Phase transitions in which crystalline solids undergo structural changes present an interesting problem in the interplay between thecrystal structure and the ordering process that is typically nonlinear. Intended for readers with prior knowledge of basic condensed-matter physics, this book emphasizes the physics behind spontaneousstructural changes in crystals. Starting with relevant thermodynamic principles, the textdiscusses the nature of order variables in collective motion instructural phase transitions, where a singularity in such a collectivemode is responsible for lattice instability as revealed by soft phonons. In this book, critical anomalies at second-order structural transitionsare first analyzed with the condensate model. Discussions on thenonlinear ordering mechanism are followed with the soliton theory,thereby interpreting the role of long-range order.Relevant detailsfor nonlinear mathematics are therefore given for minimun necessity.The text also discusses experimental methods for modulated crystalstructures, giving examples of structural changes in representativesystems. This book is divided into two parts. The first part includes suchtopics as the landau theory of phase transitions, statistics, correlations,and the mean-field approximation, pseudospins and their collectivemotion, soft lattice modes, condensates and their nouliuear growth,and lattice imperfections and their role in phase transitions of realcrystals. The second part discusses experimental studies of modulatedcrystals using X-ray diffraction, neutron inelastic scattering, lightscattering, dielectric measurements, and magnetic resonancespectroscopy. While the presence of modulated structures in thecritical region is not particularly suggested in the published resultsof these studies, it is notable that many observed anomalies indicateevidence for pinned pseudospin condensates.
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目录
Preface to the Second Edition Preface to the First Edition Part I Basic Concepts 1 Thermodynamical Principles and the Landau Theory 1.1 Introduction 1.2 Phase Equilibria in Isotropic Systems 1.3 Phase Diagrams and Metastable States 1.4 The van der Waals Equation of State 1.5 Second-Order Phase Transitions and the Landau Theory 1.5.1 The Ehrenfest Classification 1.5.2 The Landau Theory 1.6 Susceptibilities and the Weiss Field 1.6.1 Susceptibility of an Order Parameter 1.6.2 The Weiss Field in a Ferromagnetic Domain 1.7 Critical Anomalies, Beyond Classical Thermodynamics 1.8 Remarks on Critical Exponents 2 Order Variables, Their Correlations and Statistics: the Mean-Field Theory 2.1 Order Variables 2.2 Probabilities, Short-and Long-Range Correlations, and the Mean-Field Approximation 2.2.1 Probabilities 2.2.2 The Concept of a Mean Field 2.3 Statistical Mechanics of an Order-Disorder Transition 2.4 The Ising Model for Spin-Spin Correlations 2.5 The Role of the Weiss Field in an Ordering Process 3 Collective Modes of Pseudospins in Displacive Crystalsn and the Born-Huang Theory 3.1 Displacive Crystals 3.2 The Landau Criterion for Classical Fluctuations 3.3 Quantum-Mechanical Pseudospins and their Correlations 3.4 The Born-Huang Theory and Structural Ordering in Crystals 3.5 Collective Pseudospin Modes in Displacive Systems 3.6 Examples of Collective Pseudospin Modes 3.6.1 Strontium Titanate and Related Perovskites 3.6.2 Tris-Sacosine Calcium Chloride and Related Crystals 3.7 The Variation Principle and the Weiss Singularity 4 Soft Modes, Lattice Anharmonicity and Pseudospin Condensates in the Critical Region 4.1 The Critical Modulation 4.2 The Lyddane-Sachs-Teller Relation 4.3 Long-Range Interactions and the Cochran Theory 4.4 The Quartic Anharmonic Potential in the Critical Region 4.4.1 The Cowley Theory of Mode Softening 4.4.2 Symmetry Change at a Continuous Phase Transition 4.5 Observation of Soft-Mode Spectra 4.6 The Central Peak 4.7 Symmetry-Breaking Fluctuations in Binary Phase Transitions 4.8 Macroscopic Observation of a Binary Phase Transition; λ-anomaly of the Specific Heat 5 Dynamics of Pseudospins Condensates and the Long-Range Order 5.1 Imperfections in Practical Crystals 5.2 The Pinning Potential 5.3 The Lifshitz Condition for Incommensurate Fluctuations 5.4 A Pseudopotential for Condensate Locking and Commensurate Modulation 5.5 Propagation of a Collective Pseudospin Mode 5.6 A Hydrodynamic Model for Pseudospin Propagation 5.7 The Korteweg-deVries Equation 5.7.1 General Derivation 5.7.2 Solutions of the Korteweg-deVries Equation 5.8 Soliton Potentials and the Long-Range Order 5.9 Mode Stabilization by the Eckart Potential Part II Experimental Studies 6 Diffuse X-ray Diffraction and Neutron Inelastic Scattering from Modulated Crystals 6.1 Modulated Crystals 6.2 The Bragg Law of X-ray Diffraction 6.3 Diffuse Diffraction from Weakly Modulated Crystals 6.4 The Laue Formula and Diffuse Diffraction from Perovskites 6.5 Neutron Inelastic Scattering 7 Light Scattering and Dielectric Studies on Structural Phase Transitions 7.1 Raman Scattering Studies on Structural Transitions 7.2 Rayleigh and Brillouin Scatterings 7.3 Dielectric Relaxation 7.4 Dielectric Spectra in the Ferroelectric Phase Transition of TSCC 8 The Spin-Hamiltonian and Magnetic Resonance Spectroscopy 8.1 Introduction 8.2 Principles of Magnetic Resonance and Relaxation 8.3 Magnetic Resonance Spectrometers 8.4 The Crystalline Potential 8.5 The Zeeman Energy and the g Tensor 8.6 The Fine Structure 8.7 Hyperfine Interactions and Forbidden Transitions 9 Magnetic Resonance Sampling and Nuclear Spin Relaxation Studies on Modulated Crystals 9.1 Paramagnetic Probes in a Modulated Crystal 9.2 The spin-Hamiltonian in Modulated Crystals 9.2.1 The g Tensor Anomaly 9.2.2 The Hyperfine Structure Anomaly 9.2.3 The Fine-Structure Anomaly 9.3 Structural Phase Transitions in TSCC and BCCD Crystals as Studied by Paramagnetic Resonance Spectra 9.3.1 The Ferroelectric Phase Transition in TSCC Crystals 9.3.2 Structural Phase Transitions in BCCD Crystals 9.4 Nuclear Quadrupole Relaxation in Incommensurate Phases 10 Structural Phase Transitions in Miscellaneous Systems 10.1 Cell-Doubling Transitions in Oxide Perovskites 10.2 The Incommensurate Phase in ß-Thorium Tetrabromide 10.3 Phase Transitions in Deuterated Biphenyl Crystals 10.4 Successivc Phase Transitions in A2BX4 Family Crystals 10.5 Incommensurate Phases in RbH3(SeO3)2 and Related Crystals 10.6 Phase Transitions in(NH4)2SO4 and NH4AlF4 10.7 Proton Ordering in Hydrogen-Bonded Crystals Epilogue Appendix The Adiabatic Approximation Index
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