.R., Zeit. Elekrochemie, 58, 25 0 954); V. Stackelberg M., and Meinhold W., ibid., p. 40; V. Stackelberg M., ibid., p. 104; V. Stackelberg M., and Jahns W., ibid., p. 162; Pauling L. and Marsh R.E., Proc. Nat. Acad. Sci. (U.S.A.), 38, 112 (1952). (7) Dianin A.P., J. Soc. Phys. Chim. Russe, 46, 1310 (1914); Baker W. and McOmie J.F., Chem, and Ind., 256 (1955).; Powell H. M. and Wetters B.D.P., ibid., p. 256. (8) Palin D. E., and Powell H. M., J. Chem. Soc., 208 (1947); Dryden J.S., and Meakins R.J., Nature, 169, 324 (1952) Dryden J.S., Trans. Faraday Soc., 49, 1333 (1952); Cooke A.H, Meyer H., Wolf W.P., Evans D.F., and Richards R.E., Proc. Roy. Soc., A 225, 112 (1954). (9) Schlenk W., Annalen, 565, 204 (1949); Angla B., Compt. rend., 224, 402, 1166 (1947); Schlenk W., Annalen, 573, 142 (1951). (10) Schlenk W., Refs. 9; Smith A.E., /. Chem. Phys., 18, 150 (1950) Acta Cryst., 5, 224 (1952). (11) Smith A.E., Ref 10 ; Lenne H.U., Acta Cryst., 7, 1 (1954); Borchert W., and Dietrich H., Heidelberger Beitrage zur Minéralogie u. Pétrographie., 3, 124 (1952). (12) Cramer F., Ber., 84, 855 (1951); West C.D., J. Chem. Phys., 15, 689 (1947); 17, 219 (1949); 19, 1423 (1951); V. Dietrich H. and Cramer F., Ber., 87 ,806 (1954). (13) Mcintosh A.O., Robertson J.M., and Vand V., Nature, 169, 322 (1952). (l'i) Wild H. and Brandenberger E., Helv. Chim. Acta, 29, 1024 (1946); (15) Powell H.M., Nature, 170, 155 (1952). (10) Cramer F., Angew. Chem., 64, 136 (1952). 07) Schlenk W., Experientia, 8, 337 (1952).

216

Discussion M. Schlenk. — 1. Is the inclusion-lattice of P quinol and that of Dianin’s compound stable also without guest molécules, and if it is the case, how is the empty crystal to be got? 2. Can you tell some details regarding the structure of the tri-o-thymotide molecular compounds? 3. Is the structure of pure tri-o-thymotide without guest molécules known ? 4. Hâve you succeeded in resolving other racemic mixtures than 2-bromobutane by means of tri-o-thymotide?

5. Is it possible to say, which of the two enantiomorphous forms of the inclusion-lattice of tri-o-thymotide belongs to the (-f)-form of the host molécule? In the case of urea adducts it was possible to déterminé the relative configuration of corresponding (CH3) — (OH) —, (Cl) —, (NH2) — and (SH) — compounds by including these compounds into one and the same form of the host-lattice.

M. Powell. — 1. Yes. The p-quinol structure without included molécules has been obtained by cooling solution of quinol in n-propyl alcohol to températures about — 20° C. It may also be obtained at room température from a solution, free of a-quinol seeds, by seeding with the p form or with the argon clathrate. Dianin’s compound without included molécules may be obtained by sublimation. Another method is to dissolve it in sodium hydroxide solution — it is a phénol — and then to blow in, carbon dioxide. The Dianin’s compound which is insoluble in water cornes out, free of included material. 2. The detailed crystal structures, i.e. the exact location of atoms, hâve not been determined. They are very complex and of low symmetry in some cases. known for two sériés.

The general arrangement of molécules is

217

In one, formed by molécules, such as n-alcohols and n-alkyl halides, provided the molécule does not exceed a certain length, there are closed cavities as in the quinol clathrates. If longer molécules are used there is a slight rearrangement of the molécules to give channel structures very similar to the urea adducts. If molécules either short enough for the first sériés, or too long to be accepted in it, are too much branched, they do not form adducts belonging to these sériés. But they are not simply rejected by the tri-o-thymotide, as urea rejects many branched molécules. Instead they often form an adduct, but of a structure that may hâve no apparent relation to the two already mentioned. 3. The channel structure obtained when long molécules are included, is too open to form without guest molécules. The closely related structure, with closed cavities, obtained with short molécules, can form without guest molécules. 4. No, but there should not be great difficulties in the clathrate type. In the channel type, there hâve been obstacles such as failure of a particular adduct to grow a suitable crystal for seeding, or inefficiency of the seeding process. 5. This could be donc by first using a molécule of known enantiomorphous form to déterminé the nature of the cavity. It is relevant that the surrounding cage of tri-o-thymotide must fit the guest molécule rather closely, since it entirely rejects one of the enantiomorphous forms. M. Timmermans. — a) Les cristaux de complexes présentant une résolution spontanée, possèdent-ils des facettes hémiédriques et un pouvoir rotatoire mesurable? b) La résolution est-elle vraiment spontanée, c’est-à-dire, se pro­ duit-elle en l’absence complète de germes énantiotropes ? M. Powell. — d) The crystals of those tri-o-thymotide adducts which are known from X-ray examination to belong to enantiomor­ phous space groups hâve so far not developed any faces that could reveal the hemihedrism. They hâve been examined for optical rotatory power since at one time it was necessary to détermine whether they could be sorted into left and right forms by use of this property.

218

The main sériés of adducts are uniaxial and thus

favourable for such a procedure, but although the optical activity bas been observed it is very weak. Since other methods became available, the method was never attempted. Some of the crystals showed optical anomalies, possibly due to inhomogeneities of composition, and these might interféré. b) It is scarcely possible to demonstrate that an experiment has been carried out so that no enantiomorphous material of any kind could hâve been présent. Havinga carried out experiments with great care and obtained spontaneous resolution of a tetra substituted ammonium compound, but he mentions the difficulty.

M. Schlenk. — We hâve measured the rotation of urea-inclusion crystals. The optical rotation of the crystal is of the same order as that of (B-quartz.

M. Bénard. — L’observation que je désire faire se rapporte, dans une certaine mesure, à celle qui vient d’être faite par le Professeur Timmermans. L’existence des composés moléculaires non stoechio­ métriques n’est pas, en effet, l’apanage des combinaisons orga­ niques et l’on connaît maintenant de nombreux exemples de com­ posés d’addition tels que iode-benzène, anhydride carbonique, protoxyde d’azote, iode-brome, etc. Dans ces systèmes l’étendue du domaine de variation de la composition paraît reliée d’une façon assez nette à la forme générale et aux dimensions des molécules qui sont appelées à se substituer les unes aux autres. Ainsi la miscibilité est totale, si mes souvenirs sont exacts, entre CO2 et N2O, dont les configurations sont très voisines. Il n’apparaît pas dans un tel système une composition particulière qui corresponde à un rapport moléculaire dicté par la géométrie du réseau, comme c’est le cas dans les composés décrits par le Docteur Powell.

M. Timmermans. — Un autre exemple de série continue entre cristaux énantiotropes est celui des carboximes ^/ + /, dont la courbe de congélation passe par un maximum (pseudo-racémique, formant deux séries continues de cristaux mixtes avec chacun des antipodes). Il serait très intéressant de rechercher si les antipodes ont des 219

facettes hémiédriques et, éventuellement, à partir de quel pour­ centage celles-ci disparaissent dans les cristaux mixtes. M. Chaudron. — Les mécanismes d’inclusion permettent certaines séparations, par exemple de gaz rares. Je voulais demander au Professeur Powell s’il a eu l’occasion de pousser ses recherches dans cette voie. M. Powell. — Some of the host structures are indiscriminate in the sélection of guest molécules. This is the case with Dianin’s compound on account of its large cavities. Tri-o-thymotide forms adducts with nearly ail the solvents that hâve been used for it. Consequently it is not likely to be very useful for separating substances, except in the spécial case where it séparâtes dextro and laevo molécules. The urea and thio-urea inclusion compounds of Docteur Schlenk hâve been much used for séparations based on molecular shapes. As a spécial case, the quinol clathrates hâve been used to separate the rare gases. The method does not dépend on exclusion through shape or size, since both gases concerned form the clathrate. A 3 : 1 (volume) mixture of Kr and Xe gives crystals of quinol clathrate from which a 1 : 3 mixture is recovered. M. Barrer. — I would like to ask Dr. Powell the following questions. In experiments in which solid thiourea was exposed to CCI4 vapour, or solid potassium benzene sulphonate was exposed to various organic vapours, we hâve observed an induction period in formation of the complexes, an accelaration period and a slowing down of reaction, i.e. the typical auto-catalytic rate of formation of the complexes. Tri-o-thymotide which recrystallises so readily to give diverse complexes seems to présent an analogous case. Hâve such autocatalytic kinetics of formation of complexes been observed? My second question concerns the geometry of the cages in P-quinol or in Dianin’s compound. The « Windows » leading to and from these cages are rings of six — OH groups.

What is the free

diameter of these rings and hâve any measurements been made of rates of escape of small guest molécules through them?

220

Also what are the free volumes in cm^, per cm^ of crystal, in P-quinol and in Dianin’s compound?

It would be interesting to

know these and to compare them with the free volumes found in zeolites, which may exeeed 0.5 cm^ per cm^ of crystal in exceptional cases. M. Powell. — First question : No. Second question : The distance across the hexagon between oxygen O centres is 5.5 A. Allowance must be made for the effective radius of each oxygen in the hexagon. e

This will not be less than 1.4 A so that the diameter of the free O

space is not more than 5.5 — 2 X 1.4 = 2.7 A. Rates of escape hâve not been measured. The densities of empty P-quinol and the empty Dianin’s compound are not very low in comparison with organic compounds of similar formulae. This is partly because although they hâve cavities they also hâve hydrogen bonds which bring some parts of the struetures doser together than the normal intermolecular séparations in organic crystals. From these densities it can be seen that the free volumes amount to a few per cent of the volume of crystal i.e. they are a good deal less than those mentioned by Professer Barrer. M. Kuhn. — In connection with the remarks made by Professer Hâgg and by Professer Timmermans with respect to spontaneous resultion and to a virtual continuity of the composition of crystals containing d- and /-molécules of optically active substances, it is ôf interest to mention that Docteur K. Vogler and Docteur M. Kofler in Basle hâve recently found an example of such a sub­ stance (1). It is a dérivative of piperidine :

CH,

(1) K. Voghr and M. Kofler; to appear in Helvetica Chemica Acta.

221

When this substance was synthesised from inactive material, a small optical activity was found, amounting to (a)^ = 4° in 5 % solution in water. By about 400 crystallisations, the rotatory power was increased to (a)o = 124°. The melting point of the optically active compound was 84°, while the racemic substance melts at 74-76°. The melting point of the partly active substance varies continuously with optical purity with a fiat minimum for the racemic mixture. The solidus and liquidas curves are separated over the whole range by about 1-2° C. The fact that it is not possible to obtain racemic crystals from a racemic solution and that the crystals separating from a racemic or from a partly optically active solution are neither pure antipodes, the degree of optical purity increasing slowly and continuously as the optical activity in the mother liquid increases, seems to indicate 1° : that the substance forms at room température two kinds of lattices, a É?-lattice; and a/-lattice; 2° : that the ^/-lattice prefers to a certain extent t/-molecules, présent in the mother liquid, being at the same time a host for /-molécules which are taken up from the mother liquid, though relatively less than the £/-molecules ; 3° : that a

continuous variation in the content from 50 % to

100 %

^/-molécules is thus possible for the crystallographic d-form and that a corresponding statement holds for the crystallographic /-form. It should be remarked that according to the preference of the crystallographic d-form for ^/-molécules, a crystal of the crystall­ ographic ^/-form containing e.g. 75 % ^/-molécules, will not be in thermodynamic equilibrium with a solution, or melt, containing 75 % (/-molécules; a crystal with 75 % (/-molécules would indeed grow from a solution containing e.g. 70 % of (/-molécules. A cor­ responding statement would also hold for a crystal of the crystal­ lographic (/-form, containing about 50% of (/-molécules. It is possible that this might be the reason for the différence of solidus and liquidas curve mentioned. M. Hâgg. — There seems to exist another class of crystalline phases, counted to solid geneous because

which, according to Dr. Powell’s définition, should be among the optically non-stoichiometric compounds. I refer solutions between optical antipodes, which represent homophases with varying composition. Such solutions are rare, the two antipodes must be so similar in size that they can

replace each other in the lattice.

222

They are, for instance, formed

between optical antipodes of certain camphor dérivatives as found by Knipping more than fifty years ago.

In this case the similarity

is probably due to rotation of the molécules in the lattice. M. Timmermans. — Je désire attirer l’attention sur un groupe de systèmes qui ne rentrent pas à proprement parler dans la catégorie des combinaisons non stoéchiométriques, mais cependant pas complètement étrangers, en ce comme dans les clathrates, de remplir certaines d’une substance par les molécules d’une autre

qui ne leur sont sens qu’il s’agit, cavités du réseau substance, comme

dans les systèmes isomorphes. Je veux parler tout d’abord des cristaux mixtes « anormaux » que forment entre eux des couples de composés globulaires. On sait que j’ai baptisé ainsi les substances organiques et minérales, dont l’entropie moléculaire de fusion est inférieure à 5, et qui présentent un grand nombre de particularités permettant de les classer à côté des liquides anisotropes, comme intermédiaires entre



l’état cristallin et l’état liquide : pour un liquide anisotrope, à la température de fusion, le réseau disparaît, mais l’orientation molé­ culaire subsiste jusqu’à la température d’éclaircissement du liquide; dans les composés globulaires, l’orientation moléculaire disparaît déjà dans le cristal, à partir d’un point de transition énantiotrope, mais le réseau ne disparaît qu’au point de fusion. Les phases globulaires, entre le point de fusion et le point de transformation, dont je viens de parler, cristallisent toutes dans le système cubique, et si leur grandeur moléculaire n’est pas trop différente, elles donnent des cristaux mixtes, quelle que soit leur constitution chimique : un exemple classique est celui de la série isomorphe méthane -f- argon. S’il s’agit d’antipodes optiques, ceux d’une même substance, mélangés en toutes proportions, ne donnent pas de racémique, mais une série continue de cristaux mixtes, qui ne se distinguent pas par leur point de fusion : c’est le cas des deux camphres d + l. J’ai cru utile de signaler ici ce type de système curieux, dont la signification paraît avoir échappé jusqu’ici, surtout aux purs cristallographes. M. Caglioti. — Je désire attirer l’attention sur la chimie des phos­ phates de calcium et particulièrement : 22.'!

a) du phosphate tertiaire hydraté, qui présente un réseau lacu­ naire dans lequel peuvent trouver place des molécules d’eau ou de carbonate de calcium, etc.; b) de l’hydroxyapatite, qui peut former avec les aminoacides et les protéines des complexes de surface, dont la formation est proba­ blement facilitée par l’identité de certaines dimensions, phénomène qui joue un rôle essentiel dans la structure même des os. Dans ce deuxième cas, nous sommes aux limites et nous ne pou­ vons plus parler de formation d’un composé d’insertion, mais nous devons plutôt supposer qu’il s’agit d’un cas d’épitaxie.

224

Complex Compounds of the Transition Metals by R. S. NYHOLM

I. — INTRODUCTION

This report deals with the présent State of the chemistry of the coordination compounds of the transition metals, with particular reference to developments which hâve taken place during the last two décades. During this period the approach to inorganic chemistry in general, and coordination chemistry in particular, has changed from an essentially préparative one to a more purposeful attack in which valency theory, structure and reactivity are of major interest. As will emerge from this, and other, reports the reason for this change is the application of physical methods of investigation and of the results of quantum mechanics — these two being largely complementary. With the wealth of material available one must necessarily be sélective if the report is not to be too long. Following this intro­ duction, Part II will be devoted to a brief survey of the historical development of the subject of complex compounds tracing the reasons leading to the rapid growth of interest at the présent time. In Part III a qualitative picture of the modem theory of valency as is relevant to discussion of complexes will be given. In particular the develop­ ment of the présent position will be discussed. Part IV deals with the magnetic behaviour of métal complexes. Finally in Part V we

Statement on Report by R. S. Nyholm. This report has been written in close collaboration with Dr. L. E. Orgel. It was agreed that a generalised introductory treatment of the part on valency in these complexes should be given in this paper, to be followed by a more detailed discussion on spectra by Dr. Orgel. I am very grateful to Dr. Orgel for his critical comments and advice in writing this section.

225

survey the data concerning transition métal complexes under each group with spécial référencé to the valence State, stereochemistry and magnetic behaviour. 11. — fflSTORICAL It is convenient to regard the development of the chemistry of complex compounds as falling into four periods. During the first of these, the pre-Werner period, a large number of what are now recognized as co-ordination compounds were isolated and analysed. They were recognized as “addition com­ pounds” of greater or lesser stability resulting from the combina­ tion of two or more stable inorganic compounds. No satisfactory or acceptable theory to account for their structure was available. Then followed the Werner period during which time the essential principles of co-ordination number, direct métal to ligand bond and simple stereochemistry were laid down and developed. The octahedral, tetrahedral, planar and linear arrangements were visualised and the first three established more or less firmly by classical methods. Such an advance occurred during this period that experimental work outstripped the theoretical workers and in the absence of applicable physical techniques for further structural studies we pass into the Quiescent period extending until the nineteen thirties. During this time certain préparative and classical studies (e.g. optical resolution) of complexes continued, but no really striking advances occurred. From about 1932 onwards we move into the Modem period, of rapid advancement. The developments in quantum mechanics in the late nineteen twenties were applied by Pauling in particular to inorganic chemistry and although there hâve been modifications in detail since the early nineteen thirties, it is fair to say that Linus Pauling (1) enunciated the principles which provided the main stimulus for later developments. Of spécial importance was the fact that quantum mechanics gave a sense of purpose to physical measurements and enabled magnetic moments, electric dipole moments and spectral measurements to be correlated with structure. It is of interest to note that the basis of the crystal field theory was also laid down by Bethe (2), Penney and Schlapp Q) Van Vleck (4) and Gorter (5) in the late nineteen twenties and early nineteen thirties, but it is only during the past five years that this approach has found favour with many chemists.

226

III. — VALENCY THEORY Before dealing with the complex compounds in the Periodic Table we summarise first the basis for discussion. Ligands can be classified conveniently as follows (Table I).

TABLE I Types of ligand ------------------------- Ligand ------------------------- ^

a) With lone pairs of électrons

I

-----------------------!---------------------- i

1

(0

Possessing no va­ cant orbitals for réception of 7t élec­ trons from the métal E.g. :NH3

:0H2 ;C1H

b) Without lone pairs of électrons but possessing tz bonding électron pairs. E.g. Ethylene; cyclopentadienyl ion.

(<0 With vacant orbitals or orbitals capable of being made available for réception of tt électrons from the métal E.g. —N“ in dimethylglyoxime (“p” orbital) or the donor P in PMes (“d” orbital).

[:C1:]-

In discussing the type of metal-ligand bond in complex compounds we must recognize that we are at an important stage of development in our views on this subject. For a long time chemists took the view that there were two main types of bond, and “electrostatic” or “ion-dipole” bond on the one hand, and one involving électron sharing — the so-called “covalent” bond — on the other. The metals of the first transition sériés were known to give two kinds of co-ordination compounds, “normal” and “pénétration” complexes respectively. These were distinguished in idéal cases, e.g. Fe’“, by a différence in the number of unpaired non-bonding 3d électrons as determined by the magnetic moment.

Then followed the view that

in many instances in complex compounds the distinction was often not between “ ionic ” and “ covalent ” bonds but frequently between “ outer orbital ” complexes involving no électron pairing on the central métal atom, and “ inner orbital” complexes with strong pairing on the other. Thus in comparing potassium ferrioxalate and potasium ferricyanide the electronic configuration of the Fe™

227

228

P O 3 CTO

3



Fe+++ in an “ ionic ” complex

4j

in an “ outer ” orbital complex

{4s4p^4d^

orbitals)

4p

Œi

(for bonding)

I fil

•4-

Fe“’ in an “ inner ” orbital complex

{3dHs4p^ orbitals)

(for bonding)

4

(4--------------------^ =

> bonding orbitals.)

Fig. I. — Electronic configuration o f ferrie atom in complexes.

3d

St s

In order to account for certain complexes in which électron pairing occurred but where an insufficient number of M orbitals were available to allow of inner “d” orbital binding the process of promotion of électrons was postulated. This was considered necessary in the case of octahedral “ covalent ” Co” complex ions like [Co(N02)ô]‘*“- The postulated electronic configuration of varions Co” complexes are shown in Fig. 2. In addition to the necessity for promotion of électrons difficulties arose in certain compounds in deciding the stereochemistry of complexes wherein no électron pairing occurred. hedral [C0CI4]

Thus the tetra-

and the square [Cu(H20)4]++ ions hâve respectively

three and one unpaired électrons. doubly and three singly filled

In the first case there are two orbitals.

This means that there

are no vacant M orbitals available for bond-formation.(*)

If in

each case the empty orbitals immediately above these filled or partly filled non-bonding orbitals were used for bond formation we would in both compounds expect a tetrahedral arrangement based on the use of bond orbitals. The fact that the four covalent complexes of Cu'i are square rather than tetrahedral shows that this rule is not of general validity. The original Pauling theory made no serions attempt to décidé which “ outer ” orbitals (if any) were employed when the number of unpaired électrons was the same in the complex as in the free ion. Generally speaking the bonds were regarded as “ ionic ” or essentially ionic using sp^ bonds. Octahedral complexes were consider­ ed to involve either ionic binding although the possibility of some covalent character by allowing the four bonds to resonate among the six positions was envisaged. The basic principles of the Pauling theory relation magnetic moment and stereochemistry in the first transition sériés are as follows. 1° For most purposes the number of unpaired électrons in an atom may be computed from the “ spin only ” formula.C'*) i.e. (♦) We are not considering Pauling’s (‘) earlier suggestion that one orbital might be used in bond formation by électron promotion. Although logical when first proposed there are Sound objections on the basis of electronegativity of the ligand to this proposai. Ligands with donor atoms of high electronegativity give square Cu>I complexes. As will be discussed later the use of a 34 orbital should be favoured by the use of donor atoms of low electronegativity.(**) (**) The size of the orbital contribution rarely gives rise to any doubt as to the number of unpaired électrons.

229

230

Fig. 2. — Electronic configuration of cobaltous complexes.

Complex type of ion

Unpaired

Electronic configuration

Binding

électrons

observed

3d Free ion i.e. Co+ +

A T

''

Y

IT

4i Tetrahedral

“ Ionie

5.6

3

4.3-4.S

3

4.S-5.2

1

2.1-2.9

1

1.7-1.9

4p

À A 1 1 1

yy

3

Y

''

4d Octahedral

“ Ionie ”

Planar

Covalent

n t-' 1 À

1

T

>K '' l-tl

4-

lii

A

Y

>w

1

>. T

T

T

5s

Octahedral

Covalent

T

A A A If A T

T

T

T

A

T

A

Y

H m

--------------------------------------------^

magnetic moment (i, = ^/nin + 2) Bohr Magnetons (B.M.) where n = number of unpaired électrons. 2° When the magnetic moment of a complex is essentially the same as that of the free ion (*) (i.e. no spin coupling occurs) the bonds do not involve 3d orbitals. In the Pauling terminology the binding is “ ionic 3° Spin coupling with a réduction of either two or four in the number of unpaired électrons indicates that 3d orbitals are being used for (“ covalent ”) bond formation. This nécessitâtes the transfer of unpaired electron(s) originally occupying the 3d orbital(s) now used for bond formation.

Usually these displaced electron(s) pair

off with other unpaired non-bonding 3d électrons. 4° If no vacant 3d orbital(s) are available to accommodate the displaced electron(s) referred to in 3 then electron(s) may be promoted to vacant orbital(s) above those used for bond formation. 5° The orbitals used for a bond formation are usually those immediately above those occupied by non-bonding électrons provided that these are a permissible combination for bond formation. This assumption is unreliable in certain cases where no électron pairing occurs (c/ square Cu“ discussed above). In the above theory the possible use of 4d orbitals was not considered. There were many, however, who considered that the properties of certain so-called “ ionic ” complexes warranted the view that some kind of covalent bonds were présent. Thus Sugden (7) drew attention to the similarity of cobaltic and ferrie tris-acetyacetone in their physical properties other than magnetism and suggested that some kind of covalent bonds were présent in both cases. Earlier Huggins (8) had suggested that 4d orbitals might be involved in the binding of ligands in so-called “ionic” transition métal com­ plexes. The idea was discussed by other workers, particularly Taube (î*) in relation to reactivity of transition métal complexes and Burstall and Nyholm (lo) in regard to magnetism.

Then followed

a theoretical study of the problem (ii) and using the overlap intégral

(•) Provided that the free ion contains more than 2d électrons; this proviso is necessary because magnetic moments do not distinguish between 4s4p^4d^ and 3dHs4p^ octahedral binding when three 3d électrons or less are présent e.g. Crin.

231

as a criterion of covalent bond formation, based in turn, on reasonable postulâtes as to the nature of the wave fonctions involved, qualitative support for the view that Ad orbitals might be involved in a binding was adduced. Noteworthy results included the conclusion that Ad orbits were much more elongated than the 2>d type; this correlated with the well known fact that ligands of low electronegativity favour électron pairing and “ inner ” d orbital binding whereas those of high electronegativity favour the so-called “ ionic ” binding. It became apparent that the terms „ ionic ” binding and „ overlap at a greater distance using Ad orbitals ” were more similar than they might appear at first sight. Nevertheless exchange is implicit in the latter description but not in the former. Support for the view that d^ binding using non-bonding électron pairs of the métal atom was feasible on the basis of the size of the overlap intégral was also obtained. As expected this was found to be more favourable in “ inner ” rather than “ outer ” orbital complexes. At this point it might fairly be said that the Pauling picture with additions to include the use of Ad orbitals could explain satisfactorily the stereochemistry and magnetism of both “ covalent ” and “ ionic ” complexes and also the reason why the ligands of low electronegativity tended to give “ covalent ” complexes and those of high electro­ negativity to give “ionic” complexes. d) failure

to predict

Its chief limitations are :

whether four-covalent

“ outer ”

orbital

complexes would be tetrahedral (e.g. [C0CI4]—) or square planar (e.g. [Cu(H20)4]++); b) inability to interpret spectra of métal complexes; c) inability to explain quantitatively variation in magnetic mo­ ments when values in excess of spin only values are observed. In short, it is limited to qualitative phemonena and does not account for quantitative features such as the intensity and observed frequency of spectral transitions. At this stage chemists and physicists began to take a renewed interest in the Crystal Field Theory originally developed by Bethe, Penney and Schlapp and by Van Vleck. We shah be concerned here primarily with its application to stereo-chemistry and magnetism but some introductory discussion is called for. At the présent time most inorganic chemists think in terms of valence bond theory. Books and papers in the field are based mainly on this approach and

232

it is natural that there is some réluctance to think in terms of new concepts.

We shall attempt to translate from the Valence Bond

Theory and to emphasise that the similarities are quite substantial. In fact, once again it is a case of tackling a problem from two angles — one tending to use that approach which is most useful.

LIGAND FIELD THEORY We shall begin by proposing use of the title Ligand Field (10a) instead of Crystal Field Theory. The latter tends to emphasise too much the relationship with crystals and electrostatic bonds. Actually we are concerned with the efîects arising from the arrangement of électron pairs on charged or uncharged ligands around a métal atom. Furthermore the proximity of these électron pairs is frequently such as to warrant the concept of an ordinary covalent bond between métal and ligand. The complexes with which we are concerned usually hâve a cubic or near cubic symmetry, that is to say the métal behaves as though it were in an electrical field of equal intensity along the three x, y and Z axes. The octahedral and tetrahedral arrangement of ligands gives this type of field and the square planar and square pyramid may be regarded as imposing an extra component on the cubic field. In practice the déviations from cubic symmetry are very impor­ tant in giving rise to effects such as variable orbital contribution in paramagnetic complexes. Consider now a simple d électron in such slightly distorted cubic field. This single d électron may, when there is no field, be présent in any one of 5 degenerate d levels. These are the dxy, dyz and dzx orbitals (t/j.orbitals) on the one hand and the dz^ and^/*2—j^2(^^orbitals) on the other (*). This first group of three orbitals are oriented as (*) These

d

orbitals in terms of 0, and

9

hâve the form :

\/Î5

dxy

= —— sin*0 sin29

_

2

dxz =\/i5 dyz

sinO cos0 sin9

=

VT

dz^ =------ (3 cos2 0 — 1)

2 a/Ts

------ sin^ 0 cos29

dx^—yi =

2

233

shown in Fig. 3, only one of the dxy, dxz and dyz orbitals being shown (**).

2

Z

Z

It will be seen that the d^ orbitals are concentrated along the diagonals between the axes x, y and z, — along which the électron pairs of the ligands would be found in an octahedral complex. However, theclz^ and dx'^-y^ OThitsAs are definitely concentrated along the three orthogonal axes as shown. Now under the influence of an essentially cubic field, such as is produced in an octahedral complex, these 5 degenerate d orbits are split apart as shown in Fig. 4, there being a lower triplet of the d^ orbitals and an upper doublet known as dy orbitals. The more stable dxy, dyz and dxz orbitals occupy the lower triplet whereas the less stable upper doublet consists of the two axial orbitals. Consider now what happens as we gradually add d électrons to an atom with five empty d orbitals : Fig. 4. — Splitting of d levels in a nearly cubic field.

__dy orbitals ------------------ d^ orbitals

Axial — Pointing along bond directions. Pointing along the bisectors of the x, y and Z axes — between the bonds.

The first three will occupy the lower triplet level, one in each sub-level giving three unpaired électrons.

This arrangement is

expected naturally from a considération of the requirements of (*) Reproduced from Orgel and Sutton (a>a).

234

minimum electrostatic potential energy; in an octahedral complex there are six pairs of ligand électrons around the métal atom, one pair along each of the six co-ordinate axes. These will naturally tend to repel the the

dxy, dyz

and

2>d dxz

électrons of the métal which therefore go into orbitals.

On adding the fourth électron — as

say in Cr++ this could go either into the lower of the two d orbitals or begin to pair off within the d^ orbitals. If the bonds are such that the ligand pairs are not exerting a very strong répulsive effect the électron will go into a dy orbital giving 4 unpaired électrons. This is the situation in the [Cr(H20)e]++ ion. This State corresponds with Pauling’s “ ionic ” bonds. If, however, the ligand électrons are very close to the métal as when strong “ covalent ” bonds are formed (*), the fourth électron might be forced to pair off in one of the d^ orbitals resulting in two unpaired électrons only on the atom. This occurs in the [Cr(Dipyridyl)3]++ ion. Similarly with five 3d électrons we obtain either three singly occupied d^ and two singly occupied dy orbitals or two filled and one singly occupied d^ orbitals.

The

former situation corresponds with K3FeFg and the latter with K3Fe(CN)g, there being 5 and one unpaired électrons respectively. An early criticism (*2) of the Van Veck theory was based on the view that the F~ ion should create a stronger field than the CN~ ion and hence spin coupling might be expected more readily in K3FeFg than in KjFefCNlg. However it has been pointed out by Orgel (13) that polarisability of the ligand is of great importance; the capacity to produce high électron densities close to the métal is the ail important factor and the “ soft ” CN“ ion can do just this. Factors which will favour this are naturally (i) a high positive charge on the métal ion (ii) low electronegativity on the part of the ligand atom (giving rise to readily polarised électron pairs) and (iii) the extent to which d^ — or d^ — d^ bonds may be formed between métal and ligand. In the example quoted (K3Fe(CN)g) d^ —

binding making

use of 3d^ électron pairs of the Fe atom and a p^ orbital of the C atom must be very important. This gives rise to stronger binding between the Fe and C atoms resulting in a shortening of the Fe — C a bond with a conséquent increase in électron density close to the Fe

(*) This is équivalent to saying that the incoming électron pair of the ligand wish to make use of the rfy orbital occupied by the unpaired électron.

235

atom along the x, y and z axes. This further enhances the tendency to repel non bonding électrons from the i.e. to effect électron pairing.

and dx^-y^ orbitals,

It may be seen by référencé to the dxy orbitals in Fig. 3 that the shape of this is idéal for „ sideways ” overlap with a vacant d orbital (or a P orbital which is made available) on the donor atom which forms a cr bond along the x, y ov z axes in an octahedral or square planar complex. As discussed by Kimball simple geometry indicates that, provided that the métal atom has the requisite number of d^ électron pairs we can expect a maximum of three strong d^ bonds from the métal atom in an octahedral complex and two in a square planar compound. Fig. 5.

I I

d^^ orbitals

X X X X

dy

orbitals

d^

orbitals

Id^ orbitals

I I

ti-

Electronic Configuration K3FeF6

Electronic Configuration of

K3Fe(CN)6 XX Bonding Electron Pairs from Ligands

4- Non-bonding Electrons from Fe+++ ion

It should be mentioned that the arrangement of the nondegenerate d orbital levels in Fig. 5 is inverted if the ligands are arranged tetrahedrally, for example as in the [CoCla]" ion. The séparation of the levels, however, is much smaller. If one examines the arrangement of the orbitals with respect to the ligands it becomes clear that in a tetrahedral complex the électrons in the dxy, dyz and dzx orbitals are those which are nearest to the ligands and hence become the least stable. The changeover from the octahedral arrangement as the more stable with ligand H2O in [Co(H20)6]'*"'' and tetrahedral as the more stable with ligand Cl~ in [C0CI4]” indicates that there is a fine balance between size of charge on the ligand and the position of the ligands in deciding which is the more stable arrangement. Returning to the case of électron pairing in the case of K3Fe(CN)6 it will be seen from Fig. 5 that two dy orbitals are made available

236

as the resuit of électron pairing. These orbitals point in the direction of the ligands and are obviously the bonding orbitals of the Pauling theory. The two théories thus become very similar when discussing “ covalent ” complexes. However, it is important to réalisé that in applying the ligand field theory to complexes in which no électron pairing occurs, nothing has been said concerning the possible use of any bonding orbitals above the M orbitals.

In a sense, like the

Pauling theory, it offers no guidance on this point.

In fact varions

workers reject altogether the idea of covalent bonds in this “ ionic ” type of complex. It seems to be largely a matter of opinion however whether out 4j, Ap and Ad orbitals are to be regarded as occupied. It is at least a convenient way of looking at the explanation of stereochemistry of these “ionic” complexes and in no way affects the previous arguments. The results of x-ray spectroscopy need to be mentioned in this connection. Examination of the K x-ray absorption edge (15) shows that what is presumably the 1 j Ap transition is absent in K3Co(CN)g but it may be observed in the [Ni(NH3)g]++ ion and similar socalled “ ionic ” or “ outer orbital ions ”. This, however, may be taken to mean that the Ap orbitals are vacant part of the time — which is consistent with the work of Craig and alii (ii) and paramagnetic résonance studies (20-21-22) since the latter work indicates that the binding is partially covalent. The overlap intégral is smaller than in the spin-paired i.e., the “ inner orbital ” K3Co(CN)g type complex. A problem where the valence bond and the ligand field theory appear to be in some conflict is in connection with octahedral diamagnetic complexes of bivalent nickel. Examples of these include the [Ni(Diarsine)3]++ ion, the [Ni(Tri-arsine)2]++ ion and certain other Ni” complexes (i*). In these the nickel atom has a d^ configur­ ation and the usual octahedral coordination would suggest that there would be two unpaired électrons in the d^ orbitals. On the Pauling theory one could explain the diamagnetism in one of the following three ways, as shown in Fig. 6. Taking each of these in turn; the objection to (a) is the difficulty of promotion.

This is expected to lead to électrons of high energy.

Some support for this is to be adduced from the fact that oxidation occurs fairly readily. However exact values for the ionisation potential are difficult to assess. Explanations (b) and (c) really regard the com-

237

238

Fig. 6. — Possible electronic configurations of octahedral diamagnetic Niii complexes

Ap

Ad

(a) y

(b)

À

A

T

• 'id'^AsAp^-

Promoted pair of

bonding orbitals

électrons

M

45

À T

T

Y

tTTTTT

Tt

T

T

4-

T

55

El

4

Ap Y

4

E

Y

4

<--------------------- hdAsAp^------------------------------------- >bonds in plane of square

(c)

3d

45

:îir£îl ŒE

Ap

nu

3dAsAp^ bonds ---------- ><-----------------in plane of square ApAd

The Ap orbital to be used on both sides of the square, to form two “ half ” (and necessarily longer) bonds. Ad

ŒT] linear pd bonds normal to plane of square.

plexes as derived basically from a square arrangement. The remaining two ligands are then attached on either side of the square by slightly longer bonds using either the single Ap orbital or a Ap and a Ad orbital. Support for this approach is provided by the existence of many apparently 5 covalent complexes of Pd“ (i**) such as [Pd(Diarsine)2l] CIO4 and of Au“^ e.g. [Au(Diarsine)2l] [004)2. Iri the case of gold, however, one may also obtain six covalent complexes of the type [Au(Diarsine)2l2] [004)2 (*^)- These are iso-electronic (in the valency Shell) with the [Ni (Diarsine)3)++ complex and in this case of these gold complexes there is no reason at ail for postulating promotion of two électrons to the outer s orbital. It is probably most significant that in ail of these complexes which show six-covalency the ligands are of low-electronegativity, the cation has a positive charge and

y Axis

X Axis

Figure

VII

double bonds from métal to ligand are feasible. The last two of these conditions favour a strong polarising effect on the ligand and the drawing out of lone pairs of the latter to form a covalent bond is a reasonable hypothesis. The ligand field theory would predict that for a regular octahedron there should be two unpaired électrons. If, however, the arrangement of the ligands departed from the perfect octahedral arrangement to

239

one in which two longer co-axial bonds were présent we would be dealing essentially with a square arrangement with some modifica­ tions. Consider the arrangement shown in Fig. 7. Place four équi­ distant A atoms in the plane xy along the x and y axes in a square. Also put two A atoms (Ai and A2) at a much longer distance along the Z axis. Now consider the arrangement of the five d orbitals as Al and A2 are steadily brought from a long distance until they form a regular octahedron around M. When a long way off the field at M is due almost entirely to the four A atoms in the xy plane. The orbital pointing towards these four, the dx^~y^ orbital, is clearly destabilised, whereas the dP-, dxy, dyz and dxz orbitals will not differ much in energy. At first sight the d^ orbitals might be expected to hâve the maximum stability, but as against this there is the small annular ring of charge density in the xy plane which will sufîer some repulsion by the four A atoms (*). We represent the splitting of the five d orbitals then as in Fig. 8.

Fig. 8.

dx^_yi- and rdz^ both variable

\_dxy

and dxz

(a) Energy levels of d orbitals for square arrangement of ligands

and d%z (degenerate levels) dxy^ dyz

{b)

Energy levels of d orbitals for perfect octahedral arrangement

As Al and A2 gradually move towards M the dz'^ level moves steadily upwards — becomes less stable — until we reach the perfect octahedral case again. The simples! ligand field explanation of the diamagnetism of the [Ni (Diarsine)3]++ compound is to suppose that the situation most nearly approximates to (a) in Fig. 8. The eight

(*) Both Maccoll (“) and Orgel (>’) estimâtes the amount of charge in the annular ring as about 35 % of the total charge in this dzi orbital.

240

Fig. 9.

Energy Levels of d Orbitals in Varions Ligand Fields.

K >

1

------- [dx^-y^

dxy

Intermediate

dxz

between I and

_dyz

W

--------

II and probably

ble

fd.2

much doser to I than II

1 variable

r

•-------

VJ^xy]

[dx^-y^

j ï

dxy dyz

rdyz



-dz^

rdxy

_dxz

------- \jxz



W-y^

\-dyz

I

II

III Tetrahedron

Regular

Square

Octahedron

Plane

E.g. KjFeFg

[NiCl2,2Et3P]o

IV Square Pyramid

[C0CI4]--

K3Fe(CN)e

241

* The height of the dx^.y^ relative to the other orbitals is uncertain.

[NiBr3,

2Et3P]o

V Trigonal Bipyramid M0CI5

3d électrons are then ail paired in the dxy, dyz, dxz and leaving only one orbital (dx^-y^) for bond formation.

orbitals Agreement

with (b) or (c) in Fig. 6 then becomes very close (*). We now summarise in Fig. 9 the splitting of the levels which take place in varions common types of stereochemical arrangement met with in transition métal complexes. In ail cases it is assumed that ail metal-ligand distances are equal and that ail ligands are identical. For intermediate cases one would need to alter levels accordingly. No attempt is made in the diagrams to represent the splitting in a quantitative manner. However in ail cases of octahedral splitting the séparation between the degenerate d^ and dy levels is smaller when very electronegative ligands (e.g. F~) are used than when covalent double bonding ligands like CN~ are présent. Naturally a stage may be expected when the energy séparation d^ -> dy is large enough to become equal to or greater than the energy required to pair électrons in d^ orbitals and leave one or both d^ orbitals free for bond formation. This leads us naturally to a considération of the effect of electronegativity upon spin-pairing. A study of the magnetic behaviour of pentagonal bipyramidal molécules with from three to seven d électrons would therefore prove of great interest. The magnetic behaviour of RuFs (d^) is being studied over a range of température as part of such an investiga­ tion (51).

SPIN PAIRING IN METAL COMPLEXES We hâve referred previously to the varions names given to the bonding complexes in which two kinds of magnetic behaviour are observed.

Thus the terms “ ionic ” and “covalent”, “ outer ”

and “ inner orbital complexes “ higher ” and “ lower level covalent bonds”; “normal” and “pénétration complexes”. Henceforth we suggest that these names be dropped in favour of the terms “spin-free” and “ spin-paired ” complexes. Among the reasons for this are the following: (a) The terms “ ionic ”, “ outer orbital

(*) Explanation (a) is compatible with ligand field theory if one postulâtes that the 5s level is intermediate between the dz and dy levels.

242

complex ” etc. suffer from the defect that they group together ail complexes in which no spin pairing occurs, irrespective of whether there is a possibility of covalent binding or not. Sometimes this dilemma is apparently avoided by saying “the term ‘ionic’ is used simply to imply that the magnetic moment is the same as that of the free ion This of course, is often not true. Thus the [CoCl4]“ and [Co(H20)e]++ ions with p, = 4.7 B.M. and 5.2 B.M. respectively are both“ ionic ” in the sense that no spin pairing occurs but their moments are not the same as the free ion. {b) In certain cases more than two kinds of magnetic behaviour are observed.

For example

[Cr“(H20)6] CI2, [Cr"(Dipyridyl)3], [C104]2 and [Cr"(CH3COO)2]2 contain 4, 2 and 0 unpaired électrons respectively. It seems best to differentiate between “ spin-free ” and “ spin-paired ” complexes first and then discuss the nature of the binding in each case as a separate problem. Perhaps the most studied complexes wherein spin-pairing may occur are those of Ni“((/8). Four-covalent complexes of two types are known, those which are diamagnetic, e.g. K2Ni(CN)4 and those which are paramagnetic with two spins e.g. (*) [Ni(N03)2 2Et3P]o.

On the Pauling theory these are represented as follows,

(Fig. 10). Fig. 10.

4s

3d Diamagnetic four covalent Ni” complexes

I tll tll tll tlf

covalent N” complexes

ont

Square bonding orbitals 3d

Paramagnetic four

n

4/7

Y

TT Y

4j

4/7

1 -<------------------------------>Tetrahedral Bonding orbitals

On examining (a) in Fig. 8 we see that if the attached ligands can get close enough to the Ni atom then the dx^-y^ orbital — pointing in the direction of the ligands — can feasibly be used for bond forma­ (*) Many of the supposedly four-covalent paramagnetic Ni” complexes are probably octahedrally co-ordinated.

243

tion. This requires that the eight d électrons now be squeezed into the remaining four d levels giving diamagnetism. This use of the 8) has previously stressed that, pending confirmation, the assumption that four-covalent paramagnetic Ni” complexes are tetrahedral is not at ail proven. Even the high electric dipole moment of Ni(N03)2, 2Et3P, which is indisputably a four-covalent complex could be due to a c/i-planar instead of a tetrahedral arrangement of the ligands. However both the ligand field and Pauling théories agréé on the basic results for spin-paired complexes : in perfect octahedral complexes i.e. those in which the six métal ligand bonds are equal in length, two d^ orbitals are left free for octahedral bond formation, whilst in square complexe one dy orbital is available to form square bonds with the ligands. THE MOLECULAR ORBITAL APPROACH A third approach to métal complexes is the method of molecular orbitals originally developed by Mulliken. This will be summarised briefly. Essentially this method treats the molécule formed by the union of two or more atoms as an assemblage of positive ions with varions molecular orbitals, some bonding and some antibonding. These molecular orbitals are in turn formed by a combination of atomic orbitals. They are arranged in an energy sequence and will be filled by électrons in order to the relative potential energies of the orbitals. We shall confine our attention here to the combination of a métal ion (or atom) M with six ligands each represented by X. We shall follow the discussion given by Owen and Stevens (20. 21, 22) and confine our attention to the octahedral molécule or complex ion MXô. In Fig. 11 we represent on the left hand side the atomic orbitals of the métal atom or ion M and on the right those of the ligand. In the middle column are shown the molecular orbitals which resuit from a combination of these. With the métal atom only nd, (n -)- 1)5

244

Fig. 11 (*)

^\p)

(6)

Kn + \)p

(2)

__________ (« +

1)5

/ (1)

▲ empty orbits eqn (1)-

----------------------------a*(d,^) ndy

~(4)

(4)''

magnetic (antibonding) v:*(d^)

nd^

=

(6)^"

orbits partly filled with d

eqn (3)

électrons

(6) 21________ S/771

(18)-.^

S,/77t

(24)

^2/70

’(I2)

eqn (4) = n (de) /


(12)

eqn (2) = a («'y), (4),

245

Orbital

Orbital

Orbital

levels of M

levels of

levels of

MX,



(*) I am grateful to Dr J. Owen (21) for permission to reproduce this diagram.

filled orbits (bonding e ▼ non-bonding)

and (n + \)p atomic orbitals will be considered.

The value of n

is 3, 4 or 5 according as we are concerned with a métal of the first, second or third transition sériés. In the case of the ligand we are almost invariably concerned with a lone pair in a hybrid sp^ orbital — c.f. Cl~, H2O, NHj. For convenience we shall call this a p orbital of the ligand, but the above proviso is implicit. The lowest orbitals are the bonding ct orbitals which are of the usual d^sp^ type with which the Pauling theory has made us familiar. Next there are bonding tt orbitals followed by the varions antibonding orbitals. Making molecular orbitals from linear combinations of the métal and ligand orbitals involves the use of a term \/1__called the admixture coefficient; = 1 if the binding is purely ionic and for a “ purely covalent ” bond = 0.5. Paramagnetic résonance studies give valuable information about a^. For this brief survey it is relevant to point out that in [Ni(H20)g]++ and [Cu(H20)g]++ paramagnetic résonance leads to values of «2 = 0.83 and 0.84... giving support for the view held on other grounds that the bonds in this hydrated ions hâve some covalent character. The effects of a and tt binding are summed up according to Owen as follows : a Bonds. The net transfer of électrons from the six X atoms to the M atom evens out charge distribution and enhances stability. The magnetic properties are then affected, 1. By increasing the splitting between d^ and d^ levels; 2. By partial transfer of unpaired dy électrons from M to the six X atoms. 7t Bonds. Considering only the d^ orbitals which are suitably shaped for TT binding, the contribution to the total binding from this source

is smaller than with ct binding because overlap is smaller. Owen distinguishes between two cases; one in which ligands like Cl~, H2O, NH3, etc., are employed for which there are no vacant orbitals available or capable of being made available. In this case partial transfer of p^ électrons from X to M and of d électrons from M to L is envisaged.

With CN~, however, transfer of d^ électrons from

M to X can be envisaged on a large scale. This, of course, is essentially the Pauling picture. Perhaps a most important feature stressed by Owen is the effect of TT binding upon the size of ihe orbital contribution to the magnetic moment. Partial transfer of a d^ unpaired électron to a ligand

246

atom L is expected to reduce the orbital contribution to the moment.

The observed moment of (NH4)2 Ir Clg , which is close

to the spin only value for 1 unpaired électron, is attributed by Owen and Stevens (20) to this cause.

IV.

MAGNETIC BEHAVIOUR OF TRANSITION METAL

Before discussing the complexes in each Group of the Periodic Table, a general survey of the types of magnetic behaviour which will be encountered is essential.

These metals ail contain M élec­

trons and in those valency States wherein the binding involves no électron pairing or where the number of d électrons is odd, paramagnetism is generally observed. Even when électron pairing occurs paramagnetism is observed when there is an odd number of élec­ trons, and in certain other cases. With the exception of type I, quoted as idéal, ail the kinds of magnetism shown below are to be found among transition éléments. They are summarised first and in certain cases will be discussed in more detail (see Nyholm (23) for detailed references on magnetochemistry). Type 1. Rare Earth and arises (a) when magnetism are well the ground State of

Type. — This is the idéal magnetic behaviour the unpaired électrons responsible for para­ shielded from external forces and (b) when the atom is separated from the next higher

excited State by an energy différence large compared with kT, i.e. >> kT. The magnetic moment is then given by the équation p = g Vj(J + 1). by the expression ;

8

the Lande Splitting Factor given

J(J + 1) + S(S + 1) — L(L + 1) ^ ^

2J(J + 1)

For substances showing this type of magnetic behaviour p, is independent of the stereochemical environnement and the magnetic dilution. Magnetic moments of this type are not shown by the iron group éléments but it is the idéal behaviour from which dévi­ ations occur to a greater or lesser extent.

(♦) The expression the lowest and next J values.

is used to indicate the energy interval between

247

Type 2. Small Multiplet Séparation. — When the energy séparation between successive J values (/îv) is very small compared with kT i.e. < kT it is found that L and S no longer couple together to give a résultant J but each reacts separately with an external field.

Under these circumstances the calculated value of

p. is given by \/4S(S + 1) + L(L + 1). This is the opposite extreme to case 1 and is the limit towards which p approximates as approaches zéro. Type 3. Intermediate Multiplet Séparation.— i.e. comparable with kT. When this situation arise, there is a distri­ bution of the molécules over the various J values decided by the Boltzmann équation.

Examples include NO, Sm+++ and Eu+++.

Type 4. Iron Group Type. — It has been known for a long time that the magnetic moments of the irons of the éléments of the first transition sériés (Ti -> Cu) agréé neither with the large multiplet séparation formula p = gy'J(J + 1) nor the very small multiplet séparation formula p = \/4S(S + 1) + L(L -f 1)*. Agreement between theory and experiment is best given by the simple expression = -v/^SCS -fl), at least for the first half of the sériés, the whole of the orbital contribution L(L -f 1) being ignored. This is shown P

in Table II on page 25. However, the quenching of this orbital contribution is often not complété and this déviation from the “ spin-only ” formula p = ^48(8 -f 1) can be used to assist in determining stereochemistry ih idéal cases as discussed on page 27. The calculated values of p for 1 to 5 unpaired électrons are given in Table II. Type 5. Covalent Bond Type. ■— It is often found that the moments of certain complexes are much less than those predicted from Hund’s rules on the spin-free formula. Thus, whereas the Fe+++ ion has the expected 5 unpaired électrons in K3FeF6, in K3Fe(CN)g the moment of 2.34 B.M. indicates only one unpaired électron. This “ électron pairing ” occurs in many complexes of the first transition sériés with ligands of low electronegativity and is the norm for complexes, of the 2nd. and 3rd. transition sériés.

(♦) Actually this formula does agréé with the experimental peff values for certain octahedral Co** complexes. See p. 27.

248

TABLE II Transition ion moments.

Term

2d3/,

Ion

Ti+++

Actual value of V cm~i

385

Y+++

V++

(i using actual value of V

Spin only

i.e.gVJy + 1)

tx if V = 0 i.e. V4S(S + 1) + L(L + 1)

1.55

3.0

2.18

1.73

1.63

4.47

2.73

2.83

2.75 — 2.85

[i if V = 00

fXeff

Observed tAeff.

^F3/,

Cr+++ Mn++++

580 912 852

0.77 0.77 0.77

5.20 5.20 5.20

3.60 2.97 2.47

3.87 3.87 3.87

3.8 —3.9 3.7 —3.9 4.0

^Do

Cr++ Mn++^

566 852

0.0 0.0

5.48 5.48

4.25 3.80

4.90 4.90

4.8 —4.9 4.9 —5.0

5.92 5.92

5.92 5.92

5.92 5.92

5.92 5.92

5.9 —6.0 5.9 —6.0

Mn++ Fe+++

249

^D4

Fe++

998

6.70

5.48

6.54

4.90

5.0 —5.4

4p9/,

Co++

1,890

6.64

5.20

6.56

3.87

4.3 —5.2

3p4

Ni++

2,347

5.59

4.47

5.56

2.83

2.9 —3.4

2d3/j

Cu++

2,130

3.55

3.0

3.53

1.73

1.7 —2.2

Type 6. Heavy Atom Type. — In certain of the heavy atom com­ plexes, e.g. K20sC1(5, the moment is less than the number of unpaired électrons predicted even for “ covalent bond ” formation. Thus Fe++, Ru++ and Os++ ions hâve a configuration. If two d orbitals are left free for bond formation (using the Pauling picture) two unpaired d électrons are expected in the resulting complex, giving a moment of 2.8-2.9 B.M. However in K2OSCI6 the moment of 1.4 B.M. is much less than this. This is discussed further on page 49. Type 7. Antiferromagnetism. — This behaviour is often found in certain types of lattice, e. g., the perovskite structure, when paramagnetic atoms are connected by 0“ or F~ ions. Good examples include the complex fluorides of type KM“F3 (24), where M = Cr, Mn, Fe, Co, Ni and Cu. They may be regarded as consisting of two interlacing ferromagnetic networks the spins of which point in exactly opposite directions. On gradually increasing the temp­ érature from very low températures the susceptibility rises at first owing to the graduai destruction of the antiparallel cancelling spins. At higher températures the normal température dependence of paramagnetism is observed, which is characterised by a graduai fall in susceptibility, in accordance with the Curie-Weis law

1 X a .J.

This results in a maximum in the susceptibility-

temperature curve, which is characteristic of antiferromagnetics.

Further Remarks on the Iron Group Type 4. For a discussion of the moments of the first transition sériés Table II is relevant. As mentioned earlier, the magnetic moments of the métal ions of the first transition sériés as a rule do not agréé with the large /;V(j^

> J.)

interval formula

interval formula

= g\/J{J+ 1), with the small

= \/4S(S + 1) -|- L(L -|- 1)], nor with the

more complicated formula wich uses the actual multiplet séparation intervals. In general the moments are accounted for most satisfactorily by assuming that the orbital angular momentum [L(L + 1)] is largly or completely quenched leaving only the spin momentum

250

TABLE III Magnetic moments of first transition sériés.

Métal Ion

Ti++

V++

Cr++

Mn++

Fe++

Co++

Ni+++

Cu++

Spectroscopic State and unpaired électrons

F

F

D

S

D

F

F

D

2

3

4

5

4

3

2

1

IxeffCalc.

2.83

3.88

4.90

5.92

4.90

3.88

2.83

1.73

3.83.9

4.84.9

5.26.0

5.15.7

4.35.6

2.83.5

1.8-* 2.2

Y+++

Cr+++

Mn+++

Fe+++

Co+++

Ni+++

V4S(S + 1)

t^eff Observed

Métal ion

Ti+++

Cu+++

D

F

F

D

S

D

F

F

1

2

3

4

5

6

7

8

^48(3 4- 1)

1.73

2.83

3.88

4.90

5.92

4.90

3.88

2.83

t^eff Observed

1.71.9

2.72.9

3.83.9

4.75.0

5.46.0

Spectroscopic State and unpaired électrons (AeffCalc.

2.8

operative. For bi- and tervalent ions agreement with the formula f^eff = V4S(S + 1) is very good for the first half of the sériés (i.e., Ti+++ to Mn++ or Fe+++) but the déviation is much more marked for Fe++ and for the bi- and tervalent States of the metals Co, Ni and Cu. This is illustrated by the figures given in Table III. In order to understand how the stereochemical arrangement of the ligands attached to the métal ion affect the size of the orbital contribution, it is first necessary for us to examine the way in wich the energy levels of an ion are affected by the electrical field produced by the charged groups surrounding the métal ion.

The electrical

(*) Certain recently discovered Ave-covalent Cu++ complexes hâve moments up to 2.6 BM. (see p. 59.)

251

field may be considered to arise mainly from the groups directly attached to, or in immédiate proximity with, the métal ion, but longer range forces also appear to hâve a definite but smaller efîect. We shall confine this discussion to the first of these two. Reference to Table II shows that for the ions of the first transition sériés, the spectroscopic ground States are S, D or F States (*). In the first of these the orbital angular momentum (L) is zéro and hence there is no orbital contribution to the moment. For the ions in this S State the value of is given by the spin only formula irrespective of the arrangement of the ligand around the métal ion; small dévi­ ations which do occur resuit in moments less than the spin only value. These involve effects (**) which are of no diagnostic value so far as inorganic stereochemistry is concerned. However, for both D and F States the position is quite different. In the following dis­ cussion we shall confine our attention mainly to Fe, Co, Ni and Cu, particularly when bivalent. Let us consider first of ail the simpler case, that of an ion in an F State, taking as our example the Co++ ion. The arrangement of electrically charged particles about a métal ion, e.g. the four Cl“ ions in the tetrahedral [C0CI4] ” complex ion, give rise to a ligand field about the central métal ion.

This electrical field has

two main effects (***). Firstly, the coupling of the L and S vectors is largely broken up so that the ion is no longer specified by a particular J value.

Secondly, the 2L + 1 sublevels associated with

the particular L value, which are degenerate in the normal ion, with no electrical field superimposed, are usually split apart with séparations between levels which hâve important effects upon the contribution which the orbital momentum makes to the magnetic moment. It should be recalled that for an ion with narrow mul­ tiplet séparation, i.e. < kT, having no electrical field operating, the effect of an external magnetic field is to react separately with S and L lifting the degeneraties of these into their 2S + 1 and 2L + 1 sublevels. The distribution over the degenerate 2L -b 1 levels is what gives rise to the large orbital contribution to the magnetic

(*) The spectroscopic terms S, P, D and F refer to the value of L for the ion. The values are respectively 0, 1, 2, and 3. (**) Both metal-metal interaction (as in the Hga++ ion) and antiferromagnetism can cause réduction in the moment of S State ions.

(♦♦»)

252

pq|-

d.'tailed reference to original work see Nyholm (23).

Fig. 12.

Free Ion

. +Cubio Pield

+Rhombio ' Component

I

I d

Octahedral Co++ Oubio Fleld Constant D, Positive

Tetrahedral Co*'*’

Octahedral Pe**

Octahedral Cu**

Cubic Piald Constant O, Négative

Cubic Pield Constant, D, Positive

Cubic Pield Constant D, Positive

Tetrahedral Ni**

Octahedral Ni**

Tetrahedral Cu**

Tetrahedral Pe**

Cubic Pield Constant D, Négative

Cubic Pield Constant O, Positive

Cubic Pield Constant0, Négative

Cubic Fleld Constant, D, Négative

253

STAfiE

PATTERNS

FOR

0

AND

P

STATE

IONS

moment in the formula [x = \/4S(S +1) + L(L + 1). Now if the ligand field should split the L value so that the séparation between any two sublevels is large compared with kT, then only the lowest (or lower) levels will be populated. Furthermore, should this lowest level be only a singlet then the orbital contribution to the magnetic moment should be very small (*). Penney and Schlapp (}) examined by group theory methods the effect of varions kinds of electrical crystalline fields on F and D States for transition métal ions. They found that if an ion is in an F State, e.g. Co++ when at the centre of a cubic (**) electrical crystalline field, such as is produced when the Co++ ion is at the centre of a perfect octahedron of H2O molécules, the single tnergy level is split into three new levels, the séparation between successive levels being about 10^ cm~i (A:T at 20 °C is approximately 204 cm~i, small compared with 10^ cm~i). Usually small departures from cubic symmetry occur owing to slight distortion of the octahedron. This may be regarded as équi­ valent to imposing on the field a small component of lower symmetry, e.g. tetragonal or rhombic. (***) This rhombic component causes a further splitting of two adjacent energy levels into triplets; the energy séparation between the sub-levelsof the triplet is of the order kT. This gives seven levels in ail for an F State. An example of this kind of séparation is given by [Co(H20)e]++ ion, shown in Figure XII. In this case the triplet level is lowest and the singlet is highest. This means that the populations of ail three levels of the lowest lying triplet are appréciable whereas the intermediate triplet and upper singlet State hâve a negligible population. The distribution over the three sub-levels of the lowest lying triplet is according to the usual Boltzmann température dépendent function.

(*) For a magnetic moment degeneracy of spin or orbital States is essential. The spin degeneracy can never be lifted by an electrical field alone however a sufficient splitting of orbital levels can destroy orbital magnetism entirely. (**) Cubic field — three axes at right angles, ail equal; tetragonal field — three axes ar right angles, two equal; rhombic field — three axes at right angles, ail unequal. Trigonal field — two equal axes at 120“ (X and Y) NOT equal to a third perpendicular to these two. (♦**) The most usual distortion if for two co-linear métal — H2O bonds to be slightly longer than the other four bonds in the plane at right angles to this axis.

2 54

TABLE V Crystalline Field Effects on Ions of flrst transition sériés. Ion

Ti+++

Spectroscopic ground State.

2d3/2

Ti++ Y+++

3f2

V++ Cr+++

Cr++ Mn+++

Mn++ Fe+++

Fe++ Co+++

Co++ Ni+++

Ni++ Cu+++

Cu++

4F3/2

5do

6S5/2

5d4

4f«/2

3F4

2d5/2

1

2

3

4

5

4

3

2

1

2

3

3

2

0

2

3

3

2

Lowest orbital level in cubic field (-1small rhombic component). Positive field constant, i.e. 6 octahedral charges.

Triplet

Triplet

Singlet

Non magnetic doublet (equiv. to singlet

Singlet

Triplet

Triplet

Singlet

Non magnetic doublet (equiv. to singlet)

Lowest orbital level in cubic field (-1small rhombic component). Négative field constant i.e. 4 tetrahedral charges.

Non magnetic doublet (equiv. to singlet)

Singlet

Triplet

Triplet

Singlet

Nonmagnetic doublet (equiv. to singlet)

Singlet

Triplet

Triplet

Unpaired trons.

élec­

L =

255

Van Vleck (4), Penney and Schlapp (^), Bethe (2) and others (5) hâve attempted to explain quantitatively the splitting of the original single F level using expressions for the potential of the electrical crystalline field such as : V =-- Ax2 + By2 — (A + B)z2 + D(x4 +

+ z4).

