Geometry and Thermodynamics

1. Front Matter

   Pages i-x

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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

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.

• aluminium
• barium
• bismuth
• crystal
• crystal structure
• diffusion
• electron
• electron microscopy
• fields
• microscopy
• nuclear magnetic resonance (NMR)
• phase transition
• quasicrystal
• sodium
• thermodynamics

• National Center of Telecommunication Studies, Bagneux, France

  J.-C. Tolédano

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