Treats phase transition theory and the analysis of phase transitions in terms of both Landau theory and fluctution theory，with particular attention given to crystals and quasicrystals.Also included is an overview of color symmetry applications in phase transition theory.A separate chapter is devoted to maertnsite transitions and this includes an analysis of soliton solutions of nonlinear equsations of elasticity.Revised and expanded translation from the Rusiian edition of 1984.
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目录
Preface Preface to the English Edition Notation Chapter 1.Introduction to Phenomenological Phase Transition Theory 1.Fundamentals of Landau's Thermodyhamic Theory Elementary thermodyhamic analysis Spontaneous symmetry breaking at a continuous phase transition The Landau condition for a second-order phase transition Further development of Landau's theory 2.Prerequisites Oil Space-group Representations Space-group irreducible representations Irreducible representations and their decomposition Refefences Chapter 2.Physical Realization of the order Parameters at a Microscopic Level of Description 3.Tensor Represeiltation of the Space Group oil a Basis of Localized Atomic Functions Constructing crystal space group reducible representations The stabilizer method Constructing basis functions for star arms 4.Permutational Representation and its Basis A summary of formulas The OP for ordering in AB type alloys The OP for ordering in Nb-H and Ta-H hydrides 5. Vector Representation and its Basis A summary of formulas The OP at a structural phase transition in A-15 compounds The OP at a structural phase transition in C-15 compounds 6. Pseudovector Representation and its Basis A description of the magnetically ordered state The OP at a magnetic phase transition in a garnet References Chapter 3. Symmetry Change at Phase Transitions 7. Change in Translational Symmetry The Brillouin zone and the symmetric points in it Arm mixing and the transition channel Magnetic lattices 8. The Total Symmetry Change Principles for finding the symmetry group of a new phase An example of a group-theoretic method of searching for dissymmetric phases 9. Domains Domains as a consequence of the Curie principle A symme-try classification of domains Arm, orientational and antiphase domains Examples of an analysis of the domain structure 10. The Paraphase The initial phase and the paraphase Major criteria for path-phase search An example of choosing the paraphase References Chapter 4. Analysis of the Thermodynamic Potential 11. Invariant Expressions of the Thermodynamic Potential A straightforward (direct) method of constructing polynomial invari-ants Constructing the φ for the structural phase transition in C-15 compounds Constructing the φ for the structural phase transition in A-15 compounds 12. Integral Rational Basis of Invariants General remarks The IRBI construction algorithm Solv-ability of the group and the minimal IRBI 13. Examples of the Construction of an IRBI Constructing the IRBI for the structural transition in C-15 com-pounds Construction of the IRBI for the structural transition in A-15 compounds Constructing the IRBI for the structural transition in MnAs 14. Irreducible Representation Images and Thermodynamic Potential Types General information on the I groups Two- and three-compon-ent order parameters A multicomponent order parameter I groups and rotation groups in multidimensional space Uni-versal classes References Chapter 5. Phase Diagrams in the Space of Thermodynamic Potential Parameters 15. Theoretical Fundamentals of the Phase Diagram Construction Method Major physical principles Requisite theorems from the algebra of polynomials 16. The One-Component Order Parameter The form of the thermodynamic potential The л6 model The л8 model Succession of solutions to equations of state 17. The Two-Component Order Parameter The л4 model The л6 model Cubic invariants in the л4 model Cubic invariants in the л6 model 18. The Three-Component Order Parameter The phases and the stability conditions The phase diagram in the л4 model 19. The Role of the IRBI in the Construction of Phase Diagrams The two-component order parameter The three-component order parameter 20. Coupling Order Parameters The interplay of two one-component order parameters Phase transitions in MnAs Phase transitions in KMnF3 Ori-entation transitions References Chapter 6. Macroscopic Order Parameters 21. Transformation Properties of the Order Parameters Physical realization of the macroparameters Construction of basis functions Constructing the thermodynamic potential 22. Interplay of Micro- and Macroparameters Constructing the thermodynamic potential Improper transi-tions Examples of structural transitions in perovskite-type crystals 23. Ferroics Classification of dissymmetric phases according to macroproperties Ferroelectrics Ferroelastics Ferrobielectrics