Phonons: Theory and Experiments III: Phenomena Related to Phonons

ISBN-13: 9783642522734 / Angielski / Miękka / 2012 / 249 str.

Peter Bruesch;J. Bernasconi;U.T. Höchli

Opis

The first volume of this treatment, Phonons: Theory and Experiments I, was devoted to the basic concepts of the physics of phonons and to a study of models for interatomic forces. The second volume, Phonons: Theory and Experiments II, contains a study of experimental techniques and the inter pretation of experimental results. In the present third volume we treat a number of phenomena which are directly related to phonons. The aim of this book is to bridge the gap between theory and experi ment. An attempt has been made to present the descriptive as well as the analytical aspects of the topics. Although emphasis is placed on the role of phonons in the different topics, most chapters also contain a general intro duction into the specific subject. The book is addressed to experimentalists and to theoreticians working in the vast field of dynamical properties of solids. It will also prove useful to graduate students starting research in this or related fields. The choice of the topics treated was partly determined by the author's own activity in these areas. This is particularly the case for the chapters dealing with phonons in one-dimensional metals, disordered systems, super ionic conductors and certain newer aspects of ferroelectricity and melting. I am very grateful to my colleagues J. Bernasconi, V.T. Hochli and 1."

Spis treści

1. Introduction.- 1.1 General Remarks.- 1.2 Piezoelectricity.- 1.3 Ferroelectricity.- 1.4 Thermal Conductivity.- 1.5 Phonons in One-Dimensional Metals.- 1.6 Phonons in Disordered Systems.- 1.7 Ion Dynamics in Superionic Conductors.- 1.8 Melting.- 2. Piezoelectricity.- 2.1 General Remarks.- 2.2 Macroscopic Electroelastic Relations.- 2.3 The Method of Homogeneous Deformations.- 2.4 The Method of Long Waves.- 2.5 Application to Crystals with ZnS-Structure.- 2.6 Problems.- 2.6.1 The Method of Long Waves.- 2.6.2 Elastic Constant of a Piezoelectric Crystal for Short-Circuit and Open-Circuit Conditions.- 2.6.3 Piezoelectric and Optic Effective Charges for the Shell Model.- 3. Ferroelectricity.- 3.1 General Properties of Ferroelectric Materials.- 3.2 Classification and Properties of Selected Ferroelectrics.- 3.3 Thermodynamic Theory of Ferroelectrics.- 3.3.1 General Considerations.- 3.3.2 First-Order Transitions.- 3.3.3 Second-Order Transitions.- 3.4 Lattice Dynamics of Displacive Ferroelectric Phase Transitions.- 3.4.1 Ferroelectricity and the LST Relation.- 3.4.2 Origin of Instability and Polarizability Catastrophe.- 3.4.3 Soft Modes for Ferroelectric and Antiferroelectric Phase Transitions.- 3.4.4 Lattice-Dynamical Basis of Devonshire’s Theory.- 3.5 Lattice Dynamical Models for Ferroelectric Phase Transitions.- 3.5.1 The Anharmonic Lattice Model.- 3.5.2 Electronic Theory of Soft-Mode Instability.- 3.5.3 The Polarizability Model.- 3.5.4 Range of Validity of the Landau-Devonshire Theory.- 3.6 Soft-Mode Spectroscopy of Selected Ferroelectrics.- 3.7 Quantum Ferroelectrics.- 3.8 Disordered Polar Systems.- 3.9 Problems.- 3.9.1 Temperature Dependence of the Soft Mode in Displacive Phase Transitions.- 3.9.2 Polarizability Catastrophe for a System of Two Neutral Atoms.- 3.9.3 Classical and Quantum Ferroelectrics.- 3.9.4 Polarizability Model.- 4. Thermal Conductivity.- 4.1 General Remarks.- 4.2 Experimental Determination of Thermal Conductivity.- 4.3 Lattice Thermal Conductivity: Elementary Kinetic Theory.- 4.4 Formal Theory of Thermal Conductivity.- 4.5 Relaxation Times in Insulators.- 4.5.1 Boundary Scattering.- 4.5.2 Defect and Impurity Scattering.- 4.5.3 Phonon-Phonon Scattering.- 4.6 Thermal Conductivity of Glasses.- 4.7 Thermal Conductivity of Metals and Alloys.- 4.8 Second Sound.- 4.9 Problems.- 4.9.1 Three-Phonon Interactions.- 4.9.2 Relation Between Heat Flow and Phonon Momentum.- 4.9.3 Approximate Expression for ?t Based on Frequency Dependent Relaxation Times.- 5. Phonons in One-Dimensional Metals.- 5.1 Interesting Aspects of One-Dimensional Metals.- 5.2 Basic Properties of One-Dimensional Conductors.- 5.3 The Electronic Susceptibility.- 5.4 The Electron-Phonon Hamiltonian.- 5.5 Discussion of Selected Experiments for KCP.- 5.5.1 Chemistry and Structure.- 5.5.2 Transport Properties, Diffuse X-Ray Scattering and Band Structure.- 5.5.3 Inelastic Neutron Scattering Studies.- 5.5.4 Optical Properties of KCP.- 5.6 Effects of Fluctuations and Three-Dimensional Coupling.- 6. Phonons in Disordered Systems.- 6.1 The Effects of Defects and Disorder on Phonons.- 6.2 Green Functions.- 6.3 The Linear Chain with Isolated Defects.- 6.3.1 The Single Mass Defect.- 6.3.2 The Double Force Constant Defect.- 6.4 The Random Binary Mass Chain.- 6.4.1 General Features.- 6.4.2 The Coherent Potential Approximation.- 6.4.3 Cluster Approximations.- 6.4.4 Renormalization Group Approaches.- 6.5 Three-Dimensional Lattices and More Complicated Types of Disorder.- 6.6 Experimental Results and Comparison with Theoretical Calculations.- 7. Ion Dynamics in Superionic Conductors.- 7.1 General Aspects of Superionic Conductors.- 7.2 Basic Facts and Examples of SIC.- 7.3 Ionic Interactions and Dynamical Models.- 7.3.1 Free-Ion Model.- 7.3.2 Hopping and Lattice Gas Models.- 7.3.3 Continuous Stochastic Models.- 7.3.4 Continuum Models for the Hydrodynamic Region.- 7.3.5 Molecular Dynamics Calculations.- 7.4 Brownian Motion of a Particle in a Periodic Potential.- 7.5 Disorder-Induced Infrared Absorption and Raman Scattering.- 7.6 Phonons in a-AgI and Other SIC.- 7.6.1 Phonons in ?-AgI.- 7.6.2 Phonons in Other SIC.- 7.7 Lattice Dynamical Calculation of Jump Frequencies.- 7.7.1 Dynamical Theory of Diffusion in Crystals with a Small Defect Concentration.- 7.7.2 Jump Frequencies for SIC.- 8. Melting.- 8.1 Nature of the Melting Transition.- 8.2 Lindemann Relation.- 8.3 Anharmonicity and Instability of the Solid Phase.- Appendix: Constants and Units.- References.