A, B and D are constants which dépend upon the charges on the ligands and their arrangement about the central métal ion. Usually the more simple expressionV = A(x2 -j- y2 — 2z2) + r>(x‘* + y'* +z4) suffices. Thls expression represents a field which is symmetrical about the z axis; the effects of more distant atoms and powers other than those shown are ignored. The term involving the fourth power of X, y and z represents the field of cubic symmetry which is responsible for the initial séparation of an F State into three levels (~ 1Q4 cm apart). For the first transition sériés the constants A and B are of the order of 0 to 400 cm- i, whilst D lies somewhere between 1,000 and 1,500 cm-h If one is dealing with an arrange­ ment of négative charges about a métal ion it can be shown that D changes in sign in passing from the cubic field arising from six octahedral ligands to the cubic field due to four tetrahedral ligands. This change of sign results in an “ Inversion of the Stark Pattern this is shown in Figure 12. The shape of the Stark pattern is also affected by the number x of d électrons; thus, if we consider the Ni++ ion instead of the Co^-^ ion the situation is exactly reserved, 12a arising from tetrahedral Ni++ and \2b arising from octahedral Ni++.

The patterns expected for the varions bi- and tervalent first

transition ions in a cubic field with a rhombic component are summarised in Table V. For an ion in a D State the cubic crystalline field splits the orbital level into two levels, the séparation between which is large, cf. with kT. These two levels are in turn split by a small rhombic component into a triplet and a doublet. Where the triplet lies lowest, as for exampl ; with the Fe++ ion (see Table V) when surrounded by six octahedrally co-ordinated négative charges, a large orbital con­ tribution is expected. If the doublet is lowest, e.g. for Cu++ (Figure I2d) in the same field only a small orbital contribution can be expected because the doublet is said to be “ non-magnetic ”, for it behaves effectively as a singlet.

256

For the first half of the first transition sériés observed orbital contributions are negligible. For V++, Cr+++, Cr++ and Mn+++ this is in any case what we would expect for octahedral co-ordination. However, for octahedrally co-ordinated Ti++, Ti+++, and V+++, which bave a triplet lying lowest, a large orbital contribution might be expected. This has never been observed, moments corresponding to the spin only value being obtained ; we may attribute this complété orbital quenching to the small and positive values of the spin orbit coupling which, together with a rhombic field, resuit in the séparation even of the orbitally degenerate levels to widths large compared with A:T. For the ions of Fe, Co, Ni and Cu data are more interesting, most Work having been done with Co++. Octahedrally co-ordinated Fe++ and Co++ should hâve the large orbital contributions, which is in general true (see Table V). On the other hand, for octahedrally co-ordinated Ni++ and Cu++ small orbital contributions are expected; as shown by Table V this is, broadly speaking, what is found experimentally. For tetrahedrally co-ordinated Fe++ and Co++ a small orbital contribution would be predicted Data are not available for Fe++ but for Co++ it is correct to say that the orbital contribution is much smaller than in the octahedral complexes. In theory tetrahedral Co++ might be expected to hâve a close to 3.88 B.M., since the singlet is lowest; Bose and Mitra (25) propose that high frequency contributions are partly responsible for the déviations from the spin only value in this case (*). They suggest that since kT becomes steadily larger as T increases, the high frequency con­ tribution should increase with T and, in fact, be proportional to T. This implies that there should be a fall towards the spin only value of 3.88 B.M. as T decreases. Data are scarce but a definite decrease in for the tetrahedral Co++ complexes as T decreases has been observed. It is of interest to note that the large orbital contribution in octahedrally co-ordinated cobaltous salts, e.g. [Co(H20)g] CI2, is associated with marked anisotropy in the susceptibility.

On the

(*) This orbital contribution is proportional to T/D; in addition another orbital contribution arises from X, the spin-orbit coupling constant. This eflFect

X is proportional to —. D

257

other hand, the blue tetrahedrally co-ordinated salts are nearly isotropie. Thus, Krishnan and Mookherjie (26) found that anisotropy in blue Cs2 Co CI4 was only about 5 %, whereas in the pink hexahydrated cobaltous salts it is of the order of 30 %. Data for tetrahedrally co-ordinated Ni++ are not available . Similarly, no certain case of tetrahedral co-ordination to Cu++ has been reported. However, some new five-covalent complexes of bivalent copper (14), which hâve a very large orbital contribution = 2.6 B.M.) may be due to the ligand field resulting from a bipyramidal arrangement of five ligands. As yet only in the case of bivalent cobalt complexes has any serions examination been made of the use of the orbital contributions as a guide to stereochemistry. Broadly speaking, a moment between 4.3 and 4.74 indicates tetrahedral co-ordination, whereas a moment in excess of 4.85 indicates an octahedral arrangement. It is obvions that uncertainty must remain for complexes having a in the vicinity of 4.7-4.S B.M. It has become increasingly apparent that, since the field constant is affected by several other factors besides the stereochemistry, these must be borne in mind. These factors include the charge on the complex ion, the attachment of heterogeneous groups, e.g. Co CI2 X2, the electronegativity of attached groups, and the possibility of longer range electrical forces arising from atoms surrounding the complex. Data available at présent suggest that the higher the electronegativity of the attached the larger the orbital contribution; thus the moments of the [Co C^", [Co Br4]“ and [Co 14]“ ions are respectively 4.76, 4.62 and 4.56 B.M. This may possibly be explained by the intensity of the ligand field increasing as electronegativity decreases. This will increase the energy interval between lowest lying singlet and next upper triplet. A simple illustration of the application of these ideas to a stereochemical problem is provided by a study of the magnetic moments in the complexes of cobaltous halides with aniline. An. It is pos­ sible to préparé blue compounds having the formulae Co Cl2.2A«, Co Br2.2An and Co I2.2A«. In addition, a pink di-alcoholate of the chloride Co Cl2.2An.2EtOH, and of the bromide can be isolated. If the alcohol in these really coordinated with the Co“ atom to form an octahedral complex, magnetic moments greater than 4.8 B.M. are expected.

258

On the other hand, if the blue

complexes Co X2 Ah2 are really tetrahedral then they should hâve moments ~ 4.7 B.M. The actual values given in Table VI indicate

TABLE VI Magnetic moments and physical properties of cobaltous aniline complexes.

Colour in solid State

P’eff solid State

Co CI2.2 An

Blue

4.40

Co Br2.2 An

Blue

4.46

Green-blue

4.61

Co CI2.2 An . 2 C2H5OH

Pink

5.0

Co Br2.2 An . 2 C2H5OH

Pink

5.0

Co(SCN)2.2 An

Pink

5.11

Complex

C0I2.2 An

that this is so and support the hypothesis that the Co X2.2 An (X = Cl, Br and I) complexes are tetrahedral and the di-alcoholate octahedral. However, as an apparent exception to the above génér­ alisations the thiocyanate Co(SCN)2.2 An is found to be pink in the solid State and has the magnetic moment (5.11 B.M.) corresponding with an octahedral complex. This can be explained, however, by postulating that the Co(SCN)2An is polymerised in the solid State, each -SCN group being co-ordinated to a second cobalt atom. This kind of behaviour occurs in the compound Hg Co(CNS)4, the -CNS being co-ordinated to the mercury atom as well as the cobalt, although in this instance the Co atom retains its tetra­ hedral configuration. This hypothesis is being tested by studying the colour and magnetic moment and electrical conductivity of the Co(SCN).2 An complex in various solvents (26“) (*). (*) M.eff in acetone solution is 4.57 B.M., the solution being blue in colour as expected for tetrahedral complex.

259

Another interesting application is in connection with the structure of the blue and violet forms of cobaltous chloride bis-pyridine complex, Co CI2.2 Py. The violet forms has a magnetic moment of 5.24 B.M. suggesting octahedral co-ordination. This form exists only in the solid State and cannot be dissoveld in solvents without a change over to the blue form taking place. The blue form, on the other hand, has a magnetic moment of 4.51 B.M. and 4.47 B.M. in the solid State and in nitrobenzene respectively. In the latter solvent it is monomeric and a non-electrolyte and undoubtedly exists as tetrahedral Co CI2.2 Py molécules. Under the circumstances, it is reasonable to suggest that the violet form has a polymeric structure with octahedrally co-ordinated cobaltous atoms connected together by halogen bridges in an infinité polymeric lattice (*). It is probable that as more data on Fe, Cu and Ni salts bearing on the relationship between orbital contribution and stereochemistry become available the orbital contribution will serve as a useful guide to the stereochemistry of these ions also.

Further Remarks on Co-valent Bond Type — (Type 5). To understand the magnetic behaviour of those complexes of the iron group in which électron pairing occurs, one can use the Pauling or Ligand Field theory and the same resuit is obtained. Thus we consider as examples two cases of octahedral co-ordination. The complexes of Cr“ in which no électron pairing occurs hâve four d électrons. These may be regarded on the ligand-field theory as giving rise to one doubly filled and two singly filled orbitals. This results in two unpaired électrons as in [Cr(Dipyridyl)3]++. On the Pauling picture, we get the same resuit. In the latter case the two dy orbitals are available for bond formation. As with the complexes of the iron group, in which no électron pairing occurs, some orbital contribution still remains. This is greater with some stereochemical rearrangements than with others. Thus spin-paired cobaltous complexes, if four-covalent, hâve large orbital contribu-

(•) Note added in proof : Preliminary investigations by X-ray crystallography of the violet form of CoCl2.2Py confirm the postulated halogen bridged polymer, the pyridine groups being trans.

260

lions, [A being as high as 2.9 B.M.

However with the (presumably)

octahedral spin-paired Co“ complexes values doser to the spin only value of 1.73 B.M. are observed.

In the absence of spin-orbit

coupling data we shall not attempt to interpret these orbital contributions here.

Further Reniarks on the Heavy Atom Type (Type 6). As mentioned earlier it is often found that in the Pd and Pt groups the moments are even less than those expected by the Pauling or simple Ligand-Field theory*.

Thus K2 Os Clg has a moment of

only 1.4 B.M. even though there are four d électrons in Os*'', and the Pauling theory predicts p, = 2.83 B.M. To understand the further réduction we must take into account the much larger spin-orbit coupling conséquent upon the large value of z, the nuclear charge. This spin-orbit coupling constant is proportional to (z — ) (see page 49), for a cubic field arising from an octahedral arrangement of ligands. For and de* |Xeff approxes zéro as T approaches absolute zéro. For de^ and de‘ (Aeiï approaches the finite values 1.22 BM and 1.73 BM as T approaches zéro. Forde^ the spin only value is expected at ail températures.

261

combine vectorially to give a moment of 2.00 B.M. Since the sépar­ ation between the States is only 120.9 cm~i the observed moment is température dépendent reaching a value of 1.84 B.M. at room températures and only slowly rising with T thereafter.

V.

SURVEY OF VALENCE STATES, STEREOCHEMISTRY

AND MAGNETISM OF TRANSITION METAL COMPLEXES In this section we shall summarise the data available for complexes of the transitions metals shown in the modified Periodic Table hereafter. In this Table we list also the valency States which may be regarded as established beyond reasonable doubt. It would be impossible to deal with more than a fraction of the experimental data available and therefore we shall summarise with the following principles in mind. (i) Valency States which hâve been established will be indicated and complexes of the Ist, 2nd and 3rd transition sériés compared. (a) Stereochemistry if difïering from the usual octahedral arran­ gement will be discussed. (iü) Magnetic behaviour will be indicated and in particular its importance in determing a) spin pairing, and b) stereochemistry as evidenced by orbital contribution, will be emphasised. (iv)

The relevance of the type of ligand so far as (iü) is concerned

will be discussed. In the Table hereafter zerovalency is found in most cases. As a rule this occurs most readily with carbonyls (See Table VIII) but other ligands of the same type will also give rise to zero-valency. We shall not attempt to discuss zerovalent compounds under the varions groups but certain points of general interest should be mentioned. The métal carbonyls are invariably diamagnetic; where the métal atom has an odd number of électrons the carbonyl dimérisés in order to eflfect spin pairing. Thus both cobalt and manganèse carbo­ nyls are dimeric, e.g. Co2(CO)g, Mn2(CO)io. Experimental data suggest that CO may hâve one or both of two rôles in carbonyl complexes, as a terminal ligand as in Ni(CO)4 or as a bridging ligand as in Co2(CO)g. In the latter compound one

262

TABLE VII Transition metals. Group

IV

Ist

Ti

V

I

V

VI

VII

VIII A

VIII B

VIII C

I b

Cr

Mn

Fe

Co

Ni

Cu

s

II

I II V

0 IV

0 IV

0 IV

0 IV

0 IV

I

e r

III

III

I

I

I

I

I

II

e

IV

IV

II VI

II VI

II

II

II

III

III VII

III

III

III

2nd S e r i e

3rd S e r i e

Zr

V

Cb

Mo

III

Il(?)

0 V

IV

III

II VI

IV

III

V

IV

Hf

Ta

V

Te

VI

Rh

Ru 0 V

VI (and I VI others) II VII

Re

Os

III

Pd

Ag

0

0

I

I

I

II

III

II IV

III

III VIII IV IV

w

VI

III

Ir

Pt

Au

II

0 V

0(-l)

0 V

0 III

0

I

III

III

II VI

III VI

II VI

IV

II

III

IV

IV

III

IV VII III VII

VI

IV

V

IV

V

IV VIII

VI

finds two C-0 absorption bonds in the infra-red spectrum which can be attributed to iwo different C-O stretching frequencies suggesting that in one case the carbon-atom is two covalent and in the other three covalent. It is generally considered that a major reason for the stability of carbonyls is their capacity to form double bonds using d électrons of the métal. This not only results in stronger bonds owing to more overlap but removes an improbably high négative charge from the métal. Carbonyls are the best examples of a wide range of similar complexes formed by ligands capable of forming similar double bonds with the métal. Ligands of this type include isonitriles (e.g.CôHsNC), the phosphorous trihalides (PF3, PCI3), and certain complex cyanides e.g.K4Ni (CN)4. It is important to note that these

263

TABLE VIII The métal carbonyls and their properties. Cr(rf4i2)

Fe(rf6i2)

Co(d^s2)

Ni(rf8i2)

Cr(CO)6

Mn2(CO)io

Fe(CO)5

C02(CO)8

Ni(CO)4

Sublimes

M.P. 154-155°

M.P. — 20°

M.P. 51°

M.P. — 25°

Colourless

golden yellow

B.P. 103°

golden yellow

yellow

(Co(CO)3)n

Fe2(CO)9

décomposés 60°

décomposés 100°

B.P. 43° colourless

jet black

golden yellow Fe3(CO)i2 décomposés 140° dark green Mo

Te

Ru

Rh

Mo(CO)6

Ru(CO)s

Rh2(CO)8

sublimes

M.P. — 22°

M.P. 76° (décomposés)

colourless

colourless

orange

RU2(C0)9

[Rh(CO)3]n

orange

red

RU3(CO)i2

[Rh4(CO)ii]m black

Pd

W

Re

Os

Ir

Pt

W(CO)e

Re2(CO)io

Os(CO)5 M.P. — 15°

Ir2(CO)s sublimes



sublimes

M.P. 177°

colourless 0$2(C0)9

yellow-green ([Ir(CO)]3)n

colourless

colourless

M.P. 224° bright yellow

décomposés 210° yellow

I am indebted to Professer R.K.Sheline for the compilation of this table.

264

ligands stabilise lower valency States, whereas many other common ligands like NH3 fail to achieve this or do so only under very exceptional circumstances. There seems to be little doubt that the major reason for their ability to stabilise the zerovalent State is their capacity to receive électrons from the métal in forming dn bonds.

This had

the effect of increasing the strength of the binding but more important still is the removal of négative charge from the métal.

Thus in the

compound Ni (CO)4 the “ formai ” charge on the Ni atom if equal sharing of units.

ct

bonding pairs between Ni and C atoms occurs is — 2

Even allowing for the différence in electronegativity between

Ni and C the former would still hâve a charge of the order of — 1 units. The formation of the dn bonds can return some of this charge to the C and N atoms. In the process of making the Ni atom positively charged (or less negatively charged) a greater attraction for the cr bonding électrons is expected hence helping to strengthen the ti bond. It is well known that carbonyls, isonitryls etc., are formed by the transition metals — a phenomenon which can be correlated with the presence of unpaired d électrons on the métal atom, available for dv: bond formation.

Cyclo-pentadienyl complexes. Reference should also be made to the extensive recent literature upon complexes of cyclopentadiene (*). This molécule gives rise to compounds in which the cyclopentadienyl ion [CsHs]- is attached

to metals.

The simples! example is ferrocene Fe(CsH5)2.

At first

sight a normal covalent Fe — C a bond might be expected leading to the structure : If this were correct the diamagnetism would suggest t/2 binding and hence two Fe — C bonds at right angles. (*) For a review see Pauson (2’).

265

However Chemical properties and recent X-ray studies indicate quite definitely that this is the case; indeed the molécule involves a “ sandwich ” structure in which the Fe atom is placed in between two parallel C5H5 residues. Clearly a simple valence bond structure for this molécule cannot be visualised. There are, of course, no lone pairs of électrons in the résonance hybrid of the [CsHs]- ion(*) and we are clearly dealing with a bond of the type obtained in metalolefine complexes in which -k bonding pairs of électrons of the ligand are used to bond the ligand to the métal. A molecular orbital picture of the resulting structure has been put forward by Dunitz &. Orgel (28). A large number of oxidation products such as the [Fe(C5H5)2] + ion hâve been prepared and their properties investigated. At this stage the field is developing very rapidly and unless one can deal adequately with the conflicting views of the varions workers in the field one cannot do the subject justice. We shall not therefore discuss these complexes further in this report. GROUP IV (Ti, Zr, Hf) These éléments in the ground State hâve the configuration d'^s'^ the stable valency State of four corresponding to the loss of these four électrons. Quadrivalent State. — Ti forms a large number of Ti*'' complexes in which the métal atom is octahedrally co-ordinated. These are exemplified by the halogeno complexes of the type K2TiCl6. However Zr and Hf, in addition to forming such six-covalent complexes give rise to seven-covalent compounds such as K3ZrFv. As ail compounds are diamagnetic magnetic data give no help in deciding stereochemistry. The tervalent State. — Titanous complexes appear to be primarily six-covalent and undoubtedly octahedral e.g. the hexahydrate TiCl3, 6H3O (29). The single unpaired électron gives rise to a magnetic moment close to the spin-only value. In the cubic field arising from the octahedral arrangement a triplet should be lowest and hence a large orbital contribution might hâve been expected. The value of the multiplet interval (384.5 cm“i) is small and we must présumé that complété quenching of the L component takes place. If we assume (80) that there is a small asymmetric component superposed (*) If we consider a single résonance structure a p lone pair of électrons occure on one of the five carbon atoms. In the résonance hybrid, however, these becoms 7t bonding électrons.

266

on the cubic field the lower lying triplet is split into a doublet and a singlet of which the singlet lies lowest. This séparation must be sufïicient to account for almost entire destruction of the orbital contribution. Zr‘“ and Hf“^ undoubtedly exist and hâve been prepared in impure compounds but as yet no well defined complexes hâve been described. The bivalent State. — Tp is less stable than Ti”* but compounds hâve been prepared containing the required two unpaired électrons (31) .

Nothing is known of their stereochemistry; the anhydrous

halides are most probably assemblages of ions.

No Zr‘* or Hf”

compounds are known. GROUP V (V, Nb, Ta) d^s'^ Pentavalent State. — In this valence State ail complexes are diamagnetic. It is the most stable State in ail cases and is best known in anionic complexes e.g. KVO3 and K3VO4. Similar Nb and Ta compounds are formed but the tendency to polymérisation — already évident with V — is présent to an even greater degree. Quadrivalent State c/h — A large number of V''*' complexes are known, rangingfrom the complex fluoride K2VF6 ((Xett 1.5 — 1.8 B.M.) (32) to (presumably) five-covalent complexes such as VO (acetylacetone)2 (33). The latter may also be obtained with one molécule of H2O, NH3, pyridine, etc., added. These latter complexes are then six-covalent. Their magnetic properties hâve been studied by Asmussen (33) who finds that p-ett is close to the spin only value. The anhydrous, presumably five covalent complexes, also hâve pert values close to the spin only value. As with Ti'‘* ail orbital contri­ bution is clearly quenched and the moment is insensitive to the stereo­ chemistry.

Relatively little is known of the stereochemistry and

magnetism of Nb and Ta. The tervalent State ^/2. — A large number of six covalent, presumably octahedral, V”* complexes are known e.g. [V En3] CI3, (NH4)3Vp5, [V(NH3)g] CI3. Asmussen (33) reports that peft is in ail cases very close to the spin only value for 2 unpaired électrons. Little is known of the complexes of Nb and Ta. The magnetic behaviour of Tap3 (32, 34) has been studied however; pctf is only 1.4 B.M. Since the figure of 2.55 B.M. is obtained for VP3 it is apparent that the spin pairing in this instance may arise from exchange interaction between métal atoms conséquent upon the high magnetic concentration.

267

Bivalent vanadium. — complexes of the type K4V(CN)6 and the double sulphates are known but are very unstable owing to the ease with which they may be oxidised. Their moments are close to the spin only value for 3 unpaired électrons (^s). Little is known of the complexes Nb" or Ta’* although simple salts such as TaCl2 hâve been reported. Univalent and zerovalent vanadium (d^ and d^). —■ Evidence for V’ has recently been obtained (36) as the compound [V(dipyridyl)3]I. The corresponding V° complex [V(dipyridyl)3]° has also been prepared. This has a moment of 1.9 B.M. indicating the single unpaired 2>d électron expected for octahedral binding. GROUP VI Cr, Mo and W(t/4j2) The univalent State {d^). — This has been reported in the case of chromium only — as the tris-dipyridyl complex [Cr(dipyridyl)3] [CIO4] (37). The magnetic moment of 2.1 B.M. is consistent with the formation of a spin-paired complex in which M'^As4p^ bonds are présent.

The complex cation is then iso-electronic with the

[Fe(dipyridyl)3]+++ ion. An unusual feature is the unexpected highco-ordination number of 6 for such a low valency State. The corres­ ponding Mo’ and W’ complexes are unknown. The bivalent State (J4). — Bivalent chromium gives rise to three kinds of magnetic behaviour in its complexes but in its stereochemistry it has a marked preference for sixfold coordination. The spin free complexes such as [Cr(H20)6] SO4 are paramagnetic with 4 unpaired électrons.

The orbital contribution to the magnetic moment is

negligible.

If one uses CN~ or dipyridyl as the ligand complexes

such as K4Cr(CNg) and [Cr(dipyridyl)3] Br2 may be formed. These hâve two unpaired électrons only (34). This indicates that the 4 électrons give rise to two singly filled and one doubly filled d^ orbitals. The two dy orbitals are free for bond formation and give the 3dMs4p^ type of binding. Use of the acetate group in Cr(CH3COO)24H2O (38) gives a red feebly paramagnetic complex. The spin pairing in this complex is attributed to metal-metal interaction (39) — an hypothesis which is strongly supported by the short Cr-Cr distance found by X-ray crystallography (39. 40). Except for the halides, which are themselves complex, no co-ordination compounds, as usually understood, are known of Mo and W.

268

The halides (M0CI2)® and (WC^a are diamagnetic and in the case of the former, X-ray examination (42) indicates that the compound should be formulated as [MogClg] CI4.

In this complex cation the

Mo atom is four-covalent — but with nearly square co-ordination. From the diamagnetism we might expect the

levels to be lowest —

and well separated from the upper orbitals. However, for the latter inversion tetrahedral co-ordination is necessary. In connection with the diamagnetism it is of interest to point out that the Mo-Mo bond distance is consistent with métal-métal bonding; thus it is possible that the diamagnetism is accounted for in this way (as with Cr“ acetate) instead of by invoking a ligand-field explanation. The tervalent State (d^). — The octahedral complexes of Cr“* are so well known that we shall not discuss them here. The magnetic moment in ail cases shows a value very close to the spin only value ; the failure of CN~ in K3Cr(CN)g to effect spin pairing is not surprising since two dy orbitals are available, if necessary, for bond formation irrespective of the type of ligand employed. Whereas even the simple salts of Cr'** show the paramagnetism characteristic of 3 unpaired électrons, the moments of M0CI3 and MoBr3 are only 0.7 and 1.23 B.M. respectively (4i). Data for the trihalides of W are not available. The complexes of Mo“^, however, e.g. K3M0CI3 (NH4)3 Mo(SCN)g hâve moments close to the spin only value for 3 unpaired électrons (3.7 — 3.9 B.M.). The only complex of K3W2CI9 has the very low moment of 0.5 B.M. As the latter would probably not arise from the spin-orbit coupling of W, metal-metal interaction is the more likely explanation. This probably takes place via the Cl atoms as in antiferromagnetism. The quadrivalent State {d'^). — The best known chromium complex in this valency State is K2CrFg prepared by E. Huss and W. Klemm (43). The magnetic moment of 2.8 B.M. is close to the spin only value for 2 spins. Mo*'^ complexes are common and are illustrated by K4Mo(CN)3 which is diamagnetic (4i). However the chlorocomplexes are six-covalent and hâve the two unpaired électrons (4i) in common with K2CrFg. This spin pairing when one uses CN~ and passes to an eight covalent state is noteworthy. The pentavalent State (d^). — In the case of Cr this valency State occurs in compounds such as KCrOF4 which contain the expected single unpaired électron (34). For Mo'' an interesting situation

269

is observed. Whereas the complexes Rb2Mo''OCl5 [PyH]2Mo''OCl5, (PyH)2Mo''OBrs ail bave moments close to 1.73 B.M. the complex anions [M02O4CI4]", [Mo204(SCN)g] and [Mo204(C204)2]“ are diamagnetic In the diamagnetic compounds spin pairing presumably occurs between neighbouring Mo atoms. The complexes of behave normally in having the expected one unpaired électron. Hexavalent State {d°). — Apart from the presence of unusually high paramagnetism (p = ~ 1.4 B.M.) in Cr'^^ complexes (e.g. K2Cr04) the compounds of the hexavalent éléments are diamagnetic. The paramagnetism of the chromâtes is generally attibuted to Van Veck paramagnetism — a température constant contribution arising from the high frequency contribution to the moment. GROUP VII. Mn, Te and Re {d^s^) The univalent State {d^’). — The complex has recently been prepared in a pure State by (44). It has the expected diamagnetism of a <7^, spin-paired complex ion. The corresponding not been investigated.

cyanide K5Mn(CN)e Treadwell and Rath. MHsAp^ six-covalent Te valency State has

No Re' complexes are known. Mn' is also

known in complexes of the type [Mn(RNC)6]I where RNC is an isocyanide (44“). The bivalent State {d^). — Mn" gives rise to spin-free (5 unpaired électrons) and spin paired complexes (1 unpaired électron). In the former category are complexes of apparently different co-ordination numbers e.g. the [Mn(H20)6]++ ion and MnCl2, 2Py. Two forms of the last compound are known; these are no doubt similar to the corresponding Co" complexes one being tetrahedral and the other octahedral co-ordinated as the resuit of chlorine bridging and poly­ mérisation. However, in the absence of orbital contribution (Mn", d^ is an S State) there is no simple way of supporting this. The spinpaired complexes are illustrated by K4Mn(CN)6. The bivalent State of Re and Te is not yet established in any simple or complex com­ pounds. The tervalent State (d‘*). — Mn'" forms spin free complexes such as [Mn(acetylacetone)3]° with 4 unpaired électrons and spin paired complexes such as K3Mn(CN)g with only two spins. Te'" has not been investigated but Re'" complexes are diamagnetic or nearly so. Thisholdsforboth(Re(NH3)6]Cl3andRbReCl4(4i> 45, 46). Aspointed

270

out by Orgel the diamagnetism of tetrahedral complexes is to be expected since the two levels will be lowest. However there is no certainty that the anion in RbReCl4 is actually tetrahedral — it may be octahedral through polymérisation. Furthermore the dia­ magnetism of [Re(NH3)6] CI3 must clearly arise from some reason other than a tetrahedral arrangement of the attached ligands. In com­ plexes of the type [Re(Diarsine)2Cl2] Cl, p values of 1.6— 1.8 B.M. are observed (47). Here the réduction from 2.83 B.M. is only partial. A temperature-susceptibility study of these complexes is being carried out (47). An interesting five-covalent Re^” complex[ReCl3, Diarsine]° has been isolated. From the diamagnetism we conclude (see Fig. 9) that it is probably a trigonal bipyramid (47). The quadrivalent State {d^). — Mn"' forms a complex fluoride K2Mn*'^Fg (48), the moment of which (3.9 B.M.) indicates the expected 3 unpaired électrons of a spin-free complex. No examples of Mn"' with spin pairing are known. Both Te and Re as their com­ plex hexa-chlorides e.g. K2ReCl6 hâve moments which vary with température (45. 46). Thus, for K2ReCl6 petr is 2.61 B.M. at 90°K, 3.05 B.M. at 195° K and 3.22 at 300° K. The Ag sait and the complex bromide behave similarly. It is apparent that the moment is approaching 3 spins as T increases. With a view to testing the effect of a change in the electronegativity on the moment Curtis and Nyholm (47) hâve recently studied complexes of the type [Re(diarsine)2Cl2] [€104)2. These are diamagnetic; this can be explained readily by assuming large spin orbit coupling. The complex K4[Re20Clio] is also being studied (47) (*). Like the ;jo-electronic Ru complex (which is diamagnetic) (49) one expects that this will contain one unpaired électron rather than three for the same reason as that which is believed to cause the diamagnetism of K4RUOCI10 (47*) (see p. 49). The pentavalent State (d^). ■— Mn^' probably occurs in complex oxides of the type Na3Mn''O4.10H2O. The magnetic data (52) support the view that Mn'^ and not a mixture of Mn"^ and Mn''^ is présent. The subject is being vigourously studied at présent (49“). Te'' has not been investigated but Re'' is well known in complexes such as K2[Re''OCl5], [Re''(NH3)6] CI5. The latter are diamagnetic

(*) Note added in proof : It has been shown that in fact K4Re20Clio is only very weakly paramagnetic and contains no unpaired électrons (4ta), whereas [Xeff of KîlReClsOH] is 3.3 B.M. The Orgel-Dunitz (476) explanation is thus not applicable here since it should lead to one unpaired électron per Re atom.

271

(45, 46). Even with strong covalent bond formation the simple Pauling theory predicts 2 spins but in these Re complexes the coupling must be due to the large value of the spin-orbit coupling conséquent on the value of (Z — a)*. The Hexavalent State (d^). ■— Where this has been observed in Manganates e.g. BaMn04 the expected unpaired électron is observed (50). Re*'' behaves in the same way (5i). The septavalent State — Diamagnetism is expected for the complexes of this valency State but in the case of Mn'^“ in perman­ ganates weak température independent paramagnetism is observed. The isolation of Re(— 1) (5ia) as the hydrated potassium sait is of great interest. The weak paramagnetism of this compound corresponds to much less than one unpaired électron; the pure compound is presumably diamagnetic. This is taken to indicate that the Re(— 1) ion is square co-ordinated i.e. K[Re(H20)4]. Re(— 1) is wo-electronic with Os°, Ir^ and the well known square forming Pt'*. GROUP VIII a) Fe, Ru and Os Triad. Uni-valency. This valence State has been claimed for certain nitrosyl complexes of Fe but real support is lacking. Recently W. Hieber and co-workers (cf. 52) hâve reported that Fe‘(CO)2l may be prepared and this on heating gives Fe*. No data are yet available as to magnetism or stereochemistry. Ru* is presumed to exist in the corresponding diamagnetic carbonyl Ru(CO)I. This is undoubtedly polymeric and of unknown complexity. The analogous Os compound is unknown. Bi-valency. Two types of Fe" complex are known (*) — those which contain four unpaired électrons and those which are diamagnetic. Compounds of the first type are either purely electrostatic e.g. FeCl2, or involve “ionic or outer orbital” binding e.g. [Fe(NH3)g]l2. Six-covalent octahedral complexes only hâve been reported so far

(*) That is, where FeU is sixcovalent. Nothing is known of four-covalent FeU except in forced square configurations. The diamagnetic presumably four-covalent iso-nitrile complexes of the type [Fe(CNR)<] [C104]2 hâve, as yet, been little investigated.

272

but attemps to make tetrahedral complexes are being pursued. These should hâve a small orbital contribution owing to a low lying singlet. Diamagnetism is observed in complexes only e.g. [Fe(Dipyridyl)3]l2. These are invariably octahedral, consistent with the use of two type M orbitals for bonding. Ru” and Os” tend to ressemble the diamagnetic type complexes of Fe” e.g. as their complex cyanides of type K4M”(CN)6.

However, in the case of

the [Ru(Dipyridyl)3]++ ion Munro (54) reports 4 unpaired électrons; this paramagnetism is difficult to account for. Ter-valency.

Fe”* behaves similarly to Fe** in giving both spin-

free complexes with 5 unpaired électrons e.g. [Fe(acetyl-acetone)3]° and spin paired complexe e.g. K3Fe(CN)6 containing 1 unpaired électron. They may be explained in the same way as for Fe**. Ail known Ru”* and Os*** complexes are similar to those of “ spinpaired ” Fe***. It is noteworthy, however, that the orbital contribution is much larger in the Fe*” complexes (ji.erf = 2.3-2.4 B.M.) than in the Ru*** and Os*” complexes ([Xeu = 1.9B.M.). The quadrivalent State d^. Fe*'' has been long suspected in complex oxides of the type BaFe*''03 (52) (*). Recently the complex ion [Fe(Diarsine)2Cl2]++ has been isolated by Nyholm and Parish (55) as its perchlorate, per-rhenate and ferrichloride. The moment of 2.9 B.M. indicates partial spin pairing of the four 2d électrons releasing the two d^ orbitals for bond formation. The corresponding K2RUCI6 behaves similarly with a moment indicating 2 unpaired électrons. sidérable interest attaches to the diamagnetism of :

Con­

K4[Cl5 Ru — O — Ru CI5] (49). The two linear bonds to the atom indicate sp bonds. If the O atom then uses 2p électron pairs for tt bond formation with the two Ru atoms then each Ru atom must release a d^ orbital to receive these électron pairs. This forces the four 4 d électrons into two only d^ orbitals giving diamagnetism (42*). K2OSCI6 however is most unusual havinga moment of 1.4 B.M. (49). The most reasonable explanation for the low moment of Os*'' is to be found in the work of Kotani (56)

(♦) See also Scholder (52a).

273

who examined theoretically the susceptibilities arising from the configurations to d^^ under the perturbation of spin-orbit coupling. His calculations showed that for the configuration d^** at temperakT tures such that — 0.2, (jLeir is proportional to -y/TA

At higher températures

the moment reaches the value

of 2.88 and remains constant at about that value.

Although the

spin-orbit coupling coefficient X for Os is not known from spectral data, and indeed it is doubtful whether the term can be applied to the inter-electronic interactions in an élément as heavy as Os, the effective value of it would be expected to be large — of the order of some thousands of cm~ — with kT at room température about 200 cm“i — it is obvious that at these températures the condition kT ~ 0.2 obtains and p, values < 2.88 occur. A recent measurement X of (NH4)2 0sBrg by Lindberg and Johannesen (57) admirably confirms Kotani’s prédictions (*). The moment of this compound is propor­ tional to \/T from low températures up to room température. A value of X = 6,000 was assumed in this work. The fluoride K20sFg (5^) shows a similar moment (1.35 B.M.) at 20 °C. The pentavalent State (d^). Fe'^ has not been reported but Ru'' is well known in the simple fluoride Ru F5 and in complex fluorides such as Cs Ru Fg (59). The moment of the latter (3.85) B.M. indicates 3 unpaired électrons, consistent with the configuration with parallel spins. As with Cr“^ this is clearly not diagnostic of bonding orbitals or stereochemistry. Os'*' exists in Na Os Fg (59) for which p = 3.05 B.M. The decrease in the moment from the spin only value of 3.88 B.M. is not easy to understand. On Kotani’s theory for a perfect octahedron no réduction of moment from the spin only value for a d\ configuration is expected. Dwyer (50) has recently described com­ plexes of the type [Os(En — H)3] I2 where En — H represents ethylene diamine less one proton from the N atom i.e. H2N.CH2CH2.NEl. These complexes contain one unpaired électron only and in this case the lower electronegativity of the N atom in the ligand must be assisting the process of spin pairing. (*) Kotani’s theory has also been confirmed for K3Mn(CN)is (=*).

274

Higher valency States. Fe''^ is known in the complex ion [Fe04]“. Hrostowski and Scott (61) succeeded in disentangling the ferro- and para-magnetic contributions to the moment and established the presence of two unpaired électrons. Nothing is known of the stereochemical arran­ gement of the O atoms. Ru''* occurs in the corresponding ruthenates of type M*2 Ru O4.

This contains the expected two unpaired élec­

trons. K2 Os O4 however once more shows diamagnetism presumably for the same reason as with K2 Os Clg (62). Fe''** is unknown but perruthenates e.g. K Ru O4 are undoubtedly tetrahedral and contain the expected unpaired électron. The corresponding Os''*' complex is unknown. As is to be expected Ru''*** and Os''*** complexes are diamagnetic, the hypothetical RuVi**+ or 0svm+ ions having lost ail d électrons. b) Cobalt, Rhodium and Iridium. Uni-valent State {d^). Although the univalent State for these éléments is iso-electronic with the well known and readily stabilised bivalent State for Ni, Pd and Pt it is only recently that stable complexes hâve been described. In the case of cobalt the simplest examples are complexes of the type [Co(Ph NC)5] Cl O4 using phenylisocyanide (63). In these they are diamagnetic compound the métal atom is five-covalent ; this means that the non-bonding électrons occupy the three dv and one d^ orbital leaving one d.^ orbital for bonding. On the Pauling theory the binding is apparently dsp^. No examples of spin-free Co* compounds are known. Four covalent diamagnetic complexes (64) of Rh* hâve been described of the type [Rh(PhNC)4]+ but the cor­ responding valence State of Ir is not yet definitely established. Chatt and Venanzi (64") hâve also recently described Rh* compounds. These complexes contain ethylene and are dimeric with halogen bridging. The bivalent State {d^). Bivalent cobalt gives rise to complexes of the spin-free and the spin-paired types. In the former category are (a) the ionic salts e.g. Co CI2 which form ionic lattices; (b) six-co-ordinated complexes such as [Co(NH3)g] CI2 wich are octahedral; (c) four-co-ordinated complexes in which the groups are arranged tetrahedrally around the Co atoms e.g. the [C0CI4] “ ion.

The magnetic data indicates

275

3 unpaired électrons in ail cases but moments vary from 4.3 to as high as 5.6. This variation is readily understood in terms of the effect of the different kinds of ligand field on the size of the orbital contribution. As discussed on page 29 the octahedral arrangement gives rise to a lowest lying triplet and hence a large orbital component whereas the tetrahedral arrangement causes an inversion with a triplet lying lowest. This means that a much smaller orbital contribution can be expected. The situation in regard to ionic salts is complicated partly by the proximity of ions wich can give rise to exchange phenomena, and on occasions, antiferromagnetism, and partly owing to the complexity of the electric field perturbing the ions. Co“ com­ plexes in which électron pairing occurs are of two types. The first of these, the four co-ordinated complexes, hâve a relatively large orbital contribution (|i. = 2.1 — 2.9 B.M.) Most of the spin-paired complexes fall into this class. Examples include Co“ phthalocyanine. The second class hâve moments of the order of 1.9 B.M.; these are mainly six-covalent e.g. K2 Pb Co(N02)e but five-covalency is also observed e.g. K3 Co(CN)5- The six-covalent complexes are usually formulated as 3J2 4^3 complexes with one électron proFig. 13. — Diagram of six-covalent spin paired CoH complex.

5

Bonds to 1, 2, 3 and 4 in­ volve 344i4pi hybrid orbitals. Bonds to 5 and 6 in­ volve 4/>44 hybrid orbitals.

moted to a orbital. However other explanations for the moments of these compounds which does necessitate the promotion of an unpaired électron are available. The formulation of these complexes is a problem similar to that arising for the iso-electronic octahedral

276

Ni’” complexes and for octahedral spin-paired Ni” and Au”’ com­ plexes which hâve one more électron. The latter require the pro­ motion of two électrons on the Pauling picture.

For ail of these

complexes a satisfactory ligand-field formalution which reconciles the Pauling and Ligand-field théories is as follows. The seven d élec­ trons of the Co” (or eight of the Ni” and Au’” complexes) are accommodated in the three and one d., orbital. We then use one dy orbital to form (with an s and two p orbitals) a square complex. Distinct from this combination are then two linear pd hybrids completing the octahedron (see also p. 13 et seq.). The five-covalent complexes of Co” are undoubtedly more common than hitherto suspected. Thus (®”^) the so-called “ [Co(CN)6]4~” ion is actually [Co(CN5)]î “. In the solid State K3 Co(CN)5 is diamagnetic but in aqueous solution the expected unpaired électron is observed. Although it is possible that the Co” atom is six-covalent in the solid State with one molécule of co-ordinated water i.e. [Co(CN)5 H20]3 - this is not considered likely. Other examples include [Co I2, Triarsine] (*) (®8). xhe latter on oxidation gives [C0I3, Triarsine]® indicating that ail three As atoms in the Co” complex are almost certainly co-ordinated to the métal atom; otherwise the arsine would be preferentially oxidised on treatment with I2. Since Co I2, Triarsine behaves as a non-electrolyte in nitrobenzene solution and is monomeric in this solvent we conclude that it is probably to be formulated as shown in Figure 14. Fig. 14.

(*) Triarsine has the formula (CH3)2As(CH2)j AsCCHalsAsCCHsIa. 1 CH 3

277

Another five-covalent Co” complex is the cobalto-nitrite ion “ [Co(N02)6]‘*“ ” in aqueous solution. Dwyer finds that this loses one N02~ group and becomes, unless an H2O molécule enters, effectively five-covalent. The bivalent State for Rh and Ir has been reported as existing in certain compounds where the analyses gave correct empirical for­ mula e.g. [Rh CI2, 3 As R3]2- However the diamagnetism of these makes this difficult to understand and it is now most likely (^6) that these compounds should be formulated as complexes of Rh’ and Rh™ e.g. [Rh'(Rj As)4][Rh"’Cl4(AsR3)2] The tervalent State (d^). Co"’ forms two types of complexes, the rare spin-free type exemplified by K3 Co Fg with 4 unpaired électrons. One 3d orbital is doubly filled and four singly. The far more common octahedral diamagnetic complexes are readily explained on both the Pauling and ligand-field théories. Jensen (69) has reported a complex Co CI3,

Et3 P which is found to contain two unpaired électrons.

2

If, as seems likely, this five-covalent one can make an attempt at predicting the stereochemistry. The Pauling theory would suggest that only one 3d orbital is available for bond formation. If the combination 3d As Ap^ is used then on the Daudel and Bûcher (™) argument (*) a square pyramid is probable.

On the ligand-field

theory again the square pyramid appears to be favoured. Both Rh’” and Ir’” are very similar to the spin-paired complexes of Co”’ being invariably diamagnetic and octahedrally co-ordinated wherever structures hâve been determined. The quadrivalent State (d^). As is to be expected this valency State increases in stability as we pass from Co -> Rh ^ Ir.

In all cases the known complexes

are six-covalent and contain one unpaired électron the only doubtful case being K3 Co F7 ('•î- cf. 52) the crystal structure of which has not been established.

(♦) This theory proposes that (n — \)d ns np’ bonding orbitals gives rise to a square pyramid whereas ns n/j^ nd bonding orbitals resuit in a trigonal bipyratnidal arrangement.

278

The pentavalent State (d*). This occurs in Ir complexes of the type Na Ir Fg, Ag Ir Fg, K Ir Fg the moments of which are of the order of 1.2-1.3 B.M. (59). Assuming that the anion is octahedrally co-ordinated these compounds should, on the simple Pauling theory contain two unpaired électrons with a p. of at least 2.8 - 2.9 B.M. A similar prédiction is made on the ligand-field theory. It is apparent that the same explanation holds as for Os^'^. The hexavalent State (d^). Only one compound of this valency State has been established with certainly — the fluoride Ir Fg.

This is almost certainly octa-

hedral and once again both the Pauling and Ligand Field theory predict 3 unpaired électrons. The observed moment of 3.35 B.M. (^i) indicates that the departure from the spin-only value is small. Zerovalency. It is of interest to note that G.W. Watt et alii hâve recently reported a zerovalent iridium complex of the formula Ir(NH3)s. Nothing is known of its stereochemistry. Similarly the Co° complex K4Co(CN)4 has recently been described by W. Hieber and C. Bartenstein C^^). From its diamagnetism we may safely conclude that the anion is probably dimeric, making it iso-electronic with the carbonyl Co2(CO)g. GROUP VIIIC — Ni,Pd,Pt d^o The zerovalent State d^^. Reference is made to this valency for these éléments because of the wide variety of ligands with which it may be stabilised, at least for Ni. The carbonyl of nickel Ni(CO)4, which is diamagnetic, is tetrahedral. On the Pauling model this can be regarded as due to the use of As Ap^ bonding orbitals. The CO may be replaced by PF3, PCI3, PBr3 and isocyanides. These are ail diamagnetic and presumably tetrahedral also. Of great interest is the complex cyanide K4Ni(CN)4 in which the Ni atom apparently has the same structure as in the carbonyl.

The corresponding complex of Pd, K4Pd(CN)4

is known but not the platinum analogue.

Other four-covalent

Pd(0) complexes hâve been described by MalatestaC^4)^e.g. Pd(CNPh)4. The presumably polymeric

complex Pd(CNPh)2 has also been

described A tetrammino Pt(°) complex has also been claimed by G.W. Watt et alii (72).

279

The univalent State d^. The best example of this is the complex cyanide of nickel of empirical formula K2Ni(CN)3. Since this is diamagnetic it is presumably dimeric. Nast and Pfab hâve claimed that the Ni atoms are square co-ordinated there being two bridging and four terminal CN groups in the dimeric [Ni2(CN)6]‘*- anion. However infra-red spectral investigations reveal only one C—N absorption band(*); this throws some doubt on the structural assignment by Nast and Pfab. Univalency has been suggested for one organo-palladium complex but no magnetic data are available Univalency has not yet been definitely established in any platinum complex.

The bivalent State d^. This is the most stable valency for these éléments. In the case of Ni four and six covalency are common and five-covalent com­ plexes which hâve frequently been postulated as kinetic intermediates, has recently been fairly well substantiated, by other physical methods of investigation. The four-covalent complexes fall into two classes — the paramagnetic group containing two unpaired électrons and those which are diamagnetic.

Wherever X-ray structural data or

electric dipole moments are available the latter hâve been shown to be square planar. The diamagnetism indicates that one dy orbital is not used by non-bonding électrons and this orbital, together with a 4j and two Ap orbitals gives rise to the Pauling picture of four 3d 4i 4p2 bonds. The stereochemistry of the less common paramagnetic four-covalent complexes, however, is much less certain. Difficulty arises because most of the compounds in which the Ni'^ atom is supposed to be four-covalent involve polymérisation in the solid State to make the Ni atom efïectively octahedral. Nevertheless the green complex nitrate [Ni(N03)2, 2E/3P]° is definitely monomeric in benzene. Its magnetic moment indicates two unpaired électrons but the absence of a large orbital contribution is a little surprising.

Référencé to Figure 12 indicates that for a tetrahedral

arrangement of the charges around a Ni” atom the triplet lies lowest and hence a large orbital contribution is to be expected. However the surrounding groups are not ail the same in this complex and the

(*) Hence presumably only one C—N stretching frequency.

280

perturbing efîects of the asymmetric field may give rise to further splitting of the triplet. The electric dipole moment (8.8 D) indicates either a tetrahedral or a cw-planar arrangement. It is most important for us to obtain X-ray crystal structure détermin­ ations of compounds of this type. Since no 3d orbitals are available for bond formation it has been widely assumed that in the paramagnetic complexes the next four bonding orbitals 45 4p^ are used to give a tetrahedral complex. However, it is important to remember that the more electronegative ligands give rise to these paramagnetic complexes and, as with Cu^*, the square arrangement is just as feasible. The six-covalent complexes are of two types, paramagnetic with 2 unpaired électrons e.g. [NiEn3]++ and [Ni(Dipyridyl)3]++ on the one hand and diamagnetic e.g. [Ni(Diarsine)3]++ on the other. The complex ion [Ni(Dipyridyl)3]++ has been resolved, thus confirming an octahedral (but not necessarily a perfect octahedral) arrangement of the ligands, and also showing that the complex is fairly “ stable ” in the kinetic sense of not reacting rapidly to give the racemate. In this tm-dipyridyl complex the binding is regarded by some as involving the use of 4s 4p^ 4d^ bonds on the Pauling model but strictly speaking the magnetic data really only tell one that no 3d orbitals are available for bond formation. Nevertheless this complex ion must be regarded as an example of covalent binding using “ outer ” orbitals. The diamagnetic six-covalent complexes however hâve, on the ligand-field theory treatment, only one dy orbital available for bond formation. As discussed on page 13 the sixcovalency and diamagnetism are comparable provided that two co-axial bonds are assumed to be longer than the other four co-planar bonds. Five-covalent diamagnetic complexes are undoubtely much more common than hitherto supposed. The red colour produced by adding excess CN~ ion to the Ni(CN)4~ com­ plex ion has been shown to involve a 1 : 1 combination and hence the formation of the [Ni(CN)5]3- ion is indicated

It has also

been shown that the [Ni(Diarsine)2]++ ion readily attaches another halogen atom to give the complex ion [Ni(Diarsine)2X] + where X = Cl, Br and I (78). Similarly the physical and Chemical properties of [Ni Br2, Triarsine] (68) (cf. the Co’^ complex on page 53) indicate that the Ni” atom is five-covalent. On the basis of the Pauling theory the use of the extra 4p orbital suggests a square pyramid.

281

The Daudel and Bûcher (™) argument also leads to a square pyramid rather than a trigonal bipyramid. Bivalent Pd and Pt form square complexes with great facility. No paramagnetic complexes of Pd” or Pt” are known. Five-covalency in complexes of the type [Pd(Diarsine)2X] Cl Oi ('5) where X = Cl, Br and I is observed in the same way as with Ni”. Ail known bivalent six-covalent complexes of these two éléments are diamagnetic. Best known example is [Pt(NH3)4(CH3 CN)2] CI2 (^^). This is undoubtedly to be formulated in the same way as the [Ni(Diarsine)3]++ ion. The most significant feature about ail of these five- and six-covalent diamagnetic complexes of Ni”, Pd” and Pt” is the fact that in ail cases they are formed with ligands which hâve a marked capacity for double bond formation using d électron pairs of the métal atom. In this way the otherwise improbably high négative change placed on the métal atom owing to the formation of so many dative a bonds can be avoided. It has recently been shown ('?*“) by X-ray methods that Pd(Diarsine) I2 is octahedral in the solid State the two I atoms being O trans. The length of the two Pd — I bonds is 3.52 A. The calculated O Pd — I bond distance in square Pd” complexes is only 2.65 A. This great increase in the bond length is attributed to the repulsion of the I atoms by the filled dz'^ orbital. Work on [Pd(Diarsine)2 I] Cl O4 is still proceeding.

The tervalent State (d''). Only in the case of Ni are complexes of this valency State known. Pd F3 has been described and has paramagnetism indicating one unpaired électron (34) but no other Pd”* compounds are known. Ni*** occurs in the unusual five-covalent complex Ni Br3, 2 Et3P which contains one unpaired électron (79). The use of 3d 4j 4p3 bonds suggests a square pyramidal structure; this is supported by the small electric dipole moment but, in the absence of X-ray studies and in view of uncertainties as to atom polarisation its structure is still not absolutely certain.

Six-covalency occurs in complexes

such as [Ni(Diarsine)2Cl2] + which contain one unpaired électron (79). They are iso-electronic with spin paired octahedral Co** complexes the structure of which are discussed on page 51.

282

The quadrivalent State (d^). With a few exceptions ail complexes of and Pt^'^ are six-covalent and diamagnetic involving the two d^ orbitals with s and three p orbitals for bond formation (80). the complex oxides such as Ba Ni O3 (8I).

Less is known of

Higher valency States. Pt''^ probably exists in complex oxides of the type M*2Pt O4 but they hâve been but little studied. GROUP IB, Cu, Ag, Au (dio^i) The univalent State (d^^). Ail three éléments give rise to univalent complexes which are either two-covalent or four-covalent *. Although four is the preferred co-ordination number of Cu* and Ag* it is two for Au*. However four-covalent Au* complexes are now quite well established. On the Pauling picture the linear two covalent complexes can be regarded as arising from sp hydrid bonds and the tetrahedral four-covalent complexes from sp^ hybrids. However it is interesting to point out that since there are no lone pairs in the valency shell ordinary electrostatic bond pair-bond pair repulsion would also lead to the linear and tetrahedral arrangements. The bivalent State (d^). This is found only in the case of Cu and Ag. The Cu** complexes are almost invariably four square planar bonds, e.g. as in the [Cu(NH3)4]++ ion, but there is a strong tendency for two longer bonds to be formed to complété the distorted octahedron. These square complexes clearly do not involve électron promotion since they are résistant to oxidation. Furthermore use of a 2>d orbital is not indicated on grounds of electronegativity of the ligand. The ligands which give rise to square Cu** are of high electronegativity — the converse of what is required to give diamagnetic square Ni**. Earlier, therefore it was suggested (23) that the binding involved 4pMd orbitals — the use of an “ outer ” d orbital being indicated by the high electronegativity of the ligands. However, an alter­ native ligand field explanation which takes into account the JahnTeller theorem is discussed by Orgel. (i3) (*) Chatt (86) and Coates (87) hâve also adduced evidence in support of a co-ordination number of three for Silver (I).

283

Five-covalent

Cu” complexes

hâve

also

been

described

e. g

[Cu(Dipyridyl)2l] Cl O4. The very large orbital contribution found in these complexes (p.etr = 2.8 B.M.) is most readily explained by the postulate that the complexes are trigonal bipyramidal in shape Bivalent silver, although rather less stable than bivalent copper gives rise to similar complexes. The tervalent State (d^). Cu”’ gives rise to both spin-free and spin-paired complexes. A good example of the former is K3CU Fg (*2 cf. 43) which contains the expected two unpaired électrons. K Cu O2 however is diamagnetic (82) and since the Cu”* atom is iso-electronic with Ni** the complexes are presumably square. Ag*** is best established in the diamagnetic complex fluoride KAgF4 (85). It is interesting to notice the transition from paramagnetic K3CUF6 to diamagnetic KAgF4 and KAUF4. This is undoubtedly due to the greater electronegativity of Ag*'* over Cu***. The first ionisation potentials for Cu and Ag are respectively 7.72 and 7.57 volts whereas the sum of the first three ionisation potentials are 57.6 and 64.9 volts respectively. Au*** has a marked preference for forming four-covalent square co-ordinated complexes which are diamagnetic. Evidence has been available for some years to show that in solution at least the co-ordination number of gold may be increased beyond four. Thus Bjerrum (84) showed that the Au(SCN)62- ion existed in solution as long ago as

1918.

More recently (14)

complexes of the types [Au(Diarsine)2X]++ and [Au(Diarsine)2X2] + where X = Cl, Br and I hâve been isolated. Conductrimetric titration of [Au(Diarsine)2l] [Cl 04]2 with 1“ ions in nitrobenzene solution results in a sharp end point after one équi­ valent of 1“ ions hâve been added. These six-covalent complexes can be made to revert to square complexes again by suitable treatment — particularly in aqueous solution. In this solvent the hydration energy of more than sufficient to effect rupture of the Au-halogen bond. If we assume that two of the bonds are different from the other four these Au*** six-covalent complexes may be formulated in a manner similar to the six-covalent diamagnetic Ni** and Pt** complexes described earlier.

To sum up, octahedral coordination

requiring the use of four square planar bonds and two longer bonds normal to the plane offers a satisfactory explanation of the sixcovalent complexes of Co”, Ni**, Pd" and Pt**, and of Au***.

284

REFERENCES (1) L. Pauling, “Nature of the Chemical Bond” 2nd. Ed., 1945, Cornell Univ. Press. Bethe, H. Ann. Physik, 1929, 3, 133; Z. Physik. 1930, 60, 218.

(2)

(3) W. G. Penney and R. Schlapp, Phys. Review, 1932, 41, 194; 1932, 42, 666, 1953, 43, 486. (“•) J. H. Van Vleck. Phys. Review, 1932, 41, 208; J. Chem. Phys. 1935, 3, 807. (5) J. Gorter, Phys. Review, 1932, 42, 437. (®) L. Pauling, “Nature of the Chemical Bond” 2nd. Ed., 1945, Cornell Univ. Press, p. 104. O S. Sugden, J. Chem. Soc., 1943, 328. (8) M. L. Huggins, J. Chem. Phys., 1937, 5, 527. (^) H. Taube. Chem Reviews, 1952, 50, 69. (10)

F. H. Burstall and R. S. Nyholm, J. Chem. Soc., 1952, 3570.

a) L.E. Orgel & L.E. Sutton “ Report of Copenhagen Coordination Chemistry Conférence ” 1953, 17. (11) D. P. Craig, A. Maccoll, R. S. Nyholm, L. E. Orgel and L. E. Sutton. J. Chem. Soc., 1954, 332.

(10)

(12)

L. Pauling, "Nature of the Chemical Bond” 2nd. Ed., 1945, Cornell Univ Press., p. 116.

(13)

L. E. Orgel, J. Chem. Soc., 1952, 4756.

(13a)

G.E. Kimball, J. Chem. Phys., 1940, 8, 194.

(!■*) C. M. Harris, R. S. Nyholm and N. A. Stephenson, Recueil 1956 - (in press. Amsterdam Conférence on Coordination Compounds); see also C.M. Harris, Ph. D. Thesis, 1955, N.S.W. cf. référencé (J^a). (15)

Professer Cauchois (University of Paris), 1956, Private Communication. For other référencés see (18).

(16)

A. Maccoll, 1955, Private Communication.

(12)

L. E. Orgel, 1955, Private Communication.

(18)

R. S. Nyholm, Chem. Reviews. 1953, 53, 263.

(1^) K. A. Jensen, and B. Nijgaard. Acta Chem. Scand. 1949, 3, 474. (20)

K. W. H. Stevens, Proc. Roy. Soc., 1953, 219, 542; see also J. Owen and K. W. H. Stevens, Nature, 1953, 171, 836.

J. Owen, Tràns. Faraday Soc., 1955, (in press). J. Owen, Proc. Roy. Soc., 1955, 227A, 183. (23) R. S. Nyholm, Quart. Reviews Chem Soc., 1953, 7, 377. (24) R. L. Martin, R. S. Nyholm and N. A. Stephenson, CAem. anrf/n^f. 1956, 83. (25) A. Bose and S. C. Mitra, Indian Journal of Physics, 1952, 26, 393. (26) K. S. Krishnan and A. Mukherjee, Proc. Roy. Soc., 1938, A237, 135. (26a) N. A. Gill and R. S. Nyholm, Unpublished experiments. (266) J.D. Dunitz, 1956, Private Communication. (27) p. L. Pauson, Quart. Reviews. Chem. Soc., 1955, 9, 391. (28) J. D. Dunitz and L. E. Orgel, Nature, 1953, 171, 121. (20) W. Klemm and L. Grimm, Z. Anorg. Chem., 1942, 249, 198. (21) (22)

(30) D. M. S. Bagguley, B. Bleaney, J. H. E. Griffith, R. P. Penrose and B. L. Plumpton, Proc. Phys. Soc., 1948, 61, 542; 1948, 61, 551. (31) C. Starr, F. Bitter and A. R. Kaufmann, Phys. Review, 1940, 58, 977.

285

(32) W. Klemm and R. Scholder, Àngew. Chemie. 1954, 16, 461. (33) Asmussen, “Studies in the Magnetochemistry of Complex Compounds” (in Danish) Copenhagen, 1944. (34) R. S. Nyholm and A. G. Sharpe, J. Chem. Soc., 1952, 3579. (35) T. van den Handel and A. Siegert Physica 1937, 4, 871. (36) S. Herzog, Naturwiss., 1956, 43, 35.

(32) Hein and Herzog, Z. Anorg. Chem. 1952, 267, 337. (38) W. R. King and C. S. Garner, J. Chem. Phys., 1950, 18, 689. (39) B. Bleaney and A. Bowers, Proc. Roy. Soc., 1952, A214, 451.

(40) Niekerk and Schoening, Nature, 1952, 171, 36. (41) W. Klemm and H. Steinberg, Z. Anorg. Chem., 1936, 227, 193. (42) C. Brosset. Arkiv. Kemm. Min. Geol. 1945, 20A, No. 7; 1946, 22A, No. 11.

(43) E. Huss and W. Klemm, Z. Anorg. Chem., 1950, 262, 25. (44) W. D. T. Treadwell and W. E. Raths, Heh. Chim. Acta., 1952, 35, 2259.

(44a) A. Sacco Atti Accad., naz Lincei, Classe Sci., fis. mat. nat. 1953, 15, 421. (45) W. Klemm and G. Frischmuth, Z. Anorg. Chem., 1937, 230, 220. (46) W. Klemm and W. Schuth, Z. Anorg. Chem., 1934, 220, 193.

(47) N. F. Curtis and R. S. Nyholm, 1956, Unpublished results. (47a) B. Jezowska-Trzebiatowska and S. Wajda, Bull. Sciences, Cl.IlI, 1954, II, 5, 249.

Acad.

Polonaise des

(47*) J.D. Dunitz and L.E. Orgel, J. Chem. Soc., 1953, 2594. (48) J, T. Grey, J. Amer. Chem. Soc., 1946, 68, 605. (49) D. P. Mellor, J. Proc. Roy. Soc. of N. S. W. 1943, 77, 145, see aiso D. P. Mellor A. Mathieson and N. C. Stephenson, Acta Cryst., 1952, 5, 185.

(49a) Ingram and Symonds, 1956. Private Communication. (50) K. A. Jensen and W. Klemm, Z. Anorg. Chem., 1938, 237, 47.

(51) N. F. Curtis, R. S. Nyholm and R. D. Peacock, Unpublished. (51a) J.B. Bravo, E. Griswold and J. Kleinberg, J. Phos. Chem., 1954, 58, 8. (52) W. Klemm, Angew. Chem. 1951, 63, 396.

(52a) R. Scholder, Angew. Chem., 1953, 65, 240; 1954, 66, 461. ^53) J. B. Bravo, E. Griswold and G. Kleinberg, Science 1952, 115, 375; J. Phys. Chem. 1954, 58, 18. See also A. V. Grosse, Naturforsch, 1953, 8b, 533. (54) A. Munro, 1956 (Private Communication).

