相变和晶体对称性：影印版PDF电子书下载

Chapter 1．Introduction to Phenomenological Phase Transition Theory 1

1．Fundamentals of Landau's Thermodynamic Theory 1

Elementary thermodynamic analysis 1

Spontaneous symmetry breaking at a continuous phase transition 7

The Landau condi-tion for a second-order phase transition 9

Further development of Landau's theory 10

2．Prerequisites on Space-group Representations 12

Space-group irreducible representations 12

Irreducible representa-tions and their decomposition 15

References 17

Chapter 2．Physical Realization of the Order Parameters at a Micro-scopic Level of Description 19

3．Tensor Representation of the Space Group on a Basis of Localized Atomic Functions 19

Constructing crystal space group reducible representations 20

The stabilizer method 24

Constructing basis functions for star arms 27

4．Permutational Representation and its Basis 28

A summary of formulas 28

The OP for ordering in AB type alloys 29

The OP for ordering in Nb-H and Ta-H hydrides 30

5．Vector Representation and its Basis 36

A summary of formulas 36

The OP at a structural phase transition in A-15 compounds 38

The OP at a structural phase transition in C-15 compounds 43

6．Pseudovector Representation and its Basis 45

A description of the magnetically ordered state 45

The OP at a magnetic phase transition in a garnet 47

References 51

Chapter 3．Symmetry Change at Phase Transitions 52

7．Change in Translational Symmetry 52

The Brillouin zone and the symmetric points in it 52

Arm mixing and the transition channel 56

Magnetic lattices 72

8．The Total Symmetry Change 74

Principles for finding the symmetry group of a new phase 74

An example of a group-theoretic method of searching for dissymmetric phases 77

9．Domains 82

Domains as a consequence of the Curie principle 82

A symme-try classification of domains 83

Arm,orientational and antiphase domains 85

Examples of an analysis of the domain structure 87

10．The Paraphase 91

The initial phase and the paraphase 91

Major criteria for para-phase search 93

An example of choosing the paraphase 94

References 98

Chapter 4．Analysis of the Thermodynamic Potential 100

11．Invariant Expressions of the Thermodynamic Potential 100

A straightforward(direct)method of constructing polynomial invari-ants 100

Constructing the Ф for the structural phase transition in C-15 compounds 101

Constructing the Ф for the structural phase transition in A-15 compounds 102

12．Integral Rational Basis of Invariants 104

General remarks 104

The IRBI construction algorithm 105

Solv-ability of the group and the minimal IRBI 110

13．Examples of the Construction of an IRBI 112

Constructing the IRBI for the structural transition in C-15 com-pounds 112

Construction of the IRBI for the structural transition in A-15 compounds 114

Constructing the IRBI for the structural transition in MnAs 117

14．Irreducible Representation Images and Thermodynamic Potential Types 118

General information on the I groups 118

Two-and three-compon-ent order parameters 119

A multicomponent order parameter 121

I groups and rotation groups in multidimensional space 121

Uni-versal classes 123

References 130

Chapter 5．Phase Diagrams in the Space of Thermodynamic Potential Parameters 131

15．Theoretical Fundamentals of the Phase Diagram Construction Method 131

Major physical principles 131

Requisite theorems from the algebra of polynomials 134

16．The One-Component Order Parameter 137

The form of the thermodynamic potential 137

The η6 model 137

The η8 model 139

Succession of solutions to equations of state 146

17．The Two-Component Order Parameter 148

The η4 model 148

The η6 model 152

Cubic invariants in the η4 model 156

Cubic invariants in the η6 model 159

18．The Three-Component Order Parameter 161

The phases and the stability conditions 161

The phase diagram in the η4 model 164

19．The Role of the IRBI in the Construction of Phase Diagrams 165

The two-component order parameter 166

The three-component order parameter 167

20．Coupling Order Parameters 168

The interplay of two one-component order parameters 168

Phase transitions in MnAs 170

Phase transitions in KMnF3 173

Ori-entation transitions 178

References 186

Chapter 6．Macroscopic Order Parameters 188

21．Transformation Properties of the Order Parameters 188

Physical realization of the macroparameters 188

Construction of basis functions 191

Constructing the thermodynamic potential 192

22．Interplay of Micro-and Macroparameters 197

Constructing the thermodynamic potential 197

Improper transi-tions 198

Examples of structural transitions in perovskite-type crystals 199

23．Ferroics 202

Classification of dissymmetric phases according to macroproperties 202

Ferroelectrics 204

Ferroelastics 205

Ferrobielectrics and ferrobimagnetics 205

Higher-order ferroics 206

24．Non-ferroics 211

Crystal-class-preserving phase transitions 211

Examples of non-ferroics 212

References 214

Chapter 7．Phase Transitions in an External Field 215

25．Phase Diagrams 215

Constructing a potential for a system in an external field 215

Phase diagram for the η4 model 216

Phase diagram for the η6 model 217

Singular points on the phase diagram 222

Multi-component order parameter 222

Splitting of a phase transition described by a microparameter in an external field 226

