Field Theoretic Method in Phase Transformations
The continuum, field theoretic method of study of phase transformations in material systems, also known as "phase field", allows one to analyze different stages of transformations on the unified platform. It has received significant attention in the mater
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Introduction
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What Is This Book About?
Phase transitions are significant changes in the system’s properties and symmetry, which happen as a result of changes of the external conditions (temperature, pressure, chemical potential, etc.). Although various phase transitions are discussed in the book as physical phenomena, the book is more about the method to study the phase transitions than about the phenomena themselves. A lot has been written about behavior of a system close to the critical point; it is characterized by special features such as scale invariance. However, these are rare cases and most of the systems spend most of their time far away from the critical points. Rephrasing Feynman we can say that there is plenty of room away from the critical point. Evolutions of the systems when they are not close to the critical points are characterized by completely different physical features, such as rate of nucleation and growth, microstructure or pattern formation, structure modification and coarsening, etc. Physical descriptions of these features require that special consideration is taken to the free energies of the phases involved in the transformations, which in many cases are known either from thermodynamic calculations or direct experimental measurements. All of that sets the stage for different approach to phase transitions, more phenomenological, which is the main subject of this book. One of the most convenient ways of addressing the general problem of phase transformations is the Field-Theoretic Method (FTM) based on the Landau paradigm, which assumes that the free energy, in addition to temperature, pressure, and composition, is a continuous function of a set of internal (hidden) parameters associated with the symmetry changes, which are usually called long-range order parameters (OP). Different transitions may be laid out into the same framework if proper physical interpretations of OPs are found. Although significant strides in the direction of rigorous derivation of the basic equations of the method from the first principles have already been made (see Appendix A), this task is not finished yet.
A. Umantsev, Field Theoretic Method in Phase Transformations, Lecture Notes in Physics 840, DOI 10.1007/978-1-4614-1487-2_1, # Springer Science+Business Media, LLC 2012
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1 Introduction
That is why the issue of thermodynamic consistency always played and still plays significant role in the development of FTM. This issue can be expressed as follows: whatever the equations of the method are, their implications should not contradict the basic laws of thermodynamics.
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Who Is This Book For?
This book is for researchers who are interested in all aspects of phase transformations, especially for practitioners who are involved in theoretical studies or computer simulations of the phenomena and would like to expand their knowledge in the direction of the field theory of phase transitions. This book can be used as a textbook of a graduate or upper level undergraduate course in physics of phase transit
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