(54a) G. Padoa, Ann. Chim. (Italy), 1955, 45, 28. (55) R. S. Nyholm and R. Parish, Chemistry and Industry, 1956, 470. (56) M. Kotani. J. Phys. Soc. Japon, 1949, 4, 293. (57) R. Johannesen and A. Lindberg, J. Amer. Chem. Soc., 1954, 76, 5349. (58) A. Cooke and H. Duffus, Proc. Phys. Soc., (London) 1955, 68A, 32. (59) M. A. Hepworth, R. D. Peacock and P. L. Robinson, J. Chem. Soc., 1954,

1197. (60) F. P. Dwyer and J. W. Hogarth, J. Amer. Chem. Soc., 1953, 75, 1008. (61) H. J. Hrostowski and A. B. Scott, J. Chem. Phys., 1950, 18, 105. (62) A. Godward and S. Sugden, Unpublished. (63) L. Malatesta and A. Sacco. Z. Anorg. Chem., 1953, 273, 247. (64) L. Malatesta. J. Chem. Soc., 1956, in press.

286

(6''a) J. Chatt and L. Venanzi, J. Chem. Soc., 1956, in press. (®5) F. P. Dwyer, 1956, Private Communication. (6fi) F. P. Dwyer and R. S. Nyholm, 1956, Unpublished observations. (67) A. W. Adamson, J. Amer. Chem. Soc., 1951, 73, 5710.

(68) G. A. Barclay and R. S. Nyholm, Chem, and Ind., 1953, 378. (69) K. A. Jensen, 1955, Amsterdam Conférence on Coordination Compounds. Recueil in press. (70) M. R. Daudel and A. Bûcher, J. Chim. Physique., 1945, 42, 6.

(71) R. S. Nyholm, R. D. Peacock and P. L. Robinson, Unpublished experiments. (72) G. W. Watt, M. T. Walling and P. I. Mayfield, J. Amer. Chem. Soc., 1953,

75, 6175. see also G. W. Watt and P. I. Mayfield, J. Amer. Chem. Soc., 1953, 75, 6178. (73) W. Flieber and C. Bartensetin, Z. Anorg. Chem., 1954, 276, 1.

(74) L. Malatesta Atti Accad. Lincei, Rend. Class Sci.,fis. mat., nat

54, 16, 364

(74fl) L. Malatesta, J. Chem. Soc., 1954, 3924. (75) R. Nast and W. Pfab., Naturwissenschaften, 1952, 39, 300. (75fl) M.F. Amr El-Sayed and R.K. Sheline, J. Amer. Chem. Soc., 1956, 78, 702. (756) F.G. Mann, I.T. Millar and F.H.C. Stewart, /. Chem. Soc., 1954, 2833. (76) K. A. Jensen, Z. Anorg. Chem., 1936, 229, 225. (77) B. S. Morris and R. S. Nyholm, Unpublished Experiments. (78) C. M. Harris and R. S. Nyholm, Unpublished Observations; C. M. Harris

Ph. D. Thesis, Sydney, 1955. (78fl) C. M. Harris, R. S. Nyholm and N. C. Stephenson, Nature, 1956, (79) R. S. Nyholm, J. Chem. Soc., 1950, 2061.

(80) R. S. Nyholm, J. Chem. Soc., 1951, 2602. (81) J. J. Lânder and E. A. Wooten, J. Amer. Chem. Soc., 1951, 73, 2452. (82) R. Hoppe, Angew. Chem., 1950, 62, 339. (83) K. Wahl and W. Klemm, Z. Anorg. Chem., 1952, 270, 69. (84) N. Bjerrum and A. Kroschner, Kgl. Danske Videnskab. natur. math. Afdel.

1918, (8)5, 1. (85) W. Klemm, Angew. Chemie, 1954, 66, 468.

(86) Sten Ahrland and J. Chatt, Chem, and Industry, 1955, 96. (87) R. C. Cass, G. E. Coates and R. G. Hayter, Chem, and Industry, 1954, 1485.

287

Some Applications of Crystal-field Theory to Problems in Transition-Métal Chemistry. by L. E. ORGEL

INTRODUCTION

Since the publication of Pauling’s classic papers on the nature of the Chemical hond(i) it has heen customary to discuss the electronic structure of transition-métal compounds from the point ot view of valence-hond theory.

It was realized a long time ago that

molecular-orbital and electrostatic théories could account equally well for many of the experimental observations 0, but these théories did not at first appeal to inorganic chemists. More recently it has become clear that the latter théories, which are almost équivalent in their mathematical formalism, are able to account quantitatively for the spectra and magnetic properties of divalent and trivalent tran­ sition-métal ions (3> 5. 6), In Chapter I of this paper we shall extend a previous treatment of the stabilities of transition-métal compounds and show how they too dépend on the crystal-field splitting. In Chapter II we shall discuss a number of more theoretical points concerned with the proper interprétation of the theory including, in particular, the effect of double-bonding. In Chapter III we shall make a number of applications of the conclusions of Chapter II. We shall use the language of the conventional electro­ static theory in Chapter I, although an alternative nomenclature will he suggested tentatively in Chapter IL Very little introductory material has been included in this con­ tribution. The reader is referred to the paper by Prof. R.S. Nyholm for an introduction to the theory. 289

CHAPTER I The présent Congress provides an occasion to put forward and try to justify the following, perhaps over-ambitious, daim : The failure of the Chemical properties of divalent and trivalent transition-métal ions of the first sériés to vary smoothly and systematically with the atomic number of the métal may be explained in terms of a single factor, namely, the dependence of the stabilization energy and d électron configuration of an ion in a field of given symmetry on the magnitude of the field and the number of ^/-électrons présent. If we wish to extend our discussion to the oxidation-reduction reactions of transition-métal complexes it is necessary to take account also of the third ionisation potentials of the free métal atoms.

HEATS OF HYDRATION In a previous paper we hâve shown that while the beats of hydration of transition-métal ions vary rather erratically with the atomic number of the métal, the values obtained by subtracting the stabi­ lization energies due to crystal-field elfects from the observed beats of hydration rise steadily from the titanous ion to the divalent zinc ion C^). In Figs 1 and 2 we hâve plotted the measured and corrected beats of hydration of the divalent and trivalent transition-métal ions calculated by McClure from accurate data which has recently become available (8).

The way in which the corrected values lie

on smooth curves leaves no doubt that the coordinating power of the ions increases steadily with the atomic number once the dis­ continuons efïects of crystal-field splitting hâve been eliminated. In this chapter we shall deal with two main topics, the theoretical basis for the observed corrélation and its significance with regard to the stability of transition-métal complexes other than the hydrates. Many authors hâve noted that the equilibrium constants for complex formation of a given ligand with the sériés of divalent transition-métal ions increase steadily from manganèse to copper and then fall to zinc. The generality of this behaviour was emphasized by Irving and Williams, who also noted that the hydration energy varied in the same way (9). They pointed out that the sum of the first

290

and second ionisation potentials of the metals, a quantity which they took to represent the électron affinity or electronegativity of the métal ion, also rises to a maximum at copper and then falls to zinc. From this they concluded that the stability of transitionmétal complexes of a given ligand is in large measure determined by the ionisation energy of the métal.

Similar conclusions were

reached simultaneously by a number of other workers ('•>, We believe that this simple corrélation is somewhat misleading. The électron affinity of the transition-métal ions which is relevant to their beats of hydration is the one which corresponds to the filling

S>^o 520 -

-AH

X Expérimental

• CorreeteÀ

-

Kcq l/mole -

Divalent ions -

W Fig. 1.

J___ I___l_l___L

Ca ic T< V (!r rtn FC Co Ni Cu Zn

"

Experimental and corrected beats of hydration of divalent ions (*).

Fig. 2. — Experimental and corrected beats of hydration of trivalent ions (*).

291

of the 4^ and 4/j orbitals. It is true that the vacant M orbitals of eg symmetry are also involved, but there is good reason to believe that they are less important as acceptors than the As and Ap orbitals (12). It follows that ail électron affinities should be referred to some standard configuration, by far the most convenient of which is the (3rf)“ (4j)2 configuration, i.e. ail électron affinities should be for the reaction M++ (3^/)n + 2s —^ M (3^/)n (4i)2

(1)

where the ground State of the configuration is referred to on each side of (1). Electron affinities calculated in this way differ from the sums of the ionisation potentials for Cr++ and Cu++ since the chromium and copper atoms hâve (3J)4 (4i) and {My (4^) ground States, respectively (12). When the appropriate corrections of 7750 cm “ 1 for chromium and of 11200 cm ~ * for copper are made, the électron affinities are found to rise steadily from the titanous ion to the divalent zinc ion. This indicates that it is the corrected beats of hydration and, as we shall show, the corrected beats of complex formation which should be correlated with the électron affinities of the métal ions. The following additional argument supports the use of the élec­ tron affinity defined above, rather than the sum of the ionisation potentials, in correlating beats of complex formation with the electronic properties of the métal ion. Chromium and copper hâve d^s and d^^s rather than c?'*^2 and gj-Qund States and hence larger ionization potentials because of the spécial stability of half-filled and filled électron shells (cf. the rare-earth ions). Now in the chro­ mous, chromic and cupric ions the total number of i/-electrons présent does not permit the formation of these stable shells. It would therefore be unreasonable to attribute an extra stabilisation energy to the ionic complexes which corresponds to a feature of the electronic structure which can only be important in the free atoms. It might be argued that the spécial stability of the d^ and Jio configurations is sufficient to lead to an increased donor-acceptor interaction of the type which leads to the capture of an électron from the ligands by the métal d orbitals. However, in divalent complexes, the bonding effect of the d orbitals, while by no means insignificant, is smaller than that of 4^ and Ap orbitals (12). The

292

excess stability, e.g. of cupric complexes over the corresponding nickel or zinc complexes is too large, in the author’s opinion, to be accounted for by the greater électron affinity of the cupric ion for a M électron. The use of the total électron affinity for the capture of two élec­ trons (or three for the trivalent ions) rather than the simple first électron affinity is préférable for the following reasons : a) The first électron affinities of divalent transition-métal ions often correspond to the processes

(MY + e---- ^

+1

(2)

rather than to the more relevant processes {-idY + E-----^ (3^)" (4^)

(3)

It would be possible to correct ail values so that they refer to reac­ tion (3) but even then an average would hâve to be taken over two électron affinities, those corresponding to the processes 'X

-b

£--------

^ n + 1 X

(4)

X

-b

£--------

^

(5)

- 1 X

where "X dénotés the ground State of the ion, e.g.

for Ni++.

This averaging is necessitated by the fact that in the complex the électrons shared between the ligand orbitals and the métal 4^ orbitals are, apart from second-order effects, equally likely to hâve their spins in the same or the opposite directions to that of the résul­ tant spin of the métal ion d électron core. For configurations (3rf)" (4i')2 there is obviously no need to perform such an averaging. b) The équivalent State of ionisation of a métal ion in a complex does not correspond to the formai valency. According to Pauling, the net charge on any ion is approximately zéro (l^). It is not easy to give a précisé meaning to the net charge, and so to test this hypothesis, but it is clear that the métal ions are not in electronic States at ail closely related to their free States since the 4j and Ap orbitals are partially occupied by ligand électrons. While the matter cannot

293

be settled definitely at présent it seems probable that for divalent ions the électron affinities for process (1) are nearer to the correct ones than those for capture of a single électron. In order to understand the significance of the corrélation between the corrected beat of hydration and the électron affinity of the métal ion we hâve to consider the behaviour of the 2>d orbitals in the field of the octahedron of water molécules. It has often been shown that in such an environment the degeneracy of the five d orbitals is partially removed so that there results a stable triply degencrate tig orbital and a less stable doubly degenerate eg orbital ('5). The energy séparation between these orbitals is defined to be

10

Dg.

In the case of divalent and trivalent ions it is about 30 and 60 k cals, respectively. We shall return to the theoretical basis for this séparation later; for the moment we are concerned with the sequence in which the orbitals are occupied. In the sériés of divalent ions from titanium to zinc the configur­ ations of the métal ion électrons are as shown in Table I. These configurations are exact except for Ti++ and Co++, for each of which there is a small admixture of other configurations obtained by promoting one or more électrons from the tig to the eg orbitals. TABLE I. The mode of occupation of the d orhitals in complexes with maximum spin multiplicity.

hg

Ti++ (V+++) V++

(Cr+++)

Cr++ (Mn+++) Mn++ (Fe+++) Fe++ (Co+++) Co++ Ni++ Cu++ Zn++

294

tt ttt ttt ttt t1tt tjt1t t Itltt 11 11 11 t Itltt

eg

t tt tt tt tt fit tttt

If we consider that part of the electronic energy which is specifically connected with the mode of filling of the d orbitals it is clear that increasing the number of the électrons in tig orbitals favours the stability of the hydrates while increasing the number of électrons in the eg orbitals leads to relative instability. We should, therefore, expect the stability to increase more or less steadily from Ca++ to V++ as électrons go into the tig orbital and then to decrease to Mn++ as the Cg orbital becomes occupied. At this point the stability should increase again until the tig orbital is filled at Ni++ and finally fall again until the eg orbital is filled at Zn++.

It will

be noted that these prédictions are in error for the case of Cu++, but we shall show that this is due to the non-octahedral nature of the hydrated cupric ion, which itself is readily explained by the theory. In order to eliminate the disturbing effects which these discontinuities in the d électron energy hâve on the hydration energy we hâve first to define a d électron energy which is an average over the energies of ail the States obtained by orienting the ground State of the free ion in different ways with respect to the octahedron of ligands. This mean energy can be determined empirically, once some or ail of the States into which the ground State of the free ion is split hâve been identified in the electronic spectrum of the hydrate. The différence between it and the energy of the ground State of the hydrated ion is the crystal-field stabilization energy and must be subtracted from the observed hydration energy to obtain the corrected value. The corrected values in Figs 1 and 2 were obtained in this way 0. Slight différences between the correc­ tions applied in this work and those given in référencé are due to the use of more accurate spectroscopic data which hâve recently become available. We shall show for the simples! possible case, that of a single d électron in an octahedral field, how the averaging is carried out. There are only two different States which can be obtained, a triply degenerate Tig State in which the électron is in the tig orbital and a less stable E,, State in which an eg orbital is occupied. In the case e.g. of [Ti(H20)g]+++ there is a single absorption band with its maximum at 20400 cm showing that this is the t2g—eg séparation. The mean energy for the five possible orientations of the d électron

295

measured relative to the ground State

of the

ion

is

clearly

------------------ ------------------- = 8160 cm~i and so this is the correction to the hydration energy of the Ti+++ ion. For other cases the averaging process is more complicated, but the method is the same. The corrected beats of hydration are thus the beats of hydration which would be obtained if the free ions were not allowed to adjust to the field of the ligands. The fact that they increase steadily from Ti++ to Zn++ shows that the increase in stability due to the increasing électron affinity of the métal orbitals outweighs any decrease in stability due to the fact that each électron is treated as though it spent 40 % of the time in the eg orbitals, which we shall show to be antibonding. Many cupric compounds hâve been studied by means of x-ray crystallography, and it seems to be a general rule that the métal ion is surrounded by four nearest neighbours in a plane and two more distant neighbours which complété a distorted octahedron. The reason for this is probably the instability of degenerate electronic States of non-linear molécules first noted by Jahn and Teller (16). They showed that if the electronic State of a non-linear molécule is degenerate then there is always at least one vibrational coordinate along which the molécule may distort so as to lower its energy, i.e. they showed that a non-linear molécule will always distort if its ground State is degenerate. Jahn and Teller also pointed out that the extent of the distortion is proportional to the bonding or antibonding power of the degenerate électrons. Van Vleck has studied the Jahn-Teller effect in Ti+++, and V+++, which hâve degenerate ground States and has found it to be small This does not invalidate the suggestion that it is large in the hydrated cupric ion for in the cases studied by Van Vleck the degeneracy is due to (2g électrons, while in our case it is due to an Cg électron. We shall show that in molecular-orbital theory the former orbitals are non-bonding while the latter are strongly antibonding. The only other case in which a strongly antibonding orbital is responsible for degeneracy in octahedral coordination is that of the chro­ mous ion. We think it likely that chromous complexes will be found

296

to show marked déviations from regular octahedral coordination. It seems relevant to this discussion that only the chromous ion of the divalent ions has been reported’to form a dimeric diamagnetic acetate isomorphous with the cupric compound. The physical basis of the Jahn-Teller stabilisation was explained in the following way Ç). The eg orbitals are the dx^~y^ and dz^ orbitals, the former pointing towards the ligands in the xy plane and the latter towards those along the z axis. If the four ligands in the xy plane move towards the métal ion and those along the Z axis simultaneously move away then both in crystal-field theory and in molecular orbital theory the dz^ orbital is stabilized and the dx^~y^ orbital is destabilized to an approximately equal extent. The complex can thus achieve extra stability by leaving a gap in the orbital and filling up the orbital as shown in Fig. 3. The distortion proceeds until the extra stability gained in this way is just balanced by the energy it requires to stretch and compress the bonds.

dLx2-y2

CUBIC FIELD. JAHN-TELLER DISTORTION Fig. 3. — Orbital energy level scheme for octahedral and distorted octahedral cupric ions.

297

In the absence of a Jahn-Teller splitting the beat of hydration of lhe cupric ion would be almost half-way between those of the nickel and zinc ions. In fact it exceeds this value by about

8

k cals which

we deduce is roughly equal to the Jahn-Teller stabilisation of the ion. By an extension of the previous argument the formation of planar cupric compounds is readily seen to be due to the extra stabilization energy produced by the Jahn-Teller distortion increasing steadily until the fifth and sixth ligands are completely removed. It is possible, though probably not profitable, to regard the planar diamagnetic complexes of nickel as derived by a Jahn-Teller splitting of an excited State which causes it to cross the normal triplet ground State, since the latter is not stabilized at ail by the Jahn-Teller dis­ tortion. It should be noted that this explanation of the planarity or near planarity of cupric complexes is quite different from that given by Pauling, who described the métal configuration as (3J)* (4p). It seems to us that the résistance to further oxidation which is characteristic of the cupric ion is evidence against Pauling’s suggestion (1“*).

THE STABILITY OF COMPLEXES IN SOLUTION

The experimental data on the complexes formed by ligands other than water are very incomplète. We shall therefore try to deduce how such Systems should behave and compare our conclusions in detail with such experimental evidence as is available. Our general line of argument is that water is in no way exceptional as a ligand and so that we may généralisé from the conclusions of the previous section. In particular it seems reasonable to assume. 1° That after correction for the crystal-field splitting the beats of formation of complexes of the type [M++Xg] increase smoothly from Ti++ to Zn++, provided that no complicating factors such as changes in the nature of the ground State are encountered. We may expect this généralisation to work best for ligands like water, e.g. alcohols, amines, etc., which do not form strong 7t-bonds. 2° That the true beats of formation difîer from those discussed

298

in (1) due to crystal-field splittings the magnitude of which may be estimated from the observed spectra. 3° That the cupric complexes and possibly the chromous complexes will be unusually stable owing to large Jahn-Teller splittings of the ground State. We expect there to be a good deal of variation in the behaviour of these complexes since the Jahn-Teller effect dépends rather critically on the variation of the electronic energy of the non-degenerate électrons with the distortion of the complex from a regular octahedron, and this must be determined by the nature of the ligand. In practice very few beats of complex formation hâve been measured but many sets of values for formation constants in aqueous solution are available. In order to get any check on our theory we hâve therefore to make the further assumption that : 4'’ The variations in equilibrium constants Ki for the complexing of a given ligand with a sequence of métal ions reflect corresponding changes in the beats of reaction. A similar assumption is implicit in the earlier corrélations of stability with electronic structure, for example those of Irving and Williams (9). Also, since it is only in exceptional cases that Kj, K2, ... Kg are ail known, we shall assume that the déductions which we make about the relative stabilities of [M++Xg] ions apply equally to ions [M++(H20)»Xg_n]. Our general hypothesis leads to the conclusion that, in the absence of crystal-field splittings, the beat of formation of complexes of a given ligand with different divalent métal ions should increase steadily from Ti++ to Zn++. In view of the smooth increase in the corrected beat of hydration' shown in Fig. 1 the corrected beat of the solution reaction [M++(H20)„] -f X

[M++(H20)sX] + H2O

should also increase (or possibly decrease) steadily with the atomic number of the métal, as shown in Figs Aa and Ah. The crystal-field splitting will in general hâve different values for complexes from those for the hydrates.

It follows that we may

Write the true beat of reaction AH in the form AH = AH,„„ + AH„,3,

(6)

299

where

is the différence between the crystal-field stabilization

of the complex and that of the hydrate.

Fig. 4. — Heats of hydration and complex formation (a) for ligands with large crystal-field stabilizations, (b) for ligands with small crystal-field stabilizations. — X...X beat of hydration, x — x—x corrected beat of hydration, ----- beat of complex formation, ------------------corrected beat of complex formation.

AH^ryst vanishes for Mn++ and Zn++ so that in these cases AH may be equated to AH^^^. This enables us to estimate AH^„ other ions by an interpolation method. The most suitable procedure would be to draw a curve through the values for Mn++ and Zn++ as nearly parallel to the curve for hydration energy as possible. However, in order to avoid any arbitrary procedure of this sort we hâve used linear interpolation throughout.

AHc

= AHœr'î

+ (n - 5)

AHcorr

We write

— AHœr"

where n is the number of d électrons and can vary from

(7)

0



.

10

This may be rewritten in the form n

Mn"*"*"

AHcorr = AHcorr

-|-

(jl

--- 5)

p

(8)

where is a quantity which characterizes a ligand. Turning now to the second term in (6) we note that Dj for a given ligand does not vary much for the sequence of ions Fe++, Co++, Ni++. Since crystal-field theory leads to stabilizations of

300

4Dg,

Dg and \2Dq for six, seven and eight d électrons respectively

8

we expect =

4 (D,*- - D,o)

=

8

=

where

12

Fe++ ^

(DgL — D,°)

Co++



Ni++

DjO)

J

(9a)

and Dg° are values for the ligand and for water respec­

tively. for the cupric ion complexes cannot be treated so easily because of the effect of the ligand on the Jahn-Teller stabiliz­ ation.

For many complexes we find empirically that AH„,3, ~ 24 (Dg*- - DgO)

Cu + +

(9b)

but this resuit has a different status to (9a) which is based on theoretical arguments. We rewrite (9) in the form

^^cryst

(10)

= '«'■

where m has the values 0, 1, 2, 3, 6, 0 for Mn++, Fe++, Co++, Ni++, Cu++ and Zn++, respectively and /• is a second parameter characterising the ligand and depending essentially on the magnitude of the crystal-field which the latter produces. Combining (8) and (10) we hâve, finally AH“ = AH'^'’+++ (n — 5)

p

+ mr

(11)

where p and r are parameters which can be determined experimentally from thermochemical measurements on manganous and zinc com­ plexes and from spectroscopic studies, respectively. If the latter hâve not been carried out the theory can stlll be checked by studying the consistency of the thermal data on Fe++, Co++ and Ni++ com­ plexes. Unfortunately no complété set of thermochemical data on the complexes of the six metals is available so we are obliged to make use of logarithms cf formation constants instead i.e. we use assumption (4). Since many of the ligands which we shall consider are chelating agents it is necessary to recall that log Kj for a chelating agent, in the présent context, is équivalent to Sj log Kj, where the sommation is over ail the co-ordinating groups employed, e.g. log Kl for ethylenediamine complexes is équivalent to log K] -f log K2 for simple amines.

301

The most studied ligand other than water seems to be ethylenediamine. The logarithms of the stability constants are given in Table 2*. The Dg values calculated from spectroscopic studies on ethylenediamine complexes are about 25 % higher than those for the hydrates.

(The ratios lie in the range 1.17-1.31).

The sum of the logarithms for the three successive formation constants of tris-ethylenediamine complexes of Mn++ and Zn++ are 5.67 and 12.09 respectively. The corresponding “ corrected ” values for Fe++, Co++, Ni++ and Cu++ based on linear inter­ polation are 6.95, 8.24, 9.52 and 10.80 respectively. The divergences of the actual values from these, which we write as A log K and attribute to crystal-field splitting, are 2.57, 5.58, 8.54 and 7.26 respectively. Before trying to interpret these in detail we must look at the corresponding A log Kt separately. They are .85, 1.95, 3.00 and 5.44 for AlogKi; .62, 1.72, 2.66 and 4.51 for AlogK2; .94, 1.88, 2.88 and —1.11 for A log K3. It is clear from these data that the extra stability of the Fe++, Co++ and Ni++ complexes, for each stage separately and hence for the complété three-stage process can be explained by a crystal-field stabilization which increases steadily, from Fe++ to Ni++. The extra stabilities in fact are quite close to being in the expected ratio 1 : 2 : 3. The stability constants for the cupric complexes are particularly interesting for they suggest that, on the same scale, the effect of crystal-field stabilization of TABLE II. Formation constants for ethylenediamine complexes.

log Kl log K2 log K3

Mn

Fe

Co

Ni

2.73 2.06

4.28 3.25 1.99

5.89 4.83 3.10

7.52 6.28

0.88

4.26

Cu

10.55

9.05 —1.0

Zn 5.71 4.66 1.72

Cu++ is about 6.5 for log Kj, about 7.0 for log K2 and —1.3 for log K3. These data correlate remarkably with the spectroscopic evidence which shows that the first two ethylenediamine molécules coordinated to copper produce very large crystal-field splittings,

(♦) AU values for formation constants are taken from référencé (9).

302

but that the third molécule actually decreases the crystal-field splitting in a unique fashion (18). Thus we can give a completely con­ sistent account of the spectroscopic properties and stability constants of the ethylenediamine complexes.

The first two ethylenediamine

molécules stabilise the cupric ion through a large distortion of the kind already discussed for the hydrates. The [Cu(cn)2(H20)2]++ complex must consist of a planar [Cu(en)2]++ group attached weakly (if at ail) to a further pair of water molécules. The addition of third ethylenediamine molécule causes the structure to change to a much more nearly regular octahedral complex with a résultant decrease in the crystal-field stabilization.

This is the cause of the instability

of [Cu(e«)3]++ relative to [Cu(en)2(H20)2]‘''+, (but not relative to [Cu(H20)g]++). The fact that [Cu(en)3]++ is much more nearly cubic than [Cu(E«)2(H20)2]++ is itself readily understood. The amine forms stronger bonds to copper than does water and so by means of a Jahn-Teller distortion can almost push it out of the coordination sphere. For tris-ethylenediamine nickel the spectroscopic Dg value is 1160 cm ~

while the value for the hydrate is 880 cm ~ h

We

therefore expect an excess crystal field stabilisation over that of the hydrate of 12 X 280 = 3,360 cm ~ ^ or 10 k cals. In fact the logarithm of the formation constant exceeds that to be expected in the absence of crystal-field splitting by 8.54 corresponding to about 12.3 k cals. In view of the unknown entropy factor which we hâve neglected and the approximations of the method this agreement is ail that can be expected. It would be particularly interesting to see how the observed beat of reaction compares with that estimated from crystal-field theory. Data on the simple amines are incomplète and in particular, the manganous complexes hâve not been studied. No detailed analysis of the results is thus possible, but the general impression is that they parallel those for the ethylenediamine complexes but with slightly smaller crystal-field splittings. This is consistent with the spectroscopic data. Triethylenetetramine complexes of the metals from manganèse to zinc hâve been studied and in each case log Kj has been determined. The divergences of log Ki from the values obtained by linear inter­ polation between manganèse and zinc are 1.5, 3.3, 4.9 and 9.7 res-

303

pectively.

Comparison with A log Kj + A log K2 values for the

ethylene-diamine complexes, which are 1.47, 3.68, 5.66 and 9.96 is interesting. The agreement is reasonable even for Cu++, which must mean that the Cu++-triethylenetetramine complex is as much stabilised by crystal-field effects as the ethylenediamine complex. This implies that the four nitrogen atoms are almost planar in the cupric compound, and that the complex is not destabilised by steric strain. Triaminoethylamine complexes are generally similar to those of triethylenetetramine with respect to the déviations of log K from the interpolated values, except that the cupric complex is markedly less stable than would be expected. This must be attributed to the inability of the former molécule to occupy four sites in a plane. This is important in the cupric complex, but not elsewhere, for in the other complexes the spatial distribution of the four amino groups among the six coordination positions is relatively unimportant. We turn next to molécules in which the chelating groups are oxygen donors. Salicylaldéhyde, with the usual metals, gives AlogKj’s of .34, .59, 1.03 and 3.05 and A log K2*s of .23, 35, 58 and 2.42. These values are only about 30 % of those for amines, due to the much lower crystal-field splittings of oxygen containing ligands. For malonic and oxalic acids the data are not in very good agreement with the theory but the crystal-field stabilizations are always appreciably smaller than for salicylaldéhyde. Finally we may discuss chelating agents with one nitrogen and one oxygen donor atom. The extensive data on amino-acid complexes give values for A log K1 very close to those for simple nitrogen donors augmented by the small contribution from a carboxylate group. There are many anomalies in the log K values for hydroxypteridine, folie acid, etc. which we cannot easily explain. We may also use the theory, particularly équation (11), to draw some more general conclusions about complex formation. It is immediately clear that in a complicated System containing many different kinds of ligands competing for a métal ion, the distribution of the métal ion will be determined largely by its behaviour in a crystal-field. Thus métal ions which are particularly sensitive to crystal-field stabilization will tend to coordinate with ligands which give large crystal-field splitting and métal ions which are insensitive

304

will form relatively more stable complexes with ligands which produce small crystal-fields.

In a System containing both amino and carbo-

xylate groups, e.g. in a protein solution, cupric ion should be bound preferentially by the amino groups and the manganous ion about equally by both groups. Just such regularities hâve been found experimentally and hâve been reviewed by Williams (19). This point is illustrated in Figs 4a and 4b for the case of ligands producing large and small crystal-fields respectively. The theory which we hâve developed for divalent ions should, with few alterations, be applicable to trivalent complexes. At présent there is insufficient experimental evidence to justify giving the theory in detail.

LATTICE ENERGIES It is quite clear that the crystal-field stabilization of a complex ion should be almost the same in a solid lattice as it is in a solution. The close correspondence between the solution and crystal spectra, e.g. of the transition-métal hydrates, shows that the crystal-field effects are indeed almost identical in the two environments. It is at first sight less clear that the crystal-field theory will be applicable more generally to solid transition-métal compounds, e.g. the binary halides, sulphides, etc., and so one must proceed more cautiously in these cases. Stout (20) has shown that the spectrum of crystalline manganous fluoride, in which each manganous ion is surrounded by an almost regular octahedron of fluoride ions, is analogous to that of the hydrated manganous ion, and that the small différences in the wave-lenghts of the band maxima can be accounted for if Dg is slightly smaller for F“ in the crystal lattice than for H2O in solution. The spectra of other crystalline halides do not seem to hâve been investigated. In the absence of optical data for the halides we cannot proceed quite as we did for complex ions in solution, since there is no way if making sure that the stabilizations which we attribute to crystalfield splitting do not hâve some other origins. However the general consistency of the picture and the close correspondence between the behaviour of the lattice energies for the halides, despite some

305

différences in crystal structure, and that of the beats of formation of discrète complexes gives us some confidence in our interprétation. In Figs 5a and 5b the lattice energies of the divalent and trivalent halides hâve been plotted against the atomic number of the métal atom. The following facts are immediately clear :

Fig. 5. — Lattice energies of a, divalent halides b, trivalent halides (8).

306

1° For the sériés of divalent ions there is a minimum in the lattice energy curve at manganèse for each of the halides. If we suppose that divergences from linearity in the dependence of the lattice energy on the atomic number are due to crystal-field effects then these are of the order of magnitude of 10 — 40 K-cals, just as for complex ions; 2° For the sériés of trivalent fluorides the lattice energy falls to a minimum at the ferrie ion, the ion with configuration. For the other halides the data are incomplète. The crystal-field effects are about twice as large as they are for trivalent ions, just as we hâve already found for the hydrates. A number of features of Figs 5a and 5b require spécial comment. While the stabilizations of the Mn++, Fe++, Co++, Ni++, Cu++ and Zn++ ions follow the same pattern in the anhydrous chlorides, bromides and iodides as has become familiar in the treatment of complexes, there does seem to be a différence in the case of the anhydrous fluorides, for the lattice energy of CuF2 is almost identical with that of NiF2. We hâve already remarked that the Jahn-Teller effect which stabilises the cupric complexes is much more variable than the usual crystal-field splitting. It seems probable that the discrepancy indicates that the crystal-lattice of Cu F2, which, significantly, is different from that of the other fluorides, is less déformable than the discrète complex ions so that the Jahn-Teller stabilization is smaller. If this is true one might hope that the absorp­ tion spectrum of anhydrous Cu F2 would indicate a more nearly regular octahedral arrangement than occurs in the hydrates etc. A similar situation arises in the interprétation of the lattice energies of the V++, Cr++ and Mn++ halides. The uncertainties in the lattice energies of the vanadous compounds is unfortunately large enough to prevent our reaching any definite conclusions, but the general trend of the results suggests that the Jahn-Teller effect is less important for Cr++ than for Cu++.

THE RELATIVE STABILITIES OF TETRAHEDRAL AND OCTAHEDRAL COMPLEXES The simple crystal-field theory shows that in tetrahedral complexes the set of c/ orbitals is split into a stable doubly degenerate e orbital and an unstable triply degenerate t orbital, e.g. the splitting is the

307

reverse of that for octahedral complexes, The splitting and mixing of the States of atoms with several ^/-électrons differs considerably in detail from that for octahedral complexes with the single exception of the t/5 configuration which is perturbed in the same way by the two kinds of field. Direct calculation of the electrostatic field of a set of ligands shows that the splitting in a tetrahedral complex is much smaller than in an équivalent octahedral complex. Molecular orbital theory shows that while the métal orbitals are the only ones capable of forming bonding molecular orbitals of symmetry for octa­ hedral complexes ; d orbitals must compete with the more favoured 4p orbitals in bond formation in tetrahedral complexes. This means that the antibonding t orbitals in tetrahedral complexes will be raised much less than the antibonding e orbitals in octahedral complexes. Thus both théories agréé that the crystal-field splitting will be less in tetrahedral than in octahedral complexes. Experimentally this is shown to be true by the few available spectra of tetra­ hedral complexes and by the absence of spin pairing among the tetrahedral complexes of the first transition sériés. It is interesting to ask wich configurations should particularly favor octahedral complex formation and which tetrahedral. We may use the argument of the introduction and State that in the absence of crystal-field splitting the tendency to form tetrahedral rather than octahedral complexes would increase steadily with atomic number through the transition sériés. However owing to crystal-field effects we shall find certain discontinuons changes superposed on this general trend.

In Table III we give the crystal-

TABLE III. Stabilizations of d'^ —

configurations in crystal-fields.

Octahedral t/5 t/IO

0

t/1 t/6

4 D,

6

t/2 t/2

D« 12 Dg 6 Dff

12

t/3 t/8 t/4 t/9

308

Tetrahedral

8

0

8

D, D, Dq

4 Dq

field stabilizations for each électron configuration in each type of field.

Since Dg is smaller for tetrahedral than for octahedral com­

plexes this Table suggests, other things being equal : 1° That divalent manganèse and zinc should form tetrahedral complexes more readily than the other divalent ions except perhaps titanous and cobaltous; 2° That ferrie and thallic ions should form tetrahedral complexes more readily than other trivalent ions except perhaps vanadium; 3° That there should be a change favoring octahedral complexes on going from titanous to vanadous or from cobaltous to divalent nickel complexes of the spin-free type. It is difficult to décidé from the empirical formulae of substances which hâve been prepared much about absolute stabilities. Con­ clusion 3° seems definitely correct for cobaltous and divalent nickel. The ready formation of tetrahedral [C0X4]— ions where X is a halogen or pseudohalogen is a characteristic feature of the chemistry of cobaltous cobalt, while few nickel complexes containing discrète tetrahedra [NiX4]— groups seem to be known. Similarly [FeC^] — complexes are rare or unknown, hydrated (octahedral?) ions [FeCl4.2H20]—, [FeCl3, 2,3H20]“ and [FeClg]'*” being obtained instead (21). Conclusion 2° receives some support insofar as the [FeC^]” ion is stable under many conditions, although [FeCle]^” seems also to exist. There are no [MnX4]~ complexes known, the usual empirical formulae corresponding to [MnXs]^- or [MnX5(H20)]2-, Also there seem to be no [CoX4]~ complexes. Aluminium seems to form both tetrahedral and octahedral complexes with great facility (21). Conclusion 1° is also supported by very limited experimental evidence. Tetrahedral zinc complexes are quite common and there seem to be a few [MnX4]

ions (but MnCl2.2 pyridine which if

it is monomeric we should certainly except to be tetrahedral is in fact claimed to be planar) (21). Ail in ail the experimental evidence suggests that crystal-field splittings are the important factors determining the relative stabilities of tetrahedrally and octahedrally co-ordinated métal ions. However these qualitative arguments, particularly those based only on empirical

309

formulae may well prove deceptive. More structural and thermodynamic data are required to détermine the scope of these methods. These arguments may be applied to the metals of the second and third transition sériés, but they then lead to rather different results. In the later transition sériés values for complexes are systematically larger than in the first sériés, while électron repulsion energies are systematically smaller. This leads to the well-known tendency to form spin-paired or “ covalent ” complexes. While in the first transition sériés the crystal-field effects are never large enough to cause spin pairing in tetrahedral complexes, we might expect it to be more favoured in the other sériés. If so it is clear that the configur­ ation which would most likely form a spin-paired complex is the one with four ^/-électrons, for this allows the stable e orbital to be filled while leaving the t orbital empty. This conclusion of crystal-field theory is supported by experimental evidence which does not easily receive an alternative explanation. Trivalent rhénium forms halogen complexes with the empirical formulae M+ [ReX4] “ (2>). In this it seems to differ from related ions, e.g. trivalent manganèse which, although a smaller ion, forms [MnXs] — and [MnXs (H2O)] — or Re"' which forms [ReXg] —. Since Re" has just four d-electrons we suppose the complexes to be tetrahedral and attribute the existence of [ReX4] ~ ions to the spécial stability of the configuration in strong tetrahedral fields. We therefore expect [ReC^] “ and [ReBr4] “ to be diamagnetic. While in the octahedral complexes of the first sériés électron pairing is the exception rather than the rule, the situation is reversed in the other sériés. This changes the position of maximum stability from the configurations and to the configuration d^. We can deduce that in these cases the tetrahedral d'^ complexes are relatively the most stable, but there is little experimental evidence. There are probably no Pd'" or Pt"^ complexes and only a few Rh” or Ir” complexes. Some of the latter are probably tetrahedral, e.g. [Rh (S03)2]2~ but the majority, surprisingly, seem to be octa­ hedral (21), e.g. [Ir (CN)6]4 -. We suspect that detailed x-ray work might show that, as in the case of the so-called “ [Co (CN)^]'* ~ ” ion, some of the structures hâve been ascribed incorrectly.

310

CHAPTER II It has been shown that there is a formai similarity between the electrostatic

and

molecular-orbital

théories

of

transition-métal

complexes which ensures that the general pattern of energy levels obtained is the same in the two théories, although there are quite definite différences in detail (12). Since many of the properties of the complexes, such as their relative stabilities and the broad features of their optical spectra, dépend only on the energy level diagrams it is not easy to décidé which theory gives the more accurate des­ cription of the electronic structure. The valence-bond method which, at first sight, is less closely related, in a formai sense, to the other théories can in fact be made équivalent to them by introducing the idea of three électron bonds in ionic complexes and by modifying certain conclusions about the promotion of électrons to highly excited orbitals. We shall examine more closely than hitherto the appropriateness of the electrostatic and molecular-orbital théories in different situations. The valence-bond method will not be discussed further. In its most complété form the molecular-orbital theory includes ail the electrostatic interactions between the électrons and nuclei of a molécule or ion. In this form it includes the electrostatic theory as a limiting case, that in which no mixing of métal and ligand orbitals occurs. It is therefore important to realize that it is the utility, not the correctness, of molecular-orbital theory which is at stake. If électrons are shared between métal and ligands the molecular-orbital method is useful, if not it has no advantages over the electrostatic method. There are no general experimental techniques available, even in principle, whcih détermine the distribution of a single molecularorbital over the molecular framework. However, if one or more orbitals are distinguished from the majority by containing unpaired électrons then paramagnetic résonance absorption studies give fairly direct evidence about the distribution of the latter.

Fortunately

the key orbitals involved in the theory of transition-métal complexes are just the ones which can, in principle, be studied by this method. The most direct method dépends on the measurement of the nuclear hyperfine structure of the absorption line. The magnitude of the hyperfine splitting produced by a given nucléus is propor-

311

tional to the density of unpaired électron near that nucléus. The proportionality constant can be determined fairly accurately by independent measurements, so that the actual density of unpaired électron on any nucléus which has a suitable nuclear spin can be determined.

Owen and Stephens hâve applied this technique to

the [Ir Clg]

and [Ir Brg]

ions and hâve shown that the Sd élec­

trons, usually thought of as isolated on the Ir atom, spend some 20 % of the time on the halogens (22.23). Jn principle this method could be applied to many other complexes, particularly those containing nitrogen, but this has not yet been done. The results on the iridium salts do not tell us very much about complexes of the first transition sériés for two reasons. Firstly the lower ionization potentials and larger sizes of the later transitionseries ions favour more extensive delocalization than in the first sériés. On the other hand the delocalization studied in these compounds can occur only through n bonding while in many complexes of the first transition sériés more extensive delocalization through a bonding is to be expected.

We may expect such delocalization

to be greater than 10 %, but without further information cannot estimate its magnitude in this way. Owen (6) has showed that a number of features of the paramagnetic résonance spectra of the hydrates and ammines of the first transition sériés cannot be explained by the simple electrostatic theory. In particular the spin-orbit coupling seems smaller in the complexes than in the free ions. This could be understood if the J-electrons spent only about 70-90 % of the time near the métal nucléus and the rest on the ligands. He finds that a consistent explanation of the hyperfine structure, the g-values, and of small déviations of the optical spectra from those predicted by theory can be given if deloc­ alization is assumed. Alternative explanations of certain of the discrepancies between the simple theory and experiment are possible, but the consistency of Owen’s results is convincing. There is a great bulk of experimental evidence showing that if the ligands in transition-métal complexes hâve available empty 71 orbitals of even very moderate stability then extensive doublebonding involving the t2g orbitals, occurs. This provides very strong evidence for the delocalization of t2g électrons in a variety of simple complexes, e.g. those of pyridine. More important, it suggests

312

that if the

tt

électron delocalization is important even though the

ligand 7t orbitals are much less stable than the métal orbitals, then the delocalization caused by the a bonding, which involves métal and ligand orbitals of comparable stability, is likely to be very extensive. This brings us to the theoretical approach of the problem.

In

general the condition necessary for orbitals on different atoms to be mixed together to form bonds is that they overlap strongly. Direct calculations of overlap intégrais for typical transition-métal complexes hâve been carried out and indicate quite conclusively that the 3d orbitals of a métal ion overlap quite strongly with the s and P orbitals of typical ligands (24.25). Jt is difficult to avoid the conclusion that extensive mixing must occur. We hâve now examined the evidence for mixing and must consider the arguments against it. The only one of any weight seems to be the success of direct calculations, from the electrostatic model, of the frequency of optical transitions. However, on doser examination it is seen that if the correct lengths are taken for the metal-ligand bonds then dipole moments much greater than the measured stade dipole moments must be assumed for the ligands if agreement with experiment is to be achieved. These high moments may reasonably be attributed to the polarization of the ligands by the high field of the métal ion, but, apart from the arbitrariness of this proce­ dure, in vieuw of the orthogonality requirement of quantum theory, this almost implies a mixing of the varions métal orbitals and the ligand a orbitals. It seems to us that three rather different situations may be envisaged. In the first the a orbitals of the ligands are sufficiently far from the électrons of the unfilled shell for overlap to be impossible or insignificant. In this case the electrostatic theory is applicable and nothing extra is achieved by the use of molecular-orbital theory. The rare-earth ions are the most important case of this kind. In the second extreme situation the mixing of métal and ligand électrons is so extensive that it is not even reasonable to assign configurations on the basis of a certain number of d électrons remaining on the métal ion and the rest being transferred to the ligands. In this situation only molecular-orbital (or valencebond) theory is useful. Typical examples are the Mn04~ or OsOjN" ions. Between these extremes there is a région in which

313

mixing is more or less important, but not sufficiently extensive to remove the utility of the simple classification scheme based on the electrostatic picture, despite its only partial correspondence to the true electronic structure. We believe that the di- and trivalent complexes of the first, and probably the other transition sériés, and the actinide complexes lie in this intermediate range. The methods of the electrostatic theory lead to correct qualitative and sometimes even quantitative results but only because these approximate moderately closely to the results of molecular-orbital theory. If we are correct in this conjecture it would be wise to invent a new term to replace “ crystal-field ” theory which would indicate that “ bonding ” as well as electrostatic interactions are involved. The only name that we are able to suggest is “ ligand-field theory ”. While the electrostatic theory is quite adéquate for approximate calculations on the spectra and “ bond types ” of many simple complexes, it is not capable of extension to take into account the effect of TC-bonding. Another drawback is that while it gives a good account of the internai spectra of the métal ions in complexes it can say very little about excited States in which charge is removed from the métal ion to the ligand or vice-versa. Thus in order to integrate the théories of double-bonding and of normal and photochemical oxidation-reduction reactions with the other aspects of transition-métal theory it is necessary to employ the molecularorbital theory (2>

>

6

).

12

We shall discuss those métal complexes which hâve regular octahedral symmetry. The various orbitals of the central métal ion and of the ligands transform as représentations of the octahedral group in the manner shown in Table IV. The System of numbering the ligands and the choice of axes is shown in Fig. are designated in the following way :

.

6

The orbitals

a) Métal orbitals are indicated by a symbols such as 945. The subscripts refer to the usual classification of atomic orbitals ; b) Molecular orbitals made up from ligand a orbitals are indicated by symbols such as Xa

• The subscript refers to the symmetry Ig species. If the représentation is degenerate a further subscript is employed to show with which of the métal orbitals a particular member of a degenerate set will combine, e.g. Xt will combine lu»

with cpp„ but not with Çpj, or 314

p^;

9

X

c)

Molecular orbitals made up from ligand

ated by symbols such as , ,

tt

orbitals are indic-

, the use of subscripts being the xy

same as m b).

For the orbitals of individual ligands we hâve used the symbol ct; for the CT orbital on the fth ligand and the symbol for the orbital on the /th ligand, etc.

The combined ligand molecular

orbitals hâve been normalized assuming that individual ligand orbitals are mutually orthogonal.

Fig. 6. — Numbering of ligands and choice of axes for octahedral complexes.

In the absence of

orbitals on the ligands and neglecting métal

orbitals outside the 4p shell for the first transition sériés the most general molecular orbitals are of the forms shown in Table V. The normalising factors must be chosen in the usual way, e.g. N3

= n + \2 ^ 2XS^ \ - 1/2 where ig V. '*/ overlap intégral between
= J

, Xa

94

dT is the

The requirement that the

orbitals should be mutually orthogonal leads to a set of relations of the form (V — X") + (1 — X'X") S,

Ig

= 0

315

TABLE IV.

316

Symmetry classification of orbitals for octahedral complexes (Tig and T2U orbitals neglected).

'?4s ig

n;

T,.

n;

+

Xa^

^?4p + 1^' Xt lu ^ X lu, X

}

lu

( 94p y y

+

>4p^+

y.'

N"

J

N"

J

N"

X, lu, y y

y-'

N':

Xt,„.,)

(x., - X"

(xt

lu V

( Xt

lu y

lu

Eg

N': g


T2g

93d

93d

XZ

yz

lu, X

lu, y

— y-"


— y"

94p )

1

n;

Antibonding Orbitals

Orbitals

xy

yJ

Molecular-orbitals for octahedral complexes neglecting n bonding.

Ai.

Non-Bonding

-e

Bonding Orbitals

Class

N

Symmetry

In order to explain the observed behaviour of transition-métal complexes it is necessary to assume that the order of levels is as shown in Fig. 7. This order is entirely consistent with the simplest theoretical considérations based on the energies of the different métal atomic orbitals and the magnitude of the overlap intégrais. The séparation between the t2g and eg orbitals is, of course, the critical séparation 10 Dg on which most of the arguments of Chapter I depended.

ANTIBONDINC5 ^

ti a

ANTIBONDING C.

3

lODcj, I I

b BONDING

Jt

16 ,U

g

Fig. 7. — Energy level scheme for octahedral complexes.

The t2g orbitals are pure d orbitals on the métal atom so long as no Tt orbitals are présent on the ligands. In practice this is never the case, for even with saturated ligands like ammonia hyperconjugation allows a certain amount of mixing of métal orbitals with Tt type ligand orbitals in much the same way as methyl groups hyperconjugate with unsaturated Systems. Nevertheless in this and related cases we can be sure that there is only very limited mixing between the t2g orbitals of the métal and ligands. The case of the Cg orbitals is very different, for we hâve seen that mixing of métal and ligand orbitals is extensive, that is neither v' or v" is negligible. The bonding effect of the a,g and

orbitals must remain constant

or vary continuously as the atomic number of the métal increases, for the same orbitals are occupied in every case. However while the eg bonding orbital is filled by four électrons in ail configurations

318

its bonding effect is liable to be cancelled by the occupation of the eg antibonding orbital.

If we define the d orbital bond-number

as the différence between the number of électrons in the bonding and antibonding orbitals it is obvious that it has the approximate values given in Table VI for different numbers of électrons in “ ionic ” and “ covalent ” complexes. TABLE VI. Bond numbers for d'' configurations in octahedral complexes.

No of

électrons . .

Ionie complexes

. .

Covalent complexes. .

1

2

4

4

3 4

4

4

4

4

5

6

7

8

9

3 4

2

2

2

2

1

0

4

4

3

2

1

0

10

The bond-number defined in this way should not be confused with the bond-order usually employed in molecular-orbital theory. The bond-number is a measure of the occupation of bonding orbitals, not of the extent of binding which is achieved. We shall argue however that the bonding power per électron in the eg orbitals is very roughly a constant, so that the bonding energy for ions of a given valency relative to their valence States increases steadily with the bond number. This allows us to translate into molecular orbital language the results of Van Santen and Van Weirengen (26) for we see that if the radii of transition-métal ions are plotted against the number of t/-electrons they should decrease with the decreasing size of the d orbitals except when électrons are added to the anti­ bonding Cg orbitals, e.g. in going from V++ to Mn++ and from Ni++ to Zn++.

In these cases the bond lengths should increases.

This conclusion is in agreement with the experimental facts. This idea is capable of considérable généralisation. It may readily be shown that for any State of an ion with n ^/-electrons the bond number defined in this way is related to the slope of the energy elvel diagrams in ref. (5). It was shown (12) that dE d(E>q)

4«1 --- 6/72

(12)

where nj and n2 are the number of tig and antibonding eg électrons respectively, so that «i can readily be determined for any excited State once the energy level diagram has been calculated and the

319

approximate

value determined from optical spectra.

The bond

number is simply 4 — «2should be noticed that «2 inay not be even approximately intégral, nor need it be approximately constant from one complex of a given métal to another for excited States as it is in the ground State. The calculation of the energy level diagram for excited States, or a knowledge of their électron configurations derived in some other way, thus enables one to predict bond lengths. This has proved useful in interpreting phosphorescence spectra (2'?), and as we shall show is important in understanding the effect of the Franck-Condon principle on the rates of électron exchange reactions. Another application of the idea of bond number is to the change in ionic radius which occurs on going from an ion of maximum spin multiplicity, e.g. the Fe++ ion with four unpaired électrons, to an ion in which électrons hâve been paired in the orbital, e.g. diamagnetic [Fe(CN)g]4-. The bond number in this case changes from two to four and so there should be a very considérable decrease in the ionic radius. We shall return to this point later.

DOUBLE BONDING Table VI shows that if the ligand hâve reasonably stable

tz

orbitals

then the tm and t2g molecular orbitals of the métal ion and the a framework can combine with them. The orbitals then become rather complicated, but fortunately this has little effect on those properties of the ground States of the complexes which are particularly dépendent on the métal d orbitals, although it may lead to a systematic stabilization of ail the métal complexes of a given ligand. If the ligand tc orbital is isolated on a single atom the simple tig orbitals given in Table VII must be replaced by bonding and antibonding linear combinations. If the ligand has delocalized n orbitals the situation is more complicated. When the ligand t: orbital is unoccupied and rather unstable as it is in phosphines, arsines, mercaptans, etc. il is energetically(*)

(*) For a discussion of the magnetic criterion of bond type from the présent point of view, see reference 11.

320

unstable relative to the métal orbitals so that the molecular orbitals hâve the forms

(13)

N" N"

(14)

N"

in which k' < 1 and k" < 1. The first of these orbitals is bonding, i.e. it is stabilized relative to the d orbitals of the métal ion ; the other is antibonding. Since the magnetic type of a complex is determined by the séparation between the lower t^g and the Cg levels and since this kind of double-bonding lowers the former and leaves the latter unchanged it follows that complexes in which it can occur are likely to be diamagnetic. We believe that the “ covalency ” of phosphine and arsine complexes is in large measure due to the effect of doublebonding on the occupied t^g orbitals of the métal ion, rather than to a particularly strong interaction between the ligand and métal Cg orbitals. The importance of this kind of double-bonding in determining the stability of métal complexes has been recognized for some time (28) and has been discussed theoretically (24). If the ligand

t:

orbitals are of the stable occupied type, as for

example in the halogen ions, then they are energetically more stable than the métal orbitals. The combined orbitals may still be described as in (13) and (14) but now k' > 1 and k" > 1. The bonding orbital (13) is occupied by ligand électrons and any métal ci-electrons are obliged to occupy the antibonding orbital (14). This results in a decrease in the tig — eg séparation and hence a tendency to produce complexes with a maximum number of unpaired spins. Bonding of this kind does not seem to hâve been considered prior to the work of Stevens and Owen, but in the light of their results we may anticipate that it will prove to be very general. It should be noted that very similar double-bonding must occur in the hydrates

321

even though they hâve only one occupied n orbital which can combine with the métal orbitals. Double bonding between métal ions and molécules with delocalized Systems of t: orbitals has been considered in a number of instances, e.g. in |3-diketone complexes of cupric copper and in the complexes of heterocyclic nitrogen compounds with transitionmétal ions (21).

CHARGE-TRANSFER SPECTRA Most métal complexes hâve absorption bands in the visible or ultraviolet région which are distinguished from the internai tran­ sitions of the métal ion by their dependence on the ease of oxidation or réduction of the ligand and often by an unusually high intensity. Although there is much evidence showing that the final Chemical resuit of the absorption is often the oxidation or réduction of the ligands there is no general agreement as to the nature of the upper orbitals involved. The molecular-orbital theory enables one to describe the transitions in a satisfactory fashion. The internai transitions of the métal ions dealt with in crystalfield theory are essentially d— d transitions. It is to be expected that the next lowest électron transitions will be from the occupied d orbitals into the lowest empty orbitals, namely the antibonding a^g and orbitals, and empty ligand ti orbitals, and from the least stable orbitals beneath the d orbitals, namely the bonding ag andti« orbitals, and perhaps from occupied

tt

orbitals, into any empty

d orbitals which are présent. There will be other transitions from the bonding a,g and orbitals, to the corresponding antibonding orbitals but these will usually be at shorter wave-lenghts than the transitions involving J-electrons, except perhaps in Zn++ and other highly charged positive ions with filled d shells. A great variety of transitions is possible. They may be spinforbidden or spin-allowed, orbitally forbidden or orbitally allowed; they may involve mainly one ligand as in [Fe(H20)5l]++ or ail equally as in [Cr(H20)e]+++.

The theory has hardly begun to be

developed and the experimental evidence is also very incomplète. We shall make some general remarks here, and deal with one case in detail later.

322

The métal ci orbitals are usually fairly well localized and the eg orbitals not delocalized by more than 20-30 %. The métal 4j and Ap orbitals are likely to be delocalized to a greater extent. It follows that ail of the transitions other than those within the d shell involve more or less transfer of charge. The most intense transitions must be g — u in character, so that the lowest intense transitions of readily oxidised ions will usually be from the top occupied d orbital into the lowest empty t\u or tju orbital, e.g. in a spin-paired ferrons complex, e.g. [Fe(dipyridyl)3]++ this would be from a moderately localized t^g d orbital to a delocalized

orbital, partly ligand

•K and a and partly métal Ap in character. This is essentially a mixed charge-transfer and 3d — Ap transition. The corresponding tran­ sitions to the ai g a antibonding orbital must occur in the same general région but they will be much less intense, perhaps not much stronger than the internai d — d transitions. Jorgensen has suggested that certain transitions of the divalent transition métal ions classified by Dainton (3i) and by the author (32) as chargetransfer transitions, are in fact 3d — 4^ transitions. We are inclined to agréé that the 3d — As character of these transitions is large and that Jorgensen’s classification is perhaps the doser to the truth. The lowest transitions other than d-d transitions, in complexes of oxidising anions are likely to be from the bonding a\g and t\u orbitals into the empty ^/-orbitals. These transitions are indeed largely charge-transfer in character, since they involve the removal of an électron from a delocalized orbital, largely on the ligands, into a d orbital almost localized on the métal atom. They will vary widely in intensity, those from the tm orbital being very intense and the others much less so. The classification of these transitions involving the transfer of électrons from the d orbitals to empty antibonding orbitals, etc. is capable of giving very extensive and useful information about the energy level diagrams of complex ions and hence about their Chemical properties, e.g. in the case of the planar complexes of pal­ ladium and platinum we hâve identified the position of the vacant 5d and 6p orbitals and hâve been able to study d — p mixing by following the change in position and intensity of the 5d^ — 6pz transition as the ligands are changed (33).

323

CHAPTER III The molecular-orbital method developed in the last section can be applied both in a qualitative and a quantitative way to a variety of problems in transition-métal chemistry. We shall discuss a number of examples. It must be emphasized that similar results may in some cases be obtained by other methods. In particular the treatment of some of the examples owes much to the work of Taube (34). We hope to show that just as in the treatment of the spectra and magnetic properties of complexes the ligand-field method makes possible rather exact prédictions about the effects of changes in the ligands on the Chemical properties of complexes.

THE TRANSITION FROM “ lONIC ” TO “ COVALENT ” COMPLEXES We hâve shown in a previous paper that the transition from com­ plexes with maximum spin multiplicity to ones in which the spins are paired takes place when the séparation between the t^g and Cg orbitals exceeds a certain critical energy which can be calculated approximately.

We shall take up this topic again from the point

of view of molecular-orbital theory and

discuss in detail the

behaviour to be expected near the transition point, i.e. for ligands which produce crystal-field splittings very close to the critical one at which the cross-over occurs. The change from a complex with maximum spin-multiplicity to one in which spins are paired is invariably associated with the transfer of électrons from the eg antibonding orbital to the Î2g orbi­ tal. For definiteness we shall discuss the case of the ferrous ion, in which two électrons are transferred when the spin-multiplicity changes. The removal of électrons from the antibonding orbital must cause a decrease in the radius of the ferrous ion, so that the metal-ligand distance must also decrease. This agréés with the conclusion of valence-bond theory. The potential energy curves for the two States are shown diagramatically in Fig. 8. Two cases are considered, namely that in which the spin-paired State is more stable and that in which it is less stable than the State of maximum multiplicity.

324

In the former case the compound will be diamagnetic

at sufficiently low températures; in the latter it will hâve a normal paramagnetic susceptibility. If the energy séparation between the two minima is of the same order as kT a very interesting situation arises since a thermal equilibrium between the two forms should exist. The magnetic susceptibility should be a weighted average of the susceptibilities of the two forms (34) and the absorption spectrum should be composite, including bands from each form.

Fig. 8 a and b. — Energy level scheme for octahedral complexes near crossover point.

The change in radius which occurs at the cross-over point has important conséquences. Any feature of the ligand’s structure which favours the formation of long metal-ligand bonds will, other things being equal, favour the complex of maximum spin multiplicity and vice-versa. A theoretical conséquence of the change in radius with change in spin multiplicity is that while a single is sufficient to describe the ground State and the spectroscopically excited States we must expect to change when the ground State of the ion changes. It is clear from Fig. 8 that the change-over will always occur for values of

smaller than that calculated on the basis of a fixed Dq.

Unfortunately it is difficult to calculate how big this efîect will be. The one major discrepancy between the calculated and predicted spin multiplicity of simple transition-métal complexes occurred for the tris-phenanthroline complex of ferrons ion which is diamagnetic, although according to the simple calculations, it should be para-

325

magnetic.

The author is grateful to R.J.P. Williams for pointing

out that the complex of tris 2-methylphenanthroline is paramagnetic and much less stable than the simple phenanthroline complex owing to steric hindrance. Shortening of the Fe-N bonds would so compress the structure that the 2-methyl groups would interféré with the neighbouring molécules. Instead the complex remains in the State of maximum spin multiplicity. This provides a rather direct proof that the source of discrepancies between the calculated and observed cross-over points is in some cases due to the change in bond length, and hence V)q, which occurs when the spin multiplicity changes. We must next ask for what range of Dq values an appréciable thermal mixing of the two types of ground State is likely. Suppose that the crossover occurs at some definite value D^°. The crystalfield stabilizations for the types of ground State differ by 20D^ so that, neglecting other eflfects, we must hâve |20(D^° — D^)| ~ KT where T)q is the value for the ligand. At room température we may expect a tenth of the material to be in the less stable form if |D^‘’-D9| ~ 30 cm~ 1 . While there are many reasons why this resuit should be inaccurate, it should not be out by more than a factor of 2. Thus ligands whose D<7’s fall in a rather small range about the critical value will hâve anomalous magnetic properties.

It is

clear that most ligands must give either predominantly paramagnetic or predominantly diamagnetic complexes but that if one deliberately chooses a ligand giving complexes close to the cross-over point then by modifying it slightly complexes with very different properties can be obtained. We hâve already mentioned one example, that of the ferrons complexes of phenanthroline and throline.

-methyl phenan­

2

Many of the most important examples of this behaviour near a cross-over point are concerned not with regular octahedral complexes, but with octahedral complexes containing more than one kind of ligand and with planar complexes. The principles however are exactly the same. Calvin has studied the magnetic susceptibilities of a variety of planar cobaltous complexes (^5). Jhe interprétation of much of his data is complicated by the fact that planar cobaltous complexes in which the coordinating groups are nitrogen atoms lie very close to the cross-over point from complexes with one unpaired spin to

326

those with three.