26．Features Peculiar to the Temperature Behavior of Susceptibility in the Vicinity of the Second-Order Phase Transition 227

Classification of the singularities by the Aizu indices 227

Catas-trophe indices 231

27．Calculation of Susceptibilities for Second-Order Phase Transitions 233

Proper phase transitions 233

Improper phase transitions 234

Pseudoproper phase transitions 238

28．Singularities of the Susceptibility in the Vicinity of the First-Order Phase Transition 239

Classification of the first-order transitions 239

Classifying the sin-gularities of susceptibilities 240

Calculating the susceptibilities 243

29．Domains in an External Field 244

A thermodynamic description of the domains 244

Effect of an external field on domains 247

References 249

Chapter 8．Martensite Transformations 250

30．Reconstructive Structural Transitions 250

Transitions without group-subgroup relation 250

Geometric rela-tion of direct lattices 253

The b.c.c.-f.c.c.transition 255

The b.c.c.-h.c.p.transition 256

The f.c.c.-h.c.p.transition 257

Ori-entation relations 258

Interrelationship of reciprocal lattices 261

31．Thermodynamic Analysis of the Homogeneous State 266

Describing the martensitic transition in terms of deformation 266

Thermodynamic potential and phase diagram 268

Behavior in an external field 270

Shape memory effect 274

32．Inhomogeneous States in the Vicinity of the Phase Transition 275

Thermodynamic potential with gradient terms 275

Equations of motion 277

Tetragonal-strain phase transition 278

Phase tran-sition with shear strain 282

Square lattice 288

33．The Omega Phase 292

Interrelationship between the lattices at the b.c.c.-w-phase trans-formation 292

Thermodynamic potential 295

Inhomogeneous states 296

References 298

Chapter 9．Incommensurate Periodicity Phases 301

34．General Approach to the Problem 301

Commensurate and incommensurate phases 301

Expansion of a thermodynamic potential with continuous order parameters 303

35．Phases without Linear Gradient Terms in Free Energy 304

One-component order parameter 304

Two-component order pa-rameter 309

Three-component order parameter 311

Lifschitz point 316

36．Phases with Linear Gradient Terms 318

The soliton lattice 318

Soliton lattice stability 323

The devil's staircase 328

Stochastic regime 331

37．Multi-κ-structures 332

Conditions for many-arm structures to be thermodynamically favor-able 332

Multi-κ-structure in CeAl2 334

Multi-κ-structure in Nd 336

38．Incommensurate Phases in External Fields 340

Helical structure in an external field 340

Effect of external fields on the wave-vector of incommensurate phases 343

39．The Thermodynamics of Phase Transitions to Incommensurate Phases 347

Constructing a thermodynamic potential for non-Lifschitz stars 347

Phase transition from incommensurate to commensurate phase 350

Concomitant order parameters and incommensurate-phase symmetry 351

Peculiarities of susceptibilities in incommensurate phases 353

References 355

Chapter 10．Color Symmetry and its Role in Phase Transition Theory 358

40．Color Symmetry in the Theory of Magnetic Structures 358

Magnetic structures and their symmetries.Geometric aspect 358

Color symmetry and the thermodynamic-potential model 360

The hierarchy of approximations for describing the magnetic structure of FeGe2 362

41．Supersymmetry of Incommensurate Structures 365

Incommensurate structures and the paradox of the Cheshire cat 365

Phase symmetry of the thermodynamic potential and the sym-metry of incommensurate structures 367

42．Icosahedral Symmetry of CrystalsQuasicrystals 372

A new type of atomic ordering 372

The geometric aspect 374

The thermodynamic aspect 379

The symmetry of quasicrystal structures 385

Al86Mn14:A Fibonacci structure or a quasicrys-tal? 387

Conclusion 388

43．Color Groups in the Theory of Systems with a Quantum Mechanical Order Parameter 390

The quantum mechanical order parameter 390

Classification of ordered phases on the basis of color sub-groups of the normal-phase symmetry group 391

OP symmetry and the behavior of the gap in κ space 394

Thermodynamic potentials 399

References 401

Chapter 11．Fluctuations and Symmetry 404

44．Fundamentals of the Fluctuation Phase Transitions Theory 404

