Bond-Orientational Order in Condensed Matter Systems

20.12.1991

Englisch

9780387976389

Springer US

Partially Ordered Systems

Nein

388

Gebundene Ausgabe

molecule, Metall, liquid crystals, scattering, glass, Experiment

PHFC - Physik der kondensierten Materie (Flüssigkeits- und Festkörperphysik) PNR - Physikalische Chemie TGMT - Werkstoffprüfung

1 Bond-Orientational Order.- 1.1 Introduction.- 1.2 Elementary Ideas.- 1.2.1 Example: Two-Dimensional Harmonic Crystal.- 1.2.2 Mean Field Phase Diagram and Coupled Order Parameters.- 1.2.3 Modern Theory of Phase Transitions.- 1.3 Experimental Results.- 1.3.1 Thermodynamic Measurements.- 1.3.2 Static Structural Studies.- 1.4 More Complicated Systems.- 1.4.1 Crystals.- 1.4.2 Glasses.- 1.4.3 Incommensurate Crystals.- 1.4.4 Quasicrystals.- 1.4.5 Quasilattice.- 1.4.6 Quasicrystalline Glass.- 1.5 Extensions to Three Dimensions.- References.- 2 Computer Simulation Studies of Bond-Orientational Order.- 2.1 Introduction.- 2.2 Numerical Simulation Techniques.- 2.2.1 Atomistic Simulations.- 2.2.2 Simulations of Abstract Objects.- 2.2.3 Basic Problems with Numerical Simulation Studies: Short Times, Small Sizes, and the Importance of Boundary Conditions.- 2.3 Examples of Computer Simulation Studies of Bond-Orientational Order.- 2.3.1 Measurement of Bond-Orientational Order in a Two-Dimensional Atomistic System.- 2.3.2 Behavior of a Two-Dimensional Atomistic System in the Presence of a Hexatic Field.- 2.3.3 Study of the Hexatic Phase in a Defect-Based Simulation.- 2.3.4 Effects of Frustration on Glass Formation in a Two-Dimensional Lennard-Jones System.- 2.3.5 Square-Triangle Analysis.- 2.3.6 A Simple Atomistic Model Possessing an Equilibrium Quasicrystal Phase.- 2.3.7 Consequences of Nontraditional Bond-Orientational Order in a Random Tiling Model.- 2.3.8 Growth of a Perfect Quasicrystal.- 2.4 Conclusions.- References.- 3 Nature of Phase Transitions Related to Stacked Hexatic Phases in Liquid Crystals.- 3.1 Introduction.- 3.2 Fundmental Properties of the Hexatic Phase.- 3.2.1 Two-Dimensional Melting Theory.- 3.2.2 Existence of Hexatic Order in Other Physical Systems.- 3.2.3 Hexatic Phases in the Liquid Crystal.- 3.2.4 Pure Compounds and Mixtures Exhibiting Hexatic Phases.- 3.3 Thermal Properties.- 3.3.1 Heat Capacity.- 3.3.2 Nature of the SmA-HexB-SmI Point.- 3.3.3 Thermal Transport Studies.- 3.4 Criticality of the Smectic-A-Hexatic-B Transition.- 3.5 Conclusions.- References.- 4 Experimental Studies of Melting and Hexatic Order in Two-Dimensional Colloidal Suspensions.- 4.1 Introduction.- 4.1.1 Theoretical Predictions of Two-Dimensional Melting.- 4.1.2 Advantages and Disadvantages of Colloid Direct Imaging Experiments.- 4.2 Experimental Results—Melting of Two-Dimensional Colloidal Systems.- 4.2.1 Charged, Confined between Flat Plates, Wedge Geometry.- 4.2.2 Floating Monolayers on a Liquid Surface.- 4.2.3 Expansion between Rigid Plates.- 4.2.4 Dipole Holes in Ferrofluid.- 4.2.5 Wedge Geometry Revisited: Comparison of Melting in Two and Three Dimensions.- 4.3 Conclusions and Suggestions for Future Work.