The température dependence of the susceptibility

has been measured for a sélection of these compounds and it is found that some obey Curie’s law over the whole température range studied while others hâve susceptibilities corresponding to one unpaired spin at low températures and to a greater number of unpaired spins at higher températures, although there is no change in the crystal form. Clearly the former group are well clear of the cross-over point while the latter group are very close to it. As is to be expected from the theory very small modifications in the ligand efîect very large changes in the magnetic susceptibilities. A similar situation exists in the case of complexes of ferrous iron with planar four-coordinating ligands such as porphyrins and phthalocyanines.

Ferrous protoporphyrin has a magnetic moment

corresponding to four unpaired électrons at ail températures but ferrous phthalocyanine has a moment of intermediate size at room température (36). At low températures the apparent magnetic moment falls even further and it is fairly clear that the material would finally become diamagnetic. Clearly there is a paramagnetic excited State only a few hundred calories above the diamagnetic ground State. Perhaps the most important group of compounds which hâve two lowest States of comparable stability are the ferrous and ferrie porphyrins and their complexes with further ligands. Octahedral ferrous and ferrie complexes in which four co-ordination positions in a plane are occupied by the nitrogen atoms of the pyrrole rings of protoporphyrin or related porphyrins and the fifth and sixth are filled by water hâve maximum spin multiplicity. Replacement of the water molécules by ligands which produce strong crystal fields such as cyanide ion or carbon monoxide invariably produces spin-paired complexes. Ligands of intermediate character such as simple and conjugated amines, hydroxide ions and azide ions form complexes the properties of which dépend on the nature of each of the two groups and are surprisingly sensitive to very small changes in either.

We attribute the remarkable versatility of the iron proto­

porphyrin prosthetic group in the varions haemoproteins in part to the dependence of the ground States of its complexes with simple ligands such as hydroxide or hydrogen peroxide on the detailed nature of the haem-protein linkage. A small change, e.g. the replace­ ment of a histidine nitrogen atom by the aliphatic amino group of lysine would be quite sufficient to change the ground-state of

327

the complex and hence its magnetic and spectroscopic properties. The anomalous magnetic moment of methaemoglobin hydroxide, which has been interpreted by Pauling as due to partial spin pairing leaving three unpaired électrons is, we believe, due to an equilibrium between complexes with one and five unpaired spins, respectively Similarly we believe that the great complexity of the visible spectra of many ferrons and ferrie porphyrin complexes, which is in contrast to the very simple nature of other metallo-porphyrin spectra, is due in part to equilibria between different forms, although the occurrence of charge-transfer bands at long wavelengths is also almost certain. Magnetic measurements do not easily detect the presence of an equilibrium mixture of States unless the two forms are présent in comparable amounts. If the conditions are chosen carefully optical measurements can be much more sensitive. The idéal case is that of manganous and ferrie complexes, for, in the spin-free form, these hâve no spin-allowed internai transitions. The spin-paired complexes on the other hand always hâve spin-allowed internai transitions at least one hundred times more intense than the spin forbidden ones. In idéal cases they may also hâve charge-transfer spectra up to one hundred thousand times stronger than spinforbidden internai transitions. It follows that it should be possible to detect

.001

%-l % of spin-paired complex by optical methods,

i.e. one should be able, in idéal cases, to detect spin-paired complex even if D^° — ~ 150 cm~ i . This should provide a very sen­ sitive tool for studying the effect of small changes in a ligand on the ligand-field splitting which it produces. Detailed calculations hâve shown that for octahedral trivalent ions the crossover point is expected to occur at lowest Dq values for Co+++, at much higher T>q values for Fe+++ and at intermediate values for Mn+++. We are carrying out similar calculations for planar complexes but, since the crystal field can now be described only by using three parameters, the results are not so simple. The most interesting conclusion is that while divalent planar cobalt and nickel complexes require similar crystal fields to achieve spinpairing, the manganous ion requires a much larger crystal field. The ferrous ion requires a field of intermediate size. A study of spin-paired divalent planar nickel complexes shows that the ligand fields are somewhat greater than in trivalent octahedral complexes, i.e. more than twice those in divalent octahedral complexes.

328

This,

at first sight, surprising resuit is connected with the much less efficient shielding of the ligands by the M électrons in the planar complexes. Another way of putting this is to say that the ligands are more strongly polarized or form stronger, more “ covalent ”, bonds, a point of vieuw which is supported by much experimental evidence

THE MECHANISM OF SOME ELECTRON-TRANSFER REACTIONS Libby (38) has pointed out that the Franck-Condon principle requires that a reaction involving the transfer of an électron between the same élément in different valency-states, e.g. [M*(u^m)]"+ + [M(u^m)]

^

_|_ [M(u9m)]''+

must proceed via a symmetrical transition State. We shall investigate the activation energy required for such a transfer process from the point of view of molecular-orbital theory and then examine in detail those reactions which proceed via bridged binuclear complexes. Let us suppose that the radii of the di- and trivalent ions of a métal which forms octahedral complexes in both valencies are r" and r”* respectively, and let K,j and K„i be the force constants for the metal-ligand bonds. Then the tranfer of an électron from M^*to M'“, while maintaining the internuclear distance at the values corresponding to the forms présent before transfer, requires the expenditure of an energy 3 (K,j + Kj|,)(r“ — r*“)2. This is the energy which would be required for a direct photo Chemical oxidationreduction reaction. Thermal électron exchange can proceed much more readily via a transition-state in whieh each ion adjusts prior to the reaction. The activation energy for this process is roughly about

1/4

of the energy absorbed

in the corresponding photochemical reaction. We can see from the expression for the activation energy for thermal electron-transfer that a direct exchange of the kind contemplated is most likely to occur rapidly if (r” — is small. Now (/■“ — r”‘) will dépend very largely on whether the électron transferred cornes from an Cg or a tig orbital.

In the former case

329

(r” — will tend to be larger than in the latter, since the eg orbital is antibonding. Thus we expect reactions such as the exchange between ferrons and ferrie ion to be relatively rapid whether the ions are spin-paired or not. written

In the former case the reaction can be

Fe++(/2?)4(É’i,)2+ Fe+++(/2ÿ)3(ej)2->Fe+++(t2»)3(ey)2+ 'pQ++{t2gY{egY

and in the latter Fe++(/2?)® + Fe+++(t2?P ^ Fe+++(t2ÿ)5 + Fe++(r2g)® On other hand the reaction between chromons and chromic ions shonid be mnch slower since it can be formnlated as Cr++(t2ff)^(e») + Cr+++(t2ff)2 ^ Cr+++(r2ff)3 + Cr{t2g)Keg)

Similarly the cobaltons-cobaltic exchange reaction shonid be slow since it may be written C0 ++(/2ff)5(e?)2 + C0 + + +(?2ÿ)® ^

C0 + + +(t2ff)® + Co++{t2g)\egY

This reaction, it will be noticed, involves not only the transfer of an électron bnt also the rearrangement of the other d électrons of both ions. It is partially spin-forbidden and shonid proceed very slowly indeed. In fact most electron-transfer reactions involve bridged binnelear intermediates

However, in these too the same general considér­

ations shonid apply, namely that if an eg électron is transferred the reaction shonid go more slowly than otherwise. Experimentally there is one serions exception to this rnle, namely that the manganons and manganic ions exchange mnch more rapidly than we shonid hâve expected. On the whole, however, Libby’s snggestion that it is the Franck-Condon principle that is responsible for the energy barrier to électron exchange seems to acconnt for most of the evidence if it is snpposed that the ionic radius dépends on the number of électrons in the eg orbitals [cf. Taube, ref.(34)]. In a bridged chromium complex of the type shown in Fig. 9 the électron distribution can be determined with some confidence.

330

The chromic ion is in the configuration (?2y)^ or more precisely {dxyY (dy^^, with ail électron spins parallel. The chromous ion has the configuration {t2gY (eg) in the particular State (dxyY (dxzY (dyzy (dz^)^ also with ail électron spins parallel. The first three électrons automatically go into the tig orbitals in the way shown. The dz^ orbital is occupied rather than the dx'^ _ because the chloride ion produces a smaller ligand field than the H2O molécule, particularly as it is being polarised by a positive Cr“‘, so that the dj^ orbital is destabilised to a smaller extent than the dx"^ by the ligands. H2O

H2O

H2O

H2O Fig. 9. — The structure of binuclear intermediates in electron-exchange reactions.

Direct transfer of an électron from Cr'** to Cr'” would, as we hâve seen, require an unnecessarily large activation energy. It is far more economical to create a symmetrized complex before transferring the électron. The transfer involves the simple removal of an électron from the Cr" dz^ orbital to the Cr"* dz~^ orbital, so that we can neglect ail the other d électrons. The assumption that the dz'^ électron is isolated on one chromium atom or the other is only approximately justified. When the chloride ion is at its equilibrium position the approximation is quite good, but as the ion approaches a position half-way between the chromium atoms it becomes less valid until when the complex is symmetrical the électron is equally likely to be on either métal atom. In Fig. 10 we show the energy level diagram for the two critical orbitals as

331

a function of the displacement of the chloride ion from its equilibrium position, it being assumed that the other bond lengths adjust to the equilibrium values for each position of the chloride ion.

Fig. 10. — The orbital energy scheme for electron-exchange reactions.

The left-hand side of the diagram shows the Cr'* «z^ orbital stable and the Cr’“ dz'^ orbital unstable. The distance E is the activation energy for direct électron transfer. As the chloride ion approaches the symmetric position the two orbitals become more nearly equal in energy and may become mixed together if the interaction between them is strong. In the absence of mixing the two levels would cross at the symmetric position O, but if mixing can occur then the two curves repel each other as shown in the diagram. The course of the reaction can now be understood in some detail.

As

the

chloride

ion

moves

from

left

to

right,

the

électron moves from right to left. In the symmetric configuration the dz^ électron is equally distributed between the two chromium atoms. Two things can now happen : either the chloride ion moves back to its original position and the électron proceeds in the opposite direction, so that no reaction occurs, or the chloride ion continues moving to the right and finally reaches the equilibrium position for Cr”* + Cr”, the électron meanwhile having been transferred

332

in the opposite direction.

This mechanism explains why the bridg-

ing group is transferred in an electron-exchange reaction of this type, as was shown by Taube. It can be summed up by saying that the électron always prefers to stay as far away as possible front the bridging chloride ion ; if the latter moves in one direction the former move in the opposite direction. One might next ask what elfect substituents would hâve on this process;

for

example,

would

oxidation-reduction

reactions

go

more quickly with a cis or trans isomer in the pair of reactions cis trans

[Cr(NH3)4 (H2O) Cl]++ + [Cr(NH3)6]++ ^ [Cr(NH3)s (H20)]++ + [Cr(NH3)s Cl]++

if they are assumed to go via bridged intermediates. To solve this problem we must consider the energy level diagram in some detail. Since the ligand field of a water molécule is smaller than that of ammonia in the trans position it stabilizes the dz^ orbital rather strongly and the dx’^-y^ orbital rather little. A water molécule in the cis position has little elfect on the critical dz'^ orbital. It is seen that the reaction with the trans form should be more rapid than that with the cis form. Siihilar considérations also apply to the equilibrium properties of complexes and enable one to make certain prédictions about the relative stability of cis and trans forms of those ions which hâve degenerate ground-states in a regular octahedral field. It is very important to realize that while methods of this kind are quite general they must be applied very carefully to each particular System. Quite different rules might apply, e.g., in the électron exchange reaction between V+++ and V++, since in this case it is a tig électron which is transferred.

Similarly in the case of cis-trans

isomers the exchange reaction should be slower for the trans isomer than for the cis in a reaction such as [Cr(H20)4 (NH3) Cl]+++

[Cr(H20)6]++^

[Cr(H20)s (NH3)]++

+ [Cr(H20)s Cl]++ since NH3 molécule, having a larger ligand field than the H2O molé­ cule, destabilizes the orbital pointing towards it.

333

We shall deal with one more class of electron-transfer reactions, since it involves further theoretical considérations of some interest. During the réduction of spin-paired cobaltic complexes, such as the [Co(NH3)5]+++ ion, not only is an électron tranferred to the cobalt, but in addition the arrangement of the électrons already présent is altered.

In fact, as we hâve seen, the reaction is Co (t2ff)®+ e

Co

A reaction of this sort should be extremely slow both on account of the great change in bond length to be expected when two électrons are introduced into the eg orbital and on account of the change in spin multiplicity from one to four. There is a second mechanism which could be considered for some reactions of cobaltic cobalt, namely one which produces the cobaltous ion in an excited State : Co

e -> Co {t2gY {eg)

This reaction is favoured for two different reasons, namely because the Franck-Condon principle is violated to a much lesser extent since only one extra électron is placed in the Cg orbital, and because there is no violation of the spin sélection rules.

On the other hand

the promotion energy from the {î2gY {eg)'^ to the (?2ÿ)® {eg) State will often be large, and so increase the activation energy. It is not possible to make exact prédictions about the relative importance of the two mechanisms in any particular case, but the general variation as ligands with progressively greater ligand fields are used can be anticipated. If the ligand is such that the cobaltic sait is spin-paired, but the cobaltous sait is far from being spinpaired, then the first mechanism will predominate. It will hâve a very low frequency factor and a high activation energy. If the ligand is such that the cobaltous complex is very close to the crossover point to a spin-paired complex (perhaps phenanthroline) then the second reaction should predominate. It should hâve a normal frequency factor and an activation energy comparable to that for réduction of chromic complexes. In between there should be a range of ligands such that the cobaltic complexes react by both mechanisms with comparable speeds. Such anomalous behaviour might be revealed by a study of the température dependence of the

334

reaction rate. Finally, if the ligand field is such that both the cobaltous and the cobaltic ions are spin-paired, then the reaction should proceed by the second mechanism, and the reduced complex be formed in its ground-state, i.e. in the spin-paired State.

CHARGE-TRANSFER SPECTRA We hâve already remarked that a great variety of charge-transfer transitions is to be anticipated.

We shall discuss only two types

of molécule, the pentammine halides of trivalent chromium and cobalt, which are fairly typical complexes of oxidizing cations.

We

hâve chosen these Systems mainly because a great deal of experi­ mental evidence is available. The methods employed are general and could be applied to many other Systems, e.g. cupric, cuprous or ferrie complexes with oxidizable or reducible inorganic or organic molécules or ions. The simple hexammine cobaltic ion has two moderately weak absorption bands in the visible and near ultraviolet and one very strong band further in the ultraviolet at about

2000

À C'**’).

It is

generally believed that the latter is associated with the transfer of an électron from the ligands to the métal ion, reducing the latter to the divalent State. As we hâve seen, a more accurate description of this transition is given by molecular orbital theory, which describes it as being from one of the occupied bonding orbitals into the antibonding Cg orbital which is actually largely cl orbital in character. In view of the high intensity of the band we believe it to be fully allowed so that it must involve the tm bonding orbital which has a high density on the ligands. Our description of the transition is therefore substantially the same as the conventional one, the transfer of charge in the transition being considérable, and from the ammonia molécules to the métal. We believe this to be the most probable assignment, but it must be noted that it is entirely based on theory, and the experimental evidence does not exclude, e.g. the transfer of an électron from the filled ?2èt shell of the cobalt ion to the empty antibonding t\u orbitals. The situation is a good deal clearer in the pentammine cobaltic halides. The fluoride has substantially the same spectrum as the hexammine, but the chloride, bromide and iodide bave intense absorption bands at much longer wavelengths, the wavelengths

335

increasing from cliloride to bromide to iodide.

There can be little

doubt that these bands are connected with a transition in which an électron is removed from an orbital concentrated on the halogen and transferred to one concentrated on the métal ion. A doser inspection of the spectra reveals that the intense absorp­ tion is not due to a single band but to pairs of bands at 26000 and 35000 cm~ 1 in the iodide, at 32000 and 39000 cm- i in the bromide and at 36000 and 44000 cm- i in the chloride. In each halide the longer wavelength band is much weaker than the other (^O). There are a number of possible explanations for the appearance of two bands under these conditions. They might correspond to the formation of the halogen atom in the 2P1/2 and 2P3/2 States respectively, to the removal of different kinds of électrons from the halogen, e.g. a and tt, to the transfer of an électron to two different kinds of empty orbital, or to a pair of transitions arising from dif­ ferent kinds of empty orbital, or to a pair of transitions arising from different States of a single configuration. The first possibility is ruled out by the appearance of a pair of bands in the chloride separated by several thousand wave-numbers. since the séparation between ^Pj/j and 2P3/2 States of chlorine is only 880 cm- *. The fact that transitions of this type occur at long wavelengths only in trivalent transition-métal complexes and not, for instance, in trivalent aluminium or gallium complexes suggests that the acceptor orbital involves the métal d orbitals.

Since the tig d orbitals are

already filled in trivalent cobalt it seems almost certain that the Cg antibonding orbital is the acceptor in each case. The donor orbitals on the halide ion are of two types, almost localised n orbitals and largely delocalized cr orbitals. The former group are less stable than the latter and so might be expected to be involved in the longest wavelength transition. It would be plausible therefore to assign the first band to the almost completely chargetransfer transition from a halogen orbital to a métal eg orbital and the second to a less completely charge-transfer transition from the bonding a orbital of the cobalt-halogen bond, to a métal eg orbital. A doser study of the problem shows that, if we define the Z axis to be in the cobalt-halogen direction, it is predominantly the

orbital which acts as acceptor in each case.

This theoretical assignment is consistent with the observation

336

that the long wavelength band is always weaker of the two.

The

intensity of a transition will be large only if the donor and acceptor orbitals overlap strongly. Detailed calculation here shows that in most cases a overlap is larger than tt. It seems likely qualitatively that the transition moment is larger for the g than for the n transition. It is interesting that the longer wavelength transitions should be polarized in the x and y directions and the shorter ones in the Z direction. In the pentammine chromic halides there is one new feature which must be considered in the theory, namely the occurence of vacancies in the (2g orbital.

These vacancies make possible two

new types of transition, from the halogen a and

orbitals to the

Î2g orbital. In fact the charge-transfer bands of the chromic complexes are extremely similar to those of the cobaltic ones, except for a systematic shift to shorter wavelengths which is caused by the greater résistance to réduction of the chromic ion. This suggests that in the chromic complexes, even though the t2g orbital is available, it is not used in the lowest energy transitions, but the eg orbital is used instead. The energy required for spin pairing of the électrons in the t2g orbital, more than balances the extra energy obtained by putting an électron in one of the stable orbitals. This is consistent with the fact that chromous complexes are usually spin-free. The nature of the transitions of lowest energy in the spectra of complexes of this kind is relevant to the mechanisms of spontaneous oxidation-reduction reactions. In each case an électron is transferred from the least stable orbital concentrated on the ligand to the most stable one on the métal. It follows that a detailed experi­ mental and theoretical examination of the charge-transfer spectra of stable complexes should throw a great deal of light on the précisé electronic changes which take place, e.g. in the reaction of Cu++ with I“. ACKNOWLEDGEMENTS This contribution was developed in close collaboration with Prof. R. S. Nyholm to whom the author is indebted for many helpful suggestions. The author is also indebted to Dr D.P. George, Mr. J. S. Griffith and Dr. D. McClure for permission to mention material developed independently by them which will be the subject of more detailed joint publications.

337

REFERENCES (1) L. Pauling, J. Am. Chem. Soc., 53, 1367 (1931). (2) J. H. Van VIeck, J. Chem. Phys., 3, 807 (1935). Q) H. Hartmann and H. L. Schlâfer, Z. Naturforsch., 6A, 760 (1951). (“*) C. K. Jorgensen, Acta Chem. Scand., 9, 1362 (1955) and many référencés therein. (5) L. E. Orgel, J. Chem. Phys., 23, 1004 (1955). (6) J. Owen, Proc. Roy. Soc., 227A, 183 (1954). (7) L. E. Orgel, /. Chem. Soc., 4756 (1952). (8) D. McClure, Private communication. (9) H. Irving and R.J.P. Williams, Nature, 162, 746 (1948); J. Chem. Soc 3192 (1953). (10) M. Calvin and N. Melchior, J. Am. Chem. Soc., 70, 3270 (1948). (11) G. Schwarzenbach, H. Ackermann and J. E. Prue, Nature, 163, 723 (1949). (12) L. E. Orgel, J. Chem. Phys., 23, 1819 (1955). (13) «AU data on atomic spectra are from Atomic Energy Levels», by Charlotte E. Moore, National Bureau of Standards Circulars, 467 (1949 and 1952). (!■•) L. Pauling, « Tbe Nature of tbe Chemical Bond », Cornell University Press (1945). (15) R. Schlapp and W. G. Penney, Phys. Rev., 42, 666 (1932). (10) H. A. Jahn and E. Teller, Proc. Roy. Soc., A, 161, 220 (1937). (17) J. H. Van VIeck, J. Chem. Phys., 7, 472 (1939). (18) J. Bjerrum, «Métal Ammine Formation in Aqueous Solution», Copenhagen (1941). (19) R. J. P. Williams, Biological Reviews, 28, 381 (1953). (20) J, W. Stout, Private communication. (21) N. V. Sidgwick, «Chemical Eléments and Their Compounds», Oxford (1950). (22) J. Owen and K. W. H. Stevens, Nature, 171, 836 (1953). (23) J. H. Griffiths and J. Owen, Proc. Roy. Soc., 226A, 97 (1954).

(29)

D. P. Craig, A. MacColl, R. S. Nyholm, L. E. Orgel and L. E. Sutton, J. Chem. Soc., 332, (1954).

(25) H. H. Jaffe, J. Chem. Phys., 21, 258 (1953). (20) J. H. Van Santen and S. Van Weiringen, Rec. Tran. Chim., 71, 420 (1952). (27) L. E. Orgel, /. Chem. Phys., 23, 1958 (1955). (28) See for example J. Chatt, J. Chem. Soc., 4300 (1952); R. S. Nyholm, J. Chem. Soc., 3245 (1951). (29) M. Calvin and K. W. Wilson, J. Am. Chem. Soc., 67, 2003 (1947). (30) C. K. Jorgensen, In press. (31) F. S. Dainton, J. Chem Soc., 1533 (1952). (32) L. E. Orgel, Quarterly Reviews, 8, 422 (1954). (33) J. Chatt and coworkers, Unpublished work. (39) H. Taube, Chem. Reviews, 50, 69 (1952). (35) M. Calvin and C. H. Barkelew, J. Am. Chem. Soc., 68, 2267 (1946). (30) G. Frischmuth, Z. anorg. Chem., 230, 220 (1937). (37) R. R. Fergusson & B. Chance, «The Mîchanism of Enzyme Action », Johns Hopkins University Press (1954). (38) W. F. Libby, J. Phys. Chem., 56, 863 (1952). (39) H. Taube, H. Myers and R. L. Rich, J. Am. Chem. Soc., 25, 4118 (1952)(90) M. Linhard and M. Weigel, Z. anorg. Cnem., 266, 49 (1951).

338

Discussion des rapports de R. S. Nyholm et de L. G. Orgel M. Bjerrum. — I should like to add some comments to the paper of Prof. Nyholm. 1) The fact that we hâve some kind of directed Chemical bonds in more labile transition complexes as well as in the robust Co^“complexes has been recognized by several chemists for the last twenty years. Therefore, I agréé with Nyholm that names as “ ionic ” and “ covalent ”, “ outer ” and “ inner orbital complexes ”, etc., are inadéquate, and should be dropped in favour of terms as “ spin-free ” and “ spin-paired ” complexes which directly refer to experimental facts. 2) I also agréé with Nyholm that ligand field is a better name than crystal field in so far as molécules and ions in the second sphere contribute but very little to the colour of the substances. In fact, this more adéquate name has already been proposed several times. (Sutton and Orgel, 1953; Ballhausen, 1954, etc.) but until now with little success. 3) In his contribution Prof. Nyholm mentions (e.g. p. 258), that the intensity of the ligand field increases as the electronegativity of the ligand decreases. This statement, however, is not compatible with the position of the ligand in the famous Tsuchida sériés : J-
In this connection I may mention that Dr Schâffer

in my laboratory has found that the basic rhodo complex [(NH3)5Cr—O—Cr(NH3)s]4+ first prepared by S.M. Jorgensen is either diamagnetic or very close to be so; it is very hard to under-

339

stand that a d^~ complex can be diamagnetic, and I should like to ask Prof. Nyholm if he is able to explain this fact.

I may add

that Selwood in a recent paper {J. Am. Chem. Soc., 76, 6207, 1954) bas found diamagnetism of what he supposes to be [a94FeQ[j in a hydrolysed ferrie solution. In our opinion this suggests that the complex also has an oxygen bridge, i.e. it has the constitution [aqs Fe—O—Fe aq5]‘*+. M. Nyholm. — In reply to Prof. Bjerrum I would like to emphasize that the electronegativity of the ligand is only one factor influencing the strength of the ligand field. As mentioned on p 258 other factors are also important; these include double bond formation. They are discussed by Dr Orgel. The diamagnetism of the [(NH3)sCr—O—Cr(NH3)5]4+ ion is indeed surprising, since the simple theory applied to the Ruthénium case would suggest that one unpaired électron per Cr atom would still be présent unless some kind of coupling akin to antiferromagnetic exchange occurs; I cannot suggest a simple explanation. M. Orgel. —

Prof. Wilmeel daims that a quite large moment

is observed for [(NH3)sCr—O—Cr(NH3)5]++++ at room tempér­ ature, although it is complexes.

much less magnetic than simple chromic

M. Bjerrum. — I hâve studied Orgel’s contribution and especially his section on “ The stability of complexes in solution ” with great interest. At the conférence on coordination chemistry in Amsterdam last year I put forward similar ideas, but the paper worked out in coopération with Jorgensen to be published in Rec. Trav. Chim. Pays-Bas has not yet appeared. Dr Orgel discusses the values of the complexity constants for the ethylenediamine Systems determined by me.

In Table I the

gross stability constants of these conplexes are compared with gross constants for other selected Systems. In case of the ethylenediaminetetraacetate, ethylenediamine and o-phenanthroline Systems the ligand field stabilization is estimated in a way similar to that employed by Orgel. According to the ligand field theory the stabiliz­ ation for octahedral complexes should be for Fe’* 1/3, forCo'* < 2/3 and for Cu’* 1/2 of the stabilization found for Ni**. The stabilities

340

TABLE I. Gross complexity constants for some Systems of transition métal ions

(from Prof. Bjerrum, Tables of complexity constants). Ki_|y[

= Ki.K2...Kfj

dO

d^

enta gly en tn

= = = =

d^

d6

d^



d9

rfio

V++ Mn++ Fe++ Co++ Ni++ Cu++ Zn++

Ca++

enta : log Kl 10.6 stabilization gly : log Ki_3 NH3 log K,+6 —5.7 en : log Ki_3 stabilization den : log Ki_2 dip : log Ki_3 phen log Ki_3 stabilization Sc+++ enta : log K, 23.1

[maIn [M] [A]N

12.7 0.4

13.4

14.2

16.1

0.2

1.6

5.7

9.5 2.5 10.3 ~6.3 17 ~7.4 21.3 12.0

V+++ 25.9

ethylenediaminetetraacetate aminoacetate ethylenediamine trimethylenediamine

10.9 5.1 13.8 5.5 14.6

18.5 18.4 3.4 2.8 14.2 ~16 8.7 10 18.1 18.6 8.6 7.8 18.9 21.3 17.0 18.3 18.0 5.2 2.9

16.2 11.5 12.1

14.4 13.3 17.0

Fe+++ 25.1

den dip phen

= diethylenediamine = a, a’-dipyridyl = o-phenanthroline

are of the right order of magnitude, and the data show the strong tetragonal distortion normally found in cupric Systems. Only the Cu"-phen System seems to be very nearly octahedral, and this is in complété agreement with the spectra as shown by Jorgensen. Table II gives some data for the ratios between the consecutive constants. The data given for the ammonia Systems show that the nickel ion has six, and the cupric ion four uniform coordination places. This is in agreement with what is to be expected from the ligand field theory. For the cobaltous ion a weak rhombic distortion of the octahedron should be expected, and the irregularities found in the residual effects are not in disagreement with such an inter­ prétation. The négative values of the residual effects in the zinc ammonia System are due to a change from octahedral configuration of the hexaquo ion to tetrahedral configuration of Zn(NHj)4++, and the abnormally high stability found in the Fe” Systems of the aromatic diamines are due to the pairing of the spins by the uptake of the third ligand. In the ethylenediamine Systems the data show

341

TABLE II. Total effect (Tn,n + 1), statistical effect (Sn,n I 1) and residual elTect (Rn,n + 1) for some métal amine Systems. Rjî.n+i — log

*»>n+l Sl,2 = $5,6 = 0.38,

Ri,2 Co++, NH3 Ni++, NH3

= 0.27, R3.4

82,3 = 84,5 R20

0.10

0.21

0.18

0.24

Cu++, NH3 Zn++, NH3

R2,3

0.22

0.26 — 0.4

— 0.5 Sl,2 = en

Tl,2 T2,3

0.67 1.18

Fe++,en

0.68,

Co++, en

1.03 1.26 Fe++, dip

Ti,2

T2,3

<0

<-3

1.06 1.73

= 0.25 R4,5

R516

0.31 0.17

0.42 0.34

R4.5

T4,5

Ts,6

0.33

2.76 —

~2.3 —

83,4

0.04 0.29

Si,2 = S3, 4 = 0.43 Ri,2

^«+1

82,3

— 82,3

= 0.35

0.1

= 0.97

NP’*', en

1.16 1.93 Ni++, tn

Cu++, en

Zn+"'‘, en

1.41 10.3

0.77 3.29

Cu++, phen Zn++, phen

2.00

0.15

0.71

3.16

0.65

0.87

that steric strain increases from Mn++ to Zn++ and from the nickel ethylenediamine to the niekel trimethylenediamine System. In the cupric and the zinc o-phenanthroline Systems there seems to be less steric strain than in the corresponding ethylenediamine Systems, but this is not suffieient to explain that the tetragonal distortion has dissappeared in the Cu“-phen System, and I should like to ask Dr Orgel for an explanation. I hâve discussed the matter with Dr C.E. Schâffer in my laboratory, and one could think of the possibility that the strong rr-bonding in this case stabilitzes the cis-configuration of the bis-diamine complex to a higher extent than the trans-configuration ?

M. Orgel. — In the trans form of diaquobispyridyl Cu + + only one Tl bond can be formed, but in the cis form two are possible. Perhaps this faetor is suffieient to account for the différence between the complexes of the simple and conjugating amines.

342

M. Kuhn. — Is the magnetic moment rigidly connected to the framework of the molécule or is the central atom carrying the magnetic moment free to rotate inside the rest of the molécule? Paramagnetism is due to an orientation of the electric moment présent in the atom or molécule with respect to a magnetic field applied from outside. Which is then the unity whcih undergoes orientation? Are there cases in which orientation of the magnetic moment implies orientation of the entire molécule? M. Nyholm. — Both spin angular momentum and orbital angular momentum contribute to the total angular momentum hence the effective magnetic moment. In so far as we separate these the moment arising from the former is anisotropic; and thus Fe"* compounds hâve moments arising from spin only, hence no orientation with the magnetic field is expected. However the vector, when présent, is oriented by the molecular field, and hence magnetic anisotropy occurs, e.g. as in octahedral CO'* complexes. Molécules of the latter do, therefore orient in a magnetic field. M. Bénard. — Le Prof. Bjerrum nous a dit, il y a un instant, que la commission de nomenclature de l’Union Internationale de Chimie avait décidé d’adopter pour l’élément W le nom wolfram à l’exclusion de tout autre. En tant que membre de cette commission, je crois nécessaire de préciser que la situation ne correspond pas exactement à cela. En fait, au cours des réunions qui eurent lieu ces dix dernières années, à Amsterdam, New York et Stockholm en particulier, de longues discussions eurent lieu sur cette question, et il est exact que dans certains textes provisoires, la solution à laquelle le Prof. Bjerrum fait allusion, fut préconisée. Mais une opposition très forte s’éleva entretemps dans certains pays. Aussi fut-il décidé à la dernière réunion de cette commisison (Reading, avril 1956) de laisser la question en discussion, jusqu’à nouvel ordre. M. Bjerrum. —

I agréé with Dr Orgel that changes in enthalpy

give a more correct measure of the ligand field stabilization than changes in free energy. Until now the beats of complex formation hâve been determined only in a few cases, and it is therefore désirable that more thermochemical measurements be made in the nearest 343

future. It should be mentioned that the beats are less dépendent upon the sait concentration than are the free energies and it is further a possibility that they can be determined also in reactions with robust complexes where equilibrium in most cases cannot be established.

M. Chatt. — Our expérience in platinum (II) chemistry indicates that the halogen atoms, especially iodine, hâve a definite tendency to form double bonds with the métal. The tc type bond might occur either by a drift of /?-electrons from the halogen to the métal or of
These are known to be linear

in such ions as [Ag(NH3)2]+ and [Ag(CN)2]“ in the solid State. When a ligand which can form strong (/^-bonds is taken up, however, its use of two of the J^-orbitals in the silver ion will reduce the availability of the same rf^-orbitals for attaching the second molécule of ligand in the position diametrically opposed to the first. Thus we may expect the second molécule of a (/.,^-bonding ligand to be taken up less readily than the first. We (Ahrland, Chatt, Davies and Williams, unpublished) find this to be true when the ligand is a phosphine where strong -bonding between silver and phosphorus is to be expected. Leden finds that iodide ion behaves similarly, the first complex (n = 1) being very stable relative to the second (n = 2). This we consider to be evidence of strong n-type bonding between the silver and iodine atoms; the third complex (n = 3) is also surprisingly stable and the formation of mononuclear complexes continues to « = 4.

Probably the relatively

great stability of this third complex is also caused by double bonding, although the exact reason is not clear; it may be connected in some way with the use of d^p hybrid orbitals for the formation of dative 344

7i-bonds from a trigonally sp'^ hybridised silver ion (cf. Ahrland and Chatt, Chem, and Ind., 1955, 96). Dr Orgel bas admirably synthesized from crystal field theory and molecular orbital theory a very satisfactory theory of bonding in métal complexes and I wish to emphasize that the great success of cristal field theory alone in interpreting the ultra-violet spectra and magnetic properties of transition métal complexes must not blind us to the importance of covalent bonding.

Therefore I wish

to présent data which are difficult to explain on the basis of an electrostatic theory of bonding in complexes.

We hâve recently

examined the formation of silver complexes by water-soluble organic dérivatives of nitrogen, phosphorus, arsenic, oxygen, sulphur and sélénium. We found a great variety of formation curves. These are shown in the figure together with a list of the ligands studied. The “ normal ” curve of complex formation with ammonia taken from J. Bjerrum’s thesis, and Leden’s curve showing complex formation with chloride ion are also included for comparison. The latter has an inflection at n = 2. None of the new curves show the inflection, which was thought to be characteristic of the formation curves of the complexes of silver and related ions, at n = 2. The variation in the curves is not connected so far as we know with the pairing or unpairing of électrons in the li-shell and dépends largely on the donor atoms involved. Silver (I) has just sufficient électrons to fill ail its rf-orbitals and to leave only s and p-orbitals for o-bond formation. These may be used as sp, sp^ or sp^ hybrids to give linear, trigonal or tetrahedral complexes respectively. The d^ orbitals are available for dative 7t bonding which would be enhanced by some p-hybridisation in the linear and trigonal complexes. This means that silver (I) can give a great variety of complex types according to the electronegativities and double bonding tendencies of the donor atoms. The change in the relative stabilities of these different complex types with change in the covalent bonding characteristics of the donor atoms undoubtedly accounts for the variety of formation curves which we hâve found. The “ arsine curve ” is peculiar in having a very strong inflection or a final “ stop ” at n = 1. No further complex formation took place at the highest concentrations of the sulphonated arsine which it was possible to investigate. This “ stop ” at n = 1 may be caused by the high négative charge carried by the ligand, As(C6H4S03~)3.

345

Ligand Number ^

Fig. 1

LIGANDS, L. P = 3 - P Ph2C6H4S03Na

Et S = 4-S Et CgH4S03Na

As =- As (3 - C6H4S03Na)3

Ph S = 4 - S Ph CgH4S03Na

Se = 4 - Se Ph CeH4S03Na

N = 3-N H2C6H4S03Na

NH3 — Ammonia Cl“ = Chloride Ion O = Anisole - 4 - Sulphonate

The first complex (AgL)” carries two négative charges, and the second complex (AgL2)5~, if it were formed, would involve the addition to this of another three négative charges. This may account for the évident difficulty in attaching a second molécule of the sulphonated arsine. The arsine is not strictly comparable with the other ligands studied, but owing to difficulty in synthesising the sulphonates it was not possible to get a strictly comparable sériés. The relative magnitudes of the first stability constants Kj, relating to the complex formation equilibria Ag+ + L = AgL+ and Cd2+ + L = CdL2+ are also indicative of the covalent character of the bonds. The constants relating to Ag+ are listed in Table I. TABLE I. Stability Constants, Kj, of the Ligands, L, with Silver Ion in Aqueous Solution at Ionie Strength, [x(NaC104) and 25”. Ligand L.............................................................

IJ-

Kl

PhS03Na+........................................................

1.0

0.9

3—NH2C6H4S03Na*............................................

1.0

17

4—NH2C6H4S03Na*........................................

0.1

14

4—NMe2C6H4S03Na*....................................

0.1

5.7

3—PPh2C6H4S03Na*...........................................

0.1

1.4 X 108 2 X 105

As(3—C6H4S03Na)*........................................

0.2

4—0MeCeH4S03Na+........................................

1.0

4—SEtC6H4S03Na*........................................

0.1

415

0.2

390

4—SPhC6H4S03Na»........................................

0.1

47

S(4—C6H4S03Na)2*........................................

0.2

25

4—SePhC6H4S03Na*........................................

0.1

430

0.76

+ = The co-ordinating atom is not known with certainty, but it is probably an 0 atom of the sulphonate group. * = the co-ordinating atom is underlined.

The important points about these stability constants are the much greater affinities of the silver ion for the heavier donor atoms than for nitrogen and oxygen, and the very great différences between

347

the constants for the ligands containing nitrogen and those containing phosphorus and arsenic.

If the entropy factors remain constant,

the différence between the constants indicates a différence of bond energy between the Ag — N and the Ag — P bonds of the order of 11 k cal.

If the différences between the stabilities of the amine

and phosphine complexes are due to dative 7r-bonding in the Ag — P bond, we might expect the différence between the corresponding complexes in the cadmium sériés to be much smaller.

This we

find to be so. The cadmium ion is isoelectronic with the silver ion, but because of the greater positive charge on the nucléus we might expect électrons from its d/e-orbitals to be much less readily available for dative TT-bond formation than in the case of silver. We therefore measured the first stability constants in the System : Cd2+ + NH2C6H4SO3- and Cd2+ + PPh2C6H4S03". Both ligands are weak complexing agents with cadmium, and the constants, Ki, are of the order 10 in each case. This contrast between silver and cadmium cannot be explained on any electrostatic theory of complex formation, but is very strong evidence that covalent bonding, and especially double bonding, is important in the complexes of silver with the heavier donor atoms.

M. Jorgensen.— 1.

By what methods is the trigonal bipyramidal

configuration of (Cu dip2J) CIO4 supported? In the rare cases, where four nitrogen atoms are not bound co-planar to copper (II), the spectra (of Cu tren++, Cu phen2++, Cu dip2++ and Cu tren++ with one or two ammonia molécules) might rather suggest a cisoctahedral configuration. However, due to the Jahn-Teller effect, the tetrahedral complexes of copper (II) [and of nickel (II)] may be distorted such that they resemble cis-octahedral complexes much. 2. If R11F5 is monomeric and trigonal-bipyramidal, it is one of the few cases where a System is not a 6-coordinated in a regular octahedron. Is there anything known about its absorption spectrum? 3. General remarks of nomenclature : I agréé that “ligand field theory” is a better name than “ crystal field theory ” but will the two words be used synonymously, or

348

will the “ crystal field theory ” dénoté the electrostatic theory with pure i/-orbitals, which are not intermixed with the orbitals of the ligands? A name does not necessarily hâve the intrinsic significance of its parts; thus, I do not agréé with Voltaire in his criticism of the Holy Roman Empire, which was neither holy, nor roman, nor an empire. Thus the name “ crystal field theory ” does not necessarily imply a connection with crystals.

However, the

exclusive importance of the first co-ordination sphere for the energy levels of transition group complexes suggests much the better name “ ligand field theory The energy différence between the two levels of a J-electron in an octahedral complex is denoted by 10 Dq

10 by Schlapp and Penney, (Ej — E2) by Use and Hartmann, — K by Owen, Q by Williams, and A by Owen and Griffith. The first Symbol seems too complicated, since the factors 10, D and q no longer hâve a clear meaning. (Ei — E2) might be substituted by (E3 — E5) as the energy différence between y3~ and Y5~ électrons. However, it would probably be better to choose a single letter for the quantity, and A is proposed. I hope that we ail agréé in Mulliken’s proposai to use capital letters for the quantum numbers of Systems (atoms, ions, molécules) and small letters for électrons and orbitals. Finally,

it may be discussed, if the Mulliken nomenclature

a\,ü2, e, t\ and ti is to be substituted for the Bethe nomenclature and Ys for orbitals in complexes with the cubic symmetry On- It is the only point where I hesitate to conform with the viewpoint of Dr Orgel, since y» is an useful expression for an arbitrary orbital, and since the majority of ligand field theoreticists

Yb Ï2> Ï3> Ï4

(Van Vleck, Van Santen and van Wieringen, Hellwege, in later papers Hartmann, and the Chemical physicists of Copenhagen) actually utilizes the quantum numbers y^ which reminds an atomic spectroscopist of the angular momentum quantum number 1. However, it can cordially be recommended to refer to both sets of quantum numbers in papers, which are on the border-line to infra-red spectroscopy and general molecular theory. M. Nyholm. — I shall reply to the points raised in turn. 1. As yet ail know of (Cu Dipy2 I) CIO4 is that the Cu“ atom is five covalent in nitrobenzene (unless a PhN02 molécule occupies

349

the sixth position) and that a moment of 2.8. B.M. is observed. According to Prof. D.P. Craig, the large orbital contribution in the latter is not expected in a square, an octohedral or a square pyramidal molécule. It is however expected in a trigonal bipyramidal molécule. Unless we hâve X-ray evidence our suggested structure must be regarded as tentative. 2. Nothing is known of the absorption spectrum of RuFs, at least to my knowledge. 3. One of my reasons for suggesting that we use the term “ ligand field ” instead of “ crystal field ” theory is to overcome the very serions effects that it has on those first looking into the field. There is a great need for the présentation of quantum mechanical ideas to chemists who are unfamiliar with the more mathematical details that any phrases which are likely to give erroneous first impressions are best avoided. I certainly agréé with the need for a generally accepted symbol for the energy séparation between the dz and dy orbitals in a cubic field.

Personnaly I prefer A.

M. D’Or. — Je voudrais demander aux spécialistes du domaine des complexes formés par les métaux de transition si de nouveaux travaux ont été effectués récemment au sujet des interactions entre ions centraux dans les cristaux de complexes paramagnétiques et notamment si l’effet du champ magnétique dû aux ions métalliques se marque par une démultiplication observable du niveau fondamental de ces ions lorsque l’on passe d’une solution solide diluée du complexe avec une substance diamagnétique, au complexe pris à l’état de cristal pur.

M. Orgel. — I am not aware of any recent work on this subject. There is a good deal of work on the interaction of ions in magnetically concentrated solids. In general one gets a broadening rather than a splitting of the paramagnetic résonance absorption, although there are a few cases where bonds are split. These interactions desappear if the paramagnetic ion is diluted by forming a solid solution in a diamagnetic crystal.

350

M. Ubbelohde. Introducing various discussions — “ Stable ” — “ Stability 1. It would be useful if a clear distinction were made between various meanings of the words “ stable ” and “ stability Front the quantitative aspect, “ stability ” could be measured for complex contpounds either in terms of free energy différences, or entropy differenees, or enthalpy différences. Whilst the last of these is probably most directly related to bond problems, a clear statement as to which nteasure is being used would be préférable to the rather vague use of “ stability 2. Crystal field and ligand field. Can contributors agréé whether a clear distinction should be made between the terms ligand field theory and crystal field theory, and if so, what is the distinction? Alternatively, are the two expres­ sions best used interchangeably ? M. Nyholm. — When dealing with complex ions like [Co(NH3)6]+++ or complex molécules like (PtCl2, 2NH3)° where we are concerned only with the field arising from the attached ligands, I prefer the term “ ligand field However I agréé that in those ionic crystals wherein the field arises from interactions throughout the whole crystal (or domain) the term crystal field theory is rightly applicable.

M. Ubbelhode. — In the case of the interlamellar compounds of graphite, the magnetic findings can probably be interpreted in terms of a transfer of électrons between the added molécules and the layers of fused aromatic nuelei. This transfer may take place either way. If graphite is regarded as a crystal with one full électron band separated by zéro energy gap from the next empty band, an approximate représentation is to regard électron donor additives, such as potassium, as transferring électrons to the empty band, whilst acceptor additives, such as bromine, probably abstract élec­ trons from the full band forming positive holes. Either process leads to a marked increase in electrical conductivity, which is what is actually observed. For additives of simple electronic structure, such as bromine or potassium, or other alkali metals, measurements of the changes

351

of electrical properties throw important additional light on the transfer mechanism. Measurements of the Kall effect verify that bromine abstracts électrons and potassium adds électrons to the aromatic macromolecules. However, the transfer is statistical and cannot be regarded as localised at particular groups. From obvions analogies with the Pauling model for metals we hâve termed these quasi-metallic bonds, involving cooperative process extending statistically over many aromatic groups in the crystal. This brings one to a doser examination of the interesting différences described by Prof. Nyholm, relating to complexes of cobalt sulphocyanide in the solid State and in solution. The fact that polymer bonds are observed in the solid, but not in the solutions described, raised the interesting and crucial question as to what would happen in really strong solutions. It must be stressed that two quite different kinds of behaviour can be foreseen, the distinction between which has a bearing on a real discrimination between “ crystal fields ” and “ ligand fields ”. Either : (1)

the strong solutions will show “ polymer bonds ” of the

type —Co—CNS—Co— in which case true ligand field effects can be discussed in terms of what happens around each CNS group independently of next nearest neighbours; Or (2) polymer bonds only develop to any appréciable extent in an ordered cooperative System, i.e. the crystal lattice, case a true cooperative crystal field is required.

in

which

An analogous instance of how the change from the ordered environment in a crystal lattice to the disordered arrangement in a melt or solution affects ligand fields can be found in the behaviour of certain acid hydrates, such as nitric acid monohydrate H2O, HNO3.

In the crystals, infra-red and other studies indicate that

the structure can be described as N03~0H3+ whereas in the melt the molécules are predominantly H2O, and HNO3. Here the order in the crystal lattice ensures a cooperative crystal field of quite high symmetry around each N03~ and OH3+. This permits the ligand stability of OH3+ to be exerted. But on melting the action of neighbours on OH3+ is much less symmetrical and the HNO3 molécule has a higher stability than N03~ under such conditions.

352

M. Nyholm. — We are at présent studying the effect of concen­ tration upon the magnetic behaviour of solutions of —NCS com­ plexes wherein association is possible.

M. Hâgg. — Referring to the thiocyanate group being coordinated to two métal atoms I want to mention that Lindqvist in my laboratory has found that the silver thiocyanate structure contains chains —Ag—SCN—Ag—SCN—.

M. Bjerrum. — To Dr Chatt I should remark that I still consider normal for the silver ion to hâve the characteristic coordination number two and the maximum coordination number four. So far as I know the silver ion exibits these coordination numbers towards ligands as Cl“, SCN~ and CN“, and has very distinctly the coor­ dination number two towards the ligands to which it is bound through oxygen or nitrogen atoms. Only in case of ligands as e.g. phosphines, arsines,etc. giving spécial possibilities of strong rr-bonding, the conditions may be changed. I should also like to emphasize that this applies still more to Au+, Cu+ and Hg++ and that I do not remenber any cases, where these métal ions deviate from having the characteristic coordination number two.

353

Absorption Spectra of Complexes with Unfilled i/-Shells Chr. KLIXBÜLL JÔRGENSEN

The complexes of the transition group metals absorb light in the wavenumber range 8.000 - 40.000 cm“>. The transition group ions are characterized either by having in a shell from one to nine of the ten possible ^/-électrons with the same principal quantum number 3, 4, or 5, or by having from one to thirteen of the fourteen possible 4/- or 5/-electrons (the lanthanides and actinides). The absorption bands of ions with partly filled /-shells are very narrow and their positions do not shift much, when the ligands are changed. These bands are comparable with the spectral Unes of gaseous atoms and ions, and the bands may be identified as transitions from the groundstate to a set of excited levels as predicted by application of quantum mechanics to /"-électron configurations (19-25-28-32-41-45-54-6768-72-73-75-78-122-130-131-138-143-144).

The situation is markedly different for

i"-systems, which will

6

be the main subject of this paper. It is known that cobalt (III) or nickel (II) form complexes of green, blue, purple, red, and yellow colours. But when the absorption spectra are measured, they are seen to consist of a low number of absorption bands, 2-3 in the case of cobalt (III) and 4 in the case of nickel (II), which are shifted when the ligands are changed. The spectra are determined almost unequivocally by the first co-ordination sphere, i.e. the nearest environ­ ment of atoms from the ligands, which « touch » the central métal ion. Tsuchida (i"*») has arranged the ligands in a spectrochemical sériés according to their shifting efîect on the spectra. This sériés is the same regardless of the central ion, and the order of ligands is

355

roughly determined by the ligand atom nearest to the central ion : Br
0.01

to

200)

which are caused by internai transitions

between the levels of the ^/''-configurations. Bethe (**) elaborated a theory of the action of crystal fields on a partly filled shell in an ion. Since the perturbations in question decrease so rapidly with the dist­ ance from the central ion, the immédiate environment, i.e. the first co-ordination sphere is sufficient, also in solution, to maintain similar electrostatic fields as in the lattice of a crystal. It is interesting that the central ions in most transition group complexes are surrounded by ligands, arranged in regular or distorted octahedrons. Since the number and relative positions of the levels of an électron config­ uration are determined by the symmetry of the crystal field, most éI"-complexes are much more similar in behaviour than expected. However, the crystal field in /"-complexes can hâve much lower symmetry.

356

Even though Finkelstein and Van Vleck(38) applied Bethe’s theory to the spin-forbidden absorption bands of chromium (III), e.g. in the ruby, and Abragam and Pryce (i) discussed cobalt (II) spectra, most applications before 1951 of the crystal field theory was made to magnetochemical problems (66-i27-i32-i49-i50-iS2)_ Then, Use and Hartmann (<52) interpreted the weak band of titanium (III) hexaaquo ions as caused by the transition between the levels formed by splitting of the 2D-level of the free ion. In the following five years, a very large number of publications hâve appeared on the interprétation of absorption spectra. Table III is a review arranged according to the number of i/-electrons in the complex. In the following, the quantum numbers of a single électron (1, Y„, ...) will be denoted by small letters and of a System (an atom, an ion or a molécule) by capital letters (L, S, F„, ...). Bethe (i») found for crystal fields of symmetry O* (found in regularly octahedral complexes) that five types of levels are possible: Fj, F2, F3, F4, and Fs, which are 1, 1, 2, 3, 3 times orbitally degenerate respectively. They are denoted by Aj, A2, E, Tj, and T2 by Mulliken (IO6). In atoms with Russell-Saunders coupling (28) the multiplet terms can be described by the électron configuration and the two quantum numbers S and L (representing the total spin and the total angular momentum). The analogous description for an ion in a crystal field is : électron configuration. S, F„. Bethe (I8) found the possible levels F„ originating from a term with a given L in the free ion (or of Ym from a given 1) e.g. for O* :

L

Spectroscopic notation

Bethe’s quantum numbers

0

S

r,

1

P

F4

2

D

T3 + Fs

3

F

F2 + F4 + Fs

4

G

Tl + F3 + F4 + Fs

5

H

F3 +

F4 + Fs

2

Thus, a ^/-electron (1=2) has two possible energy levels, Y3 and ys, of which the former has the higher energy, when the six ligands are

357

negatively charged or polarized by the positive central ion.

(Geo-

metrically, this can be visualized by y3-electrons being concentrated in space near the six ligands, while ys-electrons hâve lower potential energy in the eight directions between the ligands). The energy différence is denoted by (Ei — E2) or 10 Dq. In Systems with more than one r/-electron, the levels F„ can either be described by sub-shell configurations or by the original term L in the free ion. If g of these levels hâve the same S and F„ (denoted by 2s+ir„) their energy can be given as the eigen-values of a matrix of ^’th degree. The non-diagonal éléments of this matrix can either contain multipla of (El — E2) (cf. 38-111) or term différences, e.g. expressed in SlaterCondon-Shortley or Racah parameters (cf. 9-109-146). it is proposed to name the two types of matrices weak-field-diagonal and strongfield-diagonal matrices according to the asymptotes represented by the diagonal éléments. The final results of the two types of calculation are of course équivalent, but the concepts “ weak ” and “ strong ” crystal field hâve been much applied in literature for the approxima­ tion introduced by using the diagonal éléments of the appropriate matrices only. If the term différences are not changed from their free ion values, and if other électron configurations are not intermixed, the energy levels in O* will vary as a fonction of one crystal field strength (Ei — E2) only.

More parameters are necessary in crystal

fields of lower symmetry. Tanabe and Sugano (*^9) completed the electrostatic calculations on ^/''-Systems in O* by giving the full strong-field-diagonal matrices. In Table I are given the diagonal éléments of energy for the lowest levels to which transitions from the groundstate can be observed as absorption bands. The levels are arranged in groups with identical sub-shell configuration and hence with equal values of the coefficient a in the energy expression a (Ei — E2) + hB -f cC. In the cases, where for small values of (Ej — E2) the connection of a level with a given value of L is obvious, the term is given in parenthesis after the appropriate level, viz. ^F2(F). The Racah parameters B (= F2 — 5F4 after Slater, Condon, Shortley) and C (= 35F4) describe the energy différences between the terms in the free ion, and Table II gives a représentative set of terms for some Systems. The ratio F2/F4 is at least 9 and is for hydrogen-like 3^/-wave fonctions 14, corresponding to C/B = 8.75 and 3.89, respectively. Generally, C/B is assumed to vary between 5 and 4.

358

As pointed out by van Santen and van Wieringen (129) d^- and Ji.systems can exhibit different groundstates with differing

TABLE I The energy of the lowest ys^ysb levels in octahedral complexes expressed in the Racah parameters B and C of electrostatic interaction between rf-electrons] and the crystal field strength (Ei — E2). The corresponding Slater-Condon-Shortley parameters (^8) are B = F2 — 5 F4 and C = 35 F4. The energy différence between the actual level and the groundstate in the gaseous ion is given. The non-diagonal éléments between levels with the same Fn of different sub-shell configurations are not considered. The table can be implied from the results of Tanabe and Sugano (i46)^ but the content has earlier partly been discussed by many authors (9-i8-38-42-47-7i-74-i09-iu-ii6).

Electron configuration

d2

Sub-shell configuration

Level

o(Ei

Ys Y3

2F5 (D) 2F3 (D)



Y52

3F4 iFa 'Fs iF, 3Fs 3F4

(F) (D) (D) (G) (F) (P)



Y3^

3f/(F)

Y5^

-h

6B

“h

C

C

0 0

0.8 0.8 0.8 — 0.8 -h 0.2 -h 0.2

+ 3 + 9 + 9 + 18 0 + 12

-h

1.2

0

IF2 (F) 2F3 2F4 2F5 “Fs (F) 4F4 (F)





1.2 1.2 1.2 1.2 0.2 0.2

0 + 9 + 9 + 15 0 + 12

4F4‘(P)

+

0.8

-h

3

0

3F4



1.6

+

6

-h 5

Y5^Y3

SFs'CD)



0.6

0

0

Ys^Ys^

SFs'cD)

-h 0.4

0

0

è

Ys^Ys YsYs^

d*

E2)

0.4 + 0.6

Y5Y3

di



y54

— -

— — — —

0 0

0

+ 2 + 2 -f 5 0 0 0

0

H" 3 -h 3 + 5 0 0

359

TABLE I (continued)

Electron configuration

Sub-shell configuration

Level

ds

a(Ei —E2)

+6B

+ cC

+ 15 + 10

+ +

+ 18

+

Y5‘‘Y3

(G) 'Ts (G)

— 2.0 — I.O — 1.0

Ts^Ys^

«ri'(S) -Tl (G) 4T3 (G) 4P5 (D) -Tj (D) 4P4 (P) (F)

0.0 0.0 0.0 0.0 0.0 0.0 0.0

+ 10 + 10 + 13 + 17 + 19

+ + + + +

+

22

+

7

Yj2y33

10

6 6 0

0

5 5 5 5 7

4r4'(F) 4F5 (F)

+ +

1.0 1.0

+ 10 + 18

+ +

6 6

2.4 1.4 1.4 1.4 1.4 0.4

+ 5 + 5 + 13 + 5 + 21

+ + + + +

8

0

0

0

0

• d6

di



Y56

'r,

Y5^Y3

3F4 3F5 T4

Yj4y32

sFs (D)

— — — — — —

Y5^Y3^

=r3'(D)

+ 0.6

Y5«Y3 Y5^Y3^

2F3 4F4 (F)

— —

Ys'*Y33

“Fs’CF) 4F4 (P)

+ 0.2 + 0.2

Y5^Y3''

^r2'(F)

+ 1.2

Y5*Y3^

3F2 iF3 'Fl 3F5 3F4 iFs ‘F4 3F4

— — — — — — —

Y5^Y33

Y5‘*Y3‘‘

irs

(F) (D) (G) (F) (F) (D) (G) (P)

1.8 0.8

1.2 1.2 1.2 0.2 0.2 0.2 0.2 + 0.8

+ +

7

+

5 5 7 7

4

3

0

0

+ 12

0 0

0

0

0

+ 8 + 16

0

+ +

S values (which déterminés the magnetic properties).

4 0 0

0 + 12

+ 8 + 12 + 3

2

+ +

2 2 0

This can be

explained from the purely electrostatic crystal field theory (even

360

though covalency, i.e. intermixing of molecular orbitals, may be actually important) by the compétition between the levels : :

TjCÜ) and

r/5 :

6ri(S)

r/6 : r/7 :

5r5(D)

and

and Ti 4r4(F) and 2rj

It is seen from Table I that for increasing values of the crystal field strength (Ei — E2), the magnetically anomalous States with lower

TABLE II Energy levels in the free gaseous ions, expressed in Racah’s parameters B and C of electrostatic interaction between r/-electrons. The energy is given with the groundstate as zéro-point. In multiplet terms with several levels with varions J. the energy refers to the centre of gravity (21). In actual cases, 4 B ('4i).

00

III

di = d^

r/5

3F

0

iD

5 B + 2c

3p

15 B

IG

12B -f 2C

IS

22 B + 7 C

4F

0

2G

4B + 3 C

4P

15 B

2P

9B

-h

3 C

2H

9B

-h

3 C

6S

0 -h

5 C

4G 4P

10 B

7 B -h 7 C

4D

17 B

4F

22 B + 7 C

-f

5 C

361

362

TABLE III Absorption Bands of Transition Group Complexes with one to nine rf-electrons. In each group with the same number of rf-electrons, the ions are arranged according to increasing atomic number.

Electron configuration

The ox— glyata“3 enta""*

following abbreviations will be used for the ligands : = oxalate en = ethylenediamine = aminoacetate temeen = C, C, C’, C’ tetramethyl-ethylenediamine = nitrogentriacetate tren = P, (3’, p” tris(ethylamino) amine = ethylenediaminetetraacetate py = pyridine

Ion

3 rfi

Titanium (III)

3 rfi

Vanadium (IV)

3rfi 4 t/l

Manganèse (VI) Niobium (IV)

4 t/l 4 t/l 3 t/2

Molybdenum (V) Ruthénium (VI) Vanadium (III)

41/2 4 t/2 5 t/2 3 t/3

Niobium (III) Ruthénium (VI) Wolfram (IV) Vanadium (II)

Ligands

6H2O enta“‘i 3 SCN- 3 H2O? 2 OH-, XH2O enta-'i, O ( ?) 2 ox—, 0— (?) SCN-, 0— 4 Cl4 0— ?, 13 MHCl ?, 8 MHCl 0—, 5 Cl4 0— 6 H2O 3 ox enta-4 5 H2O, OH6 SCN?, 10 MHCl 4 0— ? .12 MHCl 6 H2O

Wavenumbers of maxima and assignment of excited level

20300 2E3(D) 18400 18900 13100, (15800) 12800, 17200 12600, 16200 13900, 17200 9000 électron transfer bands 20900 14300 14000 tetragonal splitting of cubic 2rj(D) électron transfer bands 17700 3rs(F), 25600 3r4(P) 16500 îEsfF), 23500 3E4(P) < 8000?, 12500, 19400, 22600 second band at 23200 very high 16700 srjfF) 15400, 18900, 22500 électron transfer bands 19100 (e ~ 600) 12600 4F5(F), 18200 4F4(F), 26500 4E4(P)

dip = a, a’-dipyridyl phen = o-phenanthroline

Remarks

Référencés

rhombic splitting

49, 62, 77 82

not octahedral unknown structure » » tetrahedral »

39, 125 82 51 39

88

tetrahedral

peculiar

cf. Ventatetrahedral électron transfer?

