- 原书名：The Physics of Structural Phase Transitions
- 原出版社： Springer
Phase transitions in which crystalline solids undergo structural changes present an interesting problem in the interplay between the crystal structure and the ordering process that is typically nonlinear. Intended for readers with prior knowledge of basic condensedmatter physics, this book emphasizes the physics behind spontaneous structural changes in crystals. .
Starting with relevant thermodynamic principles, the text discusses the nature of order variables in collective motion in structural phase transitions, where a singularity in such a collective mode is responsible for lattice instability as revealed by soft phonons. In this book, critical anomalies at second-order structural transitions are first analyzed with the condensate model. Discussions on the nonlinear ordering mechanism are followed with the soliton theory, thereby interpreting the role of long-range order. Relevant details for nonlinear mathematics are therefore given for minimum necessity. The text also discusses experimental methods for modulated crystal structures, giving examples of structural changes in representative systems. ..
This book is divided into two parts. The first part includes such topics as the landau theory of phase transitions, statistics, correlations. and the mean-field approximation, pseudospins and their collective motion, soft lattice modes, condensates and their nonlinear growth, and lattice imperfections and their role in phase transitions of real crystals. The second part discusses experimental studies of modulated crystals using X-ray diffraction, neutron inelastic scattering, light scattering, dielectric measurements, and magnetic resonance spectroscopy. While the presence of modulated structures in the critical region is not particularly suggested in the published results of these studies, it is notable that many observed anomalies indicate evidence for pinned pseudospin condensates. ...
Preface to the First Edition
Part I Basic Concepts
1 Thermodynamical Principles and the Landau Theory
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 Order Variables, Their Correlations and Statistics: the
2 Mean-Field Theory
2.1 Order Variables
2.2 Probabilities, Short- and Long-Range Correlations, and the Mean-Field Approximation
Solid-state physics of perfect crystals is well established, and lattice imperfections are treated as minor perturbations. The basic theories are adequate for most problems in stable crystals, whereas in real systems, disrupted translational symmetry plays a fundamental role, as revealed particularly in spontaneous structural changes. In their monograph Dynamical Theory of Crystal Lattices, Born and Huang have pointed out that a long-wave excitation of the lattice is essential in anisotropic crystals under internal or external stresses, although their theory had never been tested until recent experiments where neutron scattering and magnetic resonance anomalies were interpreted with the long-wave approximation. Also, the timescale of observations is significant for stow processes during structural changes, whereas such a timescale is usually regarded as infinity in statistical mechanics, and the traditional theory has failed to explain transition anomalies. Although emphasized in the first edition, I have revised the whole text in the spirit of Born and Huang for logical introduction of these principles to structural phase transitions. Dealing with thermodynamics of stressed crystals, the content of this edition will hopefully be a supplement to their original treatise on lattice dynamics in light of new experimental evidence. ..
We realize that in practical crystals, a collective excitation plays a significant role in the ordering process in conjunction with lattice imperfections, being characterized by a propagating mode with the amplitude and phase. Such internal variables are essential for the thermodynamic description of crystals under stresses, for which I wish to establish the logical foundation, instead of a presumptive explanation.
Constituting a basic theme in this book, the collective motion of dynamical variables is mathematically a nonlinear problem, where the idea of solitons casts light on the concept of local fields, in expressing the intrinsic mechanism of distant order involved in the collective motion in a wide range of temperature. While rather primitive at the present stage, I believe that this method leads us in a correct direction for nonlinear processes, along which structural phase transitions can be elucidated in further detail. I have therefore spent a considerable number of pages to discuss the basic mathematics for nonlinear physics.
I thank Professor E. J. Samuelsen for correcting my error in the first edition regarding the discovery of the central peak. ...