- 4.3.1 Equilibration and System Size.- 4.3.2 Possibility for Studying Driven Nonequilibrium Phase Transitions.- 4.3.3 Relevant Energy Scales.- 4.3.4 Other Predictions of KTHNY.- 4.3.5 Substrates and Their Effects.- 4.3.6 Other Analog Molecular Dynamics Experiments.- References.- 5 Faceting in Bond-Oriented Glasses and Quasicrystals.- 5.1 Introduction.- 5.1.1 What Have Quasicrystals Brought Us?.- 5.1.2 The Problem of Quasicrystal Facets.- 5.1.3 Organization of This Chapter.- 5.2 Quasicrystal Facets.- 5.3 The Conventional View of Facet Formation.- 5.3.1 The Determination of the Equilibrium Shapes of Solids: The Wulff Construction.- 5.3.2 The Origin of Facets: Cusps in the Surface Energy.- 5.4 Faceting in Perfect Bond-Oriented Systems.- 5.4.1 Sufficient Conditions for Facet Formation.- 5.4.2 The Herring Algorithm.- 5.4.3 The Equilibrium Shape of Simple Bond-Oriented Systems with Icosahedral Symmetry.- 5.5 Equilibrium Shapes of Perfect and Random Quasicrystals.- 5.5.1 Tiling Model of Perfect and Disordered Quasicrystals.- 5.5.2 The Surface Energy of Perfect and Disordered Quasicrystals.- 5.6 Final Remarks.- References.- 6 Icosahedral Ordering in Supercooled Liquids and Metallic Glasses.- 6.1 Introduction.- 6.2 Three-Dimensional Sphere Packings and Frustration.- 6.2.1 Frank—Kasper Phases.- 6.3 Structure Factor of Monoatomic Supercooled Liquids.- 6.3.1 Sphere Packings in Curved Three-Dimensional Space.- 6.3.2 Order Parameter.- 6.3.3 Landau Free Energy.- 6.4 Application to Real Metallic Glasses.- 6.4.1 Metal-Metalloid Glasses.- 6.4.2 Metal-Metal Glasses.- 6.5 Conclusions.- References.- 7 Orientational Order and Quasicrystals.- 7.1 Introduction.- 7.2 Bond-Orientational Order Parameter.- 7.2.1 Definition.- 7.2.2 Symmetries.- 7.2.3 Measures.- 7.3 Bond-Orientational Phase Diagram.- 7.3.1 Summary.- 7.3.2 Free Energy.- 7.3.3 Minimization.- 7.3.4 Phase Diagram.- 7.4 Icosahedral Quasicrystals.- 7.4.1 Summary.- 7.4.2 Landau Theory of Freezing.- 7.4.3 Orientational-Translational Coupling.- 7.5 Conclusion.- References.- 8 Icosahedral Glass Models for Quasicrystals.- 8.1 Introduction.- 8.2 Icosahedral Crystals and Quasiperiodicity.- 8.3 Survey of Quasicrystalline Models for the Icosahedral Phase.- 8.3.1 Perfect Quasicrystalline Tilings.- 8.3.2 Entropically Stabilized Structures.- 8.3.3 Quasicrystalline Tilings as Higher-Dimensional Periodic Structures.- 8.4 Icosahedral Glass Structures.- 8.5 The Decagonal Glass in Two-Dimensions.- 8.5.1 The Basic Algorithm for Numerical Simulations.- 8.5.2 Understanding the Sharp Diffraction Maxima: The HT Approach.- 8.6 The Icosahedral Glass in Three Dimensions.- 8.6.1 IG Structures Related to the SI Alloys.- 8.6.2 IG Structures Related to the FCI Alloys.- 8.7 The Success and Failure of the Icosahedral Glass Model: Comparison with Experiments.- 8.7.1 Peak Broadening in Icosahedral Alloys.- 8.7.2 Modifications of the Growth Algorithm.- 8.7.3 Diffuse Scattering from the Icosahedral Alloys.- 8.8 Concluding Remarks.- References.

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