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Geometry and Thermodynamics

Common Problems of Quasi-Crystals, Liquid Crystals, and Incommensurate Systems

  • Book
  • © 1990

Overview

Editors:
  1. J.-C. Tolédano

    1. National Center of Telecommunication Studies, Bagneux, France

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Part of the book series: NATO Science Series B: (NSSB, volume 229)

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Table of contents (41 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Structure and Geometry

    1. Hierarchic Structure

      • Alan L. Mackay
      Pages 1-8

    2. The Structure of Quasicrystals : From Diffraction Patterns to Atom Positions

      • Christian Janot, Jean-Marie Dubois, Marc de Boissieu
      Pages 9-24

    3. Determination of Quasi — Crystal Structures by Higher Dimensional Analysis

      • Walter Steurer
      Pages 25-37

    4. Six-Dimensional Atoms for a Decorated Three-Dimensional Penrose Tiling

      • Sander van Smaalen
      Pages 39-48

    5. Metrical Aspects of Quasicrystal Embedding in Superspace

      • A. Janner
      Pages 49-65

    6. Landau Theory and Direct Methods for Crystal Structure Analysis

      • Alan L. Mackay
      Pages 67-71

    7. Geometry of Films of Amphiphile Molecules: A Curved Space Approach

      • J.-F. Sadoc, J. Charvolin
      Pages 73-82

    8. Geometrical Approach of Blue Phases

      • Brigitte Pansu, Elisabeth Dubois-Violette
      Pages 83-87

    9. Electron Microscopy and Quasicrystals

      • P. Guyot, M. Audier
      Pages 89-107

    10. On the Dark Field Imaging Behaviour of Icosahedral Phases in Rapidly Cooled Aluminium Alloys

      • K. M. Knowles, W. M. Stobbs
      Pages 109-117

    11. Electron Microscopy of Modulated Structures

      • J. Van Landuyt, G. Van Tendeloo, S. Amelinckx
      Pages 119-131

  3. Models for Stability and Growth

    1. Physical Models of Perfect Quasicrystal Growth

      • D. P. DiVincenzo
      Pages 133-139

    2. Generation and Dynamics of Defects in Two-Dimensional Quasicrystals

      • Marco Ronchetti, Mauro Bertagnolli, Marko V. Jarić
      Pages 141-158

    3. Intrinsic Stability of Quasicrystals and Behaviour Under a Load of Frenkel Defects

      • Johannes Roth
      Pages 159-172

    4. Reconstructive Phase Transition to the Icosahedral Phase

      • P. Tolédano, C. Katarci, V. P. Dmitriev, Yu. M. Gufan, S. B. Rochal
      Pages 173-177

    5. Structure and Growth of Two- and Three-Dimensional Hexatic Liquid Crystals

      • J. D. Litster
      Pages 179-191

    6. The Tiling Structure of Simple Liquids Squares and Triangles in Two Dimensions

      • Matthew A. Glaser, Noel A. Clark
      Pages 193-204

    7. Does Cholesteric Blue Phase III Have an Icosahedral Structure?

      • R. M. Hornreich, S. Shtrikman
      Pages 205-214

    8. Intrinsic Frustration and Space Curvature in Smectic a Liquid Crystals

      • J. B. Fournier, J. F. Sadoc, G. Durand
      Pages 215-219
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Keywords

About this book

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, aNA TO-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.

Editors and Affiliations

  • National Center of Telecommunication Studies, Bagneux, France

    J.-C. Tolédano

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