111

30 30 30 58, 59 29 47, 48, 109 51 82 39 39 30 29 88, 108 9, 71, 89, 110, 111, 116

3 d3

Chromium (III)

6 H2O

17400 '*rs(F), 24700 ‘*r4(F), 37000 *r4(P)

(ruby) 3 en 3 ox various ligands 60 (heteropolymolybdate) 6 F?, 10 MHCI 6C16 F-, 5 FCl-(W2Cl9-3) 6C16 Br6 H2O 5 SCN-? 6 H2O 3 ox 6CN-

15000 2ra, 15500 18500 *F4(F), 22000 21900 ‘*rs(F), 28600 *r4(F) 14350 2F3, 17400 ‘T5(F), 24000 *r4(F) very large number of spectra interpreted

60

3 4rf3

Manganèse (IV)

5rf3 5 rf3

Niobium (III) Molybdenum (III) Ruthénium (V) Wolfram (III) Rhénium (IV)

3 d4

Chromium (II)

3

Manganèse (III)

4di 4di

4d*

5 3
Ruthénium (IV) Rhodium (V) Rhénium (III) Manganèse (II)

7 7

4 Cl6 H2O 2 Cl-, 4 H2O enta-'*

3 rfs

Iron (III)

3 rfs 3rf5

Ruthénium (III) Iridium (IV)

3 3

Manganèse (I) Iron (II)

3 en 6 H2O xCl6CN6 Cl-? 6C16 Br6CN6 H2O

363

enta-'* 6CN-

24400 'T4(F)

14300 2F3, 21400 '*rj(F) 13200, 14200, 15200, 16700 2F3, 2F4 13700 (?) 2F3, 22700'*r5(F) 14800 2F3, 19200 “PslF), 24200 '*F4(F) predicted from colour : 16000 2F3 13200 (e ~ 25) 2F3, 16300 (e ~ 40) 2F4, 22200 (e ~ 1200) 14200 2F3, 15700 2F4, électron transfer vibrational structure 13200 2F3, 15100 2F4, électron transfer bands 13900 sFsfD) 16500 SFsfD) 21000 SFsfD) 10300 3F, 20100 SFjfD) 21000, électron transfer bands groundstate 2F5 mainly électron transfer bands électron transfer bands 19600 the band can split 18800 *F4(G), 23000 '*F5(G), 24900 *F3(G), 25150 *F,(G), 28000 '*F,(D), 29700 -*F3(D), 32400 *F4(P), 35400 '*F2(F), 36900 *F4(F), 40600 ‘‘FjfF) 19300 *F4(G), 23400 *F5(G), 24600 '*F3(G) and '*Fi(G), 27600 '*Fs(D), 29200 *F3(D), 31600 *F4(P), 18800 ‘*F4(G), 21300 ^FsfG), 23800 *F3(G), 24300 *Fi(G), 27200 “FsfD), 29200 ^Fj (D) 15900 '*F4(G), 20500 ^FsfG), 23800 *F3(G) and *F, (G) 12600 *F4(G), 18500 *F5(G), 24300 and 24600 *Fi and ‘T3(G), électron transfer bands six électron transfer bands groundstate 3F5 19200, four électron transfer bands » électron transfer bands at 17400, 20450, 23200, 24200 » électron transfer bands at 13600, 14300, 14800, 17200, 18400, 19600 » from colour : > 25000 groundstate *Fi 10400 5F3(D), 14400 ?, 19800, 21100, 22200,25900 ail 3F 9700 5F3(D) 31000 'F4, 37000 ? 1F5 groundstate *Fi

9, 53, 74, 109, 111, 137 38, 137 74, 137 51, 71, 104, 137 53, 97, 137 140 88, 137

30 27, 51 57, 93 88, 94 79, 102, 126 79, 126 71, 89, 146 3, 88 48 88

128 153, 154 4, 5, 44 15 40, 71, 80, 89. 111, 113 114,134 88, 134 88 88

71, 111, 121 121, 133 84 26, 84, 154 84 84 99, 147 71 82 88

OJ O 4^ Electron configuration

TA BLE III ( continued)

3 rfs

Ion

Cobalt (III)

Wavenumbers of maxima and assignment of excited level

Ligands

6 F6 H2O

3 ox 3 CO3-6 NH3 3 en 6 CNvarious ligands

3 rfô

Nickel (IV) Ruthénium (II) Rhodium (III)

6 F-

7

6 Br6C16 H2O

3 5 5 5

4(^6 5 r/6

Palladium (IV) Iridium (III)

ox“ NH3, ClNH3, OHNH3, H2O 6NH3 3 en trans-2ox , cis - 2 ox , trans-2 py, cis - 2py, trans-4py, 6 F6 Br6 Cl5 NH3, Cl-

2 Cl“ 2 Cl“ 4 Cl~ 4 Cl“ 2 Cl~

Remarks

predicted from colour : 18000 6F3(D) groundstate 3F5(0) 16600 1F4, 24900 1F5 ail other cobalt (III) hâve 'Fi 16500 1F4, 23800 1F5 15700 1F4, 22800 ’F; 13000 3F4, 21000 IF4, 29500 1F5 13700 3F4, 21400 1F4, 29600 'F5 32200 1F4, 38600 1F5 a large number of absorption spectra interpreted

predicted from colour ; 200(X) 1F4, 28000 1F5 strong bands tetragonal groundstate 3F? 18100 1F4, 22200 1F5 Ail groundstate 'Fj 14700 3F4, 19300 1F4, 24300 1F5 25500 1F4, 32800 1F5 19200 3F4, 25100 1F4, 30000 ? 1F5 28700 1F4, 36100 1F5 31200 1F4, 36000 1F5 31600 1F4, 38100 1F5 32700 'F4, 39100 1F5 33200 1F4, 39600 1F5 21300, 25100 tetragonal splitting of >F4 23000 IF4, 28400 1F5 20000, 23200 tetragonal splitting of IF4 22400 1F4, 28700 1F5 24300 predicted : 26000 and 32000 16800 3F4, 22400 1F4, 25800 1F5 Ail groundstate IF1 16300, 17900 3F4, 24100 1F4, 28100 1F5 27800 3F4, 35000 1F4

References

71, 93 3, 137 104 82, 137 82, 109, 146 81, 82, 109, 146 92 9, 13, 14, 16, 50, 64, 82, 96, 97, 101, 104, 109, 111, ,137, 146 148, 158 93 84 83 83 83 83 83 83 83 83 83, 95 ^6 86 86 86 86

93 83 83 83

3 en

py, 5 Cl-

5d6

3

d^

3d»

33100 3F4, 40200 1F4 18500 3F4 19400 3F4 21600 3F4 complexes prepared by M. Delépine 19100 3F4, 23000 ? tr4, électron transfer bands 22100 3F4, 28300 1F4, 38200 (e ~ 25000 électron transfer) 31500, 36400 ir4 and iPj ? 35000 3F4 ? 30000 3F ?. 38000 IF ?

365

Cobalt (II)

trans-2py, 4 Cl cis - 2 py, 4 Clvarions ligands 6Br6 Cl6 F5 NH3, Cltrans-2 en, 2 Clvarious amines NH2-, Cl-, OH6 H2O

Nickel (II)

enta”"* 6NH3 3 en 4C16 H2O

9100 'tFj(F), 16300 4F2(F), 19900, 20600, 21500 ‘»F4(P) 9000 4F5(F), 18500 4F2(F),21100 4F4(P) 9800 “FslF), 18700 '*F2(F), 21700 4F4(P) 6300 '‘F4(F), 14300-16400 4F4(P), many 2F tetrahedral 8500 3F5(F), 13500 3F4(F), 15400 1F3(D), 18400 iF, 22000 iF, 25300 3F4(P)

3 gly6NH3 3 en

10100 3Fs(F), 13100 iF3(D), 16600 3F4(F), 27600 3F4(P) 10750 3Fs(F), 13150 iFjfD), 17500 3F4(F), 28200 3F4(P) 11200 3Fs(F), 12400 'FjfD), 18350 3F4(F), 24000 iF, 29000 3F4(P)

3 dip 3 phen enta”'* enta-“t, NH3 ata“3 2 ata-3 ata-3, en tren, 2 H2O tren, 2 NH3 tren, en tren, gly“ en, 2 gly2 en, glyen, 4 H2O 2 en, 2 H2O

11500 iFjfD), 12650 3Fs(F), 11550 iFjlD), 12700 3Fs(F), 10100 3Fs(F), 12700 iFjfD), 10200 3Fs(F), 12700 iFjID), 9500 3F;(F), 13300 iFjfD), 10400 3Fs(F), 13000 iFj(D), 9400 3Fs(F), 13100 iFsfD), 10500 3F;(F), 12800 iFjfD), 11000 3Fs(F), 12750 iFjID), 11000 3Fs(F), 12500 ‘FjfD), 11200 3Fs(F), 12600 iFjfD), 10500 3Fs(F), 13000 iFjID), 10800 3Fs(F), 12650 ‘FjfD), 10200 3F5(F), 13600 iFjfD), 10000, 11100 3Fj (F), 17500,

Platinum (IV)

partly électron transfer in anion complexes 8100 ‘*F5(F), 11300 2F3, 16000 4F2(F), 19400 and 21550 ‘>F4(P)

19200 3F4(F) 19300 3F4(F) 17000 3F4(F), 17200 3F4(F), 16000 3F4(F), 17400 3F4(F), 16900 3F4(F), 17800 3F4(F), 18200 3F4(F), 18700 3F4(F), 18800 3F4(F), 17300 3F4(F), 17900 3F4(F), 15600 3F4(F), 18200 3F4(F),

26200 26900 25600 27000 27200 27800 28200 29000 28200 28100 28600 27000 29400

3F4(P) 3F4(P) 3F4(P) and 28600 3F4(P) 3F4(P) 3F4(P) 3F4(P) 3F4(P) 3F4(P) 3F4(P) 3F4(P) 3F4(P) 3F4(P)

83 86 86 86 86

84 84 156 84 12

46, 84 46, 84 1, 10, 70 71, 111, 146 82 10 10

10, 33, 91, 111 8, 20, 24, 33, 40 43,52, 70,71,74, 77, 80, 82, 85, 109, 111, 116 124, 127, 146, 82 20, 82, 111, 124 8, 70, 74 82, 111, 124 82 82, 124 82 85, 135 85 85 85 85 85 85 85 85 85 8,85

8

Electron configuration

366

TABLE III (continued)

Ion

3 t/8

Copper (III)

4£/8

Palladium (II)

5rf8

Platinum (II)

Copper (II)

Ad9

Silver (II)

Ligands

2 temeen 6 F2 JOft-s

Wavenumbers of maxima and assignment of excited level

23100 pale green électron transfer absorption 23800

4 CI21000 6 CI26300 6 H2O 16600 3E, 19900 3E, 24300 T 4 Br17700 3L, 21000 3T, 25600 lE, 30300 *r 4 CI4 NH3 35400 35800 2 en very strong bands : 35700, 38700, 39200, 41300 4 CN(9400), 12600 6 H2O 16900 4 NH3, 2 H2O (11700), 15100 6NH3 18200 2 en, 2 H2O (11800), 16400 3 en 10500, 13900 2 dip, 2 H2O 14700 3 dip 10200, 13300 2 phen, 2 H2O 14700 3 phen (9600), 11600, (14700) tren, 2 H2O (11100), 12700, (15400) tren, I or 2 NH3 18300 2 temeen 13600 enta”'* 13800 enta-'*, NH3 11400, 12900 ata-8 15200 2 ata-3 acetylacetonates with varions solvaté ligands 15800 2 gly ~ 15100 3 gly 2 dip ) > 25000, électron transfer 4 py j

Remarks

groundstate iPti » » » » » » » » » »

References

8,9,15,52,87,109 93 98 145, 159 145 145 6, 87 6, 87, 159, 160 6, 87 87 87, 95 7, 22, 111 7, 22 7, 22 21, 22 21, 22 23, 82 23, 82 23, 82 23, 82 85 85 85 82 85, 135 85 85 17 82 82 87, 111

values of S will eventually be the groundstates, because the promotion energy èB + cC does not increase, but rather decreases relative to the values for the free ion. From the absorption spectra in Table III and the theoretical prédictions in Table I, values of (Ej — E2) which are given in Table IV can be inferred.

It is seen from Table IV that Tsuchida’s spectro-

chemical sériés can be quantitatively treated, the position being determined by the ratios between the values of (Ej — E2) for the considered TABLE IV Values of the crystal field strength (Ei — E2), also denoted 10 Dq, in octahedral complexes, estimated from absorption spectra. In cases of strong intrinsic tetragonality, viz. in - and d9 - Systems, the value of (Ei — E2) has not been corrected for tetragonal contributions, demonstrating the anomalous conditions. Literature : 24-47-48-71-74-82-83-84-109-lll-U6-I46. 6 Br-

6 Cl-

6 H2O

6 NH3

3 en

6 CN-

Titanium (III)





20300







Vanadium (III)





18600







Vanadium (II)





12600







Chromium (III)



13300

17400

21600

21900

26300

4di

Molybdenum (III)



19200









3rf4

Chromium (II)





13900







Manganèse (III)





21000







Manganèse (II)





7800



9100



Iron (III)





13700







Iron (II)





10400





33000

Cobalt (III)





19100

23500

24000

34100

3rfi

3rf3

ids

3d6

4d6

Rhodium (III)

19300

20800

27700

34600

35300



5d6

Iridium(III)

23400

25300





41800



Platinum (IV)

25000

30000









^d?

Cobalt (11)





9700

10500

11300



3rf8

Nickel (II)

6000

6500

8500

10800

11600



3rf9

Copper (II)





12600

15100

16400



.

367

complex and for the hexaaquo ion. Thus, for a given central ion, the value of this ratio is for the hexabromo complex 71 %, and for the hexachloro complex 76 % of the value found for the hexaaquo ion. The corresponding ratios for the ammine complexes are 125130 %, and for the hexacyanide complex, it varies between 150-300 %. Excepting the irregular cyanide complexes, the values of (Ej — E2) are generally 40-80 % higher for a trivalent ion then for the isoelectronic divalent ion. A quadrivalent ion has an even higher crystal field strength. For the same oxidation State, the values of (Ei — E2) do not vary very much within a given transition group, except when the tetragonality effect discussed below is significant. For different transition groups (3<7, Ad, 5d) the values of (Ej — E2) increase general­ ly in the ratio 1 : 1.54 : 1.90. The decrease of Racah parameters B and C in the later transition groups amplifies the tendency towards magnetic anomaly exhibited by the complexes of the platinum metals. Several Chemical conclusions can be drawn from the crystal field theory. Already Orgel pointed out that ~ 5 % of the absolute beat of formation of hexaaquo ions in £i"-systems (n =|= 0, 5, 10) can be ascribed to the energy decrease of the groundstate (see Table I). Crystal field stabilizations hâve later been studied (23-42-76-85-137), The chelate effect on formation constants, which can mainly be ascribed to changes of entropy (2-63-85-120-136) is also caused by crystal field stabilization of complexes with partly filled cf-shells (21-85-120). However, in the following only four problems of general interest to the future development of the theory of the transition group complexes will be discussed. I. DEVIATIONS FROM THE HOLOEDRIC OCTAHEDRAL SYMMETRY Van Vleck (152) emphasized that the Jahn-Teller effect implies that ail groundstates shall be only once orbitally degenerate. Thus, only Fl and F2 can exhibit regular octahedral symmetry, while Fs must be distorted to tetragonal and F4 and F5 to rhombic or tetragonal symmetry. Thus, only the Systems without crystal field stabiliz­ ation (JO, J5 6Fi, JiO) and a few others (d^, JO iTj, and d^) will retain regularly octahedral configuration.

368

The latter class of com­

plexes are remarkable by forming robust complexes (i.e. with high activation energy) when (Ei — E2) is sufficiently large (23-76). On the other hand, characteristic co-ordination numbers below 6 occur only in the non-regular Systems (20). The tendency of tetragonal symmetry is especially pronounced in the cases of d‘^- and d^- Sys­ tems. The absorption spectra in Table III indicate excessively large wavenumbers for these complexes. Table III also demonstrates the “ pentamine efîect ” (20-22)^ the fact that mixed complexes with strong crystal field from four planar bound ligands will hâve spectra with higher wavenumbers than the complexes with six ligands with equally late position in the spectrochemical sériés. The latter effect can be explained as a systematical dépréssion of the groundstate with unsymmetrical substitution of ligands. In the first transition group, the values of (Ei — E2) in the divalent hexaaquo ions decrease regularly from 12 600 cm-i for vanadium (II) to 8 500 cm-i for nickel (II), except for chromium (II) which seems to give some 2 000 cm“i higher values than thus expected (and it is just a t/^.system). Then, in copper (II) the high value 12 600 cm-i appears. The cubic contribution (^) in the latter case is probably rather near to that of nickel (II), and the author (82) has proposed to use as a measure of tetragonality the wavenumber ratio V(-y/Vf^j. Table V therefore demonstrates that this ratio is highly varying for different types of complexes. In the case of strong tetragonality (vc^/vj.,; ~ 1.7), the condition, strongly bound nitrogen atoms in the tetragonal plane, is satisfied. When ail six atoms in the first co-ordination sphere of copper (II) are equal, moderate values of the tetragonality (~ 1.45) are obtained. Similar results are produced by several amino-acids (see Table V), which for steric reasons cannot be bound exclusively in the plane. Finally, some amine complexes are nearly cubic {'^cuhm — l-l)- In case of aliphatic amines, such as tren = [3, (3', p"-tris (ethylamino) amine, steric hindrance nécessitâtes the formation of cis-octahedral com­ plexes. More peculiar is the behaviour of bis- and tris-complexes of heterocyclic diamines such as a, a'-dipyridyl and o-phenanthroline. From the absorption spectra of Cu dip2(H20)2++ and Cu phen2 (H20)2++, it can be concluded that the trans-isomer is nearly absent. The opposite is the case by Cu en2(H20)2++. This behaviour seems to be dépendent on the ionic radius, since the complexes of silver (II) : Ag py4++ and Ag dip2++ are distinctly planar, just as Cu py4++.

369

TABLE V between Relative tetragonality of copper (II) complexes from the ratio the wavenumbers of the principal band in copper (II) and nickel (II) complexes with equal set of ligands, i.e. the apparent values of (Ei — E2). Literature : 82,85.

Low tetragonality

Medium tetragonality

Strong tetragonality

tren, 2 H2O

1.08

6H2O

1.48

4 NH3, 2H2O

1.7

tren, 2 NH3

I.ll

6 NH3

1.45

2en, 2H2O

1.72

2 dip, 2 H2O

1.1

3 en

1.46

2 gly-, 2 H2O

1.60

3 dip

1.21

3 gly“

1.5

2 acetylacetonate 2.06

2 phen, 2 H2O 1.15

enta”**, H2O

1.36

3 phen

enta-4, NH3

1.35

ata~3

1.29

2 ata“3

1.46

1.21

Diamagnetism (groundstate iP,,) is shown by nickel (II) complexes with very strong crystal fields of tetragonal symmetry (8-9-15-52 109-112-118). it is évident that particularly weak bonding on the axis perpendicular to the plane is a necessary condition. [Ni en2]

[Ag Br J]2

and Ni

temeen2++

The solid

are diamagnetic,

while

Ni en2(H20)2++ and Ni phen2(H20)2++ are paramagnetic, according to the absorption spectra. However, intermixing with the orbitals of the hgands seems to be important, since the Schifî’base-anions with two nitrogen and two oxygen atoms in the tetragonal plane would not be expected to be situated very lately in the spectrochemical sériés. However, six equal ligands can actually form diamagnetic t/*-complexes, which must be assumed to be tetragonally distorted as copper (II) complexes. Thus, Ni(CN)4— takes one (and presumably two) CN~ up in strong cyanide solutions. These complexes, and Pd Cls------- , and the solids K3CU Fg and Pt tren J2 are ail dia­ magnetic. Another resuit of tetragonal distortion in octahedral complexes is increased acidity. The causes of increased acid strength of a complex are often very complicated. Thus, the intermixing of molecular orbitals seems to enhance acidity of strongly oxidizing métal

370

ions.

It is also évident that d^- and t/^-systems are intei alia more

acidic than other complexes. Copper (II) and manganèse (III) hexaaquo ions are e.g. much stronger acids than the neighbour ions and recently (35) ethylenediamine in the d^- System Os en3+4 was found to be an acid with pK< 0 and pK = 8.2. Corresponding values are pK = 5.5 and 9.2 for Pt en3+^. It is further known (26) that the t/^.system ruthénium (IV) has a much higher tendency of forming hydroxo complexes than the c/6.system platinum (IV). Besides the intrinsic tetragonality, mixed ligands of highly different position in the spectrochemical sériés may produce tetragonal splitting of the levels in i/3-and diamagnetic J6-systems. These effects will not be discussed here [Table III gives some examples for rhodium (III)], they are generally smaller than expected and often deviate from the prédic­ tions based on the electrostatic crystal field models (i-7-8-9-13-16-17 18-22-51-52-53-62-82-86-96-97-101-109-111-116-137-148-158). Another déviation from the symmetry Oh is the démolition of the centre of inversion, whereby crystal fields of hemiedric instead of holoedric symmetry are created. Complexes without a centre of inversion e.g. cis-MA4B2 and tetrahedral MA4, hâve often somewhat higher absorption bands than complexes with a centre of inversion, e.g. MAg or trans-MA4B2 (16-77-137). it is rather surprising that the différences in band intensities are not even larger. In a gaseous ion or in a System with a centre of inversion, the parity Q of a level is a strictly defined quantum number, even or odd [usually denoted by subscripts g (= gerade) and u (= ungerade)]. While électron configurations with different parities q of the single électrons may freely intermix, it is necessary that the sum Q is either odd or even for ail interacting configurations. Laporte’s rule States that transitions as electric dipole radiation are only possible between levels with opposite Q. Since the observed absorption bands are too strong to be due to other types of radiation, e.g. magnetic dipole or electric quadrupole radiation, it is not easily explained why internai 6?”-transitions (where ail levels are even, since 1 = 2 is even) can be observed at ail. Actually, the oscillator strengths P are only lQ-5 to 10“3 for spin-allowed (/"-transitions, while the corresponding values for électron transfer bands where one of the électrons is odd or for the 5/"->-5/°“i 6d bands in the actinides are 10~i to 1. The intermixing of about 10“4 odd States to the even (/"-levels has been ascribed either to static hemiedry or to coupling with vibrations

371

(11-16-25-62-77-146-151). jhc former type of explanation nécessitâtes to assume the intermixing of odd molecular orbitals into the groundstate, decreasing the energy slightly according to the principle of variation.

IL

THE PHYSICAL SIGNIFICANCE OF (Ej — E2) The absorption spectra can be interpreted by use of the parameter (El — E2), which varies in a regular way among the complexes (Table IV). It is possible to explain the energy différence between the y3- and ys-orbitals by different models, the most prominent of which hâve been the molecular orbital theory and the electrostatic crystal field model with pure ^/-orbitals. At the moment, there seems to be no possibility of predicting the value of (Ei — E2) within a few hundred %, except from the empirical regularities of Table IV.

Already van Vleck (i50) pointed out that the molecular orbital theory and the crystal field theory both lead to a considérable energy différence (Ei — E2) between the Y3- and Ys'Orbitals. The former theory considers the intermixing of orbitals with identical y« and parity q. Thus, in octahedral complexes, the u-bonding orbitals from the ligands (even yi. odd Y4 and even Y3) intermix with 45, 4/7 and M, respectively, when the first transition group is considered. It is interesting to note that 50 % intermixing in each of the three pairs of orbitals corresponds exactly to the Pauling d'^sp^-hyhviàïzaXion (117-118). Thus, the molecular orbital theory affords the possibility to describe any case between the pure d "-Systems in the electrostatical model and Pauling’s type of covalency by choice of three independent parameters. This development can continue beyond 50 % intermixing, corresponding to électron transfer from the central ion to the ligands. This probably occurs in some cases of rr-bonding. Many authors hâve used this intermixing of molecular orbitals to explain a part of the energy différence (Ej — E2) (i7-42-50-ii2-ii6-i55) or even the whole of it, neglecting the electrostatic contribution It can be questioned if the molecular orbital theory is very adéquate for the transition group complexes without a study of interaction of configurations for each level. Slater (142) and Mc Weeny (lo^) emphasized that configuration interaction is very important in sys-

372

tems with a positive value of S (e.g. O2), especially in cases with larger nuclear distances.

These are just the conditions, prevailing

in most transition group complexes.

Several Chemical physicists

interested in the groundstate of simple molécules, apply one molecular orbital configuration with only one singlet State, while mostly contains more levels, as seen from Table 1. The energy dépréssions from other configurations are e.g. in the range 0 — 37.000 cm~i in the simple molécule HCN (6I). Actually, the déviations of absorp­ tion bands from the crystal field theory prédictions are usually less than 2.000 cm-i, and the spectra would be totally irrecognizable, if displacements as large as 20.000 cm“i often occurred. This agreement with single configuration treatment may be ascribed to some tendency of depressing ail the levels of a complex by nearly the same amount. In the next section it will be discussed, if the déviations can be ascribed to varying values of the Racah parameters B and C of electrostatic interaction between ^f-electrons, the crystal field theory thus being rescued. It would be interesting to see experimental evidence for the intermixing of t/-electrons with the ligand’s orbitals. Curiously, the clearest fact applies to rr-bonding in IrCls— and IrBrg rather than to any case of o-bonding, namely that the yselectrons in these ions are situated ~ 80 % of the time near the iri­ dium nucléus and ~ 3 % of the time near to each of the halogen nuclei, as found from the hyperfine structure of paramagnetic réson­ ance (115). As discussed below in the section on intermediate coupling, Owen (116) maintains the presence of

20 % a-bonding of y3-elec-

trons because of the decreased values of the Landé factor Generally, it can be said that the y3-part of ^/-électrons and y3-ligand électrons are subject to some kind of intermixing at low inter-nuclear distances resulting from orthogonalization alone. However, with orthogonalized orbitals, the interaction does not intermix orbitals with the same y„, but rather levels with the same 2s+ir„, originating from different configurations yn“ym'’-" Thus, the final calculations tend to be complicated. However, the results would be very interest­ ing. Use and Hartmann (®2) proposed a crystal field model, which has been used by several authors (î-8-22-47-52-53-134). a hydrogen-like 2id wavefunction with the effective charge Z, proposed by Slater (i*!!) is perturbed by 6 point charges or point dipoles in the distance R from the nucléus of the central ion.

Any hydrogen-like wave-

373

function will of course be approximative, since Z varies from e.g. 28 in the centre of a nickel (II) ion to 3 on the surface, while Slater assumes Z = 7.55. But these screening values are only good for internai électrons, while the values for external électrons are very uncertain. Further, the ionization potential for Ni++ in vacuo, 36.16 eV, suggests Z = 4.9. On the other hand this gives for the density maximum of the radial wavefunction the improbably high n

O

value of 0.96 A, while the ionic radius in crystals is only 0.7 A. It may be argued that by calculations from perturbation theory, the energy value is often determined much more correctly than the wavefunction. However, a first-order perturbation cannot be very reliable, when the radius is predicted ~ 80 % too large. Even worse, it is the outer parts of the wavefunction which are most perturbed by the crystal field and which are the most uncertainly determined in the hydrogen-like approximation. Belford (•'^) proposes a Hartree’s self-consistent wavefunction, which gives smaller crystal field contributions for copper (II). The concept of point dipole moments is entirely meaningless, since the négative end of a dipole molécule contributes from 10 to

100

end.

times more to (Ei — E2) than the opposite elfect of the positive The concept of point charges might seem more reasonable,

since we are accustomed to regard the action of the charge of nonpolarized anion as identical with the action of the same charge, placed in the centre of the anion. But this assumption is valid only for R-i potentials C^'^). Mr. O. Bostrup has kindly informed me that an intégration of the négative charge distribution on e.g. a chloride ion can give 4-10 times higher values of (Ei — E2) than the point chargeai. Generally (Ej—E2) is highly dépendent on the radius of the central ion and is inversely proportional to the radius of the anion, when similar charge distributions are considered (24). This résolves the old paradox, why neutral molécules such as H2O and NH3 can induce larger values of (Ei — E2) than anions such as Cl“ and Br“. Thus, there remains only the semi-quantitative expression that in atomic units ; (the energy unit = 2 Rydberg = 219 000 cm-i) (E, - E2)

374

where

is the average value of

(r is the distance nucleus-electron)

and R the distances from the nucléus to the six charges q. This expres­ sion may be integrated for given charge distributions of q, having the symmetry O*, by multiplication with the angular dependence factor. Thus, the electrostatic model can be made compatible with ail the observed facts, but that is of course no proof of its validity. Most peculiar is the fact

that trivalent ions hâve 1.4 — 1.8 times

higher values of (Ei — E2) than the isoelectronic divalent ions.

If

the ligands are not much more polarized, this resuit can only be explained by treatments taking intermixing of molecular orbitals into account. III. THE PARAMETERS B AND C OF ELECTROSTATIC INTER­ ACTION BETWEEN d-ELECTRONS AS MEASURED FOR COMPLEXES Orgel

Owen (il®), and Tanabe and Sugano (146) pointed

out that the parameters of electrostatic interaction may be smaller in the complexes than in the gascons ions, as determined from atomic spectra. This assumption can explain the déviations from the Orgel diagram in which the energy levels are supposed to be a fonction of (El — E2) only [see Table III, where the first bands Cr(H20)g+++ and Cr 0x3----- to ‘‘r5(F) hâve identical wavenumbers, while the band to "T4(F) is situated 700 cm~i lower for the tris (oxalate) complex than for the hexaaquo ion]. Mr. C. E. Schâlîer pointed out to me that the distance between the first and the second band is highly varying in chromium (III) complexes. If this distance is assumed to be 12 B (Table I), then B = 500 — 600 cm~i, while the value for gascons Cr+++ is B = 950 cm~i. Analogously, the first two excited singlet levels in diamagnetic J®-systems,

F4 and iFj,

1

hâve the asymptotical distance 16 B, implying B ~ 500 cm-i for cobalt (III), 300-450 cm^i for rhodium (III) and 250 cm~i for iridium (III) complexes. This is roughly half the expected values for the gascons ions, since the 4J-group generally (®®) has slightly lower values of B than the 3rf-group. It is obvions that anions [such as tris (oxalate) and hexacyanide complexes] seem to hâve lower values of B than the positively charged complexes. But it is not easy to distinguish a direct charge efîect from a tendency to form covalent bonds as

375

far the anions are concerned. It is known from the intensities that oxalate and thiocyanate complexes certainly contain small intermixings of odd molecular orbitals, but it is much more difficult to estimate the possibly much larger intermixing of even molecular orbitals. From the viewpoint of an atomic spectroscopist, the decreased values of B suggest a broader wavefunction, since the parameters of electrostatic interaction are inversely proportional to the average radius for isomorphous électron distributions.

This decrease of B

can only be explained by the perturbation theory, if more négative charge is présent between the nucléus and the considered électron in the complex than in the gaseous ion, e.g. even yi or odd Y4 élec­ trons from the ligands. On the other hand, any transfer of électrons to the ligands, conforming to an “ electroneutrality ” principle, will lower B. If only (1—X) of the original électrons remains in the central ion, the value of B would be expected to be roughly proportional to (1 — X)2, since the more remote parts of the élec­ trons do not contribute much to the parameter. However, another complication arises from the ratio C/B, which would be 8.75 for électrons concentrated on a spherical surface, and which is actually 4-5 in

the

gaseous ions (146).

By expansion

of the électron

cloud, the Slater-Condon-Shortley parameter F2 decreases relatively more slowly than F4, giving a smaller ratio C/B = 35F4/(F2 — 5F4). Therefore the observed decrease of B suggests an even stronger decrease of F4. In case of nickel (II) complexes, the non-diagonal element between 3F4(F) and ^F4(P) and the non-diagonal element

B

6

between 1F3(D) and 1F3(G) are significant. Hence, the straight Unes of Table 1 are strongly distorted for small values of (Ei — E2). But due to the diagonal sum rule, the sum of the energies of ^F4(F) and 5F4(P) should still be 0.6 (Ei — E2) + 15B, and with good approx­ imation, 1F3(D) has the energy given in Table I, —1.2(Ei — E2) + 8B 4 3 4- 2C, while the latter energy for the free ion is — (ID) + — (iQ) — (3F) = 17.900 cm~i. Table VI gives a list of the energy différences, found from nickel (II) complexes. The maxima in Table III are often displaced 200 cm~i in the cases of unsymmetrical bands, when the midpoint of area is taken. In the case of 1F3(D), correction is made for the shift due to effects of intermediate coupling, as discussed in the next section.

376

TABLE VI Effective term distances in nickel (II) complexes in cm~i.

Values implied by excited level....................

of the parameter

Ligands

377

free ion 6 H2O ata~3, X H2O enta”'*, H2O 3 gly“ en, 4 H2O enta”*, NH3 2 ata“3 en, 2 gly” 6NH3 2 en, gly” tren, 2 H2O 3 en tren, 2 NH3 tren, en tren, gly-

............................................

3r5(F)

3r4(E) + 3r4(P)

ir3(D)

(E, - E2)

15 B = (3P) —(3F)

8 B + 2 C =^1D) +y(iG) — (3E)

0

16900 14100 12800 13000 13900

17900 14800 13300 12700 13100 13600 12700 13000 12800 13100

Number of nitrogen atoms in the environment

0 1 2

3 2

3 2

4 6

5 4 6 6 6

5

8500 9500 10100 10100 10200 10200

10400 10700 10800 11300 11300 11600 11700 11700 11800

12000

13500 13400 13500 13400 12600 11700 12600 11300 12600 11500

12200 12000 12000 12000

11800 11900

It is seen from Table VI that the effective term distances do not decrease monotoneously with (Ei — E2). This is partiy connected with the définition of this parameter as the corrected wavenumber of the first absorption band. However, it is clearly seen that B eventually decreases to ~ 70 % of its value in the gaseous ion, and there is slight evidence that C/B eventually decreases to a value ~ 3.5 as predicted above. As far as term différences in nickel (II) complexes are concerned, the discussion is made somewhat uncertain by the fact that four absorption bands shall deliver the three parameters (Ei — E2), B, and C. It is interesting to note that ten absorption bands are known in the manganèse (II) hexaaquo ion. As pointed out by Orgel (113)^ the terms in the free ion (*05) which are ; 26,800, ; 29,200, '*D : 32,300, and : 43,600 cm~i, are decreased about 8 % in the hexaaquo ion (and 10 % in Mn enta—), while the corresponding decrease is 18 % for the nickel (II) hexaaquo ion (Table VI) and ~ 40 % for the chromium (III) and cobalt (III) complexes. While it cannot be excluded that these changes are subtle effects of covalent bonding, it seems at the moment more probable that the electrostatic crystal field theory actually is applicable with (Ej — E2) as empirical parameter together with smaller electronic repulsion parameters.

IV. EFFECTS OF INTERMEDIATE COUPLING In gaseous ions, the Russel-Saunders’ coupling with definite values of L and S for the terms may break down, when individual levels each with a definite value of J (the quantized vector sum of L and S) differ much in energy. This behaviour is évident in heavier atoms (25-28-72-73-78-8t-i23) and can be described by increasing values of Lande’s multiplet splitting factor

As in the case of (S, FJ

levels discussed above, the q levels with identical J of an électron configuration can be described by a matrix of ^’th degree. The non-diagonal éléments of this matrix hâve the order of magnitude ^ni. The values for 1 = 2, viz. are strongly increasing with three quantifies : the external charge Zq — 1 ; the number of équi­ valent ûi-electrons ; and the principal quantum number n. Thus,

378

is roughly proportional to Zq^, and the following relationship is approximately valid for the three transition groups : ~2

^ 5

The absorption spectra of complexes support strongly the analogous influence of

which is greatest at the end of the transition groups

and increases with n. Levels with S dilfering by one unit are intermixed in the squares of the wavefunctions to the extent = where A is the distance between the two levels, and k is about 1 and approximately constant for different complexes of the same ion. The sélection rule that transitions are only allowed between levels with the same S is mitigated to the degree as the groundstate and the excited level achieve the same S by intermixing induced by intermediate coupling. For group-theoretical reasons, levels can only be intermixed with the same value Fj of the internai vector product r^xF, = SFj, but it has not yet been possible to observe with certainty the Fj-components of the F„-levels, except in the tetrahedral Co CU—. In some cases levels with different S hâve nearly the same values of A for ail ligands, because the levels hâve the same sub-shell configuration, cf. iridium (III). In other cases, e.g. in chromium (III) and nickel (II), A assumes ail possible values down to the lower limit with resulting very high intermixing in some of the complexes. (82-85-i37)_ As A varies the intensity ratio of the intermixed bands behaves as predicted. A spécial case seems to occur in manganèse (II), where the oscillator strength P is ~ 0.5 % of that of spin-allowed bands in iron (II) or nickel (II). Since ^3d c^n be interpolated from Table VII to be 300 cm~i, the spin-forbidden bands were expected ordinary P-value, if the distance to the interacting sextet level (either the groundstate ^Fj or a level from some other électron configuration) is assumed to be ~ 20.000 cm~k The discrepancy can be explained by admixed odd States, which perhaps hâve a less strictly defined S. Owen (116) concludes from the g-values from magnetochemical measurements that

is diminished between 17 and 40 %, compared

to the free ion. It is not possible to infer différences of this size from

379

380

TABLE VII

The Landé multiplet splitting factor Çnd from atomic spectroscopÿ and the interaction constants k Çnd from absorption spectra of complexes, ail in cm.”L

Number of rf-electrons

1

2

3

4

6

7

8

9

KM

79

123

169

229

408

530

630

829

k pif













500, 800



Od

154

217

275

352









k Od





200, 300



500







4d", divalent :

K4d

290

468

560









1843

trivalent :

X,Ad

500

800

800









2325

k -QM





900



900







5(f”, divalent :

k KM













2000



trivalent :

k KM









2000







quadrivalent

k KM









2500







3(f", divalent :

trivalent :

Table VII, but they may be explained by the expansion of the electron cloud, discussed above. Hence, it is not absolutely necessary to describe this phenomenon in terms of covalency. The intermixing of S in the groundstates of e.g. diamagnetic
CONCLUSION In the period 1951-1956, the absorption spectra of transition group complexes hâve been investigated much more intensely than previously. It is generally believed that the crystal field theory gives a reliable description of the levels in terms of the crystal field strength [in octahedral complexes (Ej — E2)], and the parameters of electrostatic interaction between
381

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(83) J0rgensen, C.K., Acta Chem. Scand., 10 (1956), p. 500. (8‘‘) Jprgensen, C.K., Acta Chem. Scand., 10 (1956), p. 518. (85) Jprgensen, C.K., Acta Chem. Scand., 10 (1956). (86) Jorgensen, C.K., Acta Chem. Scand. (87) Jprgensen, C.K., Acta Chem. Scand. (88) Jprgensen, C.K., Unpublished results. (89) Kato, S. Sci. Papers In.it. Phy.i. Chem. Research (Tokyo), 13, (1930), p. 49. (90) Katzin, L., J. Chem. Phys., 23 (1955), p. 2055. (91) Kiss, A.v. and Gerandas, M., Z. physik. Chem., A 180 (1937), p. 117. (92) Kiss, A.V., Z. anorg. Chem., 246 (1941), p. 28. (93) Klemm, W., Angew. Chem., 66 (1954), p. 461. (9“*) Laudise, R.A. and Young, R.C., J. Am. Chem. Soc., 77 (1955) p. 5288. (95) Lifschitz, J. and Rosenbohm, E., Z. physik. Chem., 97 (1920), p. 1. (96) Linhard, M. and Weigel, M., Z. anorg. Chem., 264 (1951), 321. (97) Linhard, M. and Weigel, M., Z. anorg. Chem., 266 (1951), p. 49. (98) Mallatesta, L., Gazz. Chim. Jtal., 71 (1941), p. 467 and 842. (99) Manchot, W. and Gall, H., Ber., 61 (1928), p. 1135. (100) Mann, F.G. and Pope, W.J., J. Chem. Soc., (1926), p. 482. (101) Mathieu, J.P., Bull. Soc. Chim. France, 4 (1937), p. 687. (102) Maun, E.K. and Davidson, N., J. Am. Chem. Soc., 72 (1950), p. 2254. (103) McWeeny, R. « Electronic Structures of Molécules. Some recent developments. » Technical Report No. 7. Solid-State and Molecular Theory Group. Massachusetts Inst, of Technology. 1955 (104) Mead, A., Trans. Faraday Soc., 30 (1934), p. 1055. (105) Moore, C.E. « Atomic Energy Levels. » Nat. Bur. Stand. Circulât, No. 467. Vol. I and II. (106) Mulliken, R.S., J. Chem. Phys., 3 (1935), pp. 375, 506, 517, and 586. (107) Nyholm, R.S., Quart. Rev., 7 (1953), p. 377. (108) Ollson-Collenberg, O. and Backer, J., Z. Elektrochem., 30 (1924), p. 230. (109) Orgel, L.E., J. Chem. Soc., 1952, p. 4756. (110) Orgel, L.E., Quart. Rev., 8 (1954), p. 422. (111) Orgel, L.E., J. Chem. Phys., 23 (1955), p. 1004. (112) Orgel, L.E., /. Chem. Phys., 23 (1955), p. 1819. (113) Orgel, L.E., /. Chem. Phys., 23 (1955), p. 1824. (114) Orgel, L.E., /. Chem. Phys., 23 (1955), p. 1958. (115) Owen, J. and Stevens, K.W.H., Nature, 171 (1953), p. 836. (116) Owen, J., Proc. Roy. Soc., London, ITl A (1955), p. 183. (117) Pauling, L., J. Am. Chem. Soc., 53 (1931), p. 1367. (118) Pauling, L., « The Nature of the Chemical Bond. » (119) Polder, D., Physica, 9 (1942), p. 709.

(120) Poulsen, I. and Bjerrum. J., Acta Chem. Scand., 9 (1955), p. 1407. (121) Rabinowitch, E. and Stockmayer, W.H., J. Am. Chem. Soc., 64 (1942), p. 335.

(122) Racah, G., Phys. Rev., 76 (1949), p. 1352. (123) Rasmussen, E., « Serier i de ædle Luftarters Spektre ». Thesis. Copenhagen,

1932. (124) Roberts, G.L. and Field, F.H., J. Am. Chem. Soc., 72 (1950), p. 4232. (125) Rosotti, F.J.C. and Rosotti, H.S., Acta Chem. Scand., 9 (1955), p. 1177(126) Rulfs, C. and Meyer, R., J. Am. Chem. Soc., 77 (1955), p. 4505.

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(127) Russell, D.D., Cooper, G.R. and Vosburgh, W.C., J. Am. Chem. Soc., 65 (1943), p. 1301. (128) Samuel, R. and Despande, A.R.R., Z. Physik, 80 (1953), p. 395. (129) Santen, J.W.v. and Wieringen, J.S.v., Rec. trav. chim., Pays-Bas, 71 (1952), p. 420. (130) Satten, R.A., J. Chem. Phys., 21 (1953), p. 637. (131) Sayre, E.V., Sancier, K.M. and Freed, S., J. Chem. Phys., 23 (1955), pp. 2060 and 2066. (132) Schlapp, R. and Penney, W.G., Phys. Rev., 42 (1932), p. 666. (133) Schlâfer, H.L., Z. physik. Chem., 3 (1955), p. 222. (134) Schlâfer, H.L., Z. physik. Chem., 4 (1955), p. 116 and 6 (1956), p. 201. (135) Schwarzenbach, G., //e/v. Chim. Acta, 32 (1949), p. 839. (136) Schwarzenbach, G., Helv. Chim. Acta, 35 (1952), p. 2344. (137) Schâffer, C.E., Unpublished results. (138) Seaborg, G.T., Katz, J.J. and Manning, W.M., Nat. Nucl. Energy Sériés. Vol. 14 A (The Actinide Eléments) and 14 B (The Transuranium Eléments). (139) Shenstone, A.G., J. Opt. Soc. Am., 44 (1954), p. 749. (140) Shimura, Y., Ito, H. and Tsuchida, R., J. Chem. Soc. Japon, 75 (1954), p. 560. (141) Slater, J.C., Phys. Rev., 36 (1930), p. 57. (142) Slater, J.C. « Electronic Structure of Atoms and Molécules. » Technical Report, No. 3. Solid-State and Molecular Theory Group. Massachusetts Inst, of Technology, 1953. (143) Spedding, F.H., Phys. Rev., 58 (1940), p. 255. (144) Stewart, D.C. « Light Absorption... » II. ANL - 4812 (AECD - 3351). (145) Sundram, A.K. and Sandell, E.B., J. Am. Chem. Soc., 77 (1955), p. 855. (146) Tanabe, Y. and Sugano, S., J. Phys. Soc. Japon, 9 (1954), pp. 753 and 766. (147) Treadwell, W.D. and Huber, D., Helv. Chim. Acta, 26 (1943), p. 10. (148) Tsuchida, R., Bull. Chem. Soc. Japon, 13 (1938), pp. 388, 436, and 471. (149) Van Vleck, J.H., Phys. Rev., 41 (1932), p. 208. (150) Van Vleck, J.H., J. Chem. Phys., 3 (1935), pp. 803 and 807. (151) Van Vleck, J.H., J. Phys. Chem., 41 (1937), p. 67. (152) Van Vleck, J.H., J. Chem. Phys., 7 (1939), pp. 61, 72 and 8 (1940), p. 787. (153) Wehner, P. and Hindman, J.C., J. Am. Chem. Soc., 72 (1950), p. 3911. (154) Wehner, P. and Hindman, J.C., J. Phys. Chem., 56 (1952), p. 10. (155) Williams, R.J.P., J. Chem. Soc., 1956, p. 8. (156) Wheeler, T.E., Perros, T.P. and Naeser, C.R., J. Am. Chem. Soc., 77 (1955) p. 3488. (157) Wrigge, F.W. and Biltz, W., Z. anorg. Chem., 228 (1936), p. 372. (158) Yamada, S., Nakahara, A., Shimura, Y. and Tsuchida, R., Bull. Chem. Soc., Japon, 28 (1955), p. 222. (159) Yamada, S., J. Am. Chem. Soc., 73 (1951), pp. 1182 and 1579. (160) Yamada, S., and Tsuchida, R., J. Am. Chem. Soc., 75 (1953), p. 6351.

385

Discussion M. Orgel. Is there any evidence from optical absorption spectra for the réduction of the spin-orbit coupling constant in complexes relative to its value for the free ions? M. Jergensen. — The non-diagonal element k'ini can be found from adsorption spectra, from the relative intensities and in some cases the mutual repulsion of the energy levels, when their distance approaches Ik^ni- Thus, if theoretical estimâtes could be made of the number k ~ 1, it would be possible to déterminé the actual value of ^ni in the complex. Even though such calculations hâve not been performed. I guess that at least the platinum metals exhibit considérable decrease of ^ni, if k is not systematically small. Thus, ^5^ can be estimated from several gaseous ions to be larger than k^^d 2.000 cm~i observed in iridium (III) and planitum (II) complexes ; Platinum (0)

5d96s

4.050 cm~* ~4.000

Gold (I)

5d%s 5d^6s^

5.100 ~5.000

Mercury (II)

5d%s 5d%s2

Thallium (III)

5d%s

6.200

~6.000 7.450

M. Nyholm. — It is now well established that the number of tetrahedral Ni” complexes, if any, is much fewer than was formerly believed to be the case. However the compound [Ni(NÛ3)2, 2 Et3P]“ is monomeric in benzene solution. It has a high electric dipole moment. Would Dr Jorgensen give his views as to the probable structure of this compound ?

386

M. Jergensen. — This compound or cis-octahedral, but may show a oxygen atoms co-ordinated of each loosely bound solvent molécules on

is not necessarily tetrahedral distorted structure with two nitrate group, or with very the residual positions. Due

to the Jahn-Teller eflfect, a tetrahedral structure must distort, and there may be raised similar questions as to whether CUCI4 in solid K2CUCI4 is distorted planar or distorted tetrahedral. However, the inversion in sign of the energy différence between y3 and ys orbitals by going from the symmetry on to T
central atom, no optical activity, i.e. no Cotton

/ —effect would be observed. A Cotton effect only occurs if the vibrating moment of the bands has nA

//

components in distant parts of the molécule. The optical active behaviour of a band or a part of it is best characterised by the quotient £( — Zr .? =---------------£

387

where zi, Sr and e are the absorption coefficients for left and right hand circular and for ordinary light; g bas been termed anisotropy factor. The value of g dépends on the distribution of intensity and direction of the components of the vibrating moment over the varions parts of the molécule. The numerical évaluation of the ^-values and the intensity show that in the case of the molécules mentioned the vibrating moment must hâve components a few O Angstrom units apart, a resuit which is well in agreement with the enouncement in Orgels, Nyholms and Jorgensens papers according to which there must strong interaction between the peripheral substituents and the central atom. In order to give an approximate description of the distribution of the electric moment over the molécule, we hâve represented the central atom as a threedimensional isotropie oscillator in a first approximation and attributed the peripheral substituents a preferential polarisability in the direction of the long axis of ethylenediamine, etc., i.e. in the direction of the octohedral edge occupied by the molécule (■). In this case, the coupling between the central atom and the peripheral substituents removes the degeneracy. The original absorption band splits up in 2 or 3 parts, differing somewhat in frequency and differing considerably in g-value.

This is

a conséquence which has been corroborated by experimental facts : the détermination of g-values in the région of the long wave absorption bands of the Co(en)3-ion and the Co(ox)3-ion as well has shown that g varies to a great extent inside the band, revealing that the distribution and orientation of the components of the vibrating moment are different for the varions parts of the absorption band. It can therefore be considered to be proved that the long wave absorption band is as a matter of fact a superposition of several neighbouring bands. While the mean value of g keeps its sign if the central atom is exchanged, the arrangement of the peripheral substituents beeing kept constant, the relative distribution of the g-values observed in the long wave and the short wave part of the absorption band changes considerably. In the case of very week coupling (rather unstable) compound [Cr(ox)3]K3 g is slightly négative in the long wave part and strongly positive in the mean part of the band; in the case of medium coupling

388

in [Co(ox)3]K3 the g value in the long wave part is strongly, in the mean band less strongly positive; and in the case of strong coupling, i.e., in [Co(en)3]Br3 the g value is strongly positive in the long wave part and slightly négative in the short wave part of the first absorption band; this ail is in agreement with theoretical calcul­ ations made on the basis outlined (*). It is found experimentally that the next absorption band in the compounds mentioned is of similar intensity as a first mentioned absorption band, i.e., its /-value is 10^^ to 10"4 approximately. At a variance with the first band, the g-value is in ail the compounds investigated very much smaller in absolute value in the second than it was in the first absorption band; g is however found to vary inside the second band too, indicating that this band also is in reality a superposition and not a truly simple absorption band. M. Jorgensen. — It is very interesting to me to hear the inform­ ation, given by Prof. Kuhn and Prof. Orgel. I may only add that according to the calculations of Tanabe and Sugano, the spinforbidden transition to (in Mulliken’s notation 272) is situated at nearly the same wavenumber as the first spin allowed transition to *r4(iTi) in diamagnetic d(> Systems. Thus, the complicated behaviour, mentioned by Prof. Kuhn, might be connected with this superposition and the effects of intermediate coupling. My colleague, M. Schâfîer, has found some evidence for such a structure in the first strong band of cobalt (III) complexes. The non-diagonal éléments of intermediate coupling seem to be rather strong in tetragonal and lower symmetries of the complex. Thus it is rather difficult in many cases to distinguish between band splittings due to tetragonal distortions and to intermediate coupling. It would probably be interesting to study the optical rotation dispersion curves of such complexes; it is rather paradoxical that the angular déviations of Co(en)3+++ (Saito, Nakats, Shiro and Kuroya, Acta Cryst., 8, 1955, p. 729) from a regular octahedron do not correspond to larger déviations of the absorption spectrum from that of Co(NH3)ô+++. M. Orgel. — Prof. Moffitt at Harvard has shown that, in cobaltic complexes, theory predicts that the long wavelength band will be (*) See an oversight by D. Kuhn in Angew. Chemie 68, 93 (1956).

389

optically active and the shorter wavelength band much less so. bas calculated the magnitude of the effect. qualitative conclusion independently.

He

I had reached a similar

With regard to the splitting of bands, this is understandable since the States of Tjg and T29 symmetry in octahedral complexes are split in the lower C3 symmetry of the ethylenediamine complexes. I am not certain, but I suspect that the two States into which the lower State is split would hâve different optical properties, one perhaps being much less active than the other. M. Ubbelhode. — Do the bands shift appreciably with changes of température? What happens at liquid hydrogen températures in the solids? M. Jargensen. —

While the influence of low températures on

the spectra of lanthanide compounds has been much studied, there is not much information available on transition group complexes. There seems to be an increase of the wave number of the band maxima, amounting to about three percent for each lOO^ cooling, and the intensities do not seem to change drastically (cf. some recent measurements by some Japanese authors). M. C.E. Schâffer, M. Arne Jensen and the présent author hâve observed similar efîects in the opposite direction by warming solutions from 20 °C to 80 °C. Qualitatively, the coloured transition group salts may exhibit beautiful hysochromic effects by cooling with liquid air; rose-red cobalt (II) salts turn yellow and green nickel (II) salts sky-blue. This corresponds to an increased value of the parameter (Ej — E2), analogous to the exchange of water with ammonia at room température. M. Cagliotti. — Les questions sont si compliquées dans la spectographie ordinaire, que je ne sais s’il est possible d’apporter une contribution effective à ce domaine, au cours d’une étude de spectographie infrarouge. Dans mon laboratoire, on a étudié avec M. Sartori et M. Silvestroni les spectres infrarouge de quelques complexes hexaminées et tétraminés pour essayer de relever des relations entre la position de la bande correspondant à la V3 “ stretching band ” de l’ammoniac et la stabilité de la liaison Me—N dans les complexes.

390

Nous avons relevé les spectrogrammes de plusieurs complexes à l’état solide. Nous avons choisi l’oscillation V3 qui correspond, comme ont pu montrer Lecomte et Duval, Kobayashi, Mizushima et plus récemment Quagliona, à la “ Schwingungenergie ” la plus élevée et que l’on peut considérer la moins perturbée. Nous avons ordonné les complexes en fonction décroissante des valeurs des fréquences V3. Les spectres à l’état solide sont bien plus compliqués que les spectres que nous relevons, lorsque c’est possible, en solution. Mais si on a soin de choisir les bandes les moins perturbées, telles que la V3, on peut relever que les complexes se placent, sauf quelques exceptions, dans un ordre qui correspond qualitativement à la stabilité croissante de la liaison Me-N (fig. 1).

Après cet accord qualitativement satisfaisant, nous avons essayé encore d’appliquer, dans les cas où l’on pouvait attribuer avec suffisamment de certitude les quatre fréquences, la relation de Lechner, pour calculer dans les complexes, la valeur de l’angle qui vient d’être formé par la liaison N—H avec l’axe de la molécule deNH3. On voit que cet angle devient plus petit en fonction de la grandeur

391

de la stabilité du complexe, c’est-à-dire, que le volume deNH3 décroît avec la stabilité du complexe même. M. J0rgensen. — Votre observation des fréquences vj des complexes ammoniacales, entre les valeurs qui caractérisent NH3 libre et NH4+, est très intéressante; on peut proposer d’étudier les complexes encore plus stables comme Rh(NH3)e+++, Ir(NH3)g+++ ou Pt(NH3)g++++ (que l’on peut préparer selon les données de Tronev et Shumilina, Doklady Akad. Nauk SSSR, 101, 1955, p. 499). On espère qu’il sera possible de trouver un cas, où l’influence de l’ion central sur NH3 est plus grande que l’influence du quatrième proton de NH4+. Il serait aussi intéressant d’étudier les spectres de vibration de l’eau dans les ions hexahydratés des métaux. M. D’Or. — Les spectres d’absorption d’origine électronique des complexes considérés ici sont généralement relevés sur des solutions. Je pense cependant que, de même que la nature du solvant n’a probablement qu’un effet peu important sur le spectre, le spectre de la substance à l’état cristallin ne doit pas différer essentiellement du spectre des solutions. S’il en est bien ainsi, et que d’autre part, selon les indications de M. Jorgensen, une variation de la température a pour effet de produire un léger déplacement des bandes dans l’échelle des longueurs d’onde et non une modification de la forme des bandes, il semble que la largeur des bandes est due non à un effet direct de l’agitation thermique, mais à un effet d’élargissement des niveaux électroniques dû en partie à la variation de la distance entre l’atome central et les groupes coordonnés, au cours de la vibration, en partie au champ créé par ceux-ci. Le déplacement des bandes sous l’effet de la température serait dû au caractère anharmonique de la vibration des groupes coordonnés par rapport à l’atome central. M. Jorgensen. —

Je suis parfaitement d’accord avec vous sur

la faible influence de la température. Les cristaux semblent avoir presque les mêmes spectres que les solutions, mais le paramètre (El — E2) est souvent plus grand de 2 %, comme mon collègue, M. Ole Bostrup, a trouvé pour les sels du nickel (II). Parfois, il est possible d’observer l’effet visuellement. Les sels Tutton, comme

392

(NH4)2Ni(S04)26H20 sont bleu-verdâtres et Ni(H20)6++ en solu­ tion est d’un vert un peu jaunâtre. On peut les comparer avec les effets de solvation (J. Bjerrum, A.W. Adamson et O. Bostrup, Acta Chem. Scand., 10, 1956, 329).

M. Chatt. — With reference to the use of infra-red spectra for the examination of electronic effects in complex compounds, we (Chatt, Duncanson and Venanzi, J. Chem. Soc., in the press), hâve examined the spectra of a sériés of simple monoamines and mono­ amine complexes in carbon tetrachloride solution and also in the solid State. Although this sériés includes the simplest possible amines (v/z. monoamines), we found that the spectra in the région of N-H stretching frequencies (vn-h) ^^e complicated by intermolecular hydrogen bonding. Ail the N-hydrogen atoms are hydrogen bonded in such substances as tra«j-[PR3,NH3PtCl2] in the solid State. The complexes of primary amines are similar. However, in the complexes of secondary amines, e.g. of piperidine, very little, if any, hydrogen bonding occurs and the N-H stretching mode of vibration causes a single sharp absorption band both in solution and in the solid State. in the solid State is only some 20 — 30 cm~i lower than in solution, yet when the complexes trans(L, piperidine, PtCl2) (L = an unchanged ligand) were placed in the order of increasing measured in carbon tetrachloride solution and of increasing measured in the solid State, the two sequences were slightly different. It is most probable that the sequence observed in solution is the one relating the electronic effects of the different L’s, and that obtained from measurements in the solid State is perturbed as a resuit of slightly different crystal forces acting on the N-H bond. These results indicate that great caution is necessary in interpreting small différences in measured in the solid State, and that crystal forces may outweigh intra-molecular electronic effects in their effect on even in the absence of such strongly perturbing effects as hydrogen bonding.

M. Cagliotti. —- L’observation de M. Chatt est exacte : à l’état solide en effet, il y a des bandes supplémentaires, dues probablement aux phénomènes d’association : mais nous avons eu le soin de choisir la fréquence V3 qui est la moins perturbée et nous avons comparé tous les composés à l’état solide.

393

Il faut remarquer que les complexes examinés ont tous le même “ Ligand ” coordonné, c’est-à-dire NH3. Les valeurs observées présentent des variations très importantes, comme on peut le relever des nombres sous-indiqués (Tableau I). De toute façon, les relations que nous trouvons ont la valeur d’indication. TABLE I.

NH3 Fe(NH3)6+" Cd(NH3)e++

Mn(NH3)6++ Zn(NH3)6++ Co(NH3)6++

Ni(NH3)6-^ Cd(NH3)4++ Cu(NH3>4++ Cu(NH3)6++

Cr(NH3>6+++ Fe(NH3)s+++ Co(NH3)6+++

M. Jorgensen. —

V3 3.415 3.384 3.380 3.375 3.365 3.364 3.360 3.355 3.347 3.335 3.320 3.310 3.280

f f f f f f f f f f

1. Since gaseous ions with from two to eight

J-electrons présent several multiplet terms of the same électron configuration, the lowest of these will bave lower energy than the average of ail the terms. This produces a spécial stabilization of the groundstate of a gaseous ion, which is the same in rf" and ^10—n System and reaches its maximum value in d^~ Systems (which is the explanation of the stability of half-filled shells, often mentioned in Chemical textbooks). However, this stabilization of the ground­ state is not so large as might be predicted from the large number of levels, since the “ centre of gravity ” of the configuration is found by weighing with the total number of States (2S -|- 1) (2L -|- 1) in each term with a given value of S and L. Since the term différences decrease in complexes, relative to the gaseous ion, the energy of the groundstate of complexes will be increased by this spécial effect. Has Dr Orgel observed any decrease of the ligand field stabilization, which might be interpreted as caused by this counter-acting influence of the decrease of term distances in complexes?

Probably, the

CT-bonding of yi and y4-orbitals is slightly stronger in nickel (II) complexes than interpolated from the behaviour of manganèse (II) and zinc (II) complexes, since the distances from the central ion to

394

the ligands are relatively too small in the nickel (II) complex. Thus the observed ligand field stabilization which often is 20 % larger than predicted from the simple theory, may contain two further corrections : a positive contribution from the bonding orbitals, which do not contain ^/-électrons in their linear combinations, and a négative contribution, caused by the decreased values of the parameters of electrostatic interaction between the électrons in the partly filled shell. However, the first effect will to a high degree be linear in the number of y3-electrons and thus participate in (El — E2) without being distinguished. Unfortunately, I had not yet found the following argument for partly intermixing of J-electrons with the ligands’ orbitals, when I delivered the manuscript for the report. From the effective term distances, it is possible to déterminé the intégrais of the theory of Condon and Shortley {Theory of Atomic Spectra, Cambridge, 1953). The arguments will be presented in a paper in Danske Videnskab. Selskab, Mat. Fys. Medd. that it is possible to extrapolate from F2 and F^ to the intégral ; I*

00

W =

R2 — (Jr

JO r where e is the electronic charge and R2 the square of the radial fonction. For reasonable shapes of the wavefunction, F^ ~ 0.5 W, From W it is possible to define an average radius : e2

^ “w which is given for métal ions in gaseous State (in the case of the lanthanide ions for the aquo ions) and in complexes : 3 3 3 d6 3 d» 4 dà 4/2 4/3 4/5 4/7 4 P 4 fi2

Chromium (III) Manganèse (II) Cobalt (III) Nickel (II) Rhodium (III) Praseodymium (III) Neodymium (III) Samarium (III) Gadolinium (III) Dysprosium (III) Thulium (III)

0.75 A 0.83 0.64 0.78 0.72 0.84 0.80 0.80 0.76 0.74 0.59

0.97 0.89 0.92 0.91 1.2 0.84 0.80 0.80 0.76 0.74 0.59

— — — — — — — —

1.35 A 0.94 1.6 1.12 2.4 0.89 0.83 0.83

0.55 A 0.80 0.47

0.68 0.69 1.16 1.15 1.13

1.11 1.07 1.04

Thus, while 4/-electrons are screened in trivalent lanthanides (but not so much as assumed by many authors) the effective radius

395

ro of the ^/-shell is definitely larger than the ionic radius.

In my

opinion, this is strong evidence for partly covalent bonding, not only of Yi and orbitals, but also of Y3 orbitals containing cZ-electrons contributions. Eventhough the molecular orbital theory thus has proven its superiority over the llmiting case : the electrostatic theory with pure J-orbitals, it is interesting to notice the différences between the application of the molecular orbital theory to transition group complexes and to other types of molécules such as 7T-electron Systems. In the latter case, the excited levels generally agréé very modestly with calculations, and it is necessary to take large effects of intermixing of configurations of molecular orbitals into account, as pointed out by Coulson, Craig and Jacobs, Proc. Roy. Soc., A 206, 1951, p. 297. The calculations on transition group complexes generally agréé within 3 %, when the parameter (Ej — E2) in octahedral complexes and the somewhat decreased term distances are applied. Eventhough the group-theoretical results cannot be connected with the electrostatic model originally used, the theory of transition group complexes must still be considered as much more unified than earlier distinctions between “ ionic ” and “ covalent ” com­ plexes might hâve allowed. The most prominent failure of the earlier theory is in my opinion the concentration of interest on the groundstate of the complex only, with resulting desire for a single valence bond formula of the type encountered in CH4 or NH3.

