The Structures of Binary Compounds PDF
Preview The Structures of Binary Compounds
COHESION AND STRUCTURE Volume 2 Series editors F.R. de Boer University of Amsterdam D.G. Pettifor Imperial College, London NORTH-HOLLAND AMSTERDAM • OXFORD • NEW YORK • TOKYO THE STRUCTURES OF BINARY COMPOUNDS Contributors J. Hafner Technical University, Wien F. Hulliger ETH, Zurich W.B. Jensen University of Cincinnati, Cincinnati J.A. Majewski Polish Academy of Sciences, Warsaw K. Mathis ETH, Zurich P. Villars Intermetallic Phases Data Bank, Aristau P. Vogl Karl-Franzens-Universat, Graz 1989 NORTH-HOLLAND AMSTERDAM • OXFORD • NEW YORK ♦ TOKYO © Elsevier Science Publishers B.V., 1989 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher, Elsevier Science Publishers B.V., P.O. Box 211, 1000 AE Amsterdam, The Netherlands. Special regulations for readers in the USA: This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the U.S.A. All other copyright questions, including photocopying outside of the USA, should be referred to the publisher. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. ISBN: 0 444 87478 x Published by: North-Holland Elsevier Science Publishers B.V. P.O. Box 211 1000 AE Amsterdam The Netherlands Sole distributors for the USA and Canada: Elsevier Science Publishing Company, Inc. 655 Avenue of the Americas New York, NY 10010 USA Library of Congress Cataloging-in-Publication Data The Structures of binary compounds / editors, F.R. de Boer, D.G. Pettifor. p. cm. - (Cohesion and structure; v. 2) Includes bibliographical references. ISBN 0-444-87478-X 1. Molecular structure. 2. Domain structure. 3. Ionic structure. I. Boer, F.R. de (Frank R.) II. Pettifor, D.G. (David G.), 1945- III. Title: Binary compounds. IV. Series. QD471.S835 1989 541.2'2-dc20 89-23451 CIP Printed in The Netherlands PREFACE Two distinct but complementary developments have occurred this decade regarding the structure and stability of binary compounds. On the one hand, the known experimental data base has been ordered successful ly within two-dimensional or three-dimensional structure maps. These maps are proving useful both pedagogically and as a guide in the search for new alloys with a required structure type. On the other hand, first-principles theoretical calculations within the local density functional (LDF) approximation have been shown to predict the correct ground- state structures of binary semiconductors, insulators and metals. The success of LDF theory is allowing the microscopic quantum mechanical origin of structural stability to be explored in detail. In the first chapter of this volume, Villars, Mathis and Hulliger present an up-to-date compilation of the structures of binary compounds A xBr The 150 most frequently occurring structure types are found to have local atomic environments that are characterized geometrically by a limited number of different co-ordination polyhedra which they display explicitly. The data are ordered both within two-dimensional structure maps using the phenomenological Mendeleev or relative ordering number and within three-dimensional plots using physical co-ordinates reflecting atomic size difference, electronegativity difference, and average number of valence electrons per atom respectively. In the second chapter, Jensen shows that crystal co-ordination formulas can help bridge the gap between the minimum information content of the stoichiometric formula A^B^ and the maximum information contained either explicitly or implicitly in the specification of the unit cell and its dimensions. The different local co-ordination polyhedra are labelled in a simple fashion so that, for example, the co-ordination formula for rocksalt, ^[NaCl6/6], tells us immediately that we have an infinite three-dimensional framework struc ture in which both the Na and Cl sites are six-fold octahedrally co ordinated. The last two chapters of this volume deal with recent developments in our quantum mechanical understanding of the origins of structural stabili ty. Hafner presents the necessary background for understanding the highly successful local density functional (LDF) calculations. He demon strates very powerfully how far these first-principles results for sp-bonded vi Preface systems may be interpreted in terms of the well-known ideas of second- order perturbation theory which were developed by physicists during the 1960s for describing nearly-free-electron (NFE) metals and alloys. In the final chapter, Majewski and Vogl discuss the cohesion and structure of solids from the more localized or tight-binding (TB) point of view, thereby making contact with one's chemical intuition. D.G. Pettifor F.R. de Boer Chapter I ENVIRONMENT CLASSIFICATION AND STRUCTURAL STABILITY MAPS Pierre VILLARS*, Katharina MATHIS**f and Fritz HULLIGER** *lntermetallic Phases Data Bank, CH-5628 Aristau {Switzerland) **Laboratorium für Festkörperphysik ETH, CH-8093 Zürich (Switzerland) 'Present address: EM PA, CH-8600 Dubendorf (Switzerland) Contents Abstract 2 1. Philosophy of structural stability maps 2 2. A simplified classification concept based on coordination 3 