and ferrobimagnetics Higher-order ferroics 24. Non-ferroics Crystal-class-preserving phase transitions Examples of non-ferroics References Chapter 7. Phase Transitions in an External Field 25. Phase Diagrams Constructing a potential for a system in an external field Phase diagram for the л4 model Phase diagram for the л6 model Singular points on the phase diagram Multi-component order parameter Splitting of a phase transition described by a microparameter in an external field 26. Features Peculiar to the Temperature Behavior of Susceptibility in the Vicinity of the Second-Order Phase Transition Classification of the singularities by the Aizu indices Catas-trophe indices 27. Calculation of Susceptibilities for Second-Order Phase Transitions Proper phase transitions Improper phase transitions Pseudoproper phase transitions 28. Singularities of the Susceptibility in the Vicinity of the First-Order Phase Transition Classification of the first-order transitions Classifying the sin-gularities of susceptibilities Calculating the susceptibilities 29. Domains in an External Field A thermodynamic description of the domains Effect of an external field on domains References Chapter 8. Martensite Transformations 30. Reconstructive Structural Transitions Transitions without group-subgroup relation Geometric rela-tion of direct lattices The b.c.c.-f.c.c, transition The b.c.c.-h.c.p, transition The f.c.c.-h.c.p, transition Ori-entation relations Interrelationship of reciprocal lattices 31. Thermodynamic Analysis of the Homogeneous State Describing the martensitic transition in terms of deformation Thermodynamic potential and phase diagram Behavior in an external field Shape memory effect 32. Inhomogeneous States in the Vicinity of the Phase Transition Thermodynamic potential with gradient terms Equations of motion Tetragonal-strain phase transition Phase tran-sition with shear strain Square lattice 33. The Omega Phase Interrelationship between the lattices at the b.c.c.-w-phase trans-formation Thermodynamic potential Inhomogeneous states References Chapter 9. Incommensurate Periodicity Phases 34. General Approach to the Problem Commensurate and incommensurate phases Expansion of a thermodynamic potential with continuous order parameters 35. Phases without Linear Gradient Terms in Free Energy One-component order parameter Two-component order pa-rameter Three-component order parameter Lifschitz point 36. Phases with Linear Gradient Terms The soliton lattice Soliton lattice stability The devil's staircase Stochastic regime 37. Multi-k-structures Conditions for many-arm structures to be thermodynamically favor-able Multi-k-structure in CeAl2 Multi-k-structure in Nd 38. Incommensurate Phases in External Fields Helical structure in an external field Effect of external fields on the wave-vector of incommensurate phases 39. The Thermodynamics of Phase Transitions to Incommensurate Phases Constructing a thermodynamic potential for non-Lifschitz stars Phase transition from incommensurate to commensurate phase Concomitant order parameters and incommensurate-phase symmetry Peculiarities of susceptibilities in incommensurate phases References Chapter 10. Color Symmetry and its Role in Phase Transition Theory 40. Color Symmetry in the Theory of Magnetic Structures Magnetic structures and their symmetries. Geometric aspect Color symmetry and the thermodynamic-potential model The hierarchy of approximations for describing the magnetic structure of FeGe2 41. Supersymmetry of Incommensurate Structures Incommensurate structures and the paradox of the Cheshire cat Phase symmetry of the thermodynamic potential and the sym-metry of incommensurate structures 42. Icosahedral Symmetry of Crystals. Quasicrystals A new type of atomic ordering The geometric aspect The thermodynamic aspect The symmetry of quasicrystal structures Al86Mn14: A Fibonacci structure or a quasicrys-tal ? Conclusion 43. Color Groups in the Theory of Systems with a Quantum Mechanical Order Parameter The quantum mechanical order parameter Classification of ordered phases on the basis of color sub-groups of the normal-phase symmetry group OP symmetry and the behavior in k space Thermodynamic potentials References Chapter 11. Fluctuations and Symmetry 44. Fundamentals of the Fluctuation Phase Transitions Theory Critical indices The renormalization-group and e-expansion method The isotropic model 45. Critical Behavior of Anisotropic Systems Universal classes Cubic anisotropy Examples of systems with multicomponent order parameters 46. Fluctuation-Induced Break-Down to First-Order Phase Transitions The absence of stable fixed points First-order transitions in magnetic systems 47. Fluctuations in the Vicinity of Multicritical Points Systems with coupled order parameters. Bicritical and tetracritical points Lifschitz point References Appendix Index
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