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Field Theoretic Method in Phase Transformations 2012 [Minkštas viršelis]

  • Formatas: Paperback / softback, 344 pages, aukštis x plotis: 235x155 mm, weight: 545 g, 1 Tables, black and white; 27 Illustrations, color; 28 Illustrations, black and white; X, 344 p. 55 illus., 27 illus. in color., 1 Paperback / softback
  • Serija: Lecture Notes in Physics 840
  • Išleidimo metai: 20-Apr-2012
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1461414865
  • ISBN-13: 9781461414865
Kitos knygos pagal šią temą:
Field Theoretic Method in Phase Transformations 2012Didesnis paveikslėlis
  • Formatas: Paperback / softback, 344 pages, aukštis x plotis: 235x155 mm, weight: 545 g, 1 Tables, black and white; 27 Illustrations, color; 28 Illustrations, black and white; X, 344 p. 55 illus., 27 illus. in color., 1 Paperback / softback
  • Serija: Lecture Notes in Physics 840
  • Išleidimo metai: 20-Apr-2012
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1461414865
  • ISBN-13: 9781461414865
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781461414865.html
Raktažodžiai:

The main subject of the book is the continuum, field theoretic method of study of phase transformations in material systems. The method, also known as "phase field", allows one to analyze different stages of transformations on the unified platform. It has received significant attention in the materials science community recently due to many successes in solving or illuminating important problems. The book will address fundamentals of the method starting from the classical theories of phase transitions, the most important theoretical and computational results, and some of the most advanced recent applications.

Recenzijos

From the reviews:

This book is a thorough presentation of the field theoretic method of study of phase transformations in material systems. The book is well written and quite appropriate as a reference on the subject, but can also be used as a textbook for an audience interested in the physical aspects of the theory. It should also be useful to mathematicians interested in the analysis and numerics of phase transitions who want to deepen their knowledge on the physical origins of the problems they work on. (Apostolos Damialis, Mathematical Reviews, July, 2013)

The author discusses the field theoretic method in phase transitions. Phase transitions are significant changes in a systems properties and symmetry, which happen as a result of changes of external conditions . This book is aimed at researches who are interested in all aspects of phase transformations, especially for practitioners who are involved in theoretical studies or computer simulations of the phenomena. This book can be used as a textbook for a graduate or upper-level undergraduate course in the physics of phase transitions. (Nasir N. Ganikhodjaev, Zentralblatt MATH, Vol. 1252, 2012)

