Incommensurate Crystals, Liquid Crystals, and Quasi-Crystals PDF
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Incommensurate Crystals, Liquid Crystals, and Quasi-Crystals NATO ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NATO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics New York and London C Mathematical D. 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Series B, Physics; vol. 166) "Proceedings of a NATO Advanced Research Workshop on Incommen surate Crystals, Liquid Crystals, and Quasi-Crystals, held July 7-11,1986, in Boulder, Colorado"-Copr. p. Bibliography: p. Includes index. 1. Crystals-Detects-Congresses. 2. Liquid crystals-Congresses. I. Scott, J. F. (James Floyd), 1942- . II. Clark, N. A. (Noel Anthony), 1940- . III. Title. IV. Series. NATO ASI series. Series B, Physics; v. 166. QD921.N378 1986 548-dc19 87-24391 CIP © 1987 Plenum Press. New York Softcover reprint of the hardcover 1s t edition 1987 A Division ot Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher ISBN 978-1-4757-0186-9 ISBN 978-1-4757-0184-5 (eBook) DOI 10.1007/978-1-4757-0184-5 PREFACE In this NATO-sponsored Advanced Research Workshop we succeeded in bringing together approximately forty scientists working in the three main areas of structurally incommensurate materials: incommensurate crystals (primarily ferroelectric insulators), incommensurate liquid crystals, and metallic quasi-crystals. Although these three classes of materials are quite distinct, the commonality of the physics of the origin and descrip tion of these incommensurate structures is striking and evident in these proceedings. A measure of the success of this conference was the degree to which interaction among the three subgroups occurred; this was facili tated by approximately equal amounts of theory and experiment in the papers presented. We thank the University of Colorado for providing pleasant housing and conference facilities at a modest cost, and we are especially grate ful to Ann Underwood, who retyped all the manuscripts into camera-ready form. J. F. Scott Boulder, Colorado N. A. Clark v CONTENTS PART I: INCOMMENSURATE CRYSTALS A. Theory A PHENOMENOLOGICAL THEORY OF THE TRANSITION SEQUENCE INCLUDING AN INCOMMENSURATE (COMMENSURATE) PHASE SANDWICHED BY REENTRANT COMMENSURATE (INCOMMENSURATE) PHASE - Yoshihiro Ishibashi ..... 1 DAUPHINE-TWIN DOMAIN CONFIGURATIONS IN QUARTZ AND ALUMINUM PHOSPHATE - M. B. Wa lker . . . . . . . . . . 9 ELASTIC AND INELASTIC SCATTERING FROM QUASI-PERIODIC STRUCTURES - T. Janssen and R. Currat . . . . . 19 ARE EXOTIC CONSEQUENCES OF INCOMMENSURABILITY IN SOLIDS EXPERIMENTALLY OBSERVABLE? - J. B. Sokoloff. 35 B. Theory - Numerical l1ethods THE APPLICATION OF AXIAL ISING MODELS TO THE DESCRIPTION OF MODULATED ORDER - Julia Yeomans . . 45 TWO-DIMENSIONAL MODELS OF COMMENSURATE-INCOMMENSURATE PHASE TRANSITIONS - Palll D. Beale ... 55 GROWTH KINETICS IN A FRUSTRATED SYSTEM: THE QUENCHED AXIAL NEXT-NEAREST-NEIGHBOR ISING MODEL - D. J. Srolovitz and G. N. Hassold. . . . . . . . . . . . . . . . . . . .. 63 C. Experiment ELECTRON l1ICROSCOPY OF INCOMMENSURATE STRUCTURES - G. Van Tendeloo, J. Landuyt and S. Amelinckx . 75 EFFECT OF TRANSVERSE ELECTRIC FIELDS ON THE INCOMMENSURATE PHASE OF NaNOZ - H. Z. Cummins, S. L. Qiu, l1itra Dutta, J. P. Wicksted, and S. M. Shapiro . . . . . . . . . . 91 LIGHT SCATTERING FROM INCOMMENSURATE INSULATORS: MAINLY BaMnF4 - D. J. Lockwood. . . . 105 BRILLOUIN SCATTERING STUDY OF INCOMMENSURATE CRYSTALS - Toshirou Yagi ... ... 