It is very fortunate for the

Chemical physicists that there exist complexes with a partly filled Shell, where each électron configuration correspond to more than one level.

These cases are fiable to yield much more information

about the electronic structure than the closed shells which exist in only one State. M. Bjerrum. — In his paper Dr Orgel also discusses “ the mechanism of some electrontransfer reactions ” and I should like to ask Dr Orgel how it can be that the transfer of an électron from the tris-ethylenediamine cobalt (II) ion to the corresponding luteo ion is much more rapid than the électron transfer in the corres­ ponding cobalt ammonia System?

396

One might hâve expected the opposite, but perhaps the explanation is that Co(en)3++ is more close to be spin-paired than Co(NH3)g++ so that the spin rearrangement occurs more easily in case of the ethylenediamine System. M. Orgel. —

When I talk of stability, I am referring to beats

of formation. Often only free energy data are available. In such cases I assume, optimistically, that trends in free energy parallel those in beats of formation in sériés of related compounds. The reason for preferring the beat of formation is simply that it is this quantity which can be calculated. M. Nyholm. —

When discussing stabilities of métal complexes

one would prefer to hâve values of enthalpy (AH) for the heterolytic fission of the métal ligand bond (i.e. M-<-L—->M ; L) rather than free energy values (AG) . Pending the accumulation of many more AG and AS data we are forced to use free energy values in discus­ sing métal complex stability rather than AH. It must be borne in mind, however, that biological workers and those interested in the séparation of métal ions in analytical chemistry and in industrial processes are concerned mainly with the extent of dissociation of complex ions in solution. For these workers free energy values are the more important. What one needs very badly is some direct means of examining the relative strengths of métal — ligand bonds directly. For this purpose infra-red absorption spectroscopy in the 100 cm~* région will prove most valuable. A grating spectrograph is necessary for this Work. We propose to work on this subject in the near future. M. Chatt. — With référencé to Prof. Nyholm’s remark about the development of infra-red spectroscopic methods to examine the région of the spectrum where metal-ligand bond stretching occurs, my colleague Dr L.A. Duncanson is at présent constructing apparatus for that purpose. The entropy différences between isomeric complex compounds can be quite large. Some while ago we (Chatt and Wilkins, J. Chem. Soc., 1952, 4300; 1955, 525) measured the entropy changes during some isomérisation reactions of the type m-[L2PtCl2] — trans-

397

[L2PtCl2]. The différences were of the order 10-15 cal. mol.~i deg.“h Actual examples are; when L = PEt3, AS = 13.3; when L = AsEt3, AS = 14.2; when L = SbEt3, AS = 9.4, ail within oneen tropy unit. We speculate that these large différences are due to the very great dipole moments of the cA-isomers (10 D), and that the moments cause a much greater solvation of the cis- than of the /ran^-isomer. It is an effect which might be found in any complex System where large dipole moments occur, and I mention it because these dif­ férences in AS are much greater than are usually found between isomeric substances. M. Barrer. — From the thermodynamic point of view, the standard free energy of a reaction is AG° = —RT In Ka where Ka is the thermodynamic equilibrium constant. The termodynamic equilibrium constant is the quotient of activities of résultants and reactants, whereas the stability constants, K, are the corresponding quotients of concentrations. Thus the stability constants do not S Also — (RT In K) does ôT RT2 S In K not give a rigorous measure of AS° nor ------- r:r------ a rigorous oT measure of the beat of the reaction. One must be careful in introducing give any rigorous measure of AG°.

the terminology of thermodynamics that it be done exactly, since thermodynamics is an exact branch of science, and much confusion may eventually resuit from its qualitative or incorrect use. M. Jergensen. — So far crystal field theory shall dénoté the electrostatic model with pure ^/-wavefunctions, it might be questioned if “ ligand field theory ” does not simply mean “ molecular orbital theory ”. However, the partly covalent bonding also of tZ-electrons in complexes might be visualized as a resuit of the electrostatic perturbation on the partly filled ^/-shell. In most complexes outside the transition groups (except the/?2 Systems, bromine(III), iodine (III) and polonium (II) which exhibit the tetragonal symmetry predicted from the Jahn-Teller effect) there is no electrostatic field separating the energy levels of a partly filled shell. Thus, the “ ligand field ” seems to be a good name for these co-operating effects with resulting partly covalent bonding.

398

M. Nyholm. —

I believe that at first sight the term “ crystal

field ” gives rise to a mental picture of an electrical field extending throughout a whole crystal. However in complex chemistry the field with which we are concerned is that arising from the ligands directly attached to the métal atom ; the second order efïects of more distant ligands may be ignored as a first approximation. Thus in a sense a ligand field is a spécial kind of crystal field but the différence between these is importât since complex ions eg [Co(NHj)6]+++ or molécules eg [Co(N02)3(NH3)3]'' may exist in solution when no “ crystals ” are présent. There are occasions, of course, when both the ligand field and the crystal field may be involved.

This appears to be true of certain crytalline métal com­

plexes eg CS3C0CI5 where the main effect upon the magnetic suceptibility arises from the four Ch ions which are attached to the Co (II) atom but longer range forces appear also to be operating.

399

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J 11

Application of the Screening Theory to Chemical Reactions Involving Non-Metallic Solids by W. A, WEYL

I. INTRODUCTION For the past eight years the Office of Naval Research has sponsored basic research on varions aspects of solid State chemistry in the author’s laboratory. The results of this experimental program has led to a new concept of the polymerization of molécules and of the formation of solids. In solid State chemistry, e.g., in the détermination of crystal structures, the principle of electroneutrality in the smallest possible volume is well established. To this first principle of chemistry a second one is now being added. The author assumes that the nuclei of most atoms require screening by a larger number of électrons than that which neutralizes their positive charges. The author considers this need for additional screening to be the second principle which governs the chemistry of the solid State. In solid State chemistry it is not possible to operate with the conventional concept of the valency of an atom. Sodium is mono­ valent, but its reaction with chlorine is not terminated after each sodium ion has combined with one chlorine ion, a reaction which produces 120 Kcal. The reaction continues until each sodium ion is screened by six chlorine ions. The formation of solid NaCl from NaCl molécules gives an additional 60 Kcal. The condensation of NaCl molécules and the formation of solid NaCl is the resuit of the coordination requirement or the screening demand of the cation. The fact that NaCl and AgCl hâve widely different properties (melting point, solubility in water) in spite of having identical 401

structures, charges of the ions, and internuclear distances, ha-, been explained in two ways. One way to account for the différence is by the assumption of different “ degrees of covalency It became customary to describe the Ag+ — Cl~ bond as being more, and the Na+ — Cl“ bond as being less covalent. Another way has been suggested by K. Fajans (i) who describes these crystals as arrays of ions with different degrees of “ mutual polarization The Ag+ ion with its 18 électron shell is more interpenetrable for électrons and exerts a stronger polarizing effect upon the Cl~ ions than the Na+ ion with its octet shell. It is rather unfortunate that in crystal chemistry the terms “ ion ” and “ ionic size ”, etc. are used even for units such as PS+, Si^*+, 02-, N3-, etc. These symbols are used to designate the quantum State of these éléments. The use of the term 02- “ ion ” means only that the oxygen participâtes in a crystal structure with eight eletrons quantized with respect to its core. This quantum State or the “ quanticule ” 02- (K. Fajans) (2) does not exist in the free State nor is it stable as a hydrated ion, but it requires stabilization by strong positive fields, a fact which is most important in surface chemistry because in a surface the 02- ions may lack the positive environment which is essential for their stabilization. It has become customary to describe matter as consisting of atoms. In spite of the fact that we know little or nothing about the properties and the behavior of atoms of some of the most common éléments, e.g., carbon, sulfur, and phosphorus, the atomic concept has proved very useful in chemistry, especially in organic chemistry. There is only one rigorously correct approach to Chemical reac­ tions, namely, the description of the reacting Systems in terms of nuclei and électrons. This idea is the basis of the quantum mechanical treatment of compounds and their reactions. As it is too cumbersome and too complicated to use this approach even for relatively simple Chemical reactions, one dépends upon approximations. The polarizability of the électron clouds and their deformation by adjacent electrical fields gives at least a qualitative picture of what may actually happen. Recently (3) (Fritz Ephraim 1954), the Fajans approach to Chemical binding forces, i.e., the “ Quanticule Theory ”, has found its way into a textbook of chemistry. We hâve chosen this concept for our

402

approach to solid State chemistry because it offers several advantages over more conventional descriptions of Chemical binding. 1. According to K. Fajans’ quanticule theory an experimentally unique molecular species is represented by one electronic formula. •

2. The Fajans’ theory does not mix the two incompatible concepts, i.e., the classical valence bond (e.g., 0 = C=0) and the concept of charged particles (e.g., (COj)^-). 3. The Fajans’ concept of the mutual deformation of ions makes it obvions that in a solid the Chemical bond between two atoms must be affected by any change which takes place in a remote part of the molécule.

This “ depth action ” of Chemical binding does

not involve long range forces but is the resuit of a change in the State of polarization of the constituents which is relayed over long distances. Our concept of the screening demand of positive cores and its decrease with increasing température made it possible to explain a number of phenomena for which, in the past no proper approach was available. Thus, E. C. Marboe and W. A. Weyl (4) explained the widely different viscosities of simple glasses in which cations were replaced by others of different sizes and different electronic configurations. A study of the glassy State was of particular value for the development of this concept because glasses offer the advantage over the crystalline State of permitting one to change the com­ position gradually. Replacing in a glass one ion by another one which has a different charge does not produce the kind of defect which is so characteristic for crystals, i. e., the change of insulators into semiconductors. Once the general rules which govern the screening of cations were established, it became possible to use them for the interprétation of the melting points of simple compounds (5) and for their hardnesses (6). As the screening of a cation improves with the size and the polarizability of the surrounding anions and as these parameters are decreased under hydrostatic pressure, it also became possible to explain the structural changes of crystals and glasses which had been found to occur under high pressures C^). It is the object of this report to apply the screening concept to the rates of solid reactions.

For this purpose the author postulâtes

403

that the activation energy of solid State reactions which do not involve electronic transfer, i.e., change of the oxidation numbers of éléments, is the resuit of the need for partially unscreening cations before they can be rearranged into the new lattices. This atomistic picture of the activation energy of solid State reactions makes it possible to understand reaction rates in a qualitative way and to explain the characteristic properties of the intermediate phases which hâve been called “ Active Zwischenzustânde ”, by G. F. Hüttig (8).

II. THE SCREENING THEORY The author’s concept of the screening demand of positive cores is based on the following facts : 1. Most éléments are solids at ordinary température. 2. Only the noble gases exist as atoms under ordinary conditions. In order to obtain atoms of other éléments under normal pressure the energy of the system has to be raised. For some of the most common éléments, e.g., carbon, sulfur, and phosphorus, a tempér­ ature of even 2 000 °C is too low for producing a gas which under normal pressure consists of atoms. 3. Other forms of energy, e.g., electrical discharges or radiation, can take the place of beat and produce atoms at ordinary température. In order to account for these facts the author postulâtes that the formation of the éléments took place under energy conditions (température, radiation) which were very different from those prevailing on our planet today. As the energy density changed, only the atoms of the noble gases remained single. In these éléments the nuclei are sufficiently screened by the number of électrons which neutralize their charges. The octet shell seems to play an important rôle in the screening power of an électron cloud : Neio+ (e-)2,s. In the néon atom the nucléus Neio+ is well screened by a group of 10 électrons, two belonging to the K shell and eight forming the very stable L shell. It seems, however, that other éléments could not arrange their électrons in a fashion which provided sufficient screening for their nuclei.

404

These éléments began to interact in order to improve the screening of their positive cores when the energy density level dropped.

One

of the most effective means for improving the screening of cores consists of the sharing of some électrons by a very large number of atoms.

Some of the électrons of the individual atoms form and

participate in a continuons three-dimensional atmosphère of élec­ trons; the degenerated électron gas of metals. Metallicity can be assumed only if the number of atoms is very large. In metals the électron gas screens the nuclei of a three-dimensional array of atoms in a way which permits each core to be surrounded by électrons. This method of screening seems to be very effective : not only are most éléments metals, but a large number of non-metallic compounds, e.g., UO2, PbS, etc., imitate metallicity. The formation of molécules which imitate the structure of a noble gas atom is another method for improving the screening of cores.

In some molécules a small number of atoms combine and

rearrange their électrons so that they are quantized with respect to two or more cores. According to K. Fajans, two nitrogen atoms assume the configuration of néon and form the N2 molécule in which the two positive cores, N5+, screen themselves by ten électrons which move in orbits quantized with respect to the two cores :

N5+ (e-)io N5+ . The Fajans’ quanticule theory gives us the expression : C4+ (c-)io 06+

for carbon monoxide. This formula indicates that the positive cores of carbon and oxygen are screened by an électron cloud which is quantized with respect to both cores. The close similarity between CO and N2 molécules (the same van der Waals’ constant) and their Chemical inertness is expressed in this formula which can be derived from that of a néon atom by replacing the one core Ne'o+ by two cores. In these and similar molécules (CI2, P2, P4, Sg) the number of cores is usually small and the électrons which are quantized with respect to these cores are not available for carrying a current. In metallic tin the positive cores are screened by the électron gas. Tin can form a low température modification (gray tin) which is not metallic.

We assume that in this form the Sn4+ cores are

screened by an environment of anions Sn^-.

We treat gray tin as

405

a “ stannide ”, Sn4+ Sn^-; elemental germanium as the germanide, Ge‘‘+ Ge"*-; and diamond as the Carbide, C*+ C^-.

This regrouping

of électrons and formation of cations and anions, e.g., Na+ Cl~, is one of the main reasons for the existence of the solid State. In order to properly screen ail cations the array should be three-dimensional and infinitely extending. Indeed, a surface of a crystal has to be treated as defective and its Chemical properties might be considerably at variance with those of the bulk. The concept of screening or shielding of atoms has been used for structural considérations of compounds by several scientists, e.g., J. J. van Laar, W. Kossel and, more recently, by A. E. van Arkel. Especially van Arkel (®) went very far in using the screening concept and he even suggested that the mutual polarization of the ions should be introduced as a further refinement. This is being done in our approach. Another improvement over earlier attempts to use the screening concept is the reference to the core of atoms rather than to their oxidation number. Sulfur, for example, is always treated as the S^+ core, no matter whether it is hexavalent as in SO3 or tetravalent as in SO2. The use of the oxidation number instead of the core of an atom was one of the major stumbling blocks in earlier attempts to use the screening concept as can be seen from the questions which van Arkel raises in his book. For example, why is SO2 not a linear molécule resembling CO2? We use the Fajans’ quanticule formula S^+ (e^) {0^~)2 in order to describe the molécule SO2.

This formula explains why the O—S—O bond

angle in SO2 is the same as in SO3. The Fajans’ quanticule formula makes it obvious that the oxidation of SO2 to SO3 is a process which does not involve the addition of atomic oxygen but the exchange between the quanticules (ej) and 0^~. This is of particular importance for the understanding of the rôle of semiconductors as catalysts for this reaction. For most Chemical reactions of the compounds of divalent lead it is perfectly satisfactory to refer to the Pb2+ ion, because in aqueous solutions the Pb2+ ion is surrounded by water in a highly symmetrical fashion. However, PbBr2 is not linear and the bond angle Br-Pb-Br of this molécule in the vapor phase reminds us that the core is Pb">+ with an eighteen shell, so that it would be better to Write Pb4+ (e^) Brj rather than Pb2+ Brj. Using this expression for describing the lead ion we can understand why in solid PbO

406

the lead ion does not occupy the center of the prism which is formed by its surrounding eight 0^~ ions, but is much doser to one group of four 02- ions than to the other. Keeping in mind the fact that divalent lead is actually Pb4+ (e^) explains the reaction of lead chloride with Grignard reagent

:

2 Pb4+ (ej) CI2 + 4 CHjMgBr- = Pb4+ (CHj)^ + Pb« + 2 MgBr2 +

2

MgCl2

Otherwise this disproportionation of divalent lead into metallic lead and tetramethyl lead is difficult to understand. K. Fajans treats nitrates and nitrites in a similar fashion.

The

NOj and the NOj groups contain the core of nitrogen N^+ screened by three quanticules, namely : 02N5+

02-

ej N5+

and 02-

02-

02-

In aqueous chemistry it is not very important to emphasize the quantization of the nitrogen and one may use the oxidation number instead. In solid State chemistry this is not satisfactory. If one neutralizes the N5+ (ej) (02-)2 groups with interpenetrable cations, e.g., Ag+ ions, one obtains a solid in which the cation is linked to the nitrogen by the quanticule (ej)- The less interpenetrable Na+ ion, however, will be linked to the nitrogen hy an 02- ion. This dif­ férence, namely, (02-)2 N5+ (ej) Ag+ (^2) N5+ (02-)2 Na+

and

does not exist in aqueous solution where these salts are ionized but it becomes significant for the solid State. The reaction of the two solid nitrites with C2H5I leads to ethyl nitrite for the NaN02 but to nitroethane for AgN02- In the nitrite the ethyl group is linked to nitrogen by oxygen; in nitroethane it is linked “ directly ” to the nitrogen atom or, in the way we express it, the two cores N5+ and C4+ are linked together by the quanticule (e^). Trivalent phosphorus or trivalent arsenic is treated in the same fashion as trivalent nitrogen. The quanticule formula of phos­ phorus trichloride is, therefore, ciC2 P5+ Clci-

407

Its hydrolysis does not produce OHej P5+ OHOH-

02but

H- Ps+ OHOH-

because the proton is better screened in the quanticule in the quanticule 02-.

than

The corresponding ASCI3, however, gives (cj) As5+ (OH)j when hydrolyzed. This brings out the fact that the quanticule Cj is not as good a screener as an 02- ion when both are polarized by positive cores which are more interpenetrable than noble gas-type cores. The greater interpenetrability of the As^+ core causes the sub­ stance ASCI3 to behave in a “ normal ” fashion : ClctAsS+CI-

” Cl-

^

OHCjAsS+OHOH-

These few examples may suffice to illustrate the importance of referring to cores and électrons rather than to the oxidation number of an element.

III. CHARACTERISTIC FEATURES OF SOLID STATE CHEMISTRY In this section the main features are discussed which the author considers characteristic for solid State chemistry.

1. The basic principles The author postulâtes that the chemistry of the condensed State is governed by two basic principles, namely, the trends of a System toward establishing electroneutrality in the smallest possible volume and the desire to provide the maximum screening of the nuclei. Polymerization, i.e., the sharing of anions, and crystallization, i.e., the establishment of a symmetrical environment of anions around cations, are means by which a System can improve the screening of its nuclei. Sometimes electroneutrality is sacrificed in order to improve screening. The reaction between equal numbers of molécules

408

of Kl and AgNOa in water leads to negatively charged particles of Agi.

The System has improved the screening of the Ag+ ions

at the surface of the solid at the expense of electroneutrality. At its melting point a crystal is in equilibrium with a liquid phase which has a higher entropy but which provides less screening for its cations.

This différence in screening can give rise to electrical

potentials between a solid and a liquid. In Systems containing protons, e.g., the System ice-water or the System crystalline-fused salol, E. J. Workman and S. E. Reynolds (lo) found electrical poten­ tials up to 60 volts, the solid being positive. Protons leave the less screening liquid phase in order to enter the better screening solid. This shift of protons also produces pH changes which hâve been observed by the same authors. These facts should not be interpreted as indicating that electro­ neutrality is of lesser importance than screening. Water is unique as an ionizing solvent not because of its superior screening power (liquid NH3 is a better screener) or because of its high dielectric constant (the dielectric constant of anhydrous HCN is 50 % higher than that of H2O), but because it can establish electroneutrality around cations and anions of high charge. No other liquid can dissolve and ionize the sulfates of aluminium or matter how high the dipole moment of a molécule solvent molécules surround an AP+ ion, the excess in this solvaté unless a shift of protons in the water

thorium. No and how many charge remains in the direction

away from the AP+ ion brings this volume element doser to elec­ troneutrality. The principle of establishing electroneutrality in the smallest possible volume is well recognized by workers in the field of solid State reactions. Those who hâve theorized on the nature of the “ diffusing unit ”, e.g., J. A. Hedvall (H), agréé that the particles which diffuse should be electrically neutral or nearly so. In their thinking they eliminated the possibility that P5+ or W^+ ions migrate as such; they preferred to speak of P2O5 or WO3 molécules. This concept seems to be supported by experiments whenever experimental techniques made it possible to draw conclusions on the nature of the diffusing unit. We hâve added to this principle of electroneutrality a second one, namely, that of the screening demand of positive cores.

With

409

decreasing température or, more generally speaking, with decreasing energy density, the nuclei of most éléments require more électrons for screening than are necessary for neutralizing their positive charges. The screening demand of cations dépends upon their electronic configurations. For noble gas-type ions it increases with their field strengths, i.e., the screening demand of the cations is directly proportional to their excess charges and inversely proportional to their sizes. This can be seen from the boiling and melting points of the fluorides of the alkalies. The greater the field strength of the cation — i.e., for constant charge, the smaller their radii — the greater is their demand for screening by a symmetrical environ­ ment of anions. Fused CsF can maintain its more probable liquid State down to a température of 700 °C but NaF loses entropy at 1,000 °C in order to improve the screening of the smaller Na+ ions. If one plots the melting points of the compounds CsF, RbF, KF, and NaF versus the radii of the cations, one finds a straight line relationship. One can describe the melting point as the température at which two phases are in equilibrium, one having the higher entropy and another having a less probable, more symmetrical structure but better screened ions. Screening is improved in a crystal by surrounding the cations with anions in a symmetrical fashion. Increasing the field strength by increasing the charge of the cation, i.e., going from Na+ to Mg2+ and AF+, etc., has a similar effect upon the screening demand. However, as the excess charge of the cation increases, more anions are required for neutralizing their charge so that the demand for additional screening decreases. These two antagonistic changes cause the melting point of the fluorides NaF

MgF2

AlFj

SiF4

980 °C

1,400 °C

1,040 °C

—77

to go through a maximum. The gases SiF4, PF5, and SFg consist of molécules in which the positive cores are well screened. The anion to cation ratio is the most important parameter which déter­ minés the screening of a cation. Up to a certain point it is possible to treat solids as consisting of electrically charged rigid spheres. One can use the principle of electroneutrality in the smallest possible volume and deduce that a solid mixture of LiCl and KF will not be in equilibrium.

410

The

combination of the small cation (Li+) with the small anion (F~) and the large cation (K+) with the large anion (Cl~) would provide a more economical packing and thus produce electroneutrality in a smaller volume.

Indeed, the lattice energies of these halides

reveal that the mixture of LiF + KCl has a lower free energy and higher lattice energy than one of LiCl + KF : LiCl + KF = LiF + KCl 192 187 239 163 381 402

Lattice Energy in Kcal Total Energy of Mixture.

This simple treatment has its limitations when the mutual polarization becomes an important factor. The System CoO + BaS is not in equilibrium in spite of the fact that the sizes of the ions would suggest that this is the most economical packing.

The small

Co2+ ion, however, has an incomplète électron shell and, consequently, it is much more interpenetrable for électrons than the noble gas-like Ba2+ ion. As a resuit, a mixture of CoO + BaS can lower its free energy by reshuffling its ions and combining the most interpenetrable ion with the most polarizable, i.e., the largest, anion. For this reason cobalt occurs in nature in sulfidic ores rather than in silicates. Platinum and gold occur in nature only in forms which hâve highly polarizable anions, either the électron gas of the metals or as telluride (calaverite, AuTe2) and arsenide (sperrylite, PtAs2). Cations of the non-noble gas-type also are more polarizable, i.e., they hâve a more déformable électron cloud, than those of the noble gas-type. This, too, affects their screening demand. Whereas a Mg^+ ion requires complété screening in space, nonnoble gas-type ions of the same size and charge can be satisfactorily screened by an environment of anions in a plane rather than in space. Mg2+ and Be2+ ions, like other divalent ions, can be forced into a planar configuration by the phthalocyanine group which in its center has two H+ ions which can be replaced by a divalent ion. However, the Be and Mg compounds hydrate readily, taking up H2O molécules, in order to complété their screening in space, but the corresponding Cu^+, Ni^+, Co2+, Fe^+, Mn^+, and Pt^+ 2

complexes do not. This différence in the screening demands with respect to the distribution of anions around cations of the noble and non-noble

411

gas-type has a direct bearing on the formation of the solid State. K. Fajans considers the volatile boron hydride B2H6 as having a structure similar to the molécule AI2CI6 which is présent in the vapor of aluminum chloride : H-

HB3 +

H-

HB3+

H-

Gl­ and

H-

ClAP+

ci-

ClA13 +

Cl-

Cl-

Dimerization through the sharing of anions gives each cation the coordination number four, i.e., it can be screened by four anions in tetrahedral arrangement. The fact that the hydride of aluminum is solid can be explained on the basis that the AP+ ion is larger than the B3+ ion so that the cations cannot be screened in the dimer. However, it is not only the larger size of the AP+ ion but also its low polarizability which is responsible for its need to continue its polymerization and to form a three-dimensional structure. This can be seen from the fact that the larger Ga3+ with its greater polar­ izability (18 outer électrons) forms a volatile hydride Ga2Hô. Methyl and ethyl groups are better screeners than H~ ions. A1(CH3)3 and A1(C2H5)3 form dimers in the vapor phase but the corresponding gallium and even the indium compounds are monomeric. The fact that the polarizability of the anion is as important for the screening as the polarizability of the cations can be seen from the melting points of the sodium halides which decrease with increasing polarizability of the anion :

M. P.

NaF

NaCl

NaBr

Nal

Na métal

980

801

755

651

98 °C

Also, whereas Si02 in its varions stable modifications has to form a three-dimensional network, the corresponding SiS2 polymerizes only in one direction (chain structure). The screening theory is based on the postulate that the screening demand of cores increases with decreasing température. The cations of high température modifications frequently hâve a lower coor­ dination number than those of the low température forms. The effect of hydrostatic pressure on the screening demand of cations is less obvions than that of température. 412

Up to the présent

time physical chemists hâve paid little attention to pressure as a parameter beyond its effect upon concentration. Today high pressure reactions hâve become of technical importance and it might be interesting, therefore, to examine the effect of hydrostatic pressure on the screening demands of cations and, with it, the atomic struc­ ture of substances. 1. Ail ions are compressed, i.e., their électron clouds are forced doser to their respective nuclei so that their sizes and polarizabilities decrease. As a rule, anions, because of their larger sizes, are more compressible than cations. 2. The compression of an ion tightens the électron clouds.

As

a resuit of this tightening, the refractive index of a solid under hydrostatic pressure does not increase to the same extent as its density. 3. The loss of polarizability of the anions lowers their screening power with respect to the cations. For this reason, many solids undergo structural changes which improve the screening of their cations by increasing their coordination number. RbCl has NaCl structure under normal pressure (C.N. = 6) but assumes CsCl structure (C.N. = 8) under high pressures. Agi changes its coor­ dination from 4 to 6. P. W. Bridgman (12) found that CS2, a liquid which consists of molécules in which the carbon cores are well screened by two large and polarizable S^- ions, polymerizes under pressure and changes into a solid which is supposed to hâve the structure of Si02. 4. Modifications which are formed under high pressures are metastable at normal pressure. In spite of their higher energy content the high pressure forms can be less reactive. Their lower reaction rates are the resuit of the lower polarizability of their ions. The solid CS2 obtained by P. W. Bridgman is barely inflammable. A high pressure modification of silica obtained by L. Coes (i^) is not attacked by hydrofluoric acid. 2. The depth action of Chemical hinding The leaders in the field of solid State reactions, in particular H. Forestier (i^) and J. A. Hedvall (15), are aware of the influence of the atmosphère upon the rate of solid State reactions.

These

413

scientists encountered effects of gases on the Chemical reactivity, phase transformation, and melting of solids which are difficult to interpret on the basis of conventional physical chemistry. These phenomena seem to indicate that adsorbed molécules, even if they are chemically inert like N2 or the rare gases, must affect the electronic structure and, with it, the binding forces of the solid to a considérable depth. We can assume that the présent description of atoms and ions is essentially correct; they can be compared with tiny solar Systems in which the gravitational forces are replaced by electrical forces. Solids accordingly represent a three-dimensional array of these solar Systems in close proximity. Astronomers would deny the possibility that the effect of a disturbance in one solar System would be limited to its nearest neighbors. Nevertheless, many physical chemists still attempt to describe events at the surface of a solid, say chemisorption, in terms which are limited to certain lattice sites or active centers and they prefer to sacrifice the concept of a “ depth action ” in order to be able to dérivé a quantitative treatment of an interaction between two atoms. Astronomers who would firmly refuse to accept the idea of a localized disturbance would also frankly admit that they are not in a position to mathematically dérivé the extent and the magnitude of the disturbances in remote solar Systems. The mathematics is too complicated if it involves many bodies. The Fajans’ concept of the mutual polarization of ions provides a physical picture of the way in which the effect of a disturbance is relayed from one lattice site to another : induction of dipoles and changes in their magnitude and their direction. The screening concept explains the reason for the interaction of surfaces with the électron clouds of inert molécules such as N2 or noble gas atoms. It seems that the concept of a constant “ Chemical bond ” is the main reason for certain difficulties in solid State chemistry. Workers in varions industries are well aware of this “ depth action The rôle of the “ cooling liquid ” in grinding, milling, and drilling operations is too well known to be discussed here. The mechanical strength and the hardness of substances dépend upon their environment, a technical know-how which is well supported by laboratory experiments. W. von Engelhard! (i^) published several papers on the abrasion hardness of quartz as a function

414

of the “ cooling liquid

Experiments of C. Benedicks (i'^) reveal

that silica glass fibers and thin platinum wires undergo volume changes in contact with liquids (liquestriction).

C. Benedicks and

G. Rubens (i*) found that the strength of Steel, especially its fatigue strength, is strongly dépendent on the nature of the wetting liquid. The effect of the environment upon the mechanical properties of a solid, its volume, hardness, tensile strength and fatigue makes it obvious that electronic and Chemical properties also must be affected. M. Faraday in his classical treatise “ Experimental Relations of Gold and Other Metals to Light ” describes réversible color changes of gold dispersions as the resuit of alternate drying and wetting. In the manufacture of pigments (Guinet Green, Iron Oxides) it is well appreciated how particle size and surface structure affect the color. G. F. Hüttig (20) uses the color of reacting Systems, e.g., Fe203 + ZnO, to characterize the State of reaction. Disturbances emanating at a surface or interface are relayed into the interior and affect the State of polarization of the Fe^+ ions to a considérable depth as the color does not dépend upon surface ions only. Guided by the hypothesis that the visible fluorescence of CdS is due to asymmetrical units, e.g., Cd2+ ions which are located between S^- and say O^- ions in glasses, J. K. Inman, A. M. Mraz and W. A. Weyl (2i) produced luminescent materials by precipitating cadmium sulfide on suitable carriers, for example, alkali halides. Both intensity and frequency of the emitted light was found to decrease in progressing from KCl to KBr to Kl. The more polarizable the anion of the halide the more it resembles the ion and the less asymmetrical becomes the unit S2- - Cd2+ - Halogen. Also, by choosing the suitable environment (e.g., aluminium stéarate in xylene) the sulfides of tin, thallium, and mercury could be excited to visible fluorescence. None of these sulfides shows visible fluores­ cence when precipitated without a carrier from aqueous solutions. Of particular interest is the observation of W. Braunbeck (22) because it shows that even the chemically inert gases, hélium and argon, can screen a surface and thus mobilize électrons. He found that the conductivity of a thin platinum foil has its lowest value in vacuo and that it increases when gases are admitted. increases the electrical conductivity by only it by 0.3 % and oxygen by 0.5 %.

0.1

Hélium

% but argon increases

415

With respect to the Chemical properties of substances this depth action in solids has three implications. a) For any substance the Chemical reactivity changes if sub­ division is carried out to an extent that one, two or ail three dimensions decrease beyond the range of the depth action. The interactions of some clay minerais with water, i.e., ionic exchange and rheological properties, dépend more upon the thickness of the layers of these minerais than upon their Chemical composition. R. Schenck (23) emphasized the fact that the particle size of a métal or of an oxide not only affects the reaction rate but also the equilibrium with gases. For palladium oxide the dissociation pres­ sure at a given température increases with decreasing particle size. For iron oxides a similar dependence on the subdivision was discovered for their equilibria with CO2 - CO mixtures. G. Rienâcker and associâtes (24) found that sintering of fine métal powders decreases the surface area steadily but their catalytic activities go through a maximum. b) K second manifestation of this depth action is the influence of a “ carrier ” upon the Chemical properties of substances.

In

heterogeneous catalysis this phenomenon is so well known that there is no need for going into details. F.

Feigl (25) gives numerous examples for abnormal solubilities

of substances when precipitated on certain “ carriers ” : “ Numerous cases are known in which a solid loses its normal reactivity toward certain reagents because it is associated with a second solid which thus plays the part of a masking agent. Sulfide précipitâtes offer a véritable treasure trove of such abnormalities. ” c) K third manifestation of the “depth action” concerns the interaction between solids and gases. It is well established that a molécule chemisorbed at a solid has different optical and Chemical properties than the same molécule in the gaseous State or in a solution. However, it is not yet fully appreciated that the chemisorbed particle also affects the electronic structure of the surface of the solid and that this effect goes far beyond the adjacent the principle of “ depth action ” with that tione ” we may express our thoughts on by saying : A crystal of metallic nickel or

416

lattice sites. Combining of “ actio est par reacthis subject drastically of zinc oxide which has

a molécule of hydrogen chemisorbed at ils surface has changed into a different Chemical individual and, consequently, its reactivity toward a second hydrogen molécule is different. This différence, e.g., the change in the beat of absorption with increasing numbers of chemisorbed gas molécules, is, of course, known, but it is usually attributed to the existence of lattice sites which had different activities from the very beginning.

No doubt, this possibility exists, but it

is not necessarily the right explanation for the phenomenon. Again we may assume that the depth action will be a maximum for the polarizable metals and for sulfides and fluorides containing noble gas ions. however, it cannot be ignored as we can is affected by adsorbed gases. P. Stahl

a minimum for oxides and Even for the latter group, see from the fact that quartz (26) found that the tempér­

ature of the a-p-inversion of fine quartz powder changes with the nature of the ambient atmosphère. Such an inversion requires a cooperative maneuver and a change in the Chemical bonding within only one atomic layer in the surface could hâve no effect upon the nucléation of a new modification. H.

W. Kohlschütter (27) found that the nature of the ambient

gas has a pronounced influence upon the rate of inversion of the yellow into the red modification of mercuric iodide. W. A. Weyl and D. P. Enright (28) studied the transition of the metastable yellow into the red stable form on cooling. Irradiation and mechanical shear forces accelerate the transition and, depending upon the nature of adsorbed ions, the transition can be accelerated or delayed. Also, yellow Hgl2 precipitated from a hydrocarbon transforms immediately into the red form but it takes minutes when precipitated from a more polarizable solvent such as alcohol and hours from acetone. Yellow Hgl2, embedded in a matrix of rosin saturated with Hgl2, did not change into the red form at room température over a period of years. Ordinarily the red form transforms into the yellow form at 126 °C but treatment of the surface with Pb2+ or T1+ ions made it possible to superheat the red form to 131 °C. 3. Formation of defective structures Foreign atoms or other lattice defects affect the stability of a crystal in two ways. Firstly, they lower the free energy of the System by increasing its entropy. With increasing température this contri­ bution becomes increasingly important.

Secondly, any disturbance

417

increases the potential energy of a crystal.

The extent to which

it increases this energy term decreases with increasing polarizability of ail constituents. The polarizability of an ion can be looked upon as its ability to adjust its own force field to suit its environment. A lattice vacancy, for example, produces asymmetrical fields but such a defect raises the energy of a polarizable crystal less than that of a crystal which contains noble gas-type cations and anions of low polarizability. In nature we find sulfidic ores of great complexity rather than pure heavy métal sulfides. Calcium carbonate, calcium fluoride, cryolite or silica, on the other hand, often occur as very pure specimens. The degree of defectiveness which a given crystal assumes dépends upon the température, the composition of the atmosphère, and the presence of foreign atoms. Of particular interest to us is the fact that foreign atoms not only can induce lattice vacancies but they can also prevent their formation. 4. Classes versus crystals Classes represent the most generalized arrays of ions. The glassy State has a higher entropy than the crystalline State because it has no long range order.

The short range order around major cations

is essentially the same in both States so that there is no major energy différence between a glass and a crystal. If the need for screening of the cations of a fused System is very high (MgO, AI2O3 or Mgp2) the melt crystallizes on cooling in order to surround each cation by anions in a highly symmetrical fashion. If the cations are well screened by the number of anions which neutralize their charges, independent molécules are formed (SFg, PF5 or SiF4) and their condensation at low température is the resuit of van der Waals’ forces. The rear­ rangement of the liquid into crystals is too fast to permit the formation of stable glasses. Classes can form from a melt in which the screening of the major cations is intermediate between these two extremes (Si02, P2O5. or BeF2). The chemistry of glasses offers several features which can lead to a better understanding of the solid State. The author could dérivé a great deal of information concerning solid State chemistry from studies of glasses because : a)

The Chemical composition of glasses can be changed gradually

and continuously.

418

èj By chilling a glass from high température it is possible to “ freeze in ” and to examine at normal température some of its high température structure, e.g., a coordination of cations which is stable at high température only.

c) Eléments which form several States of oxidation (Fe2+ - Fe3+, Cr3+ - Cr6+) can form equilibria between these States in a glass so that it is possible to study the effect of composition, température, and atmosphère upon the State of oxidation of éléments.

d) The absence of long range order makes it impossible for glasses to form semiconductors and, as a resuit, their Chemical properties are not as sensitive to “ impurities ” as those of crystals. As an example for the usefulness of the constitution of glasses for answering basic questions in the field of solid State chemistry we will discuss the factors which déterminé the screening demands and, with it, the coordination numbers of cations which hâve field strengths sufficient to exert a major influence on the structure. W. A. Weyl and F. Thümen (29) developed an optical method for following coordination changes in glass.

The Ni2+ ion was

found to be particularly suitable for this purpose. When introduced into silicate glasses, Ni2+ ions form two distinct types of color centers which could be attributed to Ni^+ ions in sixfold and fourfold coordination. In sodium silicate glasses an equilibrium is formed between the yellow center (Fig. lA) characteristic for the NiOg group and the purple center (Fig. IB) characteristic for the Ni04 group. These glasses are gray because their absorption extends over the whole visible spectrum. Any change in composition which decreases the polarizability of the 02- ions favors sixfold coordination of the Ni2+ ions and shifts the color of such a glass toward yellow. For example : 1. Replacing some Na+ ions by the more polarizing Li+ ions. The gray color of this glass is shifted toward yellow. 2. Replacing Si4+ ions by P5+ ions. Nickel oxide produces yellow colors in a NaP03 glass or in vitreous metaphosphoric acid. 3. Replacing some 02- ions by less polarizable F- ions. Complex fluoberyllate glasses containing Ni2+ ions are yellow. 4. Replacing 02- ions by the less polarizable OH- ions. Exposure

419

EfTect of Heat Treatment

D

C

Fig. 1.

420

of alkali silicate glasses containing Ni^+ ions (K+ - silicate) to water vapor over extended periods of time causes H2O to diffuse into the glass and, as the diffusion of H2O proceeds, zones are produced in which the purple color has changed into yellow. The opposite effect, namely, the change of the yellow and gray colors toward purple corresponding to the change of the coordination from six to four, is observed if the polarizability of the O^- ions is increased. 1.

For example :

Replacing some Na+ ions of sodium silicate glass by the weaker

or less polarizing K+ or Rb+ ions. Rubidium silicate glasses con­ taining NiO are pure purple and their absorption spectra reveal the absence of yellow color centers. 2) Increasing the polarizability of the

ions by raising the

température. Due to thermal expansion the average internuclear distances are increased and the State of deformation of the O^- ions decreases. Increasing the température shifts the equilibrium from the yellow NiOg groups toward the purple Ni04 group (Fig. IC). 3. Chilling a glass rapidly from a high température “ freezes in ” a high température modification which is characterized by a lower density and a greater polarizability of its anions. A chilled glass is more purple than the same glass after annealing (Fig. ID). Hydrostatic pressure decreases the polarizability of the anions and, with it, their screening power. T. Fôrland, in the author’s laboratory, found that a purple-gray alkali silicate glass changes into a yellow one permanently when exposed to high pressure (30,000 atm.) at températures around 450 °C. These observations agréé with those of geochemists who associate the occurrence of aluminium in minerais in the higher coordination, i.e., sixfold, with their formation under high pressures.

IV.

ATOMISTIC INTERPRETATION

OF SOME SOLID STATE REACTIONS The concepts which were developed in the preceding chapters make it possible to présent an atomistic picture of the activated State of Chemical reactions. It is postulated that the activated State corresponds to a State in which the cations are screened to a lesser 421

extern than in the reactants and in the reaction product. The activ­ ation energy of a solid State reaction is the energy which is necessary to temporarily increase the volume of the reactants and to partly unscreen cations. This concept applies to phase transformations of the reconstructive type, to sintering and recrystallization as well as to Chemical reactions between solids. 1. Phase transformations The spectacular différences which exist between the fast a-^inversion of quartz and the sluggish inversion of quartz into tridymite or cristobalite and the pseudo-stability of cristobalite in nature led to a classification of phase transformations into two groups, “ displacive ” and “reconstruction” transformations. M. J. Buerger suggested that fast transformations involve a displacement of non-contacting atoms with respect to one another without the need for disrupting the linkage of the three-dimensional network and the formation of a new one. With respect to the recon­ structive transformation he writes : “ It necessarily involves a temporary breaking of first coordination bonds. This represents a very high energy barrier. Evidently this transformation must proceed in a sluggish fashion indeed. ” The geometry of the transformation is, no doubt, important but it is not the only rate determining factor. The red form of mercuric iodide, for example, cannot be overheated to an appréciable extent. Within a few degrees above 126 “C it changes into the yellow modification which is stable above this température. The yellow form contains Hg^+ ions surrounded by six l~ ions in a distorted octahedral arrangement. The red modification has a layer structure which is quite different from that of the structure of the yellow modification. The Hg2+ ions in red Hgl2 are surrounded tetrahedrally by four équidistant I~ ions. The formation of such a layer structure may be treated as the first step toward the transition from a three-dimensional infinitely-extending network into independent molécules.

In this first step electrically neutral layers are formed

which extend infinitely only in two dimensions. Considering the geometry one would expect that the change of the low température form of Hgl2 into the high température form would be a sluggish transformation. This change and similar changes

422

of complex iodides, however, are so fast that they are used as tem­ pérature indicators (silver mercuric iodide, copper mercuric iodide). In order to understand the mechanism of these modification changes and, generally speaking, of the rates of solid State reactions, we must abandon concepts such as those of “ breaking a bond ” and “ formation of a new bond ” because they hâve no physical significance in solid State chemistry. The activation energy of phase transformations of the recon­ structive type is given primarily by the energy necessary to partly unscreen the cation. In these iodides containing polarizable cations this energy term is very low. 2. Recrystallization and sintering The driving force in sintering or recrystallization is the lowering of the free energy of the System by decreasing the surface area and, with it, the surface free energy. P. A. Marshall, Jr. in the author’s laboratory studied the sintering of Cap2 and Bap2 pellets.

The

volume change of these pellets on heating reveals that Cap2 begins to sinter at a température 100 “C lower than Bap2 in spite of the fact that Bap2 has a lower melting point than Cap2- The low polarizability and the relatively high field strength of the Ca2+ ions causes Cap2 to hâve a higher surface energy than Bap2- This provides a greater driving force for Cap2 to lower its free energy by decreasing the surface area and, with it, the number of incompletely screened cations. These experiments show that in sintering, the rate of the reaction can be proportional to the driving force and inversely proportional to the résistance of the reacting System. However, one has to keep in mind that the “ driving force ” of a reaction déterminés its rate only in those cases where the equilibrium is actually an oscillation in which small volume éléments switch back and forth between both configurations, a situation which has been called “ microscopie reversibility ” by S. R. De Groot (^i). Non-noble gas-type cations because of their greater polarizability can lower the surface energy of a crystal which contains noble gastype ions. Thus, two solids in contact, e.g., AI2O3 -f- Cr203, may lower their free energy by covering the one with the least polarizable cation (AI2O3) with the one which has the more polarizable cation (Cr203).

G. P. Hüttig (32) observed this “ creep ” of one oxide

423

over another, a process which lowers the driving force for sintering. P.

W. Clark and J. White (33) found that the addition of 4 %

Cr203 to AI2O3 prior to pressing slowed down the rate of sintering of the alumina without afïecting the ultimate shrinkage. W. E. Brownell (34) in the author’s laboratory made a quantitative analysis of solid State reactions producing different spinels.

He

found that the addition of PbO slows down the rate of the reaction between MgO and AI2O3. The stabilization of a System by lowering its surface free energy is the driving force for sintering. The energy barrier or the activation energy of this process can be attributed to the partial unscreening of cations and the répulsive forces which corne into play if one cation has to pass another cation. For example, if a sodium ion has to move through the lattice of NaCl during thermal diffusion or in an electrical field, it has to squeeze through between other Na+ ions and Cl~ ions. In this position it will be strongly attracted by the Cl“ ion and repelled by the Na+ ion. We emphasize in our approach the répulsive forces between cations more than those between anions because anions exert weaker forces upon each other because of their mutual polarization. Many crystals can be described as arrays of anions which touch one another and which are held together by cations. However, noble gas-type cations as neighbors are not likely to occur in crystal structures. The volume expansion which accompanies the melting of the alkali halides is an indication of the repulsion between the cations. This has been discussed previously (35) and V. Zackay (36) pointed out that this volume effect during melting decreases with increasing polarizability of the cations as well as of the anions so that it is a minimum for the alkali metals. One might suspect that there is a simple relation between diffusion processes, e.g., sintering, and the absolute melting température.

This, however, is not the

case because of the paramount importance of vacant lattice sites for diffusion. Zinc oxide (M.P. 1975 °C) sinters at 700 °C because this crystal can form a defective structure. On heating, ZnO cleaves off oxygen and forms anion vacancies : Zn2+ 02- = Zn2+ (e-)2* (A.V.)* 0?I^ + x O.

424

The defective crystal has anion vacancies which make rapid diffusion possible. The very low polarizability of the Mg2+ ion is responsible for the fact that MgO forms lattice vacancies only at much higher températures.

However, in the presence of cations which hâve a

higher (Fe3+) or a lower (Li+) charge than the Mg2+ ion the gain in entropy causes MgO to form a solid solution at lower température (~ 1,500 °C) which contains cation vacancies or anion vacancies respectively : Fe^+ (C.V.)o,5,

-

02

and

Mg?!, Lii (A.V.)o.5, Oto.5. The addition of iron oxide to magnesite is used in the manufacture of magnesite refractories. The sintering of zinc oxide can be enhanced by the addition of Li20 (more anion vacancies) and delayed by the addition of Ga203 or AI2O3 because the latter additions prevent the lattice from developing anion vacancies at a température where the zinc oxide partly dissociâtes. Sintering and recrystallization processes are closely related to Chemical reactions and the following two examples illustrate that foreign atoms can enhance and prevent Chemical reactions in exactly the same way as they can affect sintering. The reaction of calcium Carbide with nitrogen to form cyanamide is very slow even at 1,000 °C but it can be greatly accelerated if calcium chloride or fluoride is added. According to G. Bredig Q~>) CaCl2 or NaCl catalyze the reaction but Na2C03 and CaC03 do not. At 1,000 °C the CaC2 crystal can gain entropy by forming a solid solution in which some (€2)2- ions are replaced by singly charged F“ or Cl- ions so that the lattice develops cation vacancies. Ca2+(C2)2-

^ Ca?!, (C.V.). (C2)?l2. CI2-

Replacing 2x (€2)2- ions in the Carbide by the same number of singly charged Cl- ions produces x cation vacancies per mol. The additions of foreign atoms may accelerate a Chemical reaction but they can also delay and even prevent it. NiO of stoiehiometric composition is green but on heating in air it forms a defective struc­

425

ture, a higher oxide which is black. As one would expect, the black oxide can react with metallic nickel and form the green stoichiometric NiO. Addition of Li20 is another way to change the green NiO into the black form. The two black oxides, one obtained by oxidation, the other by substitution, hâve identical electronic properties. This is expressed in their formulae by indicating that both structures lack X électrons per mol. The (+) sign indicates one “ misslng électron ” per mol. Nifis.sx (+)x (C.V.)o.5;, Nifî, U: (+),

-

02

and

-

02

The oxidized NiO contains cation vacancies and is chemically reactive. The Li+ substituted NiO does not contain cation vacancies and, consequently, it does not react with metallic nickel to form the green NiO. 3. Décomposition reactions The fact that CO2 is a gas at ordinary température indicates that the core of carbon C‘*+ is well screened by two 02- ions. A carbon core, however, may require tbree or four

- ions if the

02

latter are less polarizable. In carbonates a part of the excess charges of the 02- ions are neutralized by weak cations, e.g., Na+, K+, Ba2+, etc., therefore, the planar (€03)2- group becomes stable. As the field strength of the contrapolarizing cations and, with it, the tightening of the électron clouds of the 02- ions increases, the carbonate becomes less stable. In tbis case the carbon is better screened either by having two 02- ions of its own or it expands its coordination to four less polarizable 02- ions. The latter con­ figuration exists in the esters of the orthocarbonic acid in which each 02- ion is tightened by two carbon cores. The configuration (004)4- can also be obtained under high pressure because hydrostatic pressure decreases the polarizability of anions. W. Skaliks (28) thus prepared a potassium magnésium carbonate glass and W. A. Weyl (29) melted sodium carbonate-silicate glasses in which CO4 and Si04 groups are interlinked. The equilibria between carbonates and oxides plus CO2 illustrate how the screening power of an anion is affected by surrounding

426

positive fields. Table I gives the stability of some carbonates. BeC03 décomposés at 100°C whereas BaC03 bas a stability which compares with those of the alkali carbonates. The stabilities of the carbonates of Mg, Ca, and Sr are intermediate between these two extremes. The weaker the field of the contrapolarizing cation the greater is the stability of the (€03)2- group. Table I also shows that the Pb2+ ion and the Zn2+ ion hâve stronger polarizing effects upon the 02- ions of the CO2- group than noble gas-type ions of similar size and the same charge. If one goes to more highly charged cations one finds that only the large La3+ ion in La2Û3 provides 02- ions of sufficient polarizability to allow a direct reaction with gaseous CO2. No carbonate of aluminium has been prepared. The stability of the (€03)2- complex decreases with decreasing TABLE I Stability of some carbonates

Compound

Size of cation

Heat of formation

Décomposition température “C

CS2CO3

1.65 A

97 Kcal

very high

Rb2C03

1.49

97

very high

K2CO3

1.33

95

very high

Na2C03

0.98

78

very high

L12C03

0.78

56

1270

BaCOs

1.43

64

1360

SrC03

1.27

57

1275

CaC03

1.06

44

812

MgC03

0.78

28

500

BeC03

0.34

PbC03

1.32

23

350

ZnC03

0.83

16

300

Ag2C03

1.13

20

220



100

427

polarizability of its 0^~ ions.

The polarizability of the

ions

decreases with . increasing charge of the contrapolarizing cation, i.e., in the

1

order Na+, Mg2+, AP+ ; 2. decreasing size of the cation, i.e., in the order Ba2+, Sr2+, Ca2+; 3. changing electronic configuration of the cation from noble gas-type (Mg2+) to those with 18 outer électrons (Zn2+) and, finally, to those with incomplète électron shells (Cu2+). Some metals which cannot form stable carbonates can form basic carbonates. In these compounds the anion to cation ratio and, with it, the screening of the métal ions is increased so that the électron cloud of the (€03)2- group is less deformed. Cu2+(C03)2- is not stable but Cu2+(€03)2-(OH)j, malachite, and Cu^+(€03)2“ (0H)2, azurite, occur in nature. Because of the single charge of the OH~ ion the basic carbonates of copper hâve an anion to cation ratio which is greater than 1:1. With increasing thermal motion a Mg2+ ion in MgC03 distorts the (C03)2- group to such an extent that the carbon core is better screened by two independent 02“ ions. Leaving an 02“ ion behind, a gaseous CO2 molécule escapes and the System gains entropy; firstly, because of the formation of a gas, secondly, because of the disorder which is introduced into the magnésium carbonate crystal. Equations such as MgC03 = MgO “h CO2

do not properly describe the reaction; as a matter of fact, they hâve been misleading. They do not indicate that the process occurs in two steps, namely, first the formation of a defective structure Mg2+ (C03)2“ = Mg2+ (CO})t, (02-1 + X CO2 in which a small fraction of the (C03)2“ anions are replaced by 02“ ions and, secondly, the formation of MgO nuclei. The poor reproducibility of experimental data and the discrepancy between experimental and theoretical dissociation températures and pres­ sures hâve annoyed physical chemists for a long time. Recently, E. Cremer (40) demonstrated that only under experimental conditions

428

which keep the volume of the gas phase very small do the dissociation pressures of MgC03 agréé with the values obtained from thermodynamic data. A magnésium carbonate crystal consists of unions and cations which hâve a low polarizability so that it can lose only a very small quantity of CO2 and still retain its original structure. Thermodynamic data fix the dissociation pressure of one atmosphère at a température of 350 °C.

This température is approximately 200 °C lower than

the average of the widely scattered experimental data which were accumulated by various workers ever since H. Le Chatelier (1887) made the first comprehensive study on the décomposition of this carbonate. The thermodynamic treatment does not take into considération the fact that the first MgO nuclei which form as an independent phase require a high energy for nucléation. By choosing the proper experimental conditions, in particular a small volume of the reaction vessel, one restricts the reaction to the formation of defective magnesite and, thus, éliminâtes the nucléation of periclase. By this method E. Cremer obtained dissociation pressures for MgC03 which are close to the theoretical value and which did not change with time. 4. Metathetical reactions When heating a mixture of BaO and CaC03, J. A. Hedvall and J. Heuberger ("*i) observed an exothermic effect at 345 °C. The endo­ thermie effect at 900 °C which was expected from the dissociation of CaC03 was absent because the mixtures had reacted at 345 “C according to CaC03 + BaO = BaC03 -f CaO. In this reaction the large anion (€03)2- combines with the large cation Ba2+ and the small Ca2+ ion (greater polarizing power) combines

with the small more polarizable 0^~ ion.

Therefore

the C4+ core of the (€03)2- group improves its screening because the more contrapolarizing Ca2+ ion is replaced by the weaker Ba2+ ion. The reactions studied by Hedvall and Heuberger (Sâureplatz wechsel reaktionen) are well suited for illustrating the application of the screening theory to the equilibria and to the rates of meta­ thetical reactions in the solid State. The températures were determined

429

430

TABLE II Solid State reactions (After J. A. Hedvall an J. Heuberger) Reaction with CaO Sait

Reaction Products

Reaction with SrO Temp.

Reaction products

Reaction with BaO Temp.

Reaction products

Temp.



BaC03 + SrO

395 “

SrCOa

No reaction



No reaction

CaC03

No reaction



SrC03 + CaO

465“

BaCOs + CaO

345 “

MgCOj

CaCOs + MgO

525 “

SrC03 + MgO

455 “

BaC03 + MgO

345“

SrS04

No reaction



No reaction



BaS04 + SrO

370“

CaS04

No reaction



SrS04 “h CaO

450“

BaS04 + CaO

370“

MgS04

CaS04 + MgO

540“

SrS04 + MgO

440“

BaS04 + MgO

370“

ZnS04

CaS04

ZnO

520“

SrS04 + ZnO

425“

BaS04 + ZnO

340“

CUSO4

CaS04 + CuO

515“

SrS04 + CuO

420“

BaS04 + CuO

345 “

Sr3(P04)2

No reaction



No reaction



Ba3(P04)2 + SrO

350“

Ca3(P04)2

No reaction



Sr3(P04>2 + CaO

450“

Ba3(P04)2 + CaO

340“

Pb3(P04)2

Ca3(P04)2 + PbO

525 “

Sr3(P04)2 + PbO

455 “

Ba3{P04>2 + PbO

355 “

C03(P04)2

Ca3(P04)2 + CoO

520“

Sr3(P04)2 + CoO

465 “

Ba3(P04)2 + CoO

355 “

at which the oxides of the alkaline earths began to react with carbonates, sulfates and phosphates (Table II). In ail of these reactions an oxide of an alkaline earth reacts with a sait which contains a cation of greater field strength (greater polarizing power) than that of the oxide. The anion of the sait is larger and has a low polarizability because its O^- ions are strongly tightened by a central core of high field strength, C^+, P5+ and

®+. The driving

8

force of this group of reactions is the gain in energy by combining the smallest, i.e., the most polarizing, cation with the most polarizable anion, the 0^~ ion. If the cation of the sait is of the nonnoble gas-type, there can be an additional energy gain through the formation of a defect structure. CuO, for example, which forms from the mixture of CUSO4 + BaO does not hâve a stoichiometric composition but takes up an excess of oxygen, thus forming a semiconductor with a higher entropy. It is this gain in entropy through the formation of defective crystals which stabilizes the wustite phase in a température région where the “ perfect ” FeO should disproportionate into Fe and Fe304, according to the beats of formation. T. Fôrland and W. A. Weyl (“*2) pointed out the importance of the increase of mutual polarization as a “driving force ” in glass technology and in geochemistry. As the température of our planet decreased, éléments which are more interpenetrable, e.g., cobalt, combined in the original magma with the most polarizable anions, e.g., 82-, As2-, etc., and formed the ore bodies, whereas the less interpenetrable noble gas-type ions formed silicates, carbonates, etc. The séparation which took place in our planet on a gigantic scale is used commercially for producing certain colored glass, e.g., sélénium ruby. In such a glass, small amounts of a non-noble gastype cation (Cd2+) and of large polarizable anions (82-, 8e2-) are introduced. At high température the distribution of the anions is a random one, but as the glass cools or is reheated it “ strikes ”. The Cd2+ ions now surround themselves preferentially with 82and

e - ions, thus, producing the red pigment of this ruby glass.

8 2

Let us now turn to the rates of these reactions or to the “ tem­ pérature of beginning reactivity ”. J. A. Hedvall and J. Heuberger found that each alkaline earth oxide began to react within a relatively small and characteristic température région. 8urprisingly, the nature of the sait with which the oxide reacted had little influence upon its reactivity. Barium oxide began to react between 350 and 400 °C

431

and it was immaterial whether the other reactant was a sulfate, a carbonate, a silicate or a phosphate. Strontium oxide required a higher température, namely 450-500 °C, and calcium oxide a still higher température, 500-550 °C, in order to react. These température ranges of beginning reactivity are fairly well defined and are sufficiently far apart so that they must be significant. The reactions chosen by J. A. Hedvall and J. Heuberger are truly solid State reactions and do not involve reactions through the vapor phase or through a polyeutectic melt. This leaves surface diffusion and volume diffusion as the only possible mechanisms. For reasons which were discussed earlier, crystals such as CaO or MgC03 are not likely to form a large number of vacant lattice sites in the température région where their reactivity was observed. This minimizes the contribution of volume diffusion and makes it likely that most of these reactions begin with surface diffusion. This raises two questions : What are the diffusing units? What are the energy barriers? The first reaction listed in Table II, namely, MgC03 + CaO = MgO -f CaC03, becomes noticeable at 525 °C.

At this température MgC03 dis­

sociâtes and the CO2 creeps over the surface of the CaO where it lowers the surface energy. This creep probably takes place even at lower température but the température of 525 °C is the one where the CaO becomes sufficiently reactive in order to form nuclei of CaCO}. In contrast to the film formation in tarnishing reactions, these nuclei grow into independent crystals and do not coat and separate the reactants. The diffusing units are electrically neutral or nearly so. The central cores of these complex anions, so to speak, carry along sufficient 02- ions to be neutral or weakly charged (CO2, SO3, POj, SiOj”) and complété their coordination with the surface 0^~ ions of the oxide. According to this picture, a creeping SO3 group can always be described as an ion. The surface ions of the oxide participate in the screening of the S^+ core and the diffusion process does not involve “ breaking of bonds ” and formation of new bonds. During motion the inter­ action of the S^+ core is merely shifted from one 0^~ ion of the oxide surface to its neighbor. This concept of a graduai change of the State of polarization and, with it, of the binding forces has been

432

developed by the author in order to understand the viscosity of glasses. The crucial moment in these reactions cornes with the removal of (C03)2- or (804)2- groups from the surface of the oxide and their arrangement into a new phase. This process leaves the cations of the oxide partly unscreened.

This temporary unscreening of

the cations of the alkaline earth oxides is considered to be the major energy barrier of these metathetical reactions. This concept is akin to the ideas of J. A. Hedvall not only with respect to the low charge of the diffusing units but also to his “ predissociation ” of compounds.

5. Reaction between acidic and basic oxides The author considers the acidity of a System to be inversely proportional to the degree of screening of its cations. The acidity of SFg is zéro because the S®+ core in this molécule is completely screened. It has become customary to use pure water as a neutral point and call Systems in which the proton is better screened bases and those in which it is less screened acids. We found that the screening concept can be easily coordinated with other Systems of acidity without leading to contradictions. According to our concept, the acidity of a reacting mixture of MgO and AI2O3 goes through a maximum as the degree of screening goes through a minimum in the active intermediate State. The screening approach more than any other concept of acidity impresses upon us the deep meaning of Sir Humphrey Davy’s remark that the acidity dépends upon a “ peculiar arrangement of varions sub­ stances” (1814). One of the most important proton-donating catalysts, the alumina-silica catalyst, owes its high acidity to the peculiar arran­ gement of AP+ and 02- ions. Déhydration of the coprecipitated gel forces the AP+ ions to assume the coordination number of four without permitting the Al-0 distances to become as small as they are in stable AIO4 groups. If we keep in mind that acidity and basicity are relative and that Si02 is an acid with respect to CaO but a base with respect to P2O5,

433

we may still follow the established custom and talk about reactions between acidic and basic compounds, e.g., CaO + Si02 = CaSi03 Numerous

reactions

between

basic

and

acidic

oxides,

e.g.,

CaO + Si02 or CaO + UO3, bave been examined by G. Tammann and bis scbool. Tbe driving force of tbese reactions is tbe improvement of screening of tbe cations of tbe acidic oxide by surrounding tbem witb anions of greater polarizability. Tbese solid State reactions, e.g., tbe formation of tbe uranates of tbe alkaline eartb oxides from tbe acid UO3 and tbe base MgO MgO + UO3 = MgU04, can be treated in tbe same fasbion as tbe metatbetical reactions. Indeed, G. Tammann and W. Rosentbal (^3) found BaO to be more reactive tban CaO and CaO more reactive tban MgO. Here, too, we can assume tbat neutral UO3 molécules creep over tbe surface of tbe oxides utilizing surface ions in order to com­ plété tbeir screening. At relatively low température tbis creep coats tbe oxides witb UO^” groups wbicb lower tbe surface energy. Again, tbe beginning of tbe reactivity is determined by tbe alkaline eartb oxide.

