Disorder and Order in Strongly Nonstoichiometric Compounds: Transition Metal Carbides, Nitrides and Oxides PDF
Preview Disorder and Order in Strongly Nonstoichiometric Compounds: Transition Metal Carbides, Nitrides and Oxides
Springer Series in MATERIALS SCIENCE 47 Springer-Verlag Berlin Heidelberg GmbH ONLINE LIBRARY Physics and Astronomy http://www.springer.de/phys/ Springer Series in MATERIALS SCIENCE Editors: R. Hull R. M. Osgood, Jr. H. Sakaki A. Zunger The Springer Series in Materials Science covers the complete spectrum of materials physics, including fundamental principles, physical properties, materials theory and design. Recognizing the increasing importance of materials science in future device technologies, the book titles in this series reflect the state-of-the-art in understanding and controlling the structure and properties of all important classes of materials. 29 Elements of Rapid Solidification 41 Organic Electronic Materials Fundamentals and Applications Conjugated Polymers and Low Editor: M. A. Otooni Molecular Weight Organic Solids Editors: R. Farchioni and G. Grosso 30 Process Technology for Semiconductor Lasers 42 Raman Scattering in Materials Science Crystal Growth and Microprocesses Editors: w. H. Weber and R. Merlin By K. Iga and S. Kinoshita 43 The Atomistic Nature of Crystal Growth 31 Nanostructures and Quantum Effects By B. Mutaftschiev By H. Sakaki and H. Noge 44 Thermodynamic Basis of Crystal Growth 32 Nitride Semiconductors and Devices P-T- X Phase Equilibrium ByH.Morko~ and Nonstoichiometry By J. Greenberg 33 Supercarbon Synthesis, Properties and Applications 45 Thermoelectrics Editors: S. Yoshimura and R. P. H. Chang Basic Principles and New Materials Developments 34 Computational Materials Design By G.S. Nolas, J. Sharp, and H. J. Goldsmid Editor: T. Saito 46 Fundamental Aspects 35 Macromolecular Science of Silicon Oxidation and Engineering Editor: Y. J. Chabal New Aspects Editor: Y. Tanabe 47 Disorder and Order in Strongly Nonstoichiometric Compounds 36 Ceramics Transition Metal Carbides, Nitrides Mechanical Properties, Failure and Oxides Behaviour, Materials Selection By A.I. Gusev, A.A. Rempel, By D. Munz and T. Fett and A.J. Magerl 37 Technology and Applications 48 The Glass Transition of Amorphous Silicon Relaxation Dynamics Editor: R. A. Street in Liquids and Disordered Materials 38 Fullerene Polymers ByE. Donth and Fullerene Polymer Composites 49 Alkali Halides Editors: P. C. Eklund and A. M. Rao A Handbook of Physical Properties 39 Semiconducting Silicides By D. B. Sirdeshmukl!, 1. Sirdeshmukh, Editor: V.E. Borisenko and K. G. Subhadra 40 Reference Materials in Analytical Chemistry A Guide for Selection and Use Editor: A. Zschunke Series homepage - http://www.springer.de/phys/books/ssms/ Volumes 1-28 are listed at the end of the book. A.I. Gusev A.A. Rempel A.J. Magerl Disorder and Order in Strongly Nonstoichiometric Compounds Transition Metal Carbides, Nitrides and Oxides With 205 Figures and 107 Tables Springer Professor Dr. Se. Alexandr I. Gusev Professor Dr. Se. Andrej A. Rempel Ural Division of the Russian Academy of Sciences, Institute of Solid State Chemistry Pervomaiskaya 91, GSP-145, 620219 Ekaterinburg, Russia e-mail: [email protected];[email protected] Professor Dr. Andreas J. Magerl Lehrstuhl fiir KristaUographie und Strukturphysik, Universităt Erlangen-Niirnberg BismarckstraEe 10, 91054 Erlangen, Germany e-mail: [email protected] Series Editors: Prof. Robert Hull Prof. H. Sakaki University of Virginia Institute of Industrial Science Dept. of Materials Science and Engineering University of Tokyo Thornton HaU 7-22-1 Roppongi, Minato-ku Charlottesville, VA 22903-2442, USA Tokyo 106, Japan Prof. R. M. Osgood, Jr. Prof. Alex Zunger Microelectronics Science Laboratory NREL Department of Electrical Engineering National Renewable Energy Laboratory Columbia University 1617 Cole Boulevard Seeley W. Mudd Building Golden Colorado 80401-3393, USA New York, NY 10027, USA ISSN 0933-o33x ISBN 978-3-642-07524-7 Library of Congress Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Gusev, Aleksandr 1.: Disorder and order in strongly nonstoichiometric compounds : transition metal carbids, nitrides and oxides / A. 1. Gusev; A. A. Rempel ; A. J. Magerl. (Springer series in materials science; 47) (Physics and astronomy online library) ISBN 978-3-642-07524-7 ISBN 978-3-662-04582-4 (eBook) DOI 10.1007/978-3-662-04582-4 This work is subject to copyright. Ali rights are reserved, whether the whole or part of the material is concerned, specifica1ly the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. http://www.springer.de © Springer-Verlag Berlin Heidelberg 2001 Originally published by Springer-Verlag Berlin Heidelberg New York in 2001 Softcover reprint of the hardcover 1s I edition 2001 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regnlations and therefore free for general use. Typesetting: Camera-ready copy from the authors Cover concept: eStudio Calamar Steinen Cover production: design & production GmbH, Heidelberg Printed on acid-free