119 vii EXPERIMENTAL RESULTS RELATED TO THE NORMAL-INCOMMENSURATE PHASE TRANSITION IN A2MX4 COMPOUNDS - M. Qui1ichini ..... 127 SOME ASPECTS OF RAMAN SCATTERING FROM A2BX4 COMPOUNDS - F. G. Ullman, V. Katkanant, P. J. Edwardson and J. R. Hardy . 139 INTRINSIC DEFECTS IN INSULATING INCOMMENSURATE CRYSTALS - Pierre Saint-Gregoire. .. ........ ...... 151 THERMAL HYSTERESIS, SOLITONS AND DOMAIN WALLS - M.-G. Unruh and A. Levstik ..... 163 THERMAL MEMORY AND PHASE CONJUGATION EXPERIMENTS IN INCOMMENSURATE BARIUM SODIUM NIOBATE - W. F. Oliver and J. F. Scott. .. · . 177 PART II: INCOMMENSURATE LIQUID CRYSTALS A. Theory PHASONS IN QUASI-CRYSTALS AND INCOMMENSURATE LIQUID CRYSTALS - T. C. Lubensky. . . . . . .. . ........ 187 THE FRUSTRATED SPIN-GAS THEORY OF MULTIPLY REENTRANT LIQUID CRYSTALS - A. Nihat Berker and J. O. Indekeu. . .. 205 MACROSCOPIC DESCRIPTION OF FERROELECTRIC CHIRAL SMECTIC C* LIQUID CRYSTALS - B. Zeks, T. Carlsson, C. Fi1ipic, and A. Levstik . . . . . . . . . . . . . . . . .. ... 215 ON THE MOLECULAR THEORY OF SMECTIC-A LIQUID CRYSTALS - W. H. de Jeu . ... 223 ORDER ELECTRICITY AT SMECTIC LIQUID CRYSTAL INTERFACES - G. Durand ..... . . . 235 MACROSCOPIC VARIABLES IN COM}ffiNSURATE AND INCOMMENSURATE CONDENSED PHASES, QUASICRYSTALS AND PHASMIDS - Harald P1einer . . . . . . . . . . . . . . . . .. ... 241 HOW THE SMECTIC A PHASE ADAPTS TO TWO INCOMMENSURATE PERIODS IN ASYMMETRIC LIQUID CRYSTALLINE SYSTEMS - G. Sigaud, F. Hardouin, M. F. Achard, and H. T. Nguyen ... 249 B. Experiment AN INCOMMENSURATE SMECTIC A PHASE - B. R. Ratna, R. Shashidhar and V. N. Raja ... ...... 259 THE NEMATIC AND SMECTIC-A1 PHASES IN DB7N02: HIGH RESOLUTION X-RAY STUDY AND SYNTHESIS - C. F. Safinya and L. Y. Chiang . . . · . 271 X-RAY DIFFRACTION BY INCOMMENSURATE LIQUID CRYSTALS - A. M. Leve1ut · . 283 ANOMALOUS HEAT CAPACITY ASSOCIATED WITH THE INCOMMENSURATE SmA PHASE IN DB70CN + 80CB - C. W. Garland and P. Das .•. 297 viii THERMAL CONDUCTIVITY STUDIES AND FREE-STANDING LIQUID CRYSTAL FILM CALORIMETRY AS TWO APPLICATIONS OF THE AC CALORIMETRIC TECHNIQUE - C. C. Huang, G. Nounesis, and T. Pitchford . • . . . . . . . . . . . . . .. ... 305 PART III: INCOMMENSURATE QUASI-CRYSTALS QUASIPERIODIC PATTERNS WITH ICOSAHEDRAL SYMMETRY - A. Katz and M. Duneau. . . . .. 315 FRUSTRATION AND ORDER IN RAPIDLY COOLED METALS - Subir Sachdev ..... • •••• 327 LOCAL ATOMIC ENVIRONMENTS IN THE MANGANESE-ALUMINUM ICOSAHEDRAL PHASE - Gabrielle Gibbs Long and Masao Kuriyama . . ...............•. • ••. 337 PART IV: TWO-DIMENSIONAL AND LAYERED SYSTEMS X-RAY SCATTERING FROM TWO-DIMENSIONAL LIQUIDS MODULATED BY A PERIODIC HOST: THEORY, SIMULATION AND EXPERIMENT - George Reiter ........... . • • 349 ARTIFICIALLY STRUCTURED INCOMMENSURATE MATERIALS - Roy Clarke and R. Merlin 359 INDEX. 367 ix A PHENOMENOLOGICAL THEORY OF THE TRANSITION SEQUENCE INCLUDING AN INCOMMENSURATE (COMMENSURATE) PHASE SANDWICHED BY REENTRANT COMMENSURATE (INCOMMENSURATE) PHASE Yoshihiro Ishibashi Synthetic Crystal Research Laboratory Faculty of Engineering Nagoya University, Chikusa-ku Nagoya 464, Japan Abstract A two-sublattice model is presented for interpreting the appearance of the phase sequence Normal-Commensurate-Incommensurate Commensurate phases such as seen in (C3H7NH3)2MnC14' Temperature dependences of transition parameters, a strain component and soft mode frequencies are derived phenomenologically. The present model can be easily converted to the one reproducing the phase sequence