Geometry and Thermodynamics: Common Problems of Quasi-Crystals, Liquid Crystals, and Incommensurate Systems PDF
Preview Geometry and Thermodynamics: Common Problems of Quasi-Crystals, Liquid Crystals, and Incommensurate Systems
Geometry and Thermodynamics Common Problems of Quasi-Crystals, Liquid Crystals, and Incommensurate Systems NATO ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NA TO 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 Kluwer Academic Publishers and Physical Sciences Dordrecht, Boston, and London o Behavioral and Social Sciences E Applied Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cell Biology Paris, and Tokyo Recent Volumes in this Series Volume 227-Dynamics of Polyatomic Van derWaals Complexes edited by Nadine Halberstadt and Kenneth C. Janda Volume 228-Hadrons and Hadronic Matter edited by D. Vautherin, F. Lenz, and J. W. Negele Volume 229-Geometry and Thermodynamics: Common Problems of Quasi-Crystals, Liquid Crystals, and Incommensurate Systems edited by J.-C. TolMano Volume 230-Quantum Mechanics in Curved Space-Time edited by JOrgen Audretsch and Venzo de Sabbata Volume 231-Electronic Properties of Multilayers and Low-Dimensional Semiconductor Structures edited by J. M. Chamberlain, l. Eaves, and J.-C. Portal Volume 232-New Frontiers in Quantum Electrodynamics and Quantum Optics edited by A. O. Barut Volume 233-Radiative Corrections: Results and Perspectives edited by N. Dombey and F. Boudjema Volume 234-Constructive Quantum Field Theory II edited by G. Velo and A. S. Wightman Series B: Physics GEOMETRY AND THERMODYNAMICS Common Problems of Quasi-Crystals, Liquid Crystals, and Incommensurate Systems Edited by J.-C. Toh3dano National Center of Telecommunication Studies Bagneux, France Springer Science+ Business Media, LLC Proceedings of a NATO Advanced Research Workshop on From Geometry to Thermodynamics: Common Problems of Quasi-Crystals, Liquid Crystals, and Incommensurate Insulators, held September 4-8, 1989, in Preveza, Greece Llbrary of Congress Cataloglng-ln-Publlcatlon Data NATO Advanced Research Workshop an From Geometry ta Thermodynamlcs (1989 Preveza, Greece) Geometry and thermodynamles common problems of quasl-crystals, llquld crystals, and lncommensurate systems / edlteo by J.-C. Toledano. p. em. -- (NATD ASI serles. Serles B, PhYS1CS . v. 229) Proceedlngs of a NATD Advaneed Research Workshop an From Geometry to Thermodynamlcs, held 9/4-8/89, Preveza, Greece. Includes blbllographlcal referenees and lndex. ISBN 978-1-46l3-6702-4 ISBN 978-1-4615-3816-5 (eBook) DOI 10.1007/978-1-4615-3816-5 1. Crystals--Defects--Congresses. 2. LlqUld crystals--Congresses. 3. Molecular structure--Congresses. I. Toledano, Jean-Claude. II. North Atlantle Treaty Drganlzatlon. SClentlflc Affalrs D,v,s,on. III. Tltle. IV. Serles. QD921.N377 1989 548--de20 90-43309 CIP © 1990 Springer Science+Business Media New York Originally published by Plenum Press, New York in 1990 Softcover reprint of the hardcover 1 st edition 1990 AII 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 PREFACE Distinct scientific communities are usually involved in the three fields of quasi-crystals, of liquid crystals, and of systems having modulated crystalline structures. However, in recent years, there has been a growing feeling that a number of common problems were encountered in the three fields. These comprise the need to recur to "exotic" spaces for describing the type of order of the atomic or molecular configurations of these systems (Euclidian "superspaces" of dimensions greater than 3, or 4-dimensional curved spaces); the recognition that one has to deal with geometrically frustrated systems, and also the occurence of specific excitations (static or dynamic) resulting from the continuous degeneracies of the stable structures considered. In the view of discussing these problems, aNAT O-Advance Research Workshop has assembled in Preveza (Greece), in september 1989,50 experts of the three considered fields (with an equal proportion of theorists and experimentalists). 35 hours of conferences and discussions have led to a more detailed evaluation of the similarities and of the differences in the approaches implemented in the studies of the three types of systems. The papers contained in this NATO-series book provide the substance of this workshop. The reader will find three types of papers. Some very short papers giving the main ideas stated on a subject. Papers comprising 8-10 pages which stick closely to the contents of the talks presented. Longer papers providing more extensively the background and results relative to a given topic. It is worth summarizing the principal outputs of the workshop. "Exotic" spaces have appeared to possess a different status in the different systems. In modulated structures, Euclidian superspaces constitute a tool of mere geometrical conveniency for the determination of the crystal