Incommensurate Phases in Dielectrics2. Materials PDF
Preview Incommensurate Phases in Dielectrics2. Materials
MODERN PROBLEMS IN CONDENSED MATTER SCIENCES Volume 14.2 Series editors V.M. AGRANOVICH Moscow, USSR A.A. MARADUDIN Irvine, California, USA Advisory editorial board F. Abelès, Paris, France N. Bloembergen, Cambridge, MA, USA E. Burstein, Philadelphia, PA, USA I.L. Fabelinskii, Moscow, USSR M.D. Galanin, Moscow, USSR V.L. Ginzburg, Moscow, USSR H. Haken, Stuttgart, FRG R.M. Hochstrasser, Philadelphia, PA, USA LP. Ipatova, Leningrad, USSR A.A. Kaplyanskii, Leningrad, USSR L.V. Keldysh, Moscow, USSR R. Kubo, Tokyo, Japan R. Loudon, Colchester, UK L.P. Pitaevskii, Moscow, USSR A.M. Prokhorov, Moscow, USSR K.K. Rebane, Tallinn, USSR NORTH-HOLLAND AMSTERDAM-OXFORD-NEW YORK-TOKYO INCOMMENSURATE PHASES IN DIELECTRICS 2. Materials Volume editors R. BLINC Ljubljana, Yugoslavia A.P. LEVANYUK Moscow, USSR 1986 NORTH-HOLLAND AMSTERDAM-OXFORD-NEW YORK-TOKYO © Elsevier Science Publishers B.V., 1986 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. (North- Holland Physics Publishing Division), P.O. Box 103, 1000 AC 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 USA. All other copyright questions, including photocopying outside of the USA, should be referred to the publisher. ISBN: 0 444 86970 0 Published by: North - Holland Physics Publishing a division of Elsevier Science Publishers B.V. P.O. Box 103 1000 AC Amsterdam The Netherlands Sole distributors for the U.S.A. and Canada: Elsevier Science Publishing Company, Inc. 52 Vanderbilt Avenue New York, N.Y. 10017 U.S.A. Library of Congress Cataloging in Publication Data Main entry under title: Incommensurate phases in dielectrics. (Modern problems in condensed matter sciences ; v. 14) Includes bibliographies and indexes. 1. Dielectrics. 2. Lattice dynamics. 3. Crystal lattices. 4. Phase transformations (Statistical physics) I. Blinc, R. (Robert) II. Levanyuk, A. P., 1933- . III. Series. QC585.I53 1985 537'.24 85-29693 ISBN 0-444-86970-0 (U.S. : v. 2) Printed in The Netherlands MODERN PROBLEMS IN CONDENSED MATTER SCIENCES Vol. 1. SURFACE POLARITONS V.M. Agranovich and D.L. Mills, editors Vol. 2. EXCITONS E.I. Rashba and M.D. Sturge, editors Vol. 3. ELECTRONIC EXCITATION ENERGY TRANSFER IN CONDENSED MATTER V.M. Agranovich and M.D. Galanin Vol. 4. SPECTROSCOPY AND EXCITATION DYNAMICS OF CONDENSED MOLECULAR SYSTEMS V.M. Agranovich and R.M. Hochstrasser, editors Vol. 5. LIGHT SCATTERING NEAR PHASE TRANSITIONS H.Z. Cummins and A.P. Levanyuk, editors Vol. 6. ELECTRON-HOLE DROPLETS IN SEMICONDUCTORS CD. Jeffries and L.V. Keldysh, editors Vol. 7. THE DYNAMICAL JAHN-TELLER EFFECT IN LOCALIZED SYSTEMS Yu.E. Perlin and M. Wagner, editors Vol. 8. OPTICAL ORIENTATION F. Meier and B.P. Zakharchenya, editors Vol. 9. SURFACE EXCITATIONS V.M. Agranovich and R. Loudon, editors Vol. 10. ELECTRON-ELECTRON INTERACTIONS IN DISORDERED SYSTEMS A.L. Efros and M. Pollak, editors Vol. 11. MEDIUM-ENERGY ION REFLECTION FROM SOLIDS E.S. Mashkova and V.A. Molchanov Vol. 12. NONEQUILIBRIUM SUPERCONDUCTIVITY D.N. Langenberg and A.I. Larkin, editors MODERN PROBLEMS IN CONDENSED MATTER SCIENCES Vol. 13. PHYSICS OF RADIATION EFFECTS IN CRYSTALS R.A. Johnson and A.N. Orlov, editors Vol. 14. INCOMMENSURATE PHASES IN DIELECTRICS (Two volumes) R. Blinc and A.P. Levanyuk, editors In preparation Vol. 15. UNITARY TRANSFORMATIONS IN SOLID STATE PHYSICS M. Wagner TRANSPORT IN PHONON SYSTEMS V.L. Gurevich Oh, how many of them there are in the fields! But each flowers in its own way — In this is the highest achievement of a flower! Matsuo Basho 1644-1694 PREFACE TO THE SERIES Our understanding of condensed matter is developing rapidly at the present time, and the numerous new insights gained in this field define to a significant degree the face of contemporary science. Furthermore, discoveries made in this area are shaping present and future technology. This being so, it is clear that the most important results and directions for future developments can only be covered by an international group of authors working in cooperation. "Modern Problems in Condensed Matter Sciences" is a series of contributed volumes and monographs on condensed matter science that is published by North-Holland Physics Publishing, a division of Elsevier Science Publishers. With the support of a distinguished Advisory Editorial Board, areas of current interest that have reached a maturity to be reviewed, are selected for the series. Both Soviet and Western scholars are contributing to the series, and each contributed volume has, accordingly, two editors. Monographs, written by either Western or Soviet authors, are also included. The complete series will provide the most comprehensive coverage available of condensed matter science. Another important outcome of the foundation of this series is the emergence of a rather interesting and fruitful form of collaboration among scholars from different countries. We are deeply convinced that such international