paper SPIN: 10779025 57/3020/CU 543210 "L'o rdre est Ie plaisir de la raison, mais Ie d6sordre est Ie d6lice de l'imagination" d'apres Paul Clodel "Nur wer denkt, irrt auch" Horst Friedrich "Something there is that doesn't love a wall ... " After Robert Frost Preface In the last decades of the 20th century the physics of condensed matter significantly extended its sphere of interest to include new groups of materials in addition to those traditionally studied. One of these groups comprises a variety of nonstoichiometric compounds. Physicists paid interest to the phenomenon of nonstoichiometry only after the discovery of high-temperature superconductivity, although solid-state chemistry has been dealing with non stoichiometry for at least forty years. Nonstoichiometry occurs widely in solid-state compounds and is most pro nounced in strongly nonstoichiometric compounds, such as cubic carbides, nitrides and oxides of transition metals and related materials. Carbides, being those strongly non stoichiometric compounds that have received most study, have been known for nearly a hundred years, but their nature is still not clearly understood. This is especially true of non stoichiometry and the phenomena of disorder and order directly related to non stoichiometry. This book summarizes the 20-year experience of the authors working on the problems of disorder and order in strongly nonstoichiometric compounds. Our studies were concerned mainly with crystallographic and symmetry aspects of ordering, thermodynamics of disorder-order phase transformations, and the effect of ordering on properties of strongly non stoichiometric compounds. It did not take '1I Preface long to understand that the phenomena associated with the redistribution of interstitial atoms and structural vacancies in non stoichiometric compounds represent an excellent model of analogous phenomena arising in solid-state systems with mutual substitution of components. Therefore methods of analysis and description proposed and developed for nonstoichiometric compounds are applicable to a number of systems with substitutional disorder. In 1980, when we embarked on this work, ordering in nonstoichiometric compounds was assumed to be a rare and accidental effect, which hardly deserved close attention. Now many people understand that ordering represents a general regular phenomenon in all non stoichiometric compounds. Ordering effects, which were not even mentioned, or were referred to as something insignificant and negligible just 20 years ago, proved to be numerous and comparable in magnitude with the change of properties in the whole homogeneity interval of non stoichiometric compounds. Phase diagrams of binary systems of transition metals with carbon and nitrogen, which remained unchanged from the time they were plotted in 1950-60s and containing one or two nonstoichiometric compounds, were enriched with many ordered phases. Unfortunately, the accumulated experimental and theoretical knowledge has not so far been disseminated widely. Engineers concerned with commercial production and use of carbides and nitrides, and even many scientists, know very little or nothing about ordering and its relation to nonstoichiometry. English, German and French scientific literature has had no monographs dedicated at least partly to ordering of non stoichiometric compounds. However, hundreds of original papers on order and disorder in those compounds have been published in scientific journals. But even the latest books on carbides do not contain data on ordering. For example, one book\ which was published in 1996, discusses carbides of transition metals, but the overwhelming majority of the reported experimental results were obtained between 1950 and 1975. Out of 2090 works cited in Upadhyaya's book, only 21 refer to studies performed in the period from 1981 to 1985. No references are made to studies performed after 1985. Any issues of short-or long-range order and their relation to nonstoichiometry are not even mentioned. A handbook2 issued in 1996 contains only two sentences dedicated to ordering in carbides: "When the concentration of carbon-atom vacancies is high, long-range ordering in their arrangement within the metal lattice is usually observed. The effect of this ordering on the structure and physical properties of the carbide may be considerable in some cases but the mechanisms offormation, the structural and bonding arrangement are still not well defined." G. S. Upadhyaya: Nature and Properties of Refractory Carbides (Nova Science Publishers, New York 1996) 545 pp. H. O. Pierson: Handbook of Refractory Carbides and Nitrides: Properties, Characteris tics, Processing and Applications (Noyes Publications: Westwood, 1996) 318 pp. Preface \n[ The only books3 in the scientific literature describing disorder-order transitions in strongly non stoichiometric compounds were published in Russian and are inaccessible to readers outside the former Soviet Union. The present monograph is intended to bridge this gap. Reading this book will require