3. The generalized structure types 17 4. Two-dimensional stability maps 18 5. Three-dimensional stability maps 69 6. Discussion and concluding remarks 87 References 102 The Structures of Binary Compounds edited by F.R. de Boer and D.G. Pettifor © Elsevier Science Publishers B.V., 1989 1 Abstract This chapter gives a fairly complete and up-to-date representation of the structural knowledge on about 5500 binary compounds and alloys AB. Structure types with more than five representatives are examined x y with regard to the environment of the atoms. As a result, 147 classical structure types are classified as 97 coordination types. The structure data are arranged in six isostoichiometric two-dimensional M versus M maps A B or tables (M is the so-called Mendeleev number based on Pettifor's chemical scale χ), as well as in four three-dimensional VE-AR-AX representations (VE, AR, AX are concentration-dependent sums of the valence-electron numbers, differences of Zunger's pseudo-potential radii and Martynov and Batsanov's electronegativity of the constituent ele ments, respectively). The proposed geometrical structure-type classifica tion proved to be consistent with an approach from the VE - AR-AX representation, which underlines its general value. In the last part, we argue that a combined use of both the M versus M maps and the A B VE-AR-AX plots provides the greatest chance for solving crystal-chemi cal questions as well as for predicting the alloying behaviour of a binary system. 1. Philosophy of structural stability maps With the 100 elements of the Periodic System one can expect the formation of at least 8000 binary compounds crystallizing in about one thousand structure types (in this chapter often called "classical" structure types). It is the main goal of crystal chemistry to show up relations between the structure type of a compound and the electron configuration of its constituents, in order to explain or to make plausible the occurrence of certain structure types, or in order to give hints about possible structure types of new or hypothetical compounds. A basic property of each compound is its crystal structure. A new compound is only defined after its structure is reliably determined. Since new compounds frequently are available only in polycrystalline form, an idea about possible structure types can enormously facilitate the indexing of the X-ray powder-diffraction pattern. Moreover, particular structure types are favorable for certain properties like superconductivity and ferromagnetism, and perhaps one is interested in finding new representa tives. 2 Ch. I, §2 ENVIRONMENT AND STRUCTURAL STABILITY 3 Two numbers are sufficient to characterize the gross features of the chemical behavior of the elements: The Periodic Table of Mendeleev is a two-dimensional array in which each element is characterized by its period and group. We, therefore, expect more than two variables are needed to describe binary compounds. Several attempts have already been made to construct two-dimensional structural stability maps based on simple expressions of the atomic properties of the constituent elements (Mooser and Pearson 1959, Pearson 1962, St. John and Bloch 1974, Machlin et al. 1977, Watson and Bennett 1978a,b, Bloch and Schatteman 1981, Zunger 1981). This can at best be done for certain groups of compounds such as the non-metallic compounds or the metallic alloy phases of fixed atomic ratio. As the actual number of variables is definitely larger than two, the simplification will inevitably lead to some misplacements. Whether these structure maps are based on energy-band calculations or on empirical data, any structure prediction for a new compound is restricted to the structure types taken into consideration. The prediction becomes more probable the more structures types are taken into account but it necessarily fails if the new compound adopts an unknown structure type. However, it might be possible to predict the gross features of a new structure, i.e., the coordination polyhedra or the coordination number of the atoms. It is well-known that certain electron configurations lead to characteristic coordinations such as the square- planar surrounding of the diamagnetic d8 configuration. Recently, we have separated in a three-dimensional representation of structural stabili ty, binary, ternary and quaternary single-environment (structures which have only one type of coordination polyhedra) compounds of arbitrary stoichiometry into domains of defined coordination polyhedra, e.g., the tetrahedron type (CN 4) or octahedron type (CN 6) (Villars and Hulliger 1987). The classical structure types thus are abstracted to general struc ture types with similar (or identical) coordination polyhedra. Therefore, we call them coordination types. In the following we try to extend this simplification to classical structure types with up to four different coordi nation polyhedra. 