collabora- tion in the spheres of science and art, as well as other socially useful spheres of human activity, will assist in the establishment of a climate of confidence and peace. The publishing house "Nauka" publishes the volumes in the Russian language. This way the broadest possible readership is ensured. The General Editors of the Series, V.M. Agranovich A.A. Maradudin vii PREFACE Translational lattice periodicity is usually considered one of the most basic characterizing features of a crystal. Depending on the arrangement of atoms inside the unit cell and the symmetry of the crystal lattice, each crystal has been traditionally assigned to one of the three-dimensional crystallographic space groups. The concepts of symmetry and translational periodicity of crystals have played a central role in the development of solid state physics. By and large these concepts have come to be accepted as universal properties of the crystalline state. This is in sharp contrast to the disordered and amorphous a-periodic states where there is no long-range order in the positions of the atoms. In the past decade however, attention has focused on incommensurate materials which exhibit perfect three-dimensional long-range order but no translational periodicity in at least one direction, and which are thus inter- mediate between classical ideal crystals and a-periodic disordered or amorphous systems. In these materials a local property such as electric polarization, magnetization, charge density, mass density, atomic position or chemical composition is modulated with a periodicity q which is incommensurate to the l periodicity q of the underlying lattice, i.e. the periodicity q of the order p l parameter Q(x) and the periodicity of the basic lattice q cannot be expressed p as a ratio of two integers: 0i M — Φ—, M,yV = l,2,3... Here we are concerned with structurally incommensurate systems, where at least one atomic position is not exactly repeated from cell to cell and the translational symmetry of the crystal is lost in at least one direction, in spite of the persistence of long-range order. Translational lattice periodicity is generally restored at lower temperatures at a "lock-in" phase transition, where the lattice modulation changes from incommensurate to commensurate. Incommensurate systems are interesting from the point of view of basic physics since they show a number of new phenomena—nonlinear multi-soliton ix χ Preface lattice-type ground states, phason and amplitudon excitations, devil's staircase, solid-state chaos, etc.—which are not found in translationally periodic crystals. The study of incommensurate systems may thus lead to an improved under- standing of the a-periodic state of matter. Whereas the first volume of this monograph treats the macroscopic and microscopic theory of incommensurate systems and gives a review of the experimental techniques used to study these materials, this second volume presents the specific results obtained for some of the most representative examples. The various chapters on specific substances are written by the people who actually carried out the experiments and contributed most to the under- standing of these systems. The purpose of this book is thus to give a physical picture of incom- mensurate insulators, as well as to give the reader an idea of how the various experimental techniques can be used for a study of the dynamic and static properties of incommensurate systems on a microscopic level. R. Blinc A.P. Levanyuk Ljubljana, Yugoslavia Moscow, USSR CHAPTER 10 Phase Transformations in K Se0 and 2 4 Structurally Related Insulators J. D. AXE Brookhaven National Laboratory M. IIZUMI Japan A tomic Energy Research Institute and G. SHIRANE Brookhaven National Laboratory Incommensurate Phases in Dielectrics 2 Edited by © Elsevier Science Publishers Β. V., 1986 R. Β line and A. P. Levanyuk 1 Contents 1. Introduction 3 2. Crystal structure of the normal (high-temperature) phase and symmetry analysis of the atomic displacements 6 2.1. Crystal structure of the normal phase of K 2Se04 6 2.2. Group theoretical analysis of the symmetry of the collective atomic displacements in Κ 2 Se04 7 2.3. Use of the extended zone scheme 10 3. Phonons and fluctuations in the normal (high temperature) phase 12 3.1. K2Se04 12 3.2. Other compounds 13 3.3. Origins of the incommensurate instability 15 3.3.1. Analysis of phonon dispersion 16 3.3.2. Analysis of atomic displacements 18 4. Modulation in the incommensurate phases 20 4.1. Modulation in Κ 2 Se04 and similar compounds 21 4.2. Modulation in (NH4) 2BeF4 23 4.3. Modulation in tetramethyl ammonium compounds 23 5. Fluctuations in the incommensurate phase 33 5.1. Static critical behavior 33 5.2. Dynamical fluctuations in the incommensurate phase in K 2Se04 37 6. Lock-in phase transformations 42 6.1. The soliton limit 42 6.2. Lock-in and macroscopic properties 45 6.3. Dynamics near the soliton limit 45 References 47 2
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