Normal-Incommensurate-Commensurate-Incommensurate phases. I. INTRODUCTION One of the most characteristic features common to incommensurate (IC) phases seen in various dielectric materials is that an IC phase usually appears as a phase sandwiched by a high symmetry normal (N) phase and a low symmetry commensurate (C) phase, the stability of the IC phase thus being limited to some range of temperature, pressure and other controllable external parameters [1,2]. To obtain an overall understanding of the tran sition sequence of N-IC-C phases the continuum description is helpful. In such a description the thermodynamic potential functional is written in terms of the transition parameters which transform upon symmetry operations as the bases of an irreducible representation, which induces the N-C tran sition. To describe the IC phase it is necessary to include suitable terms consisting of spatial derivative of the parameters. It is possible to classify the IC phases into two groups according to the form of the thermodynamical potential functional. One group includes the Lifshitz invariant, as is represented by (NH4)2BeF4, while the other group does not, as is represented by NaN02. Behaviors of physical quantities in the N-IC-C transition sequence can be well described by such thermodynamic potential functionals. It is known that some physical properties of an IC phase are strongly dependent upon physical properties of the C phase which follows. If the C phase is ferro electric, for example, the dielectric susceptibility shows a tendency to divergence just above the IC-C transition temperature, while if the C phase is ferroelastic, an elastic compliance will diverge there. As is readily understood from the above, it is most important to write down the thermodynamic potential functional, based upon the symmetry con sideration of the C phase. Recently, however, an unusual transition sequence, including an IC phase, has been reported. For example, in propyl-ammonium manganese chloride (C3H7NH3)2MnC14 (abbreviated to PAMC) an IC phase is sandwiched by the same C phase, as shown in Table 1 [3], i.e., the C phase has a reentrant nature, and the transition from the IC phase to the low temperature C phase is not the lock-in type. In other words, there is no locked-in C phase, and therefore there is no clue required to construct a thermodynamic potential functional. A phenomenological theory for the transition of PAMC has already been published by Muralt et al. [3]. But it only treats the transition sequence starting at the high temperature C phase. Here, we would like to present a different interpretation of the transition sequence N-C-IC-C in the form which is more general (not limited only to the case of PAMC). 2. THEORY A basic idea of the present approach lies in adopting sublattices in the N phase [4]. These sublattices must comply with the way N-C transition takes place. If the N-C transition takes place at the r point of the Brillouin zone, sublattices must include atoms or dipoles located in a single unit cell, while if it occurs at, say, the zone boundary, sublat tices have to include atoms or dipoles located in two unit cells of the N phase. Let us take two parameters ql and q2, which are regarded to repre sent the displacement of two adopted sublattices. Next we have to examine the symmetry property of these sublattices. Based upon it, we would be able to write down a thermodynamic potential functional like [4] 2
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