2. A simplified classification concept based on coordination A crystal structure is completely determined by the following data: (1) chemical formula; (2) crystal system and unit-cell dimensions; (3) space group; and (4) occupation number and coordinates of the occupied point sets. These characteristics lead to a rather high number of different classical 4 P. VILLARS et al. Ch. I, §2 structure types [nearly 1000 binary structures are listed in Vol. 1 of the work by Villars and Calvert (1985)] impossible to manage in structure stability maps. The space group may be important for certain physical properties such as piezo- and ferroelectricity, but not so much for crystal chemistry. A minor distortion of a crystal structure can reduce its symmetry, although the resulting deformation of the coordination polyhedra may be neglig ible. If we base our structural classification on the coordination poly hedra, we can hope to achieve a substantial reduction of the number of different structure groups. In the following we restrict our considerations to those structure types that possess more than five representatives. These are 147 classical structure types adopted by roughly 5000 binary compounds. We have listed these types in table 1, sorted alphabetically according to the formula name in table la and according to the Pearson symbol and increasing space group number in table lb. By considering only-for reasons of time - the most frequent structure types, we omit about 500 classical binary structure types (collected in table 7) most of which, however, have only one or two representatives. In a conventional con sideration these omissions would represent a true inaccuracy. In our considerations, however, it can be hoped that the omitted compounds (which nevertheless will be included in figs. 5-11) do not represent different coordination types. The coordination polyhedron describes the environment of an atom in the structure. The exact geometrical shape of the polyhedron may be accidentally determined by additional edges which change the shape of the faces (e.g., if the fourth corner of a square slightly moves out of the plane, we end up with two triangles). For our coordination purpose, however, only the approximate arrangement of the corners is of import ance. As an illustration we show in fig. 1 how a small shift of the vertices transforms the polyhedra. The determination of the coordination polyhedron is sometimes a matter of controversy. We decided to use the maximum-gap method of Brunner and Schwarzenbach (1971) to derive the relevant polyhedra. All distances from the atom under consideration are plotted in a histogram as shown in fig. 2. The height of the bars is proportional to the number of the corresponding neighbors n. It is convenient to express all distances d relative to the shortest distance d of the nearest neighbors. In about nearest 80% of all cases a maximum gap shows clearly up. The coordination polyhedron then is constructed with the neighbors to the left of this gap. If no maximum gap is detectable, we have to base our decision on additional criteria. The polyhedron should be convex and have a high Ch. I, §2 ENVIRONMENT AND STRUCTURAL STABILITY 5 Table 1 Structure types treated in this work. The numb 5r of representatives is added in parentheses. The environment type is characterized by the number of different coordinations. Compli- cated structures with more than four different coordination polyhedra are marked with an asterisk. (a) Structure types sorted alphabetically. No. of Environ- No. of Environ- Structure Pearson point- ment Structure Pearson point- ment type symbol sets type type symbol sets type A1B2 (112) hP3 2 2 Be17Nb2 (9) hR19 5 4 Al4Ba (20) tllO 3 3 BiF3 (36) cF16 3 1 Al2Cu (53) tI12 2 2 Bi3Se4 (5) hR7 2 1 Al4Cu9 (7) cP52 8 3 Bi2Te3 (8) hR5 3 1 AlDy (12) 0PI6 4 3 C2Ca (28) tI6 2 2 Al2Gd3 (7) tP20 5 4 CFe2 (5) 0P6 2 2 Al3Ho (5) hR20 6 2 CFe3 (91) 0PI6 3 3 Al La (10) oI28 6 4 C Mn (34) mC28 4 3 n 3 2 5 Al6Mn (5) oC28 4 3 C3Pu2 (19) cI40 2 2 Al3Ni2 (12) hP5 3 2 CW (14) hP2 2 1 A1 0 (11) hR10 2 2 CaCu (94) hP6 3 3 2 3 5 Al3Ti (21) tI8 3 1 CaF2 (81) cF12 2 2 A1U (7) oI20 4 4 Caln (12) hP6 2 2 4 2 A1 W (5) cI26 2 2 Cd Ce (21) hP3 2 2 12 2 Al Zr (7) tP20 4 2 Cdl (31) hP3 2 2 2 3 2 Al Zr (7) tI16 4 1 Cd Sm (19) cF448 18 * 3 45 u As Co (10) cI32 2 2 CeCu (61) oI12 2 2 3 2 AsNa (25) hP8 3 3 CeCu (8) oP28 6 * 3 6 AsNb (4) tI8 2 1 CeNi (9) hP24 6 4 3 As Nd (6) mP12 3 3 Ce Ni (20) hP36 7 4 2 2 7 AsNi (71) hP4 2 2 CICs (281) cP2 2 1 AsTi (8) hP8 3 3 CINa (298) cF8 2 1 AuBe (20) cF24 3 2 Co Er (28) hR18 7 4 5 7 2 AuCd (12) oP4 2 1 CoGa3 (10) tP16 3 3 AuCu (73) tP4 3 1 Co304 (12) cF56 3 2 AuCu (255) cP4 2 1 CoSb (9) mP12 3 2 3 2 B Ca (26) cP7 2 2 Co Si (95) oP12 3 2 6 2 BCr (116) 0C8 2 2 CoSn (5) hP6 3 3 B Cr (36) tI32 4 4 CrFe (45) tP30 5 3 3 5 BFe (70) 0P8 2 2 Cr S (9) mC14 4 4 3 4 BRe (6) 0CI6 3 3 CrSi (8) hP9 2 1 3 2 B Th (17) tP20 4 2 Cr Si (71) cP8 2 2 4 3 B12U (18) cF52 2 2 CuMg2 (7) oF48 3 2 B W (5) hP12 4 3 Cu Mg (216) cF24 2 2 2 2 BaCd (10) tI48 4 4 Cu Sb (58) tP6 3 2 n 2 BaH (12) cP36 5 * Cu Si (7) cI76 3 2 gll 15 4 BaP (5) mC16 3 2 CuTi (12) tP4 2 1 3 BaPb (6) hR12 4 3 Cu Ti (25) 0P8 3 1 3 3 Be Nb (44) hR12 5 4 Cu Zn (15) cI52 4 3 3 5 8
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