Tbese reactions between an acid and a base or between

two salts (metatbetical reactions) bave two features in common. 1. Tbe anion becomes mobile at relatively low température because it can meet tbe requirements of tbe two basic principles : forming electrically neutral or weakly cbarged groups in wbicb tbe central core is sufficiently screened as long as it can utilize tbe surface anions of tbe otber reactant for additional screening. 2. Tbe reaction températures are relatively low and are deter­ mined by tbe energy necessary to partly unscreen tbe alkaline eartb ions. Otber reactions involving alkaline eartb oxides require mucb bigber températures. As compared witb tbe formation of calcium uranate (600 °C), tbe formation of calcium zirconate begins at 1000 °C. Tbe bigb température modification of Zr02 (fluorite structure) reveals tbat eacb Zr^+ ion must be surrounded by eigbt 02- ions in order to be properly screened. Tbe large Zr^+ ion cannot possibly migrate witb less tban six anions and even if we assume

434

that one of the six O^- ions belongs to the surface of CaO it still hasto “ carry along ” fiveO^-ions whereas the Zr4+ ion neutralizes only two 02- ions. The diffusion of a highly charged unit such as a (Zr04)4- or (ZrOs)^- group is not likely to occur at 600 °C. As a resuit, the reaction proceeds only at a much higher température where the screening demands are less. In reactions with oxides of the general formula X4+ it is not the alkaline earth oxide alone which détermines the beginning of reactivity. The temporary unscreening of an X"*+ ion requires a température which increases with increasing coordination number of X^+. The screening demand of these cations increases with increasing atomic weight and ionic size as can be seen from their coordination numbers : C4+ 2, Si4+ 4, Ti4+ 6, Sn4+ 6, Zr^+ 8. CaO begins to react with Si02 at 400 °C, with TiÛ2 at 675 °C, with Sn02 at 900 °C, and with ,Zr02 at 1000 °C. The screening power of the 02- ions for a Si^+ or a Ti4+ ion increases with increasing polarizability. For this reason one finds that more basic compounds, e.g., Ca2Si04, form faster even if the acid oxide is présent in a large excess. 02- ions contrapolarized by Ca2+ ions are better screeners than those exposed to another 8^+ ion. The greater the R2+ Q2-■ x‘*+ ratio, the lower is the energy barrier of the reaction. Mixtures of oxides such as BeO, MgO, AI2O3, Zr02 and Si02 react only at very high températures because the screening demand of the cations is strong and the oxygen to cation ratio is rather low. For this reason it is not possible to synthesize béryl, Be3Al2Si60ig, without a catalyst (additional screener, H2O). AU of the eleven cations of this molécule hâve a high field strength and they are neutralized by only 18 02- ions. In order to cause such a System to react, températures would be required which are above the stability région of the béryl (1450 °C).

6. The nature of Hüttig’s “ Active Intermediate State ” The formation of Ag2Hgl4 from Agi and Hgl2 is one of the few solid State reactions for which the quantitative data are in good agreement with the theory (44). In contrast to reactions involving solids with highly polarizable cations and anions such as iodides and sulfides, the reactions between the oxides MgO, AI2O3, and Si02 seem to offer greater difficulties with respect to the inter-

435

pretation of their rates.

Those who are active in the field of solid

State reactions are well aware of the experimental difficulties which are involved if one wants to follow quantitatively the formation of a spinel. However, aside from the general difficulties which lie in the nature of reactions between powders with poorly defined shape and surface area, the formulation of some solid State reactions is more compücated than of others. In the reactions which were chosen by C. Wagner and his school, the State of affairs at any moment can be described by the quantities of the reactants and that of the reaction product. For other reactions, however, such a description is not applicable. The formation of spinel from MgO and AI2O3 produces phases which are different from both the reactants and the reaction product. These phases which may hâve very characteristic physical and Chemical properties hâve been called “ Active Zwischenzustande ” by F. Hüttig who has contributed much to their identification. The formation of spinels has been studied by several workers and this reaction provides a good example for the unusual properties of the metastable intermediate State. W. Jander and K. Bunde (^S) studied the reaction of the mixture ZnO + AI2O3 in the ratio 1:1 by heating it stepwise to increasing températures until a well crystallized spinel ZnAl204 had formed. Each step was examined with respect to its catalytic activity (CO-O2 combustion), its sorbing power for an azo dye dissolved in benzene, and the solubilities of ZnO and AI2O3 in NH4CI, HCl, and H2SO4. Ail of these Chemical reactivities went through maxima for mixtures which had been treated in the température range between 600° and 900 °C. In a later paper with H. Pfister (“*6) W. Jander States : “ We must not forget that we know absolutely nothing about the State and the energy of the active film ”. In reality W. Jander and other workers in this field were amazingly well informed about the conditions which affect the formation of an active intermediate State. Thus, for example, W. Jander mentioned that éléments which form several States of valency are not conducive to produce a highly active inter­ mediate State. According to our views, the polarizability is the missing link for the understanding of the active State.

The ions

of éléments, e.g., Fe or Cr, which occur in different valencies are more polarizable than those of the noble gas-type. As a rule, éléments

436

which form noble gas-type ions hâve only one valency over a wide température région. W. Jander also mentioned the possibility that Cr3+ at a surfaee may form CrO^ groups even if the quantity of chromate ions is too small to be detected analytically. Again he had the right intuition. We were able to prove that oxidation of Cr^+ to Cr^+ and of Co^+ to Co^+ occurs when these ions are adsorbed on the surface of silica gel and the System heated in air to 300-400 °C. The formation of the magnesia spinel, MgAl204, from the oxides shows essentially the same features as that of the zinc spinel. The reactivity as a function of beat treatment seems to follow a simpler pattern than that of the System Zn0-Al203 probably because in the latter the probability of forming electronic defects is greater. Around 800 °C a State is obtained in which the mixture of MgO +AI2O3 hasits maximum reactivity. Especially the occurrence of a maximum in the dyestuff adsorption and a maximum in the hygroscopicity are direct proofs for the unscreened nature of the active State. The incomplète screening of cations also increases the cation-cation repulsion so that one must expect that the volume of the reacting System also goes through a maximum. Now we can answer W. Jander’s question concerning the structure of the active intermediate State : A mixture of oxides which contain cations with a strong screening demand, e.g., Mg2+, AP+, or SH+, has to go through an “ active State ” in order to react in the solid State because of the volume expansion (first principle) and the unscreening (second principle) which are necessary before the cation can occupy new equilibrium positions. In this active State the System exhibits a Chemical reactivity which is greater than those of both the reactants and the reaction product. The reaction with H2O from the atmosphère (hygroscopicity) lowers the free energy of the System by increasing the anion to cation ratio, i.e., by changing some 02- ions into twice the number of OH- ions. From a poorly screening liquid (benzene) the active phase attracts and chemisorbs polar dye molécules in order to improve the screening of surface cations. We mentioned earlier that the acidity of a System is inversely proportional to the degree of screening of its cations.

On this basis

we can understand another characteristic feature of the active inter­

437

médiate State, namely, its ability to donate protons.

This property

is utilized in the cracking and isomerization catalysts, e.g., the alumina-silica type, which are obtained from oxides or hydroxides which, by themselves, are not good catalysts. Neither B2O3, Si02, MgO, AI2O3 nor Zr02 are useful cracking catalysts by themselves. Coprécipitation of two of these oxides, however, produces a solid which has the ability to donate protons at about 500 °C. In their partly reacted State these oxides undergo a reaction with H2O and organic molécules which can be described as an “ oscillation of the coordination number ” in the same fashion as one can describe the catalytic activity of vanadium or iron oxide with respect to the oxidation of SO2 to SO3 as an “ oscillation of the valency ”. In the course of the proton donation reaction a surface cation improves its screening by changing an (OH)“ ion into a better screening O^ion.

This process leads to charged particles.

W. Jander also raises a question concerning the energy relations of these intermediate States. This question can be answered on the basis of two recent papers, one on the apparent surface energy of crushed quartz and the other on the beat of reaction of thoroughly degassed alumina. A. Bondi ("*■?) called attention to the discrepancy which exists between the energy requirements for producing a quartz surface by fracture and the Chemical potential of this surface. The energy consumed in the crushing of very brittle substances might be ascribable to the energy required for the création for new surfaces only since energy processes are probably negligible. Hence, the energy absorbed in crushing per unit of surface generated ought to be a measure of the total surface energy. The crushing of quartz led to a value of the total'surface energy of 70-80000 ergs/cm^ by measurement of crushing energy, and of 107000 ergs/cm^ by bail mill calorimetry, numbers which are out of proportion to the data for liquid silica (200-260 ergs/cm^). These large “ surface energies ” may, however, constitute the amount of energy stored in the surface as a resuit of the scission of Chemical bonds and the local lattice deformation. Referred to a layer depth of one Si02 molécule (3.2 A.U.) the calorimetric value gives 3.3 X 10>2 ergs/cm2 = 93 e.v. per mole of silica in the surface an altogether impossible magnitude. But, even if one assumes the energy to be stored in the three molecular layers nearest the

438

surface, the energy would still be of the order of

20

e.v. per mole,

i.e., of the order of ionization energies. According to our concepts the potential energy in the quartz is stored in a surface film which is several hundred atoms deep, the distortion of which is strongest in the surface but tapers olî very gradually toward the interior. From the viewpoint of screening, the energy requirement for producing 1 cm2 of a new surface must be greatest if the quartz is crushed in vacuo and it must decrease with increasing ability of the environment to screen the fields of the Si"*+ ions. E. B. Cornélius, T. H. Milliken, G. A. Mills and A. G. Oblad (48) dehydrated alumina and found that the beat of reaction for the first 0.3 wt. % of water is greater than 105 Kcal/mole, i.e., of the same magnitude as the reactions between chlorine and alkali metals. The beat of reaction drops off with increasing water content and reaches 10 Kcal/mole for alumina with 3 % water. Arrays of cations with insufficient screening corresponding to Hüttig’s intermediate State can be obtained in several ways : 1. Mixing of oxides and allowing the mixture to react under conditions (time, température) which do not permit the reaction to go to completion (F. Hüttig, W. Jander). 2. Déhydration of a coprecipitated gel of hydroxides, e.g., A1(0H)3 + Si(OH)4, under conditions which decrease the anion to cation ratio by the reaction 2 (OH)- = 02- + H2O. An AF+ ion can be satisfactorily screened either by six or by four 02- ions. In the latter case, however, the four 02- ions hâve to corne doser to the AF+ ions so that they can be more strongly deformed. By coprecipitating Al(OH)3 with silica, the rigid silica network prevents the 02- ions from moving into such a position so that ail cations remain insulficiently screened. 3. Déhydration of a hydrated clay minerai under conditions which decrease the anion to cation ratio by changing OH“ into 02- ions (gain in entropy) without giving the System a chance to form the equilibrium structure which would be mullite plus silica.

439

L.

Tscheichwili, W. Büssem and W. A. Weyl (‘*9) found that the

déhydration of kaolin leads to a defective lattice in which the AP+ ions are in fourfold coordination. Déhydration takes place at a température which is characteristic for the particular clay minerai. When carried out carefully the déhydration of kaolin can lead to a highly reactive, metastable phase which has been called “ metakaolin ”. If this phase is prepared at a température not exceeding 600-700 °C it can be partly rehydrated. The Chemical characteristics of the metaphases, e.g., the solubility of alumina in HCl and the reactivity of metakaolin with Ca(OH)2, resemble those of Hüttig’s active intermediate phases. The same applies to the physical characteristics. The distortion of the lattices produces a rather diffuse X-ray scattering. The cation-cation répulsive forces of the incompletely screened AP+ and SH+ is responsible for their low densities. The volume expansion of clay minerais which accompanies the déhydration is so characteristic that it can be used for their quantitative détermination. Above 700 °C the lattice of metakaolin breaks down into AI2O3 and Si02 which at higher températures form mullite.

Water vapor

catalyzes this rearrangement of the metaphase into the more stable lattices of gamma alumina and cristobalite as can be seen from the experiments of G. F. Hüttig and E. Hermann (50) who found that under optimum heating conditions in oxygen or nitrogen approximately 12 % alumina became soluble in HCl. Déhydration of the kaolin in an atmosphère of water vapor, however, caused the maximum acid soluble alumina to drop to 8 % because the water catalyzes the formation of acid-insoluble aluminium oxide. In order to make déhydration and rehydration réversible both processes should be carried out at the lowest possible température.

7. Catalysts for solid state reactions In the preceding chapter an atomistic picture has been presented of the energy barrier which has to be overcome by a mixture of MgO and AI2O3 in order to form the spinel. A reaction of this type can be described as a reshuffling of AF+, Mg^+, and ions. The energy barrier consists of the overcoming of the Coulomb attractive forces between AP+ and 0^“ as well as between Mg2+ and Q2-. In addition these cations hâve to be temporarily unscreened.

440

The partial unscreening of Mg2+ and AP+ ions suggests that additions to the mixture which can provide temporary screening should lower the energy barrier. In some industrially important reactions this is donc by means of a flux which changes the solid State reaction into one involving a liquid phase.

However, screening can also be

achieved by a suitable gas phase. The most effective way to temporarily screen AP+ and Mg2+ ions consists of increasing the anion to cation ratio by a surface Chemical reaction with HF, HCl or H2O. The protons of these molécules enter the électron clouds of surface 0^~ ions changing them into OH~ ions and the rest of the molécules attach themselves to cations which need the screening most. The efîectiveness of these gaseous molécules as catalysts for the reaction of an oxide is due to their twofold action, namely, lowering the Coloumb forces between cations and ions by changing the latter temporarily into singly charged OH~ ions, and by providing additional temporary screeners, i.e., Cl“, OH~ or F“ ions which temporarily increase the anion to cation ratio. To many chemists the formation of “ hydroxides ”, even tem­ porarily, may seem to be strange; however, these facts are well established. Whereas the déhydration of Al(OH)3 is rather complété around 1,000 °C, alumina above its melting point reacts with water because the AP+ ions lose screening when their symmetrical environment of ions is replaced by a more random one. H. von Wartenberg (^i) made this observation when he fused corundum in different fiâmes some of which contained H2O (H2 + O2) and others (CO + O2) not. In the latter case alumina did not volatilize, but in the presence of H2O it did. At its melting point two phases of AI2O3 are in equilibrium; the crystal is better screened, but the liquid has the higher entropy and its cations are less screened. Through its reaction with H2O an oxide can increase its entropy without losing too much screening. This is the principle of using H2O as a catalyst in the method of hydrothermal synthesis. The catalytic effect of H2O and HF which accelerate the formation of spinels, silicates, etc. can be described in conventional terms. However, some gases hâve an effect on the rates of solid State reactions which makes it difficult to formulate the interaction in the conven­ tional Chemical terminology.

441

Our concept that reaction rates can be increased by the presence of screening électron clouds leads to the conclusion that chemically inert molécules such as N2 and even the noble gases, e.g., argon, can be catalysts. Noble gas atoms can enhance reactions by “ lending ” électrons to cations which require temporary screening in order to move into new positions. The volatility of silicates and of alumina in the presence of H2O is the resuit of the improved screening of the Si^+ and AP+ ions which causes depolymerization. As the screening of cations can also be improved by the électron clouds of inert molécules, one may expect that the volatility of an oxide is a fonction of the atmos­ phère and that it increases from hélium to xénon. J. A. Hedvall and O. Runehagen(52) were probably the first to observe and to hâve the courage to publish the effects of apparently inert gases such as SO2, O2, and N2 on the reactivity between different forms of silica with CaO. Recently, H. Forestier (l't) presented additional pertinent experimental material. The formation of the spinel NiFc204 from the oxides was found to be slowest in vacuo and fastest in an atmosphère of H2O and CO2. This fact can be explained on a conventional basis by attributing the catalytic efîect to the temporary formation of “carbonates” and “hydrates”. However, H. Forestier also found that this reaction is faster in an atmosphère of argon than in one of hélium From the viewpoint of screening, there is no need to distinguish between the noble gas atoms on the one hand and O2 or N2 molécules on the other. The polarizability of the électron clouds is the only parameter which déterminés their screening power. The fact that nitrogen or oxygen can form several valence States whereas argon cannot, has no influence upon this catalytic activity. We assume that during the rearrangement of Ni2+, Fe^+, and 02~ ions constel­ lations arise in which cations need additional screening in order to move from one equilibrium position into another. This temporary screening can be achieved either by hydration or by “ borrowing ” an électron cloud from an atom or molécule which is sufficiently polarizable. An adsorption process of very short duration due to van der Waals’ interaction may help an ion to overcome a certain energy barrier; van der Waals’ interaction thus can accelerate solid State reactions.

442

The fact that the électron cloud of an argon atom can act as a screener in a manner similar to that of a nitrogen molécule is completely in line with the findings of H. S. Frank and M. W. Evans (53) who found a relatively high entropy loss when argon was dissolved in water. The électron cloud of the argon atom acts as a screener for some protons of the water, and this process immobilizes a certain volume of water around the soluté (iceberg formation).

V. SUMMARY AND CONCLUSIONS

In order to understand the existence of solids at ordinary tempér­ ature, the author postulâtes that under normal energy conditions the nuclei of most éléments require a more complété screening by électrons than can be achieved by the number of électrons which neutralize the nuclear charge. In order to improve their screening and still conform with the basic principle of electroneutrality in the smallest possible volume, many molécules, e. g., NaCl, Si02, AI2O3, etc., do not assume their most probable State under ordinary conditions but lose entropy and undergo polymerization or con­ densation. The principle of maximum possible screening has been added to the principle of electroneutrality and it is shown in this paper how the two principles cooperate and govern the chemistry of solids. The main factors which déterminé the screening of a cation, e.g., the anion to cation ratio, the symmetry of the environment, and the polarizability of the anions, are discussed. In order to use the screening theory for explaining solid State reactions, one has to relinquish a concept which has been useful when dealing with gaseous molécules, namely, that of a constant Chemical bond between atoms. We prefer to use the concepts of K. Fajans who speaks of “ binding forces ” rather than of “ bonds The binding forces are changed over large distances if a surface or a defect in the interior of a crystal produces a disturbance. This concept of a “ depth action ” becomes important if one wants to understand the influence which a carrier exerts upon a catalyst or that of adsorbed gases upon the properties of solids. The variance of data on the CO2 pressure of MgCOs as a fonction

443

of the température and the discrepancy between the experimental data and the theoretical values for the dissociation température of this carbonate are used to demonstrate how the formation of defects can obscure phenomena which occur in crystals.

For this reason

the author studied the fundamental relations governing the condensed State in the glassy rather than in the crystalline State. The advantages offered by the glassy State are demonstrated for the coordination or screening requirements of Ni^+ ions as a function of composition, température and pressure. Using the concepts developed in the first part of this paper a few selected solid State reactions are analyzed with respect to the nature of their “ driving forces ” and their “ energy barriers ”. A physical picture of the “ active State ” and the “ energy barrier ” of solid State reactions is derived and the varions features of Hüttig’s active intermediate State are interpreted on that basis. Our définition of the energy barrier of solid State reactions as the energy requirement for partial unscreening of cations was used to explain the mechanism of catalysts, for example, the findings of H. Forestier that even noble gases, e.g., argon, can catalyze spinel formation. Our atomistic approach to solid State reactions made it pos­ sible to explain the mechanism of hydrothermal synthesis as well as the mineralizing action of gases such as HF, HCl and H2O. These phenomena are of interest to physical chemists, geochemists and geologists. The action of these gaseous molécules is twofold. They send protons into the électron clouds of oxygen ions in silica or silicates.

This changes the structure

.... Si4+02-SH+02-Si4+ .... temporarily into one in which the Si'*+ ions are bonded together by OH- ions rather than by 02- ions. We rightly expect two fluorides, e.g., 2 NaF + BeF2 = Na2BeF4 to react at a much lower température than two oxides 2 CaO + Si02 = Ca2Si04. This, after ail, is the basic idea of V.M. Goldschmidt’s model struc­ tures. The fluorides, i.e., the weakened models, are more reactive because their valence sums are only one-half of those of the oxides.

444

Thus, the change of O^- ions into singly charged OH“ ions lowers the reaction température. In addition to this weakening of the Si-O-Si-0 “ bonds ” by the protons, the F", Cl~, and OH~ ions increase the screening of the SH+ ions by temporarily increasing the anion to cation ratio, thus aiding depolymerization. This purely ionic picture is applicable not only to oxide Systems but even to organic compounds, in particular to hydrocarbons when we use the quanticule theory of Chemical binding. K. Fajans pictures a hydrocarbon chain as a row of €“*+ cores, the répulsive forces of which are overcome by the quanticules (cj), a pair of électrons quantized with respect to two neighboring cores .... (e^) C4+ (e^) C4+ (ci) C4+ .... In order to reshuffle such a chain either relatively high tempér­ atures are required (thermal cracking) or the Coulomb forces hâve to be weakened by sending protons into the (ci) quanticules. Isomerization, aromatization, polymerization, and cracking can be carried out at lower température in the presence of acids and proton donating catalysts. Thus, the extreme ionic concept and the quan­ ticule theory make it possible to treat the reshuffling of oxides and of hydrocarbons on a par.

445

VI. REFERENCES K. Fajans, “ Chemical Forces and Optical Properties of Substances ”, McGraw-Hill Book Company, New York (1931). (2) K. Fajans, Chem. Eng. News, 27, 900 (1949). (3) F. Ephraim, “InorganicChemistry”, 6thEdit., Oliver and Boyd, London (1954) (■*) E. C. Marboe and W. A. Weyl, Trans. Soc. Glass Techn., 39, 16 (1955). (5) W. A. Weyl, J. Phys. Chem., 59, 147 (1955). (^ W. A. Weyl, Office of Naval Research Technical Report, No 65, Contract N6 onr 269, Task Order 8, NR 032-264, The Pennsylvania State University, University Park, Pennsylvania, (June 1955).
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(31) S. R. De Groot, “ Thermodynamics of Irréversible Processes ”, Inter­ science Publ. Co., New York (1951), p. 15. (32) G. F. Hüttig, Discussions of the Faraday Society, No. 8 (1950), p. 215. (33) P. W. Clark and J. White, Trans. Brit. Ceramic Soc., 49, 305 (1950). (3‘*) W. E. BrowneU, Ph. D. Thesis and Office of Naval Research Technical Report, Nb. 54, Contract N6 onr 269, Task Order 8, NR 032-264, The Pennsylvania State University, University Park, Pennsylvania, August (1953). (35) W. A. Weyl, Trans. Soc. Glass Techn., 35, 469 (1951). (36) V. Zackay, Trans. Soc. Glass Techn., 37, 18 (1953). (33) G. Bredig, Z. Elektrochemie, 13, 69 (1907). (38) w. Skaliks, Z. f. anorgan. allgem. Chem., 183, 263 (1929). (39) W. A. Weyl, Glastechn. Ber., 9, 641 (1931). (“10) E. Cremer, Proc. Internatl. Symposium on the Reactivity of Solids, Gôtheborg (1952), p. 665. («) J. A. Hedvall, Reference 11, p. 169 ff. (42) T. Fôrland and W. A. Weyl, J. Am. Ceramic. Soc., 32, 267 (1949). (43) G. Tatnmann and W. Rosenthal, Z. anorgan. Chem., 156, 20 (1926). (44) E. Koch and C. Wagner, Z. Phys. Chem., B 34, 317 (1936). (45) W. Jander and K. Bunde, Z. anorgan. allgem. Chem., 231, 345 (1937). (46) W. Jander and H. Pfister, Z. anorgan. allgem. Chem., 239, 95 (1938). (47) A. Bondi, Chem. Rev., 52, 435 (1953). (48) E. B. Cornélius, T. H. Milliken, G. A. Mills and A. G. Oblad, in print, presented at the Meeting of the American Chemical Society (1955). (49) L. Tscheichwili, W. Büssem and W. A. Weyl, Ber. Deutschen Keram. Ges., 20, 249 (1939). (50) G. F. Hüttig and E. Hermann, Z. /. Elektrochemie, 47, 282 (1941). (51) H. von Wartenberg, Z. f. Elektrochemie, 55, 445 (1951). (52) J. A. Hedvall and O. Runehagen, Naturw., 28, 429 (1940). (53) H. S. Frank and M. W. Ewans, J. Chem. Physics, 13, 507 (1945).

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Discussion M. Hedvall. — The ideas presented by Prof. Weyl are of course very interesting especially because they try to give so to say a broad and general concept or picture of the many peculiarities of the solid State of matter. Prof. Weyl has in his publications often used the Word “ picture ”. He has also mentioned the close connection of his ideas with those of Fajans and V. M. Goldschmidt. There are different ways we hâve to go in order to solve the problems of matter. You can start directly from the problems of the nuclei and their électron shells and no doubt these are places where you by means of mathematical methods, using quantum mechanical and wave mechanical calculations, will gradually find the many enigmas answered. But you can also start in another way, the way which Prof. Weyl has chosen. And this way of thinking and working is very welcome to ail those who do not master the pure mathematical sort of thin­ king.

It is welcome because it is materializing the notions of which

many chemists hâve and will keep to hâve a need. Especially of course investigators working in contact with industries, wanting and having the task to develop technical applications. We hâve heard that Prof. Weyl is the first to emphasize that his ideas do not explain the mechanism of reactions or of lattice structure in details. But no doubt they are valuable and promising as a sort of germs, from which the growth will go down to deeper layers and details.

Intimate results will be achieved when différend kinds

of thinking meet and complété each other. After this more principal introductory remarks I should like to corne back to discussion of definite “ solid problems However I shall limit myself to put only one question, leaving the other ones to my collaborator Dr Lindner, who since many years occupies himself with studying the reaction mechanism by means of radio isotopes.

448

I should like to ask you whether you consider the imperfections you hâve talked about in ZnO as corresponding to equilibria or not. And I think you mentioned something like that also for some spinel Systems? I think it is not necessary to add that from that point of view the formulas do not tell us very much, because the structure is of course always depending on the conditions (starting material, tempér­ ature, time of heating, etc.) you hâve chosen for the production of the substance. Considering this, it must also be emphasized that it is not always easy to compare the qualities of dilîerent substances in exactly corresponding States.

M. Weyl. — It is not easy to give a definite answer to your question concerning defective crystals and equilibria. A defect raises the potential energy of a crystal but it also increases its entropy. As the entropy enters this expression of the free energy as a factor multiplied by the absolute température, one can assume that a true equilibrium is established with the number of defects increasing with the température. However at low température the diffusion of defects might become so slow that one deals with crystals whose defects correspond to “ frozen in ” equilibria. Indeed one finds that this disorder of many crystals is a fonction of their past Chemical and thermal history. The terminology which Fajans introduced in -order to describe e.g. SO2 as (e~2) S6^-(02-)2 has the advantage over other description that it is obvions that this oxidation of SO2 to SO3 can be catalyzed by V2O5, etc. because it consists of an exchange of an (e~2) quanticule for an 02- quanticule. Crystals like V2O5 can easily exchange - ions for électrons and vice versa so that they become catalysts.

02

It has been reported that ozone does not oxidize SO2 to SO3 so that this oxidation reaction is not an addition of an O atom. I agréé With Dr Hâgg that in many cases the Fajans description which I use is not essentially different from other description but it has the advantage of clearly showing the values of the binding forces. M. Hagg. — Prof. Weyl has given a report which treats a great many important problems related to solid State reactions.

I am

449

sure that Prof. Weyl’s statement of such problems will be of great value to ail working in this field because of its great stimulating effect. But I don’t think that the language chosen by Prof. Weyl in describing the Chemical bond is quite suitable. It is very important that there can be given an elementary description of the quantum mechanical ideas of Chemical bonds. But such a description can certainly be brought to conform more closely to the présent State of these ideas than does Prof. Weyl’s. It can thus be made much more useful but need not be more difficult to understand nor harder to visualize. Prof. Weyl has, for instance, showed how the “ quanticule ” method could be applied to the bonding in SO3 and SO2. But is it more difficult to apply the valence bond method, using sp'^ hybrid orbitals? This gives immediately the shape of both molécules. In addition, it explains the appearance of a non-localized tt bond. Several solid State reactions, in which Prof. Weyl uses the concept of screening, can be easily treated after the relative lattice energies of the phases hâve been estimated, according to usual elementary ideas. In some cases the “ quanticule ” language is obviously dangerous. A drastic example is the diamond lattice, where it requires the existence of two non-equivalent kinds of carbon atoms. M. Weyl. — 1. I do not think that it is generally possible to replace the “ screening concept ” by the “ lattice energy ”. In many cases, of course, they both convey the same idea, but the screening applies to polymerization e.g. formation of AI2 Clg molécules in the gas phase or to di-, tri-chromic acid anions in aqueous solution, when the lattice concept could not be in order. I fully agréé with Prof. Hâgg’s comment concerning the des­ cription of the diamond. If this were an isolated case no necessity would arise to describe this form of carbon as

until an

experiment proves that not ail carbons are identical. However the high melting point and the high hardness become obvions if this element is treated formally as being a Carbide. I distinctly remember that earlier workers had serions difficulties to explain that in sériés such as NaF

450

ZnS

AIN

Ge

the hardness increased in a way which did not indicate an abrupt change of Chemical binding. The electronic properties of Ge can be so much better understood if the element is treated as the germanide of germanium Ge'^+Ge^- analogous to In^+Sb^^ and similar compounds. 2.

The change of Ti02 and WO3, etc. into defective structure

can be described as a lowering of the valency of the metals. However such a description does not account for the extremely high dielectric constant, for the semi-conductivity and other electronic properties, at least not in an obvions manner. For this reason I prefer to describe these compounds as crystals in which some ions are replaced by électrons and where the électrons cannot be “ located ” but are quantized with respect to a number of cations.

M. Jurgensen. —

1. One of the most interesting results of

Prof. Weyl’s investigations of métal ions in silicate glasses is the discovery of tetrahedrally co-ordinated nickel (II) complexes, since only anhydrous nickel (II) salicylaldéhyde is known as a dubious case. Do you think that other métal ions, which always are octahedrally co-ordinated in solution, such as chromium (III) might be provoked into tetrahedral positions in some kind of glass? 2. You mention the much higher beat of formation of solid NaCl than of gaseous NaCl molécules and ascribe it to the much larger screening of the sodium ions each by six chloride ions. Why do you not emphasize as much the reciprocal influence of each chloride ion being surrounded by six sodium ions? 3. You point out the importance of electroneutrality in the smallest possible value. Since the electrostatic energy of a sphere is Z2/r (where Z is the charge and r is the radius) it is sixteen times more difficult to understand the auto-ionization of diamond to and than the auto-ionization of an analogous monovalent System. Your argument that AI4C3 and SiC resemble much diamond does not suggest that diamond is a carbon Carbide, but rather that the carbides hâve the same type of covalent bonding as diamond. Do you agréé that diamond might be described better as cores surrounded by quanticules ef analogous to an infinité hydrocarbon structure? I must point out that the latter quanticules, which in the theory of Fajans hâve played the rôle of électron pairs in Pauling’s

451

theory of covalent bonding, are not responsible for the bonding solely by reasons of electrostatic potentials. Thus, the bonding State of a hydrogen molécule must be described by quantum mechanics in a manner, which nécessitâtes the extension of your theory with imaginary charges, attracting each other in some of the States. I do not know your opinion of a possible electrostatic model with complex charges. 4. I am very happy that you recognize nuclei and électrons as the actual particles applied by quantum mechanics. Thus, your concept of cores and quanticules such as électron pairs is only expédient method of classification into distinct units of the particles in a System, and it cannot be assigned an absolute validity in ail cases. When the concepts of your report are translated into the language of the theory of molecular orbitals, your électron distributions correspond to the single configurations for a molécule. I do not agréé with the first of the three principles p2> that an experimentally unique molecular species is represented by one electronic formula. I may guess that you would assume the presence of a quanticule, containing e.g.

6

électrons, in benzene for avoiding the considération

of the two Kékulé structures. This would be équivalent to a linear combination of two of the possible sets of molecular orbitals, which co-operate in the complété description of the benzene molécule. The transition group complexes, which hâve been discussed also by Dr Orgel and Prof. Nyholm, exhibit many cases, where it would not be very adéquate to ascribe a certain limiting electronic con­ figuration, such as the pure electrostatic case or the d’^sp^-hyhTÏàïzation of Pauling to e.g. the hexaaquo ions of trivalent metals. I hope that you agréé in the relative inadequacy of the Fajans’ theory for these cases. 5. It is very interesting that the ion O cannot exist without strong electrostatic fields from cations in lattices. I can here remind that the Fermi-Thomas statistical model for atoms, assuming spherical symmetry and no distinction between the shells, implies increasing radii for the métal ions for decreasing external charge, i.e. the différence between the nuclear charge and the number of électrons.

Even after certain assumptions, the neutral atom is the

last case, whcih is predicted to exist by Fermi-Thomas’ statistics; the électron distribution diverges for unions as function of the

452

distance.

This may perhaps be the explanation that cations are

so much more common in the periodical System than anions, which only occur in the halogen and chalcogen groups. While the ligands with tendency of a and Tc-bonding in the direction from the ligands towards the central ion, prefer high oxidation States of the metals (where the actual charge is decreased by the bonding), the ligands such as o-phenanthroline or cyanide with tendency towards 7t-bonding in the opposite direction, as discussed by Dr Orgel, stabilize the metals with low oxidation States, such as iron (II) or vanadium (II). However, the lattice energy (which stabilizes the dioxides with fluorite structure of actinides, which not elsewise is easy to hâve in quadrivalent State) and the relative difficulty of liberating elementary oxygen and fluorine may co-operate in the stabilization of some oxidation States. M. Weyl. —

1. Unfortunately we hâve no experimental evidence

for the existence of Cr^+ ions having fourfold co-ordination in glasses. As a rule, the co-ordination number of a cation decreases with increasing polarizability of the ions i.e. from B2O3 glass to alkaliborate glasses or from a lithium silicate to a potassium or rubidium silicate? However these changes from six fold to four fold co-ordination are easily observable only for Ni2+ and Co2+ ions because here they produce drastic color changes. 2. It is out of energy considérations that I center my screening theory amid the co-ordination requirements of the cations. A cation of the noble gas type rarely changes its co-ordination number with respect to O^-ions. Some éléments like Al form AIO4 and AlOs groups. However major changes of this co-ordination number of O2- ions are frequently observed. ions in silica are exposed to two SH+ ions. In Rutile the co-ordination number of oxygen is three and in periclase (Mgo) it is six. M. Ubbelohde. — In the particular case of sodium chloride, the straightforward summation of electrostatic attractions and repul­ sions shows that there is a large decrease in potential energy on passing from the gaseous ion NaCl to the crystalline assembly with 6 nearest neighbours around each ion. As Prof. Weyl says, there is no clear eut distinction between “ Chemical combination ” in the gas and “ physical interaction ” in the crystal, for the case of sodium chloride. However, the spécifie polarizability contribution

453

to the potentiel energy does not constitude more than 1 or 2 % for sodium chloride crystals. There are other crystals where the polarisability contribution is much larger fraction of the lattice energy.

M. Nyholm. — It would be very interesting to study the magnetic susceptibilities of the glasses containing varions transition métal ions which Prof. Weyl has made. In particular the “ freezing in ” of the tetrahedral configuration of the oxygen atoms around Ni" is expected to resuit in a triplet as the ground State in the Stark splitting of the orbital levels by the ligand field. We are very glad to be able to measure these moments on compounds to be supplied by Prof. Weyl. Also one feels that the screening theory, whatever be its value in connection with electrostatic substances, appears to hâve a very limited application to covalent compounds. Thus it would be interesting to see how far it enables one to understand the shape of a molécule such as CIF3 which contains three bonding pairs and two lone pairs of électrons. On the basis of simple electrostatic repulsion structures I, II and III are possible :

of which III might be thought the more likely since the lone pairs are furthest apart in the structure. However I is closest to the correct structure; this can be understood in tenus of a valency bond des­ cription. In the latter we regard the structure as intermediate between that obtained by hybridising bonding orbitals {p^d) and non-bonding orbitals (Sp) separately and that obtaining by mixing ail of these together in an Sp^d pentagonal bipyramidal arrangement. This

454

means that the lone pairs hâve a good deal of S character hence that they are to be located in the trigonal plane. 3s

<■

-------------------------—

sp

p^d ■sp^d

>

M. Weyl. — If one applies the screening theory to a compound such as CIF3 one has to assume that the positive core of the chlorine, CF+, is screened by three F~ ions and two pairs of électrons, (^2“). In this case the structure III is not likely because of the large size of the F“ ions as compared with the very small CF+ core.

It is

impossible for the CF+ core to be close to ail five négative particles. From electrostatic considération it is, therefore, most reasonable to assume that the doubly charged (c2“) quanticules will be closest to the CF+ (1.598 A.U.) and the other two hâve to assume positions which are more remote (1.698 A.U.). This arrangement corresponding to formula I seems to give the lowest electrostatic energy of any arrangement between a CF+ core, two (e2~) quanticules and three F“ ions. That this arrangement is not very satisfactory and that it produces strong repulsion forces between the five négative quanticules expresses itself in the extreme Chemical reactivity of the compound CIF3 which resembles that of elemental fluorine.

M. Lindner. — I should like to make some comments to professor Weyl’s paper, especially concerning the connections with solid State reactions : 1. Perhaps one should not overemphasize the importance of electroneutrality in the smallest possible volume in solids as it became known lately that space charges can occur and are in fact most essential for the first stage of some solid State reactions as oxidation of metals. 2. The newer interprétation of the mechanism of reactions between solids as forwarded by Hedvall and his school, does neither over­ emphasize the electroneutrality of difîusing particles. In some cases métal and oxygen seem to be mobile in the solid lattice, which

455

can more conveniently be described as a simultaneous transport of ions, possibly by means of associated vacancies. 3. The experimental proofs for the “ creeping ” of one oxide over another during a solid State reaction cannot yet be considered sufficient. As far as I know no direct surface transport of that kind has been measured, but indirect conclusions bave been drawn from experimental observations, which can be explained on a simpler basis. Several examples can be named : thus a reaction layer of zinc ferrite formed by reaction between the oxides of zinc and iron is always attached to the iron oxide although it is formed by a migration of both zinc and iron ions within the reaction layer. In the case of the reaction between the oxides of aluminum and chromium, the higher vapour pressure of chromic oxide may explain the covering of the alumina. 4. As outlined in our paper during this conférence there is actually a relation between self-diffusion and melting température in the form that the self-diffusion of cations in oxides at melting tempér­ atures shows conforming values for practically ail oxides investigated thus far. 5. As to our knowledge anion vacancies in zinc oxide hâve not been reproved experimentally. The différence in defect concentrations between the oxides of zinc and magnésium may not be so essential, as the values for self-diffusion in the oxides indicate the possiblity of comparable defect concentrations (cf.

our paper, presented

during this conférence). 6. For the so-called place exchange reactions as investigated by Hedvall and his school, an interesting mechanism has been suggested

by C. Wagner (Z. anorg. Chem., 236, 322, 1938) avoiding the necessity of diffusion transport of bigger complex ions. 7. It may perhaps not be generally valid that reactions between an acid and a base in the solid State proceed by prédominant diffusion of the anion. In the case of silicate formation e.g. no sufficient mobility of Silicon or silicate ions could be found. On the other hand self-diffusion values for Ca in Ca2Si04 are nearly comparable to those for the formation reaction. Within the température range usually investigated, the self-diffusion within the orthosilicate sur­ passes the values obtained for lower basic silicates, which may

456

explain sufficiently the prédominant formation of the high basic silicate. 8.

There may be a certain danger with an oversimplified picture

of solid State reactions. It is doubtful if a more qualitative conception like the screening demand of cations actually is sufficient for a deeper understanding of the reaction mechanism.

Naturally it is

an ultimate aim to deduce a complété picture of solid State reactions from atomic properties. These are finally rate déterminations by determining différences in Chemical potential and energies necessary for defect formation and migration. Even if a detailed description of crystals and their energy distribution would be possible, it may not be sufficient. The actual solid State reaction is strongly influenced by defects which to a lesser extent hâve been subject of exact cal­ culation as e.g. dislocations. A sensible approach to the whole field of solid State reactions is the endeavour to investigate in detail the different parameters and to establish quantitative relations. M. Forestier. — Je serais heureux de savoir si l’on peut admettre que le «screening effect » est de désordre; il semblerait en screening plus élevé que l’état de fusion). Peut-on relier les effet?

lié à la stabilité de l’état d’ordre ou effet que l’état d’ordre demande un de désordre (exemple : le phénomène transformations ordre-désordre à cet

M. Bénard. — Je tiens tout d’abord à dire l’intérêt que je porte aux conceptions du Prof. Weyl, dont le plus grand mérite est semble-t-il d’avoir attiré l’attention sur l’importance des phénomènes de polarisation dans le comportement des solides. C’est surtout, semble-t-il, pour la compréhension des phénomènes de surface que le rôle de ce facteur est le plus grand. Par contre, il me paraît difficile de suivre le Prof. Weyl lorsqu’il attribue au « screening » une importance égale dans la formation des structures lacunaires telles qu’on les rencontre dans certaines phases non stoechiométriques. Je ne me fais bien entendu aucune illusion sur le caractère, au moins partiellement formel, du langage que nous utilisons lorsque nous attribuons aux ions des charges discrètes. Cette représentation qui n’est probablement pas très éloignée de la réalité lorsqu’on considère les oxydes des métaux comme le sodium ou le calcium, s’en éloigne lorsqu’on passe des oxydes aux sulfures et des sulfures

457

aux séléniures, dans les réseaux cristallins desquels la contribution de l’énergie de polarisation est importante. Il en est de même avec un élément déterminé, lorsqu’on compare des phases dans lesquelles celui-ci est associé à un nombre variable d’anions, le caractère ionique s’atténuant lorsque le nombre des unions diminue (passage Ti02 à TiO par exemple). Mais j’éprouve l’impression que le Prof. Weyl nous propose de substituer à un formalisme auquel nous sommes habitués, un autre formalisme qui, pour le cas des phases non stoechiométriques, ne semble pas apporter des facilités nouvelles d’interprétation. 11

paraît en particulier difficile d’expliquer les différences impor­

tantes observées dans l’étendue des phases non stoechiométriques sans faire appel aux différences d’énergie qui existent entre les différents états d’ionisation des cations, toute formation de lacune cationique devant en effet s’accompagner d’un changement dans l’état quantique des cations restants, et étant par conséquent subordonnée à la possibilité d’effectuer ce changement avec une dépense d’énergie raisonnable. Adopter ce point de vue n’équivaut d’ailleurs pas à admettre une localisation des ions de valence anormale dans la structure, la répartition des charges anormales pouvant être considérée comme répartie statistiquement sur l’ensemble des sites cristallographiques aptes à les accueillir. Avec ce point de vue, l’apparition de la conductibilité électrique et de bandes d’absorption dans le visible trouve une explication satisfaisante. Un autre point sur lequel j’aurais voulu attirer l’attention est l’influence que le Prof. Weyl attribue au phénomène de « screening » sur la cinétique des transformations dans l’état solide. Il est aisé de comprendre, dès que l’on a adopté les hypothèses de base de l’auteur, que le « screening » puisse être un facteur déterminant dans le sens de la variation d’énergie libre qui accompagne une transformation solide A solide B. Il me paraît par contre dif­ ficile de le considérer comme facteur déterminant de la cinétique. En effet, toute explication de la cinétique de telles transformations doit, pout être prise en considération, établir la distinction entre le processus de nucléation et celui de croissance. L’un et l’autre possèdent des énergies d’activation qui dépendent de facteurs multiples autres que le « screening » et qui ne sont pas nécessairement identiques.

458

Some Problems of Solid State Chemistry (With spécial regard to diffusion and reaction in oxide Systems.)

by Roland Lindner

INTRODUCTION

One aim of modem solid State chemistry is the élucidation of the mechanism of solid State reactions. Very extensive work has been laid down on the investigation of the diffusion stage of some typical and important solid State reactions such as : ° the oxidation of some metals at high températures and

1

2° the formations of “ oxide compounds of higher order ” as silicates and spinels by reaction between the respective oxides in the solid State. A question of spécial importance in this connection is the State of the reaction layers at high températures. The déviation from stoichiometric composition and the degree of réversible lattice disorder, i.e. the concentration of vacancies and interstitial atoms and its dependence on température, impurities and changes in the surrounding gas atmosphère, has to be investigated by spécial experiments, which, besides, contribute to the knowledge of the solid State itself. During recent years new techniques as e.g. the measurement of the dielectric loss and of the nuclear magnetic résonance spectrum hâve been developed.

As direct and comparatively easy and reliable

methods, the measurement of atomic mobility with radioactive tracers

459

and by évaluation of electronic and ionic conductivity can, however, still be considered to be the most important ones. In the following an attempt is made to illustrate the présent situation in this field with a detailed discussion of some of the most prominent solid Systems. Référencé will be made to some unpublished results, and this summary should consequently not be considered as final, but rather as a report on the présent situation and as a survey on results, some of them not fully established and still open to discussion. The author is indebted to several colleagues, especially in the USA (C. Wagner, W.J. Moore, E. Gulbransen) for discussions during his recent visits. In the following the available information about lattice disorder and self diffusion in some oxides will be discussed as well as the corrélation of these results with the oxidation of the respective metals (reactions : solid - gas). In the second half of this paper the same procedure shall be applied to reactions between solids. The Systems discussed can be divided into the following groups : 1. a) alkaline earths (MgO, CaO and BaO) b) ZnO as example of a «-conducting métal oxidation layer c) /?-conducting oxides (CU2O, FeO, CoO and NiO) 2. a) Atomic

mobility

and

solid

State

reactions

in

Systems

Si02 + PbO and CaO respectively. b) Self diffusion and reaction in varions spinel Systems.

METAL OXIDES AND METAL OXIDATION

Ail available information on self diffusion in oxides is assembled in Table I and repeated référencé to this table will be made. The constants for the température dependence of the self diffusion coefficient D = Dq exp (Q/RT) viz. the preexponential (frequency) factor Dq and the experimental activation energy (beat of activation) are presented. Informations about crystal structure and melting point are given in connection with the évaluation of the self diffusion coefficients at the melting point (to be discussed later).

460

The alkaline earths hâve hardly any importance as oxidation reaction layers, as the oxidation of alkaline earths metals usually does not resuit in cohérent protective oxide layers (with the possible exception of magnésium at low températures). Nevertheless the knowledge of lattice disorder and self-diffusion in alkaline earths contributes to the general picture of the behaviour of oxides (and has, besides, some bearing on problems connected with alkaline earth cathodes and their électron émission). The self-diffusion of Mg^s in MgO has been measured in single crystals ('), whilst practically ail other investigations hâve been made on polycrystalline material. Only a very tentative direct détermination of the ionic conductivity has been made and a small value (a few percent at 1,300 °C) for the transfer number could be estimated. The indirect détermin­ ation by comparison of diffusion measurements with conductivity measurements (in air) (2) on crystals from the same source leads to the same order of magnitude. Measurements of the thermoelectric power (2) indicate hole conduction in Mg O, which should normally be accompanied by Mg-vacancies, although interstitials are also assumed. The self-diffusion of Ca^s in sintered samples of CaO shows an activation energy very similar to that for MgO. Conductivity and transfer numbers, i.e. the ionic conductivity has also been measured over a large range of température and been found to increase from about 1 % at 1,200 °C to about 10 % at 1,400 °C, which means that ail conductivity should be practically ionic near the melting point (‘•). The ionic conductivity and the self-diffusion coefficient, correlated by the Nernst-Einstein relation, are in fair agreement, which indicates that practically ail ionic transport is due to calcium ions. The self-diffusion of Bai‘*o in single crystals of BaO has been measured by Redington (5). The values for the activation energy at elevated températures are, however, astonishingly high (~ 250 Kcal) and should in the présent author’s opinion be considered with réservation. If these values are not accepted, measurements of the migration of excess barium in colourless barium oxide (*) crystals could be considered to give an estimate for the self-diffusion of barium with an activation energy of 65 kcal, which tentatively had been ascribed to the diffusion of oxygen vacancies.

461

Surveying the measurements on alkaline earths it can be stated that an activation energy of about 80 kcal represents an average value for the self-diffusion of the cations in these comparatively simply built oxides. The self-diffusion values can possibly be predicted empirically from the melting températures as will be described later.

Zn O AS EXAMPLE OF AN EXCESS CONDUCTING METAL OXIDATION PRODUCT Zn O is a substance of manifold interest as luminescent, catalyst, and métal oxidation layer. It has been investigated very thoroughly during the last twenty years, but no complété and consistent picture of its basic kinetic qualifies has been obtained yet. ZnO is considered to be a typical «-conductor, the excess of zinc in déviation from stoichiometric composition being accommodated in the form of interstitial zinc ions and électrons. The alternative possibility of oxygen vacancies seem somewhat less probable because of recent x-ray investigations by Gray Ç). Primarily interstitial zinc ions are considered to be the main vehicles for atomic transport under self-diffusion and oxidation of zinc métal. Table I contains two different investigations with practically the same values for the température function of the self-diffusion coef­ ficient of zinc. This coincidence is, however, surprising as in the first case polycrystalline samples in air were investigated (8), whereas in the second case the exchange between radioactive zinc oxide crystals and zinc métal vapour at

1

atmosphère pressure was

measured (P). In this last case the formation of interstitials zinc ions should require less energy (by solution of the métal in the oxide) than by dissociation of zinc oxide in the first case, and consequently a lower activation energy for self-diffusion (37 kcal for Zn++ and 22 kcal for Zn+ formation and diffusion) would be expected (^O). In fact, however, the self-diffusion was practically unaffected by the presence of zinc vapour under the spécifie experimental con­ ditions used (probably diffusion against an overall gradient of zinc). In this connection experiments (i*) are to be mentioned which indicated that the diffusion constant during the exchange of radio­ active zinc métal vapour with zinc oxide crystals is strongly con-

462

TABLE 1 Self-ditTusion in oxides

DO (cm sec-i)

Q (kcal mole-i)

T“ (OC)

log DT”’

MgO

0,23

78.7

2800

— 6,22

I

CaO

0,4

81

2570

— 6,62

II

36.1

1235

— 6,61

III

74 73

1975 1975

— 7,06 — 6,42

IV V

CU2O ZnO

4,4 .10-2 1,3 4,8

Ref.

FeO

1,4 .10-2

30.2

1420

— 5,75

VI

CoO

2,15 .10-3

34.5

1935

— 6,09

VII

CF203

4 .103

100

1990

— 6,05

VIII

FejOs

4 .10’

112

1570

— 7,7

IX

Sn02

106

119

1930

— 5,95

X

PbO

106

69

890

— 7,00

XI

NiO

0,24

62

2090

— 6,35

XII

REFERENCES TO TABLE 1 I

R.

Lindner and G.D. Parfitt, J.

Chem.Phys., inpress.

II

R. Lindner, Acta Chem. Scand., 6, 468 (1952).

III

W.J. Moore and B. Selikson, J. Chem. Phys., 19, 1539 (1951).

IV

R. Lindner, Acta Chem. Scand., 6, 457 (1952).

V

E.A. Secco and W.J. Moore, J. Chem. Phys., 21, 1117 (1955).

VI

L. Himmel, C. Birchenall and R.F. Mehl, J. Metals, 5, 827 (1953).

VII

R.E. Carter and F.D. Richardson, J. Metals, November 1954, p. 1244.

VIII

R. Lindner and A. Akerstrdm, Z. phys., Chem., 6, 162 (1956).

IX

R. Lindner, Arldv Kemi, 4, No 26 (1952).

X

R. Lindner and O. Enqvist, Arkiv Kemi, in press.

XI

R. Lindner, Arkiv Kemi, 4, No 27 (1952).

XII

R. Lindner and A. Akerstrdm, to be published in J. Chem. Phys.

463

centration dépendent, suggesting vacancy diffusion as rate determining, when the excess zinc (métal) concentration is high. Similar experiments with radioactive zinc vapour, performed in this laboratory by Spicar (*2), showed over a large range of température an activ­ ation energy of 85 kcal.

Preliminary diffusion experiments on

sintered pellets performed by Moore and Secco indicated about the same value (90 kcal). Some observations concerning the colour of zinc oxide heated to high températures or exposed to zinc métal vapour are of interest in connection with diffusion measurements. Sometimes the assumption is made, that the colour is a direct measurement of the concen­ tration of excess zinc in the form of interstitial ions. This is, however, by no means certain. According to preliminary results obtained by Lânder at Bell Téléphoné Laboratories the activation energy for the diffusion of a reducing agent in zinc oxide crystals, possibly excess zinc, requires a considerably higher activation energy than the diffusion of the coloration (about 90 against 50 kcal/mole) (*3). Endeavours were made by E. Spicar to déterminé the diffusion of interstitial zinc in zinc oxide by following the change in conductivity after quenching (i2). This change proceeds according to a diffusion law. Of course an essential experiment is the investigation of zinc self-diffusion as a fonction of oxygen pressure, which should establish a différentiation between interstitial and vacancy diffusion. Certain conclusions can already be drawn from experiments by Roberts (i**), who found that self-diffusion of zinc is enhanced by factor of 4, by the substitution of oxygen for an argon atmosphère. After this short discussion of diffusion data the oxidation of zinc métal is considered. The kinetics hâve been investigated by Wagner and Grünewald (is) and in newer work by Moore and Lee (16), who measured the oxidation of zinc foil at different oxygen pressures and obtained at the highest pressure used (10 cm Hg) as the température dependence of the parabolic rate constant k = 3.3 X 10“2 exp (— 28,000/RT) cm^ sec“i, whilst a decrease in oxygen pressure of two orders of magnitude increased the activation energy by about a factor 2, whiçh brings it near the self-diffusion activation energy. The preexponential factor is, however, 105 times higher than Dq and the values for k at 400 °C 108 times higher than for the (extrapolated) D. It should be noted

464

that the low preexponential factor indicates a négative activation entropy, which is usually considered as being proof of prevailing grain boundary diffusion. In contrast to the déficit {p—) conductors discussed below, agreement between oxidation and self-diffusion was not to be expected, as the formation of interstitial zinc ions, should require less energy in the case of métal oxidation, and the activation energy for diffusion of zinc in zinc oxide in equilibrium with solid métal was calculated to 47 kcal (lo), which figure is considerably lower than the one experimentally found for diffusion in zinc oxide in air but still higher than that observed for the oxidation. Direct measurements of the self-diffusion of zinc in zinc oxidation layers has been tried independently by both Moore (lO) and Lindner (i^), who found that this diffusion coefficient has the order of magnitude 10“i<5 cm2 sec~i at 400 °C, which is in sufficient accord­ ance with the oxidation rate at that température. Thus the original assumption that the diffusion of interstitial zinc ions détermines the oxidation rate looks sufficiently established. The fact that the activation energy for self-diffusion in zinc oxide was not considerably influenced by the presence of zinc métal vapour but well by the presence of solid zinc casts a new light on the théories of atomic mobility in zinc oxide. It does not invalidate the assump­ tion mentioned above, that the oxidation proceeds mainly by diffusion of zinc ions (although a participation of oxygen cannot yet be excluded) but indicates that grain boundary diffusion may be prevailant as already indicated by a négative entropy of activation for the oxidation constant. Lattice diffusion besides, may eventually not proceed by interstitial migration mainly and a certain indication for this possibility has been given by the results obtained by Münnich (H). He found in his experiments, as mentioned a marked decrease in the diffusion coefficient with increasing excess zinc concentration in the crystals. The conclusion is drawn, that at low concentrations the considerably faster interstitial diffusion prevails, whilst at higher concentrations vacancy diffusion becomes rate determining. The interstitial transport may be décisive and responsible for the lesser activation energy of the oxidation reactions, as in this case a continuons consumption of zinc ions takes place at the zinc oxide oxygen interface. This préservés a concentration 465

gradient for interstitials and faveurs this transport as compared with vacancy transport. The extensive work on Zn O, originated by the effort to elucidate the oxidation of zinc, has lead to a rather complex picture and some more crucial experiments seem necessary.

Such experiments are

amongst others : measurement of an eventual anisotropy for the self-diffusion, experiments in zinc oxidation layers over a larger range of température, experiments in order to establish equilibrium condition at the surface of zinc oxide crystals. An essential point is the detailed investigation of interstitial diffusion by following the migration of an excess zinc interstitial concentration forced upon the crystal by treatment with zinc vapour or by génération at high températures and subséquent quenching. The preliminary results by Lânder (*3) would give a rather high activation energy for interstitial diffusion and should be repeated as soon as pure crystals of sufficient size become available. In spite of ail complications (experiments with gas adsorption and diffusion through the oxide also contribute to the picture) there is no convincing evidence that the Wagner mechanism (i^) of prevailant cation diffusion through the oxidation layer is not rate determining for the oxidation of zinc.

P-CONDUCTING OXIDES AS REACTION LAYERS In the following some /7-conducting oxides shall be treated by comparison of oxidation and diffusion constants. The selfdiffusion in cuprous oxide (CU2O) has been investigated by Moore (19) and co-workers as shown in Table I. The comparison of the results with oxidation data obtained by Lee and Moore, shows that the activation energy for both is the same and the values of the cons­ tants are in the relation k/D ~ 2.

This indicates that there is a

uniform distribution of vacancies throughout the oxide layer, (as e.g. in the case of a linear concentration gradient the ration k/D would be 4). This contradicts results obtained by Bardeen, Brattain and Shockley (20), who assumed a gradient of vacancy concentration in a cuprous oxide reaction layer and a diffusion coefficient for cuprous ions proportional to that gradient. Their experimental evidence may not be quite sufficient and according

466

to Moore the possibility must be considered that no vacancy gradient is maintained in a growing cuprous oxide layer (grain boundaries and dislocations acting as sources and sinks for vacancies), or that otherwise the diffusion is based on another mechanism. According to Moore (2i) even the participation of copper-oxygen vacancy pairs cannot be excluded as indicated by direct measurement of the diffusion of oxygen-18 in cuprous oxide. The conditions are further complicated by the observed plastic flow of oxide layers during oxidation of copper, which makes any marker experiments for the détermination of the prevailant migrating ionic species very difïicult. The question of vacancy concentration gradients in oxide layers arises in other cases of p-conducting oxides where sufîicient agreement between self-diffusion and oxidation is found. Thus the dif­ fusion coefficient for ferrons ions in ferrons oxyde, according to Himmel, Birchenall and Mehl (22), increases linearly with increasing vacancy concentration, which latter can be easily determined, as in this case the déviation from stoichiometric composition is large. This evidence is, however, mainly based on experiments at the highest température used (1000 °C). The measurements of Carter and Richardson of the self-diffusion in wustite agréé, as shown above, very well with those by Himmel, Birchenall and Mehl, although these authors report a practically unchanged composition of the wustite, équivalent to a constant vacancy concentration over the température range 700° — 1000 °C. In cobaltous oxide (Co O), however, oxygen excess is found to increase with température and with about the 1/3 power of oxygen pressure (23), which indicates considérable association between cobaltic ions and vacancies. Such a phenomenon, i.e. that the vacancy formed is bound by an ion of deviating valency may be common and contribute little to diffusion, which argument would invalidate the calculation of vacancies from déviations of stoichio­ metric composition. The investigation of the oxidation of the cobalt métal by Richardson and Carter (24) shows that although the oxidation rates agréé with the Wagner oxidation theory the distribution of cobalt in growing oxide layers is different from that predicted by Wagner. The tracer distribution in growing oxide films corresponds to a constant dif­ fusion coefficient for approximately two thirds of the layer and

467

falls towards zéro at the oxide métal interface. In any case, the diffusion coefficient does not vary linearly with distance and there is indication that the concentration of vacancies near the gas/oxide interface is less than the equilibrium value for oxide in equilibrium with the oxidizing atmosphère. Summing up the evidence concerning the detailed mechanism of the growth of /^-conducting oxide layers on metals we can State that although the simple assumption of a linear concentration gradient for vacancies through the oxide film seems to hâve been proved by experiments by Bardeen and co-workers (20) as well as by Himmel, Birchenall, and Mehl (22), contradictory evidence has been found by Moore and co-workers as well as by Richardson and Carter (23). Another case of the oxidation of a transition métal is that of nickel. The activation energy for oxidation is according to Moore and Lee 38,4 kcal (25) and according to Kubaschewski and Goldbeck (26) 45-60 kcal/mol. The electric conductivity shows an activation energy of 23 kcal with a proportional to which indicates that only one hole is dissociated from the cation vacancy. Other observations by Baumbach and Wagner (22) indicate that the activation energy for diffusion of oxygen should be about 45 kcal (concluded from the change of conductivity as a function of change in oxygen pressure). Direct measurement of nickel self-diffusion in NiO are still incomplète. The preliminary value for the activation energy, contained in Table I and obtained for the diffusion of radioactive nickel in nickel oxide crystals does not, however, coincide with the oxidation rates at lower températures, in which case grain boundary diffusion may hâve been prevailant. (This would, however, be in contrast to the results of Richardson and Carter (23) for the diffusion in cobaltous oxide films, where no grain boundary diffusion has been found). Thus it would be possible that the activation energy for the oxidation rate changes with température. Some indication for this has been found in unpublished experiments by Gulbransen (29), who quotes an activation energy of about 60 kcal at températures between 1000 ° and 1200 °C [a similar value is given by Goldbeck (26)]. Extensive work has still to be done. Thus the dependence of the self-diffusion coefficient of nickel on the composition of the oxide and

468

on the oxygen pressure has to be investigated in detail. Experiments with pure nickel oxide single crystals are under work both in the laboratory of W.J. Moore and in our Gothenburg laboratory. The last example we shall shortly consider is the oxidation of lead métal which has been investigated by a number of authors. The activation energy for oxidation seems to be about the same as for the self-diffusion of lead in PbO (30). The self-diffusion is not appreciably affected by the presence of underlying métal (^i), which indicates that PbO is a p-conductor as should be expected. The quantitative comparison of oxidation and diffusion rates, however, shows that the oxidation rates are about three orders of magnitude higher, i.e. the ratio kjD is about 10^.

