Bond-Orientational Order in Condensed Matter Systems

One of the most important aspects of solid materials is the regularity of the arrangement of the constituent molecules, that is, the long-range order. The focus of this book is on the contribution made by the ordering of bond orientations (as distinguished from the orientations of the molecules themselves) on the behavior of condensed systems, particularly their phase transitions. Examples in which bond-orientational effects play an important role are liquid crystals, quasicrystals, and two-dimensional crystals. This book contains contributions by many of the foremost researchers in the field. The chapters are tutorial reviews of the subject, written both for the active researcher looking for a review of a topic and for the graduate student investigating an exciting area of research. The contributions include an overview by J.D. Brock, Cornell; a discussion of computer simulation studies by K.J. Strandburg, Argonne; chapters on phase transition in hexatic liquid crystals by C.C. Huang, Minnesota and C.A. Murray, Texas A&M; and chapters on quasicrystals by S. Sachdev, Yale, M.V. Jaric, A.I. Goldman, Iowa State, and T.-L. Ho, Ohio State.

Contenu

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.