1 Introduction
1(6)
1.1 What Is This Book About?
1(1)
1.2 Who Is This Book For?
2(1)
1.3 Historical Note
2(2)
1.4 Nomenclature
4(1)
References
5(2)
2 Landau Theory of Phase Transitions
7(30)
2.1 A Phase and Phase Transition
7(4)
2.2 Phase Transition as Symmetry Change: the Order Parameter
11(3)
2.3 Phase Transition as a Catastrophe: the Free Energy
14(5)
2.4 Ehrenfest Classification
19(3)
2.5 The Tangential Potential
22(5)
2.6 Phase Diagrams and Measurable Quantities
27(3)
2.6.1 First-Order Transitions
27(1)
2.6.2 Second-Order Transitions
28(2)
2.7 Effect of External Field on Phase Transition
30(5)
References
35(2)
3 Heterogeneous Equilibrium Systems
37(54)
3.1 Theory of Capillarity
37(5)
3.2 The Free Energy
42(4)
3.3 Equilibrium States
46(4)
3.4 One-Dimensional Equilibrium States
50(17)
3.4.1 Classification of the States
53(4)
3.4.2 Type-e1 Solutions: Bifurcation Off the Transition State
57(2)
3.4.3 Type-e3 Solutions: Approach to Thermodynamic Limit
59(1)
3.4.4 Type-e4 Solution: Plane Interface
59(4)
3.4.5 Interfacial Properties: Gibbs Adsorption Equation
63(2)
3.4.6 Type-n4 Solution: Critical Plate---Instanton
65(2)
3.5 Free Energy Landscape
67(3)
3.6 Multidimensional Equilibrium States
70(12)
3.6.1 Quasi One-Dimensional States: Drumhead (Sharp Interface) Approximation
70(3)
3.6.2 Critical Droplet: 3d Spherically Symmetric Instanton
73(6)
3.6.3 Small Deviations from Homogeneous Equilibrium States: Fourier. Method
79(3)
3.7 Thermodynamic Stability of States: Local Versus Global
82(6)
3.7.1 Type-e4 State: Plane Interface
84(1)
3.7.2 General Type-e and Type-n States
85(1)
3.7.3 3d Spherically Symmetric Instanton
86(2)
3.8 Gradients of Conjugate Fields
88(2)
References
90(1)
4 Dynamics of Homogeneous Systems
91(10)
4.1 Evolution Equation: The Linear Ansatz
91(3)
4.2 Solutions of the Linear-Ansatz Dynamic Equation
94(4)
4.2.1 Evolution of Small Disturbances
94(1)
4.2.2 Critical Slowing Down
95(1)
4.2.3 Nonlinear Evolution
96(1)
4.2.4 More Complicated Types of OPs
97(1)
4.3 Beyond the Linear Ansatz
98(1)
4.4 Relaxation with Memory
98(2)
4.5 Other Forces
100(1)
References
100(1)
5 Evolution of Heterogeneous Systems
101(20)
5.1 Time-Dependent Ginzburg-Landau Evolution Equation
101(1)
5.2 Motion of Plane Interfaces
102(5)
5.3 Dynamic Stability of Equilibrium States
107(5)
5.3.1 Homogeneous Equilibrium States
108(2)
5.3.2 Heterogeneous Equilibrium States
110(1)
5.3.3 Morphological Stability of Moving Plane Interface
111(1)
5.4 Motion of Curved Interfaces: Drumhead (Sharp Interface) Approximation
112(4)
5.4.1 Nonequilibrium Interface Energy
114(1)
5.4.2 Evolution of a Spherical Droplet
115(1)
5.5 Domain Growth Dynamics
116(3)
References
119(2)
6 Thermomechanical Analogy
121(6)
References
126(1)
7 Thermodynamic Fluctuations
127(24)
7.1 Classical Nucleation Theory
128(2)
7.2 Free Energy of Equilibrium System with Fluctuations
130(5)
7.3 Levanyuk-Ginzburg Criterion
135(1)
7.4 Dynamics of Fluctuating Systems: Langevin Force
136(5)
7.5 Evolution of the Structure Factor
141(3)
7.6 Drumhead Approximation of the Evolution Equation
144(6)
7.6.1 Evolution of the Interfacial Structure Factor
145(2)
7.6.2 Nucleation in the Drumhead Approximation
147(3)
References
150(1)
8 More Complicated Systems
151(50)
8.1 Conservative Order Parameter: Theory of Spinodal Decomposition
151(17)
8.1.1 Thermodynamic Equilibrium in a Binary System
151(6)
8.1.2 Equilibrium in Inhomogeneous Systems
157(2)
8.1.3 Dynamics of Decomposition in Binary Systems
159(3)
8.1.4 Evolution of Small Disturbances
162(3)
8.1.5 Role of Fluctuations
165(3)
8.2 Complex Order Parameter: Ginzburg-Landau's Theory of Superconductivity
168(10)
8.2.1 Order Parameter and Free Energy
168(3)
8.2.2 Equilibrium Equations
171(4)
8.2.3 Surface Tension of the Superconducting/Normal Phase Interface
175(3)
8.3 Multicomponent Order Parameter: Crystallographic Phase Transitions
178(10)
8.3.1 Invariance to Symmetry Group
178(1)
8.3.2 Inhomogeneous Variations
179(2)
8.3.3 Equilibrium States
181(7)
8.4 Memory Effects: Non-Markovian Systems
188(6)
8.5 "Mechanical" Order Parameter
194(5)
References
199(2)
9 Thermal Effects of Phase Transformations
201(44)
9.1 Equilibrium States of a Closed (Adiabatic) System
202(13)
9.1.1 Type-E1 States
202(8)
9.1.2 Type-E2 States
210(5)
9.2 Generalized Heat Equation
215(5)
9.3 Emergence of a New Phase
220(5)
9.4 Motion of Interfaces: Non-isothermal Drumhead (Sharp Interface) Approximation
225(14)
9.4.1 Generalized Stefan Heat-Balance Equation
227(3)
9.4.2 Generalized Kinetic Equation
230(2)
9.4.3 Gibbs-Duhem Force
232(2)
9.4.4 Interphase Boundary Motion: Heat Trapping
234(2)
9.4.5 APB Motion: Thermal Drag
236(3)
9.5 Length and Energy Scales
239(1)
9.6 Pattern Formation
240(4)
9.6.1 One-Dimensional Transformation
241(1)
9.6.2 Two-Dimensional Transformation
242(2)
References
244(1)
10 Transformations in Real Materials
245(4)
10.1 Parameters of FTM
245(2)
10.2 Boundaries of Applicability of the Method
247(2)
11 Extensions of the Method
249(12)
11.1 Cellular Automata Method: "Poor Man's Phase Field"
249(5)
11.2 Continuum Models of Grain Growth
254(5)
11.2.1 Multiphase Field Models
255(2)
11.2.2 Orientational Order Parameter Field Models
257(1)
11.2.3 Phase-Field Crystal
258(1)
11.3 Epilogue: Challenges and Future Prospects
259(1)
References
260(1)
Appendix A Coarse-Graining Procedure 261(6)
Appendix B Calculus of Variations and Functional Derivative 267(6)
Appendix C Orthogonal Curvilinear Coordinates 273(6)
Appendix D Lagrangian Field Theory 279(6)
Appendix E Eigenfunctions and Eigenvalues of the Schrodinger Equation and Sturm's Comparison Theorem 285(6)
Appendix F Fourier and Legendre Transforms 291(6)
Appendix G Stochastic Processes 297(18)
Appendix H Two-phase Equilibrium in a Closed Binary System 315(4)
Appendix I The Stefan Problem 319(6)
Appendix J On the Theory of Adsorption of Sound in Liquids 325(16)
Index 341