a certain effort, the knowledge of basic postulates of thermodynamics and solid-state theory, and a command of a body of mathematics. The point is that ordering theory is not so simple that it can be mastered without a profound scientific training. We have done our best to present today's understanding of the mutual relationship between disorder, order and nonstoichiometry in a solid, taking nonstoichiometric compounds as an example. Hopefully this book will direct the reader's attention to interesting and by far incomplete studies of a real solid. We think it will be interesting and useful for your professional research. Of course, this book does not cover all issues of non stoichiometry, disorder and order in solids. This means that we shall continue our work and, with time, interested readers will be able to read a new book about defects, nonstoichiometry and disorder-order transformations in crystals. Ekaterinburg-Erlangen, May 2001 A. Gusev, A. Rempel, A Magerl A. I. Gusev, A. A. Rempel: Structural Phase Transitions in Nonstoichiometric Compounds (Nauka, Moscow 1988) 308 pp. (in Russian) A. I. Gusev: Physical Chemistry ofN onstoichiometric Refractory Compounds (Nauka, Moscow 1991) 286 pp. (in Russian) A. A. Rempel: Effects of Ordering in Nonstoichiometric Interstitial Compounds (Nauka, Ekaterinburg 1992) 232 pp. (in Russian) V. N. Lipatnikov, A. I. Gusev: Ordering of Titanium and Vanadium Carbides (Ural Division of the Russian Academy of Sciences, Ekaterinburg 2000) 266 pp. (in Russian) Contents List of Main Notation XIII 1 Introduction 1 References 8 2 Crystal Symmetry 11 2.1 Point and Space Groups 11' 2.2 Reciprocal Lattice and Wave Vectors 22 2.3 Elements of Diffraction Theory 33 References 41 3 Strongly Nonstoichiometric Compounds 43 3.1 Preparation Techniques and Degree of Homogeneity 45 3.2 Crystal Structure and the Homogeneity Interval 52 3.3 Structural Stability Boundaries 72 3.4 Ordering in Strongly Nonstoichiometric Carbides, Nitrides 79 and Oxides References 102 4 Short-Range Order 113 4.1 Short-Range Order Parameters and Two-Particle Correlations 113 4.2 Short-Range Order in Strongly Nonstoichiometric Compounds 121 4.2.1 NMR Studies of Short-Range Order 122 4.2.2 Diffuse Scattering of Neutrons and Electrons 137 4.2.3 Short-Range Order and Magnetic Susceptibility 144 4.2.4 Short-Range Order in Carbide Solid Solutions 147 4.3 Local Atomic Displacements 149 References 172 5 Long-Range Order 179 5.1 Long-Range Order Parameters 179 5.2 Disorder-Order Phase Transition Channel 185 5.3 Transition Channel and Diffraction Reflection Intensity 190 5.4 Distribution Functions and Diffraction for Superstructures of Strongly Nonstoichiometric Compounds 195 5.4.1 Superstructures of Type M2X 195 5.4.2 Superstructures of Type M3X2 203 5.4.3 Superstructures of Type ~X3 213 5.4.4 Superstructures of Type M6XS 217 X Contents 5.4.5 Superstructures of Type MsX7 227 5.4.6 Superstructure of TisOs 232 5.5 Kinds of Disorder-Order Phase Transformations 237 5.6 Intervals of Admissible Values of Long-Range Order Parameters 239 References 243 6 Interrelation of Short- and Long-Range Orders 247 6.1 Relationship between Short-and Long-Range Orders 247 6.2 Short-Range Order in Superstructures 257 References 269 7 Nonstoichiometric Nitrides at High Temperature 271 7.1 Evaporation of Non stoichiometric Nitrides 271 7.2 Titanium Nitrides and Carbonitrides 277 7.3 Vanadium Nitrides and Carbonitrides 284 7.4 Niobium Nitrides and Carbonitrides 290 References 296 8 Order-Disorder Phase Transformation Theories 299 8.1 Thermodynamics of Phase Transformations 299 8.2 Phenomenological Theory of Phase Transformations 303 8.3 Mean Field Approximation 309 8.4 Cluster Methods in Ordering Theory 321 References 330 9 Order-Parameter Functional Method 333 9.1 Main Approaches ofthe Method 334 9.2 Energies of Clusters 342 9.3 The Choice ofthe Basis Cluster Figure 348 9.4 Probabilities of Clusters and Subfigures 351 9.5 Free Energy Minimum Conditions 355 References 368 10 Equilibrium Phase Diagrams 371 10.1 Computation of Disorder-Order Phase Transformations in Nonstoichiometric Compounds 372 10.2 Ordering of a MXy Compound in a Generalized Phase Diagram of the M-X System 376 10.3 Phase Diagrams of M-X Systems (M = Ti, Zr, Hf, V, Nb, Ta; X=C,N) 387 10.4 Phase Diagrams of Pseudo binary Systems 416 References 442 11 Effects of Ordering on the Properties of Strongly N onstoichiometric Compounds 453 11.1 The Basic Lattice Constant 454 11.2 X-Ray Photoelectron and Emission Spectra 470 11.3 Electron-Positron Annihilation 478 Contents XI 11.4 Electrokinetic Properties 496 11.5 Magnetic Susceptibility 508 11.6 Superconductivity 528 11.7 Heat Capacity 539 11. 7.1 Superposition Model of the Heat Capacity 540 11.7.2 Heat Capacity of Non stoichiometric Carbides at a Temperature Below 300 K 546 11.7.3. Heat Capacity of Nons toichiometric Carbides at a Temperature Above 300 K and Near the Point of Order-Disorder Transition 563 11.8 Microhardness 571 References 586 Subject Index 603
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