structure, and it is possible to solve the structures without recurring to them. By contrast they seem unavoidable in discussing the structure of quasi-crystals, and many a physical argumentation is based on their consideration. A different objective is pursued in the case of liquid crystals: that of estimating, with the help of curved spaces, the energy associated to the frustration of the actual 3D-structure. This difference between a geometrical point of view in the first two types of systems, and an energetic one in the last type, must be attenuated. Indeed, it is also possible to develop a unified theoretical framework which describes physical excitations (electrons, phonons) in quasi-crystals and in modulated crystals on the basis of the superspace description. Experimentally, the testing of these unified theories has not reached the same level of maturity in quasi-crystals (for which little has been done aside from the structural aspect) and in the simpler modulated structures (in which few questions remain to clmify, e.g. the existence of optical activity). The "phason" excitation is another interesting point of comparison between liquid crystals and modulated crystals. Its observation seems more generally favourable in liquid crystals due to the lack of strong pinning centers. Such an observation has even been achieved, in liquid crystals, by means of light scattering, while the same technique has been tried unsuccessfully, up to now, in the other type of system. On the other hand, the existence of a gap in the phason spectrum is still a subject of controversy. Its systematic detection by NMR techniques relies on an interpretative framework whose validation has v to be refined. It has been noted that there may be a difference of nature of the phason in the two types of systems due to the fact that there is no reference-frame for the sliding of the phase in liquid crystals, and also, that in the latter systems, there is a possible coupling to hydrodynamics degrees of freedom. In a number of substances with modulated crystal structures, reliable and accurate atomic configurations have been determined. By contrast, a central problem in quasi-crystals, and in newly discovered liquid crystal phases (e.g. blue phases) is the delicate interpretation, in the form of a detailed structural description, of the available diffraction data and of the electron microscopic observations. Many questions relative to these structures are still open. One of the promising ways to answering them is to investigate theoretically and experimentally their mechanism of formation and of growth. J.e. Toledano VI CONTENTS STRUCTURE AND GEOMETRY I Iierarchic structure ............................................................................................ . A.L. Mackay The structure of quasicrystals : from diffraction patterns to atom positions... .... ...... .... .... ...... .......... ...... ... 9 C. lanot, 1.M. Dubois and M. de Boissieu Determination of quasi-crystal structures by higher dimensional analysis ..................................................................... 25 W. Steurer Six-dimensional atoms for a decorated three-dimensional Penrose tiling ............................................................................................ 39 S. Van Smaalen Metrical aspects of quasicrystal embedding in superspace ................................. 49 A. lanner Landau theory and direct methods for crystal structures analysis ...................................................... ............................................... 67 A.L. Mackay Geometry of films of amphiphile molecules: a curved space approach ...................................... .......... ....... ......... .......... ...... .... ...... ...... ... 7 3 J.F. Sadoc and J. Charvohn Geometrical approach of blue phases .... .... ...... .... ...... .. ...... .... .......... ....... ... ...... ... 8 3 B. Pansu and E. Dubois-Violette Electron microscopy and quasicrystals ....................... .......................... ............. 89 P. Guyot and M. Audier On the dark field imaging behaviour of icosahedral phases in rapidly cooled aluminium alloys ............... ..................... ......... I 09 K.M. Knowles, and W.M. Stobbs Electron microscopy of modulated structures ...................... .............................. I 1 9 1. Van Landuyt, G. Van Tendeloo and S. Amelinckx VII MODELS FOR STABILITY AND GROWTH Physical models of perfect quasicrystal growth ...................... ............................. 133 D.P. DiVincenzo Generation and dynamics of defects in two-dimensional quasicrystals ............................................................................................... 141 M. Ronchetti, M. Bertagnolli and M.V. Jaric Intrinsic stability of quasicrystals and behaviour under a load of Frenkel defects................................................................... 