Beyond the Crystalline State: An Emerging Perspective - Couverture souple
Livre 63 sur 65: Springer Series in Solid-State Sciences
Synopsis
1. Introduction.- 2. Variety in Structures.- 2.1 Crystals.- 2.2 Incommensurate and Long-Period Structures.- 2.3 Quasicrystals.- 2.3.1 Quasiperiodicity.- 2.3.2 2D Quasicrystalline Tilings.- 2.3.3 A Brief Recapitulation.- 2.3.4 3D Quasicrystals.- 2.4 Liquid Crystals.- 2.5 Glass.- 2.6 Systems with Quasi Long-Range Order.- 2.7 Overview.- 3. Order Out of Disorder.- 3.1 Landau Theory.- 3.1.1 Transition in a System with a Scalar Order Parameter.- 3.1.2 Role of Symmetry.- 3.1.3 Systems with a Complex Order Parameter.- 3.1.4 Order Parameter Space.- 3.1.5 Generalized Landau Expansion.- 3.1.6 Fluctuations.- 3.2 Conjugate Field.- 3.3 Symmetry Breaking: Further Aspects.- 3.4 Goldstone Modes.- 3.5 Generalized Rigidity.- 3.6 Quasi LRO.- 3.7 Overview.- 4. Defects and Topology.- 4.1 Basic Strategy.- 4.2 Some Basic Concepts of Topology.- 4.3 Continuous Groups and Topological Spaces.- 4.4 The First or the Fundamental Homotopy Group and Defects.- 4.4.1 Burgers Circuit.- 4.4.2 Closure Misfit.- 4.4.3 Fundamental Group.- 4.4.4 ?1 (V) and Defects.- 4.5 Some Examples.- 4.6 Stability.- 4.7 Combination of Defects.- 4.8 Other Homotopy Groups.- 4.9 Ordered Media with Broken Translational Symmetry.- 4.10 Summary.- 5. Structures by Projection.- 5.1 Concerning Tilings.- 5.2 Regular Polytopes.- 5.3 Amorphous Structures from Mappings of Polytopes.- 5.4 Line Defects in Amorphous Structures.- 5.5 Disclinations and Frank-Kasper Chains.- 5.6 Mapping from S3 to E3.- 5.7 Defects and Star Mapping.- 5.8 Mapping by Disclination Procedure.- 5.9 Decoration.- 5.10 Defects in the CRN.- 5.11 Amorphous Structures by Projection of Hyperbolic Tilings.- 5.12 Polymers and Polytopes.- 5.13 Quasicrystals by the Projection Method.- 5.13.1 Generation of the Penrose Chain.- 5.13.2 Varying the Choice of the Unit Cell.- 5.13.3 Role of the Slope.- 5.13.4 Effect of Translating S Laterally.- 5.13.5 Role of the Orientation of ?.- 5.14 Generalization.- 5.15 Some Comments on the Projection Method.- 5.16 Miller Indices for Quasicrystals.- 5.17 Diffraction Patterns of Quasicrystals.- 5.18 Incommensurate Crystals.- 5.19 Summary.- 6. Beyond Simple Geometry.- 6.1 Some Basics.- 6.2 Landau Theory and Ordered Atomic Structures.- 6.2.1 Free Energy Expansion.- 6.2.2 Liquid-Solid Transition.- 6.2.3 BCC Versus Icosahedral Ordering.- 6.3 Orientational Ordering.- 6.4 Orientational Order Versus Translational Order.- 6.5 Landau Theory and Amorphous Structures.- 6.6 Landau Theory and Liquid Crystals.- 6.6.1 Liquid-to-Nematic Transition.- 6.6.2 Deformation Energy.- 6.6.3 Nematic-to-Smectic A (NA) Transition.- 6.6.4 Defects in Smectic A.- 6.6.5 Analogies to the Superconductor.- 6.7 Hydrodynamics.- 6.8 Fluctuations and the Landau Theory.- 6.9 Frustration and the Disruption of Order.- 6.10 Defect-Dominated Structures.- 6.10.1 Role of Topological Defects.- 6.10.2 Topological Order.- 6.10.3 Critical Behaviour of the Model.- 6.10.4 Disclinations and 2D Melting.- 6.10.5 Landau Theory and Defect-Mediated Transitions.- 6.11 Overview.- 7. Tilings in One Dimension.- 7.1 Structures and Competing Periodic Potentials.- 7.1.1 The Problem.- 7.1.2 Structures and Maps.- 7.1.3 Trajectories and Structures.- 7.2 Portrait of the Penrose Chain.- 7.3 Spatial Chaos and Amorphous Structures.- 7.4 Summary.- 8. Ergodicity Breaking.- 8.1 Basic Ideas.- 8.2 Time Scales and Broken Ergodicity.- 8.3 Broken Ergodicity and Symmetry Breaking.- 8.4 The Spin Glass.- 8.5 The Case of Glass.- 8.6 Generalization.- 9. Symmetry Breaking - A Second Look.- 9.1 Orbits and Strata in Crystal Physics.- 9.2 Symmetry Breaking and Strata.- 9.3 Isotropy Subgroups of the Euclidean Group E(3).- 9.4 More About Extensions to E(3).- 9.5 Patterns in Nonequilibrium Systems.- 9.6 Cylindrical Crystallography.- Appendix: Special Topics.- A. Hydrodynamics.- A.1 Hydrodynamic Equations.- A.2 Ordered Media with Continuous Broken Symmetries.- A.2.1 Hydrodynamics of a Solid.- A.3 The Poisson Bracket Method in Hydrodynamics.- A.4 Summary.- B. Curved Space and Parallel Transport o
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
