Ebook: Geometry and Thermodynamics: Common Problems of Quasi-Crystals, Liquid Crystals, and Incommensurate Systems

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.

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Content:
Front Matter....Pages i-x
Hierarchic Structure....Pages 1-8
The Structure of Quasicrystals : From Diffraction Patterns to Atom Positions....Pages 9-24
Determination of Quasi — Crystal Structures by Higher Dimensional Analysis....Pages 25-37
Six-Dimensional Atoms for a Decorated Three-Dimensional Penrose Tiling....Pages 39-48
Metrical Aspects of Quasicrystal Embedding in Superspace....Pages 49-65
Landau Theory and Direct Methods for Crystal Structure Analysis....Pages 67-71
Geometry of Films of Amphiphile Molecules: A Curved Space Approach....Pages 73-82
Geometrical Approach of Blue Phases....Pages 83-87
Electron Microscopy and Quasicrystals....Pages 89-107
On the Dark Field Imaging Behaviour of Icosahedral Phases in Rapidly Cooled Aluminium Alloys....Pages 109-117
Electron Microscopy of Modulated Structures....Pages 119-131
Physical Models of Perfect Quasicrystal Growth....Pages 133-139
Generation and Dynamics of Defects in Two-Dimensional Quasicrystals....Pages 141-158
Intrinsic Stability of Quasicrystals and Behaviour Under a Load of Frenkel Defects....Pages 159-172
Reconstructive Phase Transition to the Icosahedral Phase....Pages 173-177
Structure and Growth of Two- and Three-Dimensional Hexatic Liquid Crystals....Pages 179-191
The Tiling Structure of Simple Liquids Squares and Triangles in Two Dimensions....Pages 193-204
Does Cholesteric Blue Phase III Have an Icosahedral Structure?....Pages 205-214
Intrinsic Frustration and Space Curvature in Smectic a Liquid Crystals....Pages 215-219
Critical Behavior of Polymorphic Smectic-A Liquid Crystals....Pages 221-254
Universal Behavior in Phospholipid Multimembrane Systems....Pages 255-263
Pattern Formation During the Ordering Processes in Nematic Liquid Crystals....Pages 265-271
Spatially Modulated Structures in Models with Competing Interactions — Some New Results....Pages 273-279
Weakly Periodic Structures with a Singular Continuous Spectrum....Pages 281-300
The Anderson Metal — Insulator Transition: Incommensurate Versus Disordered Systems....Pages 301-305
The Origin of Polytypes in SiC and ZnS....Pages 307-309
Structural Modulations in the High-Temperature Superconductor YBa2Cu3O7-? and Semi Conducting WO3-x Aspects of Non-Equilibrium Behaviour....Pages 311-322
Incommensurate Modulations in Bismuth-Based High-Tc Superconductors....Pages 323-333
Incommensurate — Commensurate Phase Transition of Cu2-?Te. (x < 0.05)....Pages 335-345
Review of the Commensurate and Incommensurate Transitions in BCCD....Pages 347-352
Amorphous and Quasicrystalline Al-Cr and Al-Cr-Si Phases Produced by Solid State Diffusion of Alternating Thin Layers....Pages 353-369
Phasons and Amplitudons in Modulated Structures....Pages 371-381
Phonons in Quasicrystals and Related Structures....Pages 383-386
Phasons in Ferroelectric Liquid Crystals....Pages 387-394
Atomic Debye-Waller Factors and Phasons in Modulated Incommensurate Structures....Pages 395-403
The Landau Free Energy and Acoustic Anomalies in Incommensurate Insulators....Pages 405-415
NMR and NQR in Incommensurate Systems....Pages 417-428
Do We Understand Optical Activity in the Incommensurate Phase of the A2 BX4 Family ?....Pages 429-438
The Coupling Between Phason and Soft Modes Near the Smectic C* to Smectic a Phase Transition....Pages 439-445
Back Matter....Pages 447-451
Optical Measurements of Diffusivities in Incommensurate Barium Sodium Niobate....Pages 463-466
....Pages 453-462