This can hardly

be reconciled with the assumption of a linear concentration gradient for lead vacancies in the oxide layer. The concentration gradient for radioactive lead in layers of oxidized métal ought to be inves­ tigated experimentally and even the possibility of oxygen diffusion should be considered in this oxide where the ionic sizes of cations and anions are comparable. When surveying the field of métal oxidation mechanisms as described in this paper the impression is obtained that an originally clear picture has become more and more indistinct as experimental progress has been made. This is, however, no disadvantage and will finally lead to a much deeper knowledge of the oxidation mechanism as well as of the oxides concerned.

2

REACTIONS BETWEEN SOLIDS

The experimental material forestablishing definite reaction mechan­ isms is scarce compared with the amount of analogous work on tarnishing reactions. Cari Wagner assumed the diffusion of cations through the formation of “ ionic compounds of higher order ” (32). This could be verified in the case of the formation of silver-mercuryiodide (33), which is a pure ionic conductor with a high mobility of silver and mercury ions and practicafly no mobility of iodide ions. This proof, already established in 1936, was to be the only one for a long time. Based on the material about ionic mobility in silicates which was available at that time Wagner suggested that the same mechan-

469

ism (cation diffusion through the reaction layer and immobile anions) should be valid also for the formation of high melting compounds such as silicates and spinels. Investigations by Jagitsch and co-workers in the Hedvall institute, however, already showed in the years 1946-1947 that the experimental results found with the formation of lead silicates (^4) and zinc aluminium spinel (^5) were not consistent with the Wagner theory. The evidence was not based on the comparison of diffusion and reaction data, but on a very simple and effective technique, that of the marked original interface between the reactants. The markers, small particles of noble métal, not participating in the reaction, would be imbedded in the reaction layer, if the layer grows by diffusion of the two cation species in opposite direction. This was, however, not found to be the case in the two reactions mentioned, where ail transport obviously was due to the motion of lead and zinc ions respectively together with oxygen ions in the same direction. The two groups of high melting oxidic compounds, viz. silicates and spinels hâve been the subject of a larger research program using radioactive tracers and being under work in the Hedvall institute during the last eight years use of the

We intended to make full

technique of radioactive tracer atoms, which became

increasingly available during this time. 2a. SILICATES OF LEAD AND CALCIUM (37)

The formation of silicates by reaction between a métal oxide and silica in the solid State is a rather intricate reaction as several compounds are simultaneously found in varying concentrations. Usually one has to reckon with the formation of 3 Me0.Si02, 2 Me0.Si02, 3 Me0.2Si02, and MeO.Si02. AU four silicates exist in the best investigated cases, viz. the Systems PbO + Si02 and CaO -f Si02. This means that not only the direct reaction between the oxides but also intermediate reactions between different sili­ cates must be considered.

This complicates studies of silicate

formation as compared with the formation of spinels, where only one reaction product exists. Fortunately, in the beginning of the diffusion stage only orthosilicates (2 Me0.Si02) are formed with a yield surpassing that of the others. In any case, however, a quan­ titative analysis of the process is rather difficult and our research has only reached semiquantitative results.

470

LEAD SILICATES Our aim was to measure the self-diffusion coefficients for lead in ortho- and metasilicate (and if possible also the diffusion of Silicon)

and compare

them with

exact déterminations

of the

reaction rates. It contrast to métal oxidation the transport of one atomic species through the reaction layer is not sufficient for the reaction to proceed.

Consequently, diffusion of two different

cation species in opposite directions (Wagner) or the diffusion of oxygen and métal ions in the same direction is necessary. Experiments to find a mobility of Silicon in lead silicates were not successful. Silicon-31, the only tracer available at that time, has, however, a comparatively short half life and is produced with a yield small compared with that of usually présent impurities as sodium. This limits the précision of the measurements and it could only be stated that the self-diffusion of Silicon, if any, must be considerably lower than that for lead ions at the comparable températures. (In the meantime longlived Silicon-32 has become available and a rein­ vestigation of the diffusion in silicates as well as in silica itself is planned.) A rechecking of Jagitsch’s results concerning the formation of orthosilicate by reaction between lead oxide and lead metasilicate led qualitatively to the same results, i.e. the activation energy of the reaction rate is not identical with that of the self-diffusion of lead ions, but higher, as should be expected if a simultaneous trans­ port of oxygen takes place during reaction. The assumption by Jagitsch that diffusion of oxygen participâtes in lead silicate form­ ation could not be devaluated and has to be investigated direct.

CALCIUM SILICATES No very exact measurements of the reaction rates in this System are available, and the best data are still those by Jander and Hoff­ mann (38), who measured the rate of the powder reaction between calcium oxide and silica. Powder reactions, in spite of their technical and scientific importance, are far from fully explored and the participation of phase boundary reactions and surface diffusion has not yet been sufficiently investigated. The last phase of powder reactions is rate determined by diffusion through the reaction layer and, with the contact phases area sufficiently well known.

471

reaction constants can be evaluated according to a procedure suggested by Serin and Ellickson (39). In principle rate déterminations by reactions between e.g. plane crystals of the reactants are to be preferred; although the instability of the calcium orthosilicate formed usually as a loose powder (as conséquence of a crystallographic transformtaion and increase in volume) makes it difficult to follow the reaction through repeated intervals. The same effect complicates the measurement of self-diffusion in calcium orthosilicate samples. (The “ surface decrease ” method has to be used with radioactivity measurements during diffusion.) The self-diffusion of Ca-45 in Ca0.Si02 and 3Ca0.2Si02 has also been measured and the following activation energies hâve been obtained : Ca0.Si02 : a-modif. 55 kcal, (3-modif. 65 kcal;

2

3Ca0.2 Si02 : a-modif. (58 kcal), p-modif. 73 kcal; Ca0.Si02 : a-modif. 112 kcal, p-modif. (78 kcal). Comparison with the rate of the reaction CaO -f Si02 favours the self-diffusion in

2

CaO.Si02 in accordance with the prédominant formation of

this silicate. Neither in this case was it possible to find an appréciable transport of radioactive Silicon, although diffusion experiments with silicon-32 will be necessary to obtain final results. Thus oxygen diffusion has to be considered and to be experimentally investigated by means of 0-18 as a tracer isotope.

THE FORMATION OF SPINELS BY REACTION IN THE SOLID STATE (2») Spinels, i.e. solids with the same crystal structure as the minerai spinel MgAl204, should be expected to display markedly the characteristics of atomic mobility in the solid State because of their spécifie structure.

The spinel structure (shown by ferrites, chromites, and

aluminates of certain bivalent metals) is a comparatively “ loose ” structure, as the interstices of the oxygen lattice are only partly occupied with cations. In the case of a “ normal ” spinel each cation species is confined to a type of position, i.e. tetrahedral or octahedral sites. If the non-occupied lattice sites constituted

472

vacancies in the sense of the theory of réversible lattice disorder, considérable diffusion in the solid State would be expected, with an activation energy practically identical with that for the motion of lattice defects (as no energy for vacancy formation would be required). In fact, the self-diffusion of cations in spinels is usually higher than in the pure oxides but the diffusion rates are nevertheless still low at not too high températures, as would be expected when considering the fact that some spinels act as protective layers in the case of high température oxidation of alloys. The activation energies for self-diffusion in spinels is comparable with that for self-diffusion in oxides (Table II). (The respective measurements are made on sintered compacts of nearly stoichiometric composition; some of them will be repeated using single crystals which recently became available.) In ferrites and chromites both cations are mobile with comparable activation energy. In the case of aluminates Jagitsch’s method of marking the original interface between the reacting oxides had to be used.

Thus Jagitsch’s results for zinc aluminate could be repro-

TABLE II Self-difTusion in Spinels D = Docxp (— Q/RT)

Do (cm2 sec->)

Q (kcal mole-i)

(Mg in MgAl204

2 .102

86)

Zn in ZnAl204

2.5.102

78

(Ni in NiAl204

3 .10-4

55)

Zn in ZnFe204

8.8.102

86

Fe in ZnFc204

8.5.102

82

Zn in ZnCr204

60

85

Cr in ZnCf204

9

81

Ni in NiCr204

0.85

75

Cr in NiCr204

0.75

73

Sn in SnZn204

2.3.105

Zn in SnZn204

37

109 76

473

duced and also nickel aluminate (with a much smaller reaction rate) seems to show the same mechanism. Here the diffusion of both cations in opposite direction is obviously not rate determining, but the diffusion of oxygen within the aluminate lattice has to be considered and will be measured direct, which, however, may be a rather difficult experimental task, because of small rates and high températures. In the case of ferrites and chromites the comparable diffusion coefficients and the nearly identical activation energies indicate a sufficient mobility for both cations to justify the assumption of a Wagner mechanism. Both may even diffuse by the same mechanism because of the nearly identical activation energies, which of course would mean a certain exchange or even a statistical distribution between tetrahedral and octahedral positions (“ inversion ”) at high températures. A detailed comparison of reaction and diffusion rates in order to prove the Wagner mechanism quantitatively has been tried in the case of zinc ferrite, zinc chromite and nickel chromite. The agreement is rather good; the independent détermination of the change in free energy for the reactions considered by measurements of electromotoric forces has still to be made. The situation is somewhat puzzling : in spite of the same struc­ ture (as low température X-ray measurements indicate) ionic mobility and reaction mechanism in ferrite and chromite Systems are different from those in aluminate Systems. Investigations of atomic mobilities in spinels with déviations from stoichiometric composition are of spécial interst in this connection. In a close packed lattice with comparatively few vacancies the introduction of impurities with valencies different from that of the ionic constituents of the pure crystal should strongly influence the vacancy concentration as shown by Koch and Wagner (^o). The impurity atom might even associate with vacancies and form a complex of deviating mobility. The question is now, whether similar considérations are valid for the case of spinels in which geometrically a very high concentration of vacant lattice sites is assumed? If a spinel — contrary to conditions revealed by X-ray diffraction at low températures — is regarded as a structure with nearly completely occupied cation sites, the substitution of a bivalent ion

474

by a trivalent one would, for electrostatical reasons, increase the vacancy concentration of the bivalent ions and increase their diffusion and possibly even enhance the diffusion of trivalent ions associated with the generated vacancies to a sort of a complex. The essential formai différence between the ternary spinels and binary compounds is of course that such a change is in the first case only a change from stoichiometric composition and does not imply the introduction of impurity atoms as in the second case. As, however, the spinel cation sites are far from completely occupied and, besides, different types of lattice sites are assumed for the two different cationic species one should not assume a priori an increase in atomic mobility if the addition is within reasonable limits. Experiment, however, shows than an increase of concen­ tration of iron (probably as ferrie ions) of about 3 - 5 % in zinc ferrite (Zn2+Fe2'*'04) increases the diffusion coefficient of iron by about a factor 10, but does not affect appreciably the self-diffusion coefficient for zinc (4>). The same has been found for the case of zinc chromite where the addition of 3.7 % chromium increased the self-diffusion coefficient for chromium by about one order of magnitude. Spéculative assumptions concerning the increase in mobility of the trivalent ions can be made. For reasons as yet unknown the excess of the trivalent ions may partially or completely be accommodated on tetrahedral sites as favoured paths for atomic transport (“ inversion ” of the spinel). The tetrahedral sites which usually are occupied only to 1/8 of their capacity are only at lower températures considered to be smaller than the octahedral ones, whereas X-ray measurements at high températures (and possibly a detailed calculation of the potential fonctions within the different spinel lattices at hig températures) would be necessary to obtain sufficient information concerning this question. In this connection, a paper presented by Flood and Hill at the Third International Meeting on the Reactivity of solids, Madrid 1956, is of great interest. The concentrations of ferrie and ferrons ions in the spinel magnetite (FeFe204) can be calculated (with the assumption of vacancy formation by oxidation) as fonction of oxygen pressure and are found to fit experimental results. Obviously the WagnerKoch (40) procedure can be applied. The influence of the two different types of cation sites (if they are preserved at high temper-

475

aturc) on atomic mobility ought to be elucidated.

A consistent

theory of the kinetics in spinels will hâve to explain the changes in self-diffusion coefficients with déviation from stoichiometric composition and will also hâve to explain why aluminium ions should be so much less mobile than chromic or ferrie ions. In the latter case hardly différences in ionic sizes can be used for explanation, a better approach would be to consider the eventual existence of bivalent iron and chromium ions which may be generated by an électron exchange; this is less probable in the case of aluminium ions. When surveying the available data on atomic mobility in oxides (Table I), the question arises, if there is a feature common to ail Systems investigated. The activation energies can vary within wide limits (maximum ratio nearly 4), so do the preexponential factors Dq (variation over

10

orders of magnitude).

The values for the cation self-diffusion coefficients extrapolated to the (sometimes not too well known) melting points of the oxides (42) lie, however, within comparatively narrow limits around a mean value log Dq = — 6.5 ± 0.8 (with a déviation for Fe203, whose latter value might possibly change somewhat with improved exper­ imental technique). The déviation in log

is smallest for the cubic oxides of Mg,

Ca, Co, and Cu’ (the values for the cubic NiO still being somewhat uncertain) and larger for the trigonal Fe203 and Cr203 and the tetragonal PbO and Sn02, whilst the hexagonal ZnO shows a log D^,p very near to — 6.5, if the values of Moore and Secco are used. The molar ratio metal/oxygen varies from 2 (CU2O) to 0.5 (Sn O2). Obviously the only thing in common to ail syst ms are oxygen ions which are considerably larger (with the exception of PbO) than the meta! ions. The question is how to ascribe the values for cation self-diffusion at the melting points qualities of the collapsing oxygen lattice.

to

corresponding

Any self-diffusion coefficient represents the product of the lattice defect concentration and the mobility of disordered particles. The séparation of the two terms has been possible only in a few cases and more déterminations for oxides (Hall effect measurements) look highly désirable. There is not yet any quantitative basis for an argument like the assumption of corresponding values for

476

cation defect concentration and finally corresponding instability of the oxide lattice. [Similar ideas can be found in literature and are treated e.g. by Frenkel (43)].

A qualitative “ coopération effect ”,

in grouping vacancies to dislocations with conséquent decreased resistivity to shear ( = melting), bas been suggested by Rothstein (44). In this connection, ideas presented by Nachtrieb and Handler (45) are of interest. A relation between the latent beat of fusion and the activation energy for self-diflFusion in face and body centered cubic metals induced those authors to assume a “ relaxion ” model for self-diffusion, the essenfial part of which is the inward relaxation of the atoms nearest to a vacancy.

In the case of Na-metal, about

0.4 % of ail atoms are assumed to belong to relaxions immediately under the melting point. A higher concentration obviously leads to melting. A similar model might possibly explain the influence of cation vacancies on the stability of the oxygen partial lattice in oxides, although here the relation A H/L^j = const. is not fulfilled. Concluding this paper, it should be stated once more, that it is intended as a report on research in progress. It contains only a part (although an essential one) of modem solid State chemistry and leads to the following picture : Continued research has led to an ever increasing complexity in the treatment of the field.

The basic conceptions concerning the

mechanisms of solid State reactions hâve been few and ought to be enlarged in order to explain ail experimental results, although considérable progress has been made during the last few years. There is, however, no reason why the mechanism of the most pro­ minent solid State reactions should not be completely elucidated in a comparatively short time. The générons support by Prof. J. A. Hedvall and the Swedish Council for Technical Research is gratefully acknowledged.

477

REFERENCES (1) R. Lindner and G.D. Parfltt, J. Chem. Phys., in press.

E. Yamaka and K. Sawamoto, Phys. Rev., 95, 848 (1954). (3) R. Mansfield, Proc. Phys. Soc. (London), 66 B, 612 (1953). (“*) R. Lindner, Acta Chem. Scand., 6, 468 (1952). (5) R.W. Redington, Phys. Rev., 87, 1066 (1952). (6) R.L. Sproull, R.S. Bever and G. Libowitz, Phys. Rev., 92, 77 (1953). O T.J. Gray, J. Am. Ceram. Soc., 37, 534 (1954). (8) R. Lindner, Acta Chem. Scand., 6, 457 (1952). (9) E.A. Secco, W.J. Moore, J. Chem. Phys., 23, 1170 (1953). (10) W.J. Moore. J. Electrochem Soc., 100, 302 (1953). (11) F. Münnich, Naturwissenschoften, 42, 340 (1955); Diplomarbeit Erlangen (1955). (12) E. Spicar, Dissertation Stuttgart (1956). (12) J.J. Lânder, private communication. (1“*) J.P. Roberts, Trans. B~it. Ceram. Soc., 55, 75 (1956). (18) C. Wagner and K. Grünewald, Z. phys. Chem., B 40, 455 (1938). (16) W.J. Moore and J.K. Lee, Trans. Farad. Soc., 47, 501 (1951). (12) R. Lindner 8. Nord. Kjemikermôte, Oslo (1953). (18) C. Wagner, Z. phys. Chem., B 21, 25 (1933). (19) W.J. Moore and B. Selikson, J. Chem. Phys., 19, 1539 (1951). (20) J. Bardeeen, W.H. Brattain and W. Shockley, J. Chem. Phys., 14, 714 (1946). (21) W. J. Moore, Spring Meeting Am. Chem. Soc (1955). (22) L. Himmel, R.F. Mehl and CE. Birchenall, J. Metals 5, 827 (1953). (23) R.E. Carter and F.D. Richardson, J. Metals, (1954), p. 1244. (24) F.D. Richardson and R.E. Carter, J. Metals (1955), p. 336. (25) W.J. Moore and K. Lee, J. Chem. Phys., 19, 255 (1951). (26) O. Kubaschewski and O. Goldbeck, Z. /. Metallkunde, 39, 158 (1948). (27) H.H. v.Baumbach and C. Wagner, Z. phys. Chem., B 22, 199 (1933) (28) R. Lindner and A. Âkerstrdm, Z. phys. Chem., 6, 162 (1956). (29) E.A. Gulbransen, private communication. (30) R. Lindner, Arkiv Kemi, 4, No. 27 (1952). (31) R. Lindner and H.N. Terem, Arkiv Kemi, 7, No. 31 (1954). (32) C. Wagner, Z. phys. Chem., B 34, 309 (1936). (33) E. Koch and C. Wagner, Z. phys. Chem., B. 34, 317 (1936). (34) R. Jagitsch and B. Bengtson, Arkiv Kemi, 22 A, No. 6 (1946). (35) B. Bengtson and R. Jagitsch, Arkiv Kemi, 24 A, No. 18 (1947). (36) R. Lindner, Z. EL Chem., 59, 967 (1955). (37) R. Lindner, Z. phys. Chem., 6, 129 (1956). (38) w. Jander and E. Hoffmann, Z. anorg. Chem., 218, 211 (1934). (39) B. Serin and R.T. Ellickson, J. Chem. Phys., 9, 742 (1941). (40) E. Koch and C. Wagner, Z. phys. Chem., B 38, 295 (1937). (41) R. Lindner, A. Akerstrdm and F. Heinemann, unpublished. (42) R. Lindner, Proc. Internat. Symposium, Gdteborg, 1952, p. 195. (43) J. Frenkel, « Kinetic Theory of Liquids », Oxford 1947, p. 109-111. (44) J. Rothstein, J. Chem. Phys., 23, 218 (1955). (45) N. H. Nachtrieb and G. S. Handler, Acta Metallurgica, 2, 797 (1954). (2)

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Etat actuel et évolution des recherches et de l’application technique dans le domaine de la réactivité des corps solides par J. ARVID HEDVALL

A la fin du siècle dernier, quelques expériences préliminaires de Spring, Cobb et Roberts-Austen démontrèrent la possibilité de trans­ port de matière à l’état solide. Ce n’est qu’au début de ce siècle que l’étude de ce domaine, jusqu’alors inexploré, fut entreprise de façon systématique. A ce moment, les connaissances concernant le réseau cristallin étaient nulles : elles se sont développées ultérieurement grâce à la méthode de Rœntgen. Les recherches ont d’abord porté sur une série de substances oxygénées, choisies à cause de leur importance pratique considé­ rable. Ce choix est considéré aujourd’hui comme un heureux hasard. Les principaux résultats des expériences exécutées dans le but d’établir les limites « topographiques » de ce nouveau domaine de la chimie, furent les suivants : 1° Les réactions donnant lieu à la formation de composés ou de solutions solides peuvent se faire avec une vitesse considérable, à des températures de plusieurs centaines de degrés en dessous de la température de fusion ou sublimation. 2° La vitesse de la réaction est fortement influencée par le trai­ tement préalable, le mode de liaison et, en général, par les facteurs cristallographiques des différents constituants. 3° Des maxima de réactivité se manifestent lorsque de nouvelles phases apparaissent, lors de décompositions thermiques ou de modifications cristallographiques, par exemple. Ces maxima cor­ respondent à un excès d’énergie ou à un état de déséquilibre.

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Ces résultats, parmi d’autres, formaient la base des considérations théoriques concernant les états lacunaires réversibles et irréversibles. Celles-ci ont pu être développées par Frenkel, Schottky et Wagner, grâce au développement de la Rœntgenographie. 4° On a découvert de nouveaux types de réactions, qui peuvent être schématisés de la façon suivante : a) M'O + M"XO„ = M"0 + M'XO„ b) M'O + M"X

= M'X -f M"0

M'O et M"0 sont des oxydes, M'XOn et M"XOn des sels d’oxacides et M'X et M"X des halogénures, sulfures, carbures, phosphures, siliciures, borures, etc. De telles réactions, effectuées au départ de substances appropriées, peuvent être déclenchées à des températures étonnamment basses et se déroulent avec des vitesses très grandes. Ceci se présente lorsque la différence d’énergie entre le mélange réactionnel et les produits formés est grande. Les réactions du type a) présentent des régularités étonnantes quant aux températures de début de réaction. Celles-ci sont indépendantes du sel (M"XOn) et déterminées par l’oxyde (M'O). Ces régularités ont suscité les pre­ mières discussions animées au sujet de la nature des particules de transport. Pour expliquer de telles régularités, il s’avère nécessaire de faire intervenir des migrations en surface, de groupes d’atomes autres que les ions. Par contre, dans la majorité des cas, les réactions du type b) commencent aux températures auxquelles les halogénures utilisés deviennent conducteurs électrolytiques. Weyl aussi a confirmé ce point de vue dans ses travaux. On a montré, que dans les deux cas a) et b), des écarts à ces régularités apparaissent lorsque le mélange des poudres renferme un composé qui subit un changement de structure cristallographique avant d’atteindre la température normale de la réaction. Dans ce cas, la réaction débute à la température de transformation. 5° En métallographie, on connaissait depuis longtemps l’influence de traces de substances étrangères sur le comportement physico­ chimique. On a démontré que ce phénomène était général. Les atomes étrangers encastrés dans le réseau du solide influencent ainsi l’acti­ vité du cristal à cause de leurs déviations au volume, à la charge et à la structure des couches électroniques. De même, les gaz ambiants.

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chimiquement inertes, peuvent influencer la réactivité par leur présence dans le réseau cristallin. ° Après avoir constaté l’influence de chacune des perturbations

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du réseau cristallin sur l’activité physico-chimique et sur la mobilité interne des particules, il devenait passionnant de voir si une action semblable pouvait être provoquée par un changement d’état pure­ ment énergétique, sans perturbation structurale directe. D’autant plus, que pendant les vingt années antérieures, la cristallographie roentgenographique s’était développée et affinée pour devenir un outil indispensable. Suite à des discussions et à des échanges de correspondance, je sais qu’il n’est pas exagéré de dire que les théoriciens étaient étonnés par les grands changements de réactivité, d’activité catalytique ou d’adsorption que peuvent provoquer des variations d'états magné­ tiques, électriques et de rayonnement. Ceci sous-entend une compré­ hension large et approfondie des termes magnéto-, électro-, photoet phono (ultrasons) -chimie, qui ne se limitent plus à des substances isolées. Des travaux purement théoriques se sont développés, en rapport direct et en contact étroit avec les études précédentes. L’utilisation des méthodes roentgenographiques a permis de mettre en évidence, de façon précise, les différences existant entre les réseaux cristallins idéaux et ceux présentant des défauts de structure de diverses natures. On a introduit et démontré théoriquement des notions importantes connues : places inter-réticulaires, vides, formation d’assemblages moléculaires par polarisation, équilibre thermodynamique entre concentrations d’assemblages normaux et déformés dans les réseaux. On a prévu l’influence de ces facteurs sur des effets de diffusion, de transformation et de conductibilité électrique. Les défauts de structure ont été divisés en deux groupes, défauts réversibles ou d’équilibre et per­ turbations de structure irréversibles. Ces derniers défauts ne corres­ pondent pas à un équilibre et, de ce fait, les réseaux possèdent un excès d’énergie. Ils comprennent des perturbations provenant de défauts héréditaires de structure, de transformations incomplètes ou de particules étrangères réparties de façon désordonnée. La réactivité des solides appartenant à ce dernier type peut être prévue à l’avance. De ce fait, leur connaissance est importante pour l’indus­ trie en général et, tout particulièrement, pour celle utilisant la cata­ lyse ou l’adsorption.

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Dans ce bref résumé du développement de ce domaine relativement neuf de la chimie, on n’a marqué que les dates importantes. Soulignons que les résultats obtenus ne constituent qu’une porte entrouverte sur un vaste domaine, resté longtemps non prospecté. Les particularités de la chimie des solides sont sans doute plus nombreuses que celles des autres états de la matière, étant donné que les influences structurales sont naturellement plus diverses. Il sera donné, dans la partie suivante, un bref résumé des réalisations techniques existantes, des groupes de problèmes théoriques et, ensuite, quelques exemples de recherche et de réalisation les plus urgentes. Il n’existe évidemment plus de différences de principe, actuellement, entre le travail théorique et pratique, étant donné que l’industrie moderne ne peut plus travailler sans connaître exac­ tement les matériaux, les réactions et les méthodes, sous peine de s’exposer à des pertes de temps et d’argent. Ces connaissances ne peuvent s’acquérir que par la recherche approfondie. Un fait important, observé dans la chimie des silicates, en métal­ lurgie et, en général, chaque fois que l’on travaille avec des solides, est que les réactions effectuées au départ de poudres, commencent à des températures beaucoup plus basses qu’on ne le pensait aupa­ ravant. De ce fait, il y a formation de produits de réaction qui agissent, non seulement directement sur la température d’effondrement ou de fusion, mais qui, par la suite, influencent l’évolution de la réaction totale. En effet, les produits formés à des températures plus basses, par effet de diffusion, sont différents de ceux qui se formeraient normalement, à des températures plus élevées. Le fait de savoir que chaque forme de transformation ou d’état incomplet, correspond à un maximum relatif d’activité — que ce soit une attaque ou une prédisposition à l’attaque — a donné à l’industrie la possibilité d’éviter des destructions de matériaux, provenant de transformations cristallographiques. Ainsi, le quartz ou la sillimanite, utilisés pour le revêtement des fours, doivent être préalablement transformés en cristobalite et en mullite. La présence de petites quantités de substances étrangères dans la matière première, peut influencer les propriétés physico-chimiques de cette dernière. Ceci a permis d’expliquer le comportement dif­ férent, considéré longtemps comme énigmatique, de matériaux de compositions chimiques à peu près identiques.

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L’industrie a compris l’importance capitale des propriétés struc­ turales, dépassant souvent celle des analyses chimiques dont elle se contentait précédemment. La réactivité des solides est fortement influencée par des variations de composition du gaz ambiant, ne réagissant pas chimiquement. Ceci est valable non seulement lors du chauffage au four, mais aussi lors du broyage, au cours duquel la formation de couches de grains fins, freinant les chocs autour des particules non ramolies, dépend de la teneur en humidité de l’atmosphère du moulin. Notons encore que les nouveaux types de réactions cités, qui ont été appelés, plus ou moins heureusement, réactions d'échange ont permis d’expliquer le déroulement de divers procédés, utilisés depuis longtemps dans l’industrie; par exemple, les procédés de grillage et frittage ou la méthode de Bessemer. Elles ont de plus rendu possible la mise au point d’une série de nouvelles méthodes de production : la fabrication de briques hautement réfractaires sans phases de fusion, de pièces d’appareillage utilisés dans les industries électrotechnique et électronique modernes et possédant des propriétés électriques et magnétiques particulières. La possibilité de prévoir l’activité des corps solides, au départ de données concernant les perturbations de structure irréversibles, est évidemment de première importance pour l’industrie utilisant la catalyse. On a pu ainsi améliorer la durée et la sélectivité des catalyseurs, empêcher ou ralentir les processus de recristallisation et les échanges indésirables avec la substance de support. Dans l’industrie de la catalyse, dans la fabrication des pigments, des produits huileux et des vernis, l’attention se porte aujourd’hui sur les influences très diverses de certaines modifications cristal­ lographiques, telles le rutile et l’anatase. Il va de soi que la connaissance des phénomènes de diffusion à l’état solide est à la base de la préparation des produits métallur­ giques et céramiques en poudre des métaux durs et des « Cermets ». Rappelons que l’influence des gaz ambiants dissous, non liés, sur l’activité en surface, joue également un rôle important dans ces préparations. Pour ce qui est de l’extension des notions de magnéto-, électro-, photo- et phonochimie, ces effets ne sont pas exploités dans la même

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mesure, du point de vue technique. Certaines réalisations existent cependant. Ainsi, la préparation des ferrites et d’autres substances utilisées en électronique, est facilitée si l’on opère à des températures situées dans l’intervalle de la transformation magnétique. La pro­ duction de couches minces isolantes, dans les transformateurs, est favorisée par un traitement préalable du métal par les ultrasons. Depuis longtemps, j’ai attiré l’attention sur le fait qu’il est pos­ sible d’influencer la sélectivité d’un catalyseur en utilisant des champs magnétiques ou électriques externes ou d’accélérer la polymérisation de substances organiques, dans les domaines de changement spon­ tané de polarité. Les réalisations techniques que nous venons de mentionner donnent un aperçu de l’avenir. Les possibilités d’amélioration des méthodes et d’adaptation dans de nouvelles branches de la production sont extrêmement variées. Cela demande toutefois des connaissances encore plus approfondie, des facteurs suivants notamment : 1° Les particularités de la surface en rapport avec la structure; nature et formation des molécules de surface. 2° Effets de polarisation à l’intérieur du réseau par suite de chocs thermiques résultant du chauffage (par exemple, assemblages molé­ culaires dans les réseaux ioniques). 3° La propagation de certains éléments perturbateurs de l’intérieur vers la surface. 4° La nature réelle des dislocations de toutes formes. 5° Déterminations exactes des défauts irréversibles. ° Le mécanisme des transformations cristallographiques.

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1° Influence de diverses perturbations du réseau sur le mécanisme de transport (diffusion) et détermination de la nature des particules et des modes de transport. ° Déviations stoechiométriques des formules normales en surface

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et à l’intérieur et leur influence sur l’activité physico-chimique des surfaces. 9° Les conditions d’échange d’électrons ou de particules de matière à la limite des phases et leur influence sur les effets d’adsorption et de réaction.

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10° Recherches approfondies sur les nouveaux effets magnéto-, électro-, photo- et phonochimiques. Dans la suite de cet exposé, nous donnerons quelques exemples de problèmes actuels en liaison avec ces différents points spécialement en ce qui concerne les applications pratiques. Les particules situées en surface, aux arêtes et aux angles, sont plus ou moins non saturées. Elles ont tendance, suivant la nature de la substance, à se grouper autrement qu’à l’intérieur du réseau. Il en résulte une structure superficielle spécifique au sein de laquelle les particules ou les groupes possèdent des moments dipolaires propres et produisent des effets de polarisation différents de ceux qui existent à l’intérieur. On sait également que les températures de transfor­ mation, observées en surface, sont généralement très inférieures aux températures normales et que l’activité physico-chimique de la surface est influencée par le déroulement général de la transfor­ mation. La mobilité des groupes atomiques formés ou adsorbés à la surface est modifiée par les conditions de diffusion à l’intérieur du réseau. Tout ceci est important, non seulement du point de vue théorique, mais aussi du point de vue des applications pratiques dans de nombreux domaines. En effet, les phénomènes dont il vient d’être question agissent aussi bien sur les processus de recristal­ lisation et de frittage que sur l’adsorption et les réactions chimiques. Jusqu’à présent, on a étudié partiellement ces problèmes avec quel­ ques métaux et substances organiques (migration de molécules en surface). Il va de soi que les questions soulevées ne se limitent pas à ces quelques cas, bien que ceux-ci soient d’un intérêt général. Il arrive souvent, dans la littérature, de voir extrapoler des basses températures à des températures supérieures, lors de l’étude de processus dépendant des propriétés des ions d’un réseau ionique. Ceci suppose que le réseau reste constamment un réseau ionique type. Une telle manière de procéder n’est évidemment pas justifiée. Les chocs thermiques provoquent la formation de groupes molécu­ laires ou d’autres effets de polarisation. Ceux-ci tendent à perturber ou à faire disparaître le réseau ionique. Lorsqu’on chauffe du CaCO , par exemple, il faut admettre la préformation, dans le réseau, de groupe CO2. Le mécanisme de décomposition thermique, ainsi que les modifications physiques et chimiques qui l’accompagnent, n’a

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pas encore été étudié suffisamment. C’est une tâche urgentes et importante de la recherche. On s’occupe beaucoup de ces problèmes maintenant. En rapport avec ce que nous avons dit et avec ce qui suit, les vues de W. A. Weyl méritent un intérêt tout particulier. Elles sont exprimées, par exemple, dans son livre A New Approach to Surface Chemistry (1951) et dans sa conférence, présentée à ce Symposium. Il montre la nécessité de considérer de façon différente, d’une part, pour l’état solide et, d’autre part, pour les états liquides et gazeux, les notions de particules élémentaires et leurs rapports d’affinité, dans le cas de formations caractéristiques de ces états. Il est possible que la théorie de Weyl permettra une compréhension plus profonde et plus concrète des notions de vides et d’espaces inter-réticulaires, de la nature des perturbations et de leur propagation dans les réseaux. Actuellement, ces représentations se limitent en quelque sorte à des formules mathématiques, sans que nous ayons, le plus souvent une image claire de la nature des perturbations du réseau, comme c’est le cas pour le réseau régulier. Pour une même substance, on peut observer de grandes différences dans la vitesse de certaines transformations cristallographiques, suivant que l’on opère à des températures croissantes ou décrois­ santes. On a beaucoup écrit à ce propos, sans arriver toutefois à une représentation exacte du mécanisme de ce phénomène. Comme exemple, on peut citer les transformations de la Si02, très importantes du point de vue pratique dans la chimie des silicates et en métallurgie. Les transformations a ^ p se font rapidement dans les deux sens. La formation de la tridymite et de la cristobalite, bien qu’assez lente, se fait toutefois beaucoup plus vite que le retour au quartz, lorsque la température décroît. Aussi à l’Institut de Gôteborg, on s’est attaché depuis longtemps à l’étude de ces pro­ cessus ainsi qu’au problème de la migration. Ce champ de travail est immense étant donné l’individualité marquante des phénomènes de transport dans les transformation entre phases solides, ou entre phases solides et liquides ou gazeuses. A Gôteborg, nous nous sommes limités à l’étude de systèmes oxygénés, dont l’importance est vitale pour la chimie des silicates et pour la métallurgie. Jagitsch a élaboré une méthode radiogra­

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phique et mis en évidence la migration de groupes lors des « réac­ tions d’échange », dans le cas de nombreux mélanges d’oxydes. En faisant varier la dimension des particules, il a pu déterminer le rapport entre le transport en surface et la diffusion dans le réseau, pour quelques systèmes importants, du point de vue géologique, en particulier. A Gôteborg encore, Lindner a élaboré de nouvelles méthodes utilisant les radioisotopes, pour l’étude des phénomènes de diffusion. Ici également, l’importante question du rapport entre la migration de surface et la diffusion interne, a été attaquée avec succès. Les discontinuités, mises en évidence par les courbes de diffusion, ont fait découvrir quelques transformations cristallographiques, incon­ nues précédemment. L’étude du mécanisme de la corrosion par oxydation, insuffi­ samment connu dans la plupart des cas, devrait être entreprise à nouveau. Chez nous, on met au point une méthode d’investigation utilisant l’oxygène lourd. Il est évident que tous ces problèmes demandent beaucoup de travail et que celui-ci présente un intérêt tant théorique que pratique. On connaît depuis longtemps les déviations aux formules stoechio­ métriques caractéristiques seulement pour les composés hétéropolaires typiques. Dans les systèmes métalliques on a défini également les facteurs qui déterminent la composition des alliages. Les rapports sont différents dans la plupart des composés non métalliques, pour lesquels il existe des écarts déterminés plus ou moins par la température, par exemple, pour les sulfures, les séléniures et les oxydes. Dans le cas, des semi-conducteurs et des substances phosphores­ centes ou fluorescentes, ces conditions non stoechiométriques jouent un rôle très important du point de vue technique. Dans beaucoup de cas, cette influence a été justifiée de façon scientifique. La théorie de Weyl, c’est-à-dire « the maximum possible screening » d’un cation, constitue certainement un progrès important pour l’explication de ces faits. M’étendre sur ce sujet sortirait du cadre de cet exposé. Je m’atta­ cherai plutôt à attirer l’attention sur quelques résultats obtenus dans notre Institut, résultats qui peuvent comme d’autres ouvrir un nouveau champ de travail.

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On a démontré, en particulier, que les substances ou les couches superficielles pour lesquelles les conditions stoechiométriques ne sont pas respectées, possèdent des propriétés d’adsorption et de réactions particulières. L’étude approfondie de ces phénomènes est importante pour les processus catalytiques, en particulier. S. Berger s’occupe de ces recherches. Ce domaine est toutefois extrêmement vaste; il comprend également l’étude de l’influence des états cristal­ lographiques transitoires. Les vues de Weyl, de même qu’elles précisent les particularités de l’état solide, éclaircissent quelque peu les phénomènes catalytiques, y compris la question importante de la recristallisation des catalyseurs. Il y a encore d’autres problèmes importants en catalyse qui devraient être étudiés. Ils se rapportent, entre autres, à l’échange électronique entre le catalyseur et le substrat {Schwab, Suhrmann, Weyl) et à la détermination de la phase véritable du catalyseur, à savoir, par exemple, s’il s’agit du métal pur ou d’un oxyde ou d’un carbure formé. Nous dirons encore quelques mots au sujet de l’extension des notions de magnéto-, éleetro-, photo- et phonochimie. Les études poursuivies sur les phénomènes de transport à l’aide d’atomes, de groupes d’atomes, et surtout d’électrons, sont communes à ces notions et aux phénomènes envisagés précédemment. Il apparaît que, dans tous les systèmes de substances ferromagnétiques et de substrats très variés étudiés, l’état paramagnétique possède toujours la plus grande activité. H. Forestier a non seulement confirmé ces vues, mais il les a développées en démontrant — comme cela a déjà été mentionné — que l’état de transition entre le ferroet le paramagnétisme détermine, dans le cas des mélanges de poudres également, un maximum relatif de la capacité réactive, suivant le rapport des transformations de structures véritables. Ces phénomènes « magnétocatalytiques » sont certainement liés aux conditions significatives, déjà mentionnées, de mobilité et d’échange. Ces relations demandent des études physiques appro­ fondies. E. Justi a entrepris dernièrement des recherches de ce genre. Il a démontré que des champs magnétiques, placés extérieurement, exercent une influence semblable à celle déjà mentionnée, par exemple, dans le cas de la transformation de l’hydrogène ortho-para.

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Les effets « électro-Curie » correspondants constituent également un domaine de recherche attirant. Jusqu’à présent, on a seulement constaté l’apparition des discontinuités dans les propriétés chimiques lors des changements spontanés des propriétés dipolaires. De telles recherches sont à rapprocher des travaux de Timmermans. L’étude approfondie des phénomènes décrits à l’origine comme photoadsorption, contribuera certainement à résoudre la question très actuelle de la signification de l’échange électronique dans l’adsorption, et dans les processus chimiques, en général. Il est très important de noter, du point de vue scientifique, que toute substance, et pas seulement celles désignées comme photosubstances, présente des propriétés physico-chimiques différentes, suivant qu’on l’irradie avec des longueurs d’onde susceptibles ou non d’être absorbées ou encore, si elle reste à l’obscurité. Un vaste domaine de travail s’ouvre ici; il faut s’attendre aussi à des applications techniques dans de nombreux domaines. Les effets chimiques des ultrasons sont un peu mieux connus et plus appliqués. Scientifiquement, il y a ici une certaine difficulté à séparer les effets purs des ultrasons de ceux provenant de réchauf­ fement local. Cette distinction n’a pas été faite de façon assez précise dans certains travaux. L’activité accrue des surfaces cristallines soumises à l’action des ultrasons suggère, entre autres, une étude détaillée du mécanisme de la formation des germes. C’est d’ailleurs un problème d’un intérêt général : il est étroitement lié à la formation des produits de réaction à la limite des phases. Pour terminer, il faut souligner que nos connaissances actuelles des facteurs agissant sur l’activité physico-chimique des solides, ont permis de résoudre quelques problèmes sur l’utilisation plus ration­ nelle et plus économique des matières premières non métalliques et des déchets industriels. Il suffit de citer ici la production des revêtements de fours, des cermets et des produits céramiques en poudre dans le domaine des “ alliages ” non métalliques. Nous mentionnerons encore que les éclaircissements apportés au problème de la formation des roches et des minerais ont permis de renouer le lien classique qui existe entre la chimie, la géologie et la minéralogie. On a aussi commencé un travail pour élaborer des méthodes pour la conservation des monuments historiques. Mais ici encore, nous n’en sommes qu’au début.

489

Discussion des rapports de J. A. Hedvall et de R. Lindner M. Barrer. — In self-diffusion in oxides (Table I) and in spinels (Table II) there seems to be a rough corrélation between the terms Do and E in the Arrhenius équation D = Do exp — E/RT. There are exceptions (e.g. self-diffusion in PbO, according to Table I, and of course some irregularities, but the general trend seems rather clear. I hâve previously demonstrated and a linear relation between Loge Do and in rubbers; and also between Loge 6o in a large variety of liquids (0 = 6o

discussed in several papers E/T for diffusion of gases and E/T for viscous fiow exp — E/RT) :

Loge Do = A + B (E/T)

Loge 00 = C + D(E/T) It might be of interest to try similar plots of Loge Do and (E/T) for the Systems studied by Dr Lindner. The appropriate value for T is the mean température in the range studied. If one writes the Arrhenius équation in the form : Loge

D

= Loge Do — E/RT

then if the ranges in measured values of LogeD are always much less than the corresponding ranges in the values of E/RT over a variety of diffusion Systems, then to a first approximation these values on LogeD can be regarded as constant in comparison with the much greater range in values of E/RT and so : constant

=

Loge Do



E/RT

giving a function of the observed type. This situation might arise either because of limitations in the accessible range of measurements of D or because of an intrinsic property of these rate processes such that the terms E/RT will always contribute a much larger numerical range than will the values of Loge D.

490

The nature of diffusion in crystals may of course be according to several distinct mechanisms whereas that in rubbers, and viscous flow in liquids, is due to the place exchange type of mechanism. There seems therefore less likelihood of uniform behaviour in diffusion in crystals, and so I find the trends shown by Dr Lindner to be very interesting. Evidently the entropy and energy of activation alter together for a very wide variety of rate processes. M. Lindner. — If the material mentioned in this paper is arranged in the way proposed by Prof. Barrer a general trend of a nearly linear relation between log Do and E/T becomes obvions (with inclusion of lead oxide). A parallelity between the two constants Do and E can be demonstrated in different ways : 1. If a common value for the self-diffusion constants at the melting point is valid, the Unes representing the température function of the self-diffusion constants are intersecting at the melting point and by extrapolation the largest slopes (activation energies) lead to the highest values for log Do. 2. A survey of the form suggested by Prof. Barrer has been published for self-diffusion in metals as well as intermetallic dif­ fusion by Dienes {J. Appl. Phys., 21, 1198, 1950) who stated a nearly linear relation between log Do/v y2 as function of E/T^ ÇTm : melting température). Dienes assumed a sort of a local melting as an elementary activation step for diffusion and identified E/Tm with the activation entropy. 3. The relation between Do and the entropy of activation has been further developed by Zener (J. Appl. Phys., 22, 322, 1951), who derived a direct proportionality between the logarithms of Do and the entropy of activations. The practical conséquence of this treatment is that low values of Do indicate short circuiting paths for diffusion as e.g. grain boundaries, which on the other hand are known to be connected with comparatively low activation energies. 4. Similar relations between log Do and E hâve been derived by LeClaire {Acta Metallurgica, 1, 438, 1953). M. LFbbelohde. — In at least one recent group of studies we hâve been able to correlate changes of the probality term and the energy

491

term for migration processes, and to interpret this corrélation on a structural basis. I refer to the viscosities of melts of various terphenyls measured as a function of température, and represented in terms of the entropy of activation Syj* and the energy of activ­ ation Et)^ by means of the absolute reaction rate expression for viscosity

fiN ri = —- exp (— Sri'^jR) exp (Eri^/RT), where V is

the molar volume. In these polyphenyls, the force fields between molécules are closely similar in ail cases but the degree of interlocking of molécules in the melts is much greater for a molécule such as o-terphenyl

As a resuit, o-terphenyl molécules require a much greater activ­ ation energy (7.9 K cal/mole compared with 3.8 K cal/mole to move in the liquid).

This higher activation energy is associated with a

larger probability factor. For o-terphenyl the entropy of activation is + 5.7 e.u. as compared with — 4.6. e.u. for p-terphenyl. One can think of it in this way : to permit o-terphenyl to move at ail, a larger hole must be produced than in p-terphenyl. But this hole can be used in a much less sélective way so that the entropy of activation involves an increase of probability over the ground State, instead of a decrease as for p-terphenyl. This interprétation can be confirmed in a rather élégant way from studies of the same flow parameters near the melting points. p-Terphenyl shows no appréciable change, but the activation energy to “ unlock ” neighbouring o-terphenyl molécules is dépendent in a sensitive way upon the volume. As the volume contracts the activation energy rises, and near the melting point it has more than doubled : —Eyj ~ 16 K cal (mole) . Presumably a larger hole has to be produced in the melt for flow to become feasible.

And the path for flow by means of this larger

hole is even less sélective than before.

The entropy of activation

rises to the large positive value of 29 e.u.

492

A similar interprétation can perhaps be generalised. In structures with similar force fields, large activation energies are associated with less sélective reaction paths than small activation energies. Consequently entropies of activation tend to be algebraically more positive, the larger the activation energy, (cf. J. N. Andrews and A. R. Ubbelohde, Proc. Roy. Soc., 228 A, 1955, 435). M. Bénard. —

Les observations du Dr Lindner concernant la

comparaison des énergies d’activation de diffusion des deux sortes de cations dans les ferrites, sont extrêmement intéressantes. Elles méritent d’être confrontées avec les résultats des études de l’inten­ sité des spectres de rayon X, qui révèlent dans ces phases une locali­ sation des cations à la température ordinaire. Si nous admettons avec le Dr Lindner que la répartition des cations sur les différentes positions est faite au hasard aux températures élevées, il nous faut conclure que le degré d’ordre observé à basse température doit être une fonction de la vitesse de refroidissement, ce qui ne semble pas avoir été observé. Il paraît en effet difficile d’admettre qu’un ordonnancement des cations puisse se produire d’une manière instantanée. Je voudrais demander au Dr Lindner s’il considère que l’identité des énergies d’activation de diffusion des deux types de cations implique nécessairement l’équivalence des positions au point de vue énergie. Ne serait-il pas possible en effet de concilier l’égalité des énergies d’activation de diffusion des ions avec des énergies différentes pour la localisation des deux types d’ions sur les deux types de position : tétraédrique et octaédrique. M. Lindner. — En effet, il a été observé et rapporté dans plusieurs conférences du “ Colloque international de Ferromagnétisme et d’Antiferromagnétisme ” à Grenoble en 1950, que la distribution des ions dans les ferrites à structure de spinelles est une fonction de la vitesse de refroidissement. Par exemple : Pauthenet et Bochirol {J. Phys. Radium, 11, 249, 1951) signalent que l’aimantation des ferrites de cuivre et de magnésium est une fonction de la température de la trempe. Au moyen des rayons X, Bertaut (J. Phys. Radium, 12, 252, 1952) a montré, par exemple dans le ferrite de zinc, qu’une inversion partielle peut être observées après un échauffement à 1000 °C. Le mécanisme de l’autodiffusion des cations dans les spinelles est, malheureusement, insuffisament connu. Usuellement l’énergie

493

d’activation expérimentale est la somme de l’énergie de formation des lacunes (ou ions interstitiels) et de l’énergie de migration. La structure des spinelles permet de prévoir un grand nombre de lacunes, ce qui a été, d’ailleurs, vérifié grâce aux mesures effectuées par la méthode des rayons X aux basses températures, celles-ci ne sont peut-être pas décisives aux hautes températures; On peut déduire de ces expériences que l’on doit probablement tenir compte d’une énergie de formation des lacunes effectives, et ainsi que l’énergie d’activation expérimentale n’est pas identique à l’énergie d’activation de la migration (c’est-à-dire la hauteur de la barrière d’énergie à franchir pour passer d’une position d’équilibre à l’autre). C’est déjà une des raisons pour lesquelles on ne peut pas répondre à la question du Prof. Bénard au sujet de la relation entre l’énergie d’activation expérimentale et l’énergie nécessaire pour l’échange des cations A et B entre les positions à coordination tétrahédrique et octahédrique. Nous espérons obtenir d’autres évidences expé­ rimentales par des expériences sur des spinelles non stoechiométriques. M. De Keyser. — Je désire donner un bref aperçu d’expériences récentes, effectuées en collaboration avec M. René Cyprès et qui ont fait l’objet d’une communication au Symposium de la Chimie des Solides à Madrid (avril 1956). Ces expériences concernent les réactions entre AlaOj/CaO.

Si02/Ca0 et

Dans l’étude de ces réactions par la mise en contact de pastilles, deux difficultés expérimentales doivent être surmontées : 1° Lors du chauffage, le retrait des deux oxydes en présence n’est pas le même. Il ne se produit pas non plus aux mêmes tempé­ ratures. Il s’ensuit que les briquettes qui sont en contact au début de l’expérience, se séparent très rapidement et que la réaction s’arrête faute d’un contact suffisant. Cette difficulté a pu être surmontée en utilisant, comme le montre la figure 1, un creuset de marbre très pur (CaCo3) dans lequel on comprime suivant le cas, de la poudre d’Al(OH)3 ou de la silice amorphe. Le retrait de CaO étant supérieur à celui des autres oxydes, le creuset, au cours du chauffage, se contracte sur la pastille inté­ rieure. De plus, un piston en marbre, lesté, maintient un bon contact entre la pastille et le fond du creuset.

494

: E

FI0.1 CREUSET DE MARBRE 2° Les pastilles qui ont été soumises aux températures de réaction, sont extrêmement friables. Il est impossible de les manipuler sans les briser et même sans qu’elles ne tombent en poussière. Aucune méthode d’investigation de la surface réagissante n’est applicable sans un traitement préalable de la briquette permettant de figer

Fig. 2

495

l’échantillon dans son ensemble après la réaction. Ce résultat peut être obtenu en imprégnant les matières solides de méthyl métacrylate liquide qui est ensuite polymérisé.

Résultats des examens. 1° Réactions Al203/Ca0. La micrographie de la figure 2 montre l’aspect en lumière pola­ risée d’une lame mince taillée suivant le plan EF (fig. 1) pour un échantillon traité à 1250 °C durant 48 heures. Pour l’examen de cette lame mince, il faut remarquer que CaO, A3C4 et AC3 sont isotropes et que la biréfringence de l’Al203 est faible (+). Seul AC orthorhombique présente une biréfringence appréciable. Le liséré clair situé du côté de l’Al203 est constitué de AC. Entre cette couche et le CaO, se trouve une zone foncée, dans laquelle on remarque certaines bandes claires. Les examens par rayons X obtenus en faisant des coupes suivant le plan CD et par usure dans la direction de la flèche (voir fig. 1) confirment que c’est bien de l’AC qui est en contact avec de l’alumine et que la deuxième couche est constituée essentiellement de A3C5. Une étude par la méthode des traceurs radioactifs a d’ailleurs confirmé ces observations. L’épaisseur environ

0,2

de

l’ensemble

des

couches

réactionnelles

atteint

mm.

( + ) Suivant les notions habituelles AC

représente, ALOa.CaO

A3C5 représente 3(Al203).5(Ca0) AC3

Sc représente Si02.Ca0 SC2 représente Si02.2Ca0

représente Al203.3(Ca0)

La localisation de ces couches a été faite par l’utilisation d’un repère en platine suivant le procédé de Jagitsh. La position de ce repère montre la pénétration de Ca dans AI2O3.

496

2° Réactions SiOj/CaO. La figure 3 reproduit une micrographie (lumière polarisée) d’une lame mince, préparée de la même manière que pour les réactions AljOa/CaO.

Fig. 3

L’échantillon Si02/CaO a été porté à 1250 °C pendant 212 heures. Il a été nécessaire de chauffer très longtemps parce que la vitesse de pénétration de Ca dans Ci02 est très faible. Le peu d’épaisseur de la couche réactionnelle rend la détermi­ nation exacte de la composition de celle-ci fort difficile. Toutefois, les examens par rayons X y montrent la présence de C2S, CS et de tridymite. La tridymite croit au fur et à mesure que l’on pénètre, le a CS persiste. Il faut toutefois remarquer que l’échantillon est fissuré et qu’il est possible que le a CS se forme sur les bords des fissures. De toute manière, lorsque l’on se trouve à profondeur suffisante (environ 0,86 mm) le a CS disparaît presque complètement, la tridymite persiste tout en diminuant, et il y a apparition graduelle de cristobalite.

497

Le fait qu’à 1250 °C (température de cuisson de l’échantillon) il n’y a aucune phase liquide Ca0-Si02, montre nettement que la tridymite s’est formée directement en phase solide, grâce à l’inter­ vention du Ca par un mécanisme du type qui a été proposé par Weyl. Au sortir de la phase contenant de la tridymite, on constate la présence de cristobalite qui s’est formée directement à partir de Si02 amorphe, ce qui est conforme aux observations faites anté­ rieurement par de nombreux chercheurs et par nous-mêmes. En conclusion de cet examen, on peut dire que la couche réaction­ nelle située entre CaO et Si02 a probablement été obtenue par migration moléculaire de CaO. La faible vitesse de migration peut expliquer la formation de C2S. On sait en effet que dès qu’il y a du Ca en suffisance, ce composé est formé de préférence au CS, ce qui d’ailleurs peut s’expliquer par la théorie de Weyl, les tétraèdres Si04 étant mieux couverts par le Ca dans C2S que dans CS. Nos examens radiocristallographiques ayant montré qu’au-delà de cette couche, il n’y a que des traces de silicate, mais qu’il y a formation de tridymite, on peut supposer que dans cette région, il y a diffusion de Ca++ en faible quantité. Ce Ca++ facilite la trans­ formation de cristobalite en tridymite.

M. CoUongues. — Nos expériences montrent que la variation de concentration des lacunes à l’intérieur d’une couche de protoxyde de fer formée à la surface du métal n’est pas linéaire. En effet, nous avons étudié la variation de composition en mesurant par la méthode de rayons X en retour le paramètre cristallin des couches succes­ sives de protoxyde (1,2). Rappelons que les paramètres des phases protoxyde de fer de différentes compositions varient linéairement depuis a = 4,276 A (Feo,90i) jusqu’à a = 4,304 A (FeiOj). Nos pellicules étaient préparées par oxydation de fer très pur dans différents mélanges H2-H2O. Les résultats sont les suivants :

(') R. CoUongues : Thèse Paris (1954). (2) R. CoUongues et R. Lifferlen : Coll. Intern. Réact. Superficielles Paris {1956).

498

distance à l’interface en microns p\Ï2^ ° ——— = 0,7; phase FeO en équilibre a = 4,303 A P^2 /7H2O O courbe (II) —--— = 1,8; phase “ FeO ” en équilibre u = 4,280 A pWi PH2O courbe (III) —— = 6,4; phase en équilibre Fe304. P^2 On constate : courbe (I)

1° que la variation de composition à l’intérieur de la couche d’oxyde n’est pas linéaire. La composition reste sensiblement constante dans la plus grande partie de l’épaisseur de la pellicule

et varie très rapidement au voisinage de l’interface métal-oxyde. 2° que la composition de la couche externe à l’interface oxydeatmosphère ne correspond pas à la composition de la phase “ FeO ” en équilibre avec le mélange H2-H2O utilisé. Ces conclusions sont valables quelle que soit l’épaisseur de la pellicule à condition qu’une adhérence parfaite soit réalisée à l’inter­ face métal-oxyde. M. Chaudron. — La diffusion règle généralement la réaction dans l’état solide. Toutefois, il ne faut pas oublier que dans certains cas, la vitesse de diffusion peut devenir très grande et cet obstacle à la réaction devient alors négligeable. Dans la chimie des phosphates de calcium, Montel, du Laboratoire de Vitry, a mis récemment en évidence des réactions dans l’état solide où la diffusion devient un facteur secondaire (*). Certaines (*) G. Montel : Influence de petites quantités de sodium sur la cinétique d’une réaction de synthèse de la fluorapatite. Communication au Troisième Colloque International sur les Réactions dans l’Etat Solide, Madrid, avril 1956 (à paraître).

499

structures, les apatites par exemple, sont probablement favorables à une diffusion rapide. Des additions de sels de sodium, dans les expériences de Montel, favorisent également la diffusion. Ce rôle des impuretés peut être expliqué par des mécanismes de Weyl qui ont fait l’objet des précé­ dents rapports.

M. Lindner. —

Dans quelques cas, l’accélération de la diffusion

par des impuretés peut être expliquée par la théorie de WagnerSchottky et Frenkel. Dans le cas des ions interstitiels, la concentration peut être augmentée par des impuretés contribuées par des ions de valence inférieure.

M. Ubbelohde. — It is comparatively easy to understand how certain ionic impurities can increase migration velocities in ionic crystals. For example, when Cd++ is dissolved in NaCl, a proportion of the holes practically equal to the concentration of Cd++ is generated in order to preserve local electrostatic neutrality. This increased concentration of holes is in mass-action equilibrium with the NaCl lattice also. The increased proportion of holes leads to increased migration probabilities. But how does the addition of impurities decrease the proportion of holes so as to decrease migration velocities ?

M, Lindner. — The case treated, i.e. zinc oxide with additions of alumina or gallium oxide does not refer to vacancy disorder but to the occurrence of interstitial zinc ions as responsible for ionic migration and reaction in the solid State (though the alternative possibility of oxygen vacancies, preferred by Prof. Weyl, can be treated in an analogous way). By introducing e.g. alumina into the zinc oxide lattice, two zinc ions are substituted by two aluminium ions. A raise in the positive charge, is, however, prevented by interaction with the three oxygen ions introduced together with the aluminium ions, which may react not only with the two zinc ions formerly belonging to the normal lattice but also with one interstitial zinc ion of higher mobility. With this decrease in mobile carriers the overall diffusion is likewise decreased. Obviously there is a fondamental différence between the effect of impurities on lattices with cation vacanties on one hand and

500

anion vacancies or interstitial cations on the other.

In fact this

method of incorporating impurities can be used to déterminé the character of lattice disorder.

M. Weyl. — It is very difficult to compair the System NaCl + Cd++ excess with the System ZnO — Ga+++ because NaCl resembles closely an idéal crystal whereas ZnO at températures above 600 °C is defective, as can be seen from the fluorescence. Now we assume that such an oxide contains O^- vacancies and as a resuit we predicted that Ga203 or AI2O3 decreases this rate of sintering a conclusion which could be verified experimentally (Gôteborg Proceedings). The description by Lindner of the interstitial zinc atom-placing, the Zn++ between two Zn++ ions and the two électrons between the two 02- ions, violâtes the principle of electroneutrality in this smallest possible volume. The high coulomb repulsion between Zn++ — Zn++ ions in close proximity or this électron between two 02- ion would raise the energy of such a System to a very high level. I prefer to describe the interstitial Zn atom as a zincous ion, Zn2++ analogous to the mercurous ions Hg2++ and give it the quanticule formula Zn++(e2“)Zn++.

2n -métal

ZnO

501

M. Lindner. —

There has been much work and discussion con-

cerning the disorder model of zinc oxide. Many characteristics can be explained by either the occurrence of interstitial zinc ions or oxygen vacancies and a final decision between the two possibilities has not been reached yet. Lately, however, there has been some experimental evidence in favor of the assumption of interstitial zinc ions. 1. Thus Gray {J. Am. Ceram. Soc., 37, 534, 1954) found a corrél­ ation between the colour of preheated zinc oxide crystals and the lattice constant of the oxide, which is larger in the coloured crystals as compared with white zinc oxide. As the colour is assumed to be in some way related to excess zinc, accomodation of this excess in form of interstitial zinc ions looks probable. It must be admitted that such measurements ought to be combined with conventional density measurements and quantitative data for the zinc excess. 2. The lattice eonstant of cadmium oxide, which oxide is usually supposed to behave very similar to zinc oxide, has been measured — as Prof. Bénard kindly reminded us during the conférence — as fonction of vacua-preheating température by Faivre and Michel {Comptes Rendus, 207, 159, 1938), who observe a significant enhancement of the lattice constant with increasing preheating température (and subséquent quenching), whereas the constant is not changed if the sample is slowly cooled or preheated in oxygen atmosphère. 3. The self-diffusion of zinc oxidation layers is greatly enhanced as compared with the values in zinc oxide, as mentioned in our paper. Besides, approximate agreement between this rate and the oxidation rate of zinc métal has been obtained.

This supports the view that

the diffusion of interstitial zinc ions determinated the oxidation rate. The possibilities of a diffusion of oxygen vacancies cannot be completely excluded, but has in no way been experimentally proved. Summing up the evidence it can be stated that the occurrence of monovalent interstitial zinc ions in zinc oxide looks at the présent to be better established than the occurence of oxygen vacancies.

M. Bénard. —

Il me paraît intéressant d’attirer l’attention sur

un aspect des relations qui existent entre les réactions dans l’état

502

solide et la diffusion, dont il ne semble pas avoir été question jusqu’à maintenant : je pense à l’influence du mode de liaison sur l’énergie d’activation de diffusion. En effet, l’énergie requise pour transporter un atome d’une position d’équilibre du réseau cristallin à une posi­ tion d’équilibre voisine du même réseau ou d’un réseau différent dépend essentiellement de la nature des liaisons que cet atome échangeait initialement avec ses voisins immédiats. Il semble entre autres que l’existence d’une liaison de covalence forte oppose un obstacle considérable à la diffusion, comme le montre la lenteur de la diffusion dans les réseaux covalents tridimensionnels du type diamant. On pourrait dans ces conditions se demander si les études d’autodiffusion ne constituent pas un moyen commode de comparer les types de liaison dans une série homologue de composés solides. En outre cette méthode d’approche rend compte des phénomènes d’anisotropie de diffusion, dont l’importance est particulièrement marquée dans les réseaux lamellaires, mais qui apparait de f