Table Of ContentMODERN 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
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ISBN: 0 444 86970 0
Published by:
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Sole distributors for the U.S.A. and Canada:
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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