159 J. Roth Reconstructive phase transition to the icosahedral phase .................................... 173 P. Tol6dano, C Katarci, V.P. Dmitriev, Y.M. Gufan and S.B. Rochal Structure and growth of two- and three-dimensional hexatic liquid crystals .............................................. ............................................... 179 J.D. Litster The tiling structure of simple liquids: squares and triangles in two dimensions... ........ ...... ...... ...... ...... .... .... .... .... ........ ............. 193 M.A. Glaser and N.A. Clark Does cholesteric blue phase III have an icosahedral structure ? ................................................................................................... 205 R.M. Hornreich and S. Shtrikman Intrinsic frustration and space curvature in smectic A liquid crystals ............................................................................................. 215 J.B. Fournier, J.P. Sadoc and G. Durand Critical behavior of polymorphic smectic-A liquid crystals............................................................................................. 221 CW. Garland Universal behavior in phospholipid multi membrane systems ............................. 255 E.B. Sirota, CR. Safinya, G.S. Smith, R. Plano, D. Roux, and N.A. Clark Pattern. formati<?n ~uri.ng the ordering processes In nematIc hqUId crystals .................................. ........................................ 265 Y. Ishibashi, T. Nagaya and H. Orihara Spatially modulated structures in models with competing interactions -some new results ... ............. .... ................ .... ....... 27 3 W. Selke Weakly periodic structures with a singular continuous spectrum .................................................................................. 281 S. Aubry The Anderson metal-insulator transition: incommensurate versus disordered systems ................. ............................ 301 S. N. Evangelou viii Theory of phase transition between two incommensurate phases in NbTe4 ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 307 M.B. Walker and R. Morelli The origin of polytypes in SiC and ZnS ........................................................... 311 V. Heine and C. Cheng Structural modulations in the high-temperature superconductor YBa2Cu307_0 and semi conducting W03_x, aspects of non-equilibrium behaviour ................................................................ 323 E.K.H. Salje Incommensurate modulations in bismuth-based high-Tc superconductors ....................................................................... 335 lC. Toledano, J. Schneck, and L. Pierre Incommensurate -commensurate phase transition of Cu2_xTe. (x < 0.05) ............................................................................. 347 N. Vouroutzis and C. Manolikas Review of the commensurate and incommensurate transitions in BCCD .............................................................................. 353 M.R. Chaves and A. Almeida Amorphous and quasicrystalline Al-Cr and Al-Cr-Si phases produced by solid state diffusion of alternating thin layers ..... ........ ........ ......... ... ...... .... ...... ................... .... .... .................. 371 1. Levi and D. Shechtman DYNAMICS AND PHASONS Phasons and amplitudons in modulated structures ......................................... . 383 R. Currat Phonons in quasicrystals and related structures ............................................... 387 T. Janssen Phasons in ferroelectric liquid crystals.............................................................. 395 M. Copic, 1. Drevensek, 1. Musevic, and R. Blinc Atomic Debye-Waller factors and phasons in modulated incon1mensurate structures .................................................................... 405 J.M. Perez-Mato and G. Madariaga The La.ndau free energy.and acoustic anomalies in Incommensurate Insulators .... .... ...... .......... ...... ......... .... .... .... .......... ....... 41 7 H.Z. Cummins, G. Li, N. Tao, R.M. Pick, C. Dreyfus and M. Hebbache NMR and NQR in incommensurate systems ................................................... 429 F. Milia and G. Papavassiliou Do we understand optical activity in the incommensurate phase of the A BX family? ......................................... .................................. 439 2 4 R.M. Pick The coupling between phason and soft modes near the smectic-C* to smectic-A phase transition.............................................. 447 H. Pleiner and H.R. Brand IX Optical measurements of diffusivities in incommensurate barium sodium niobate ............................................................................. 453 J.F. Scott and W.F. Oliver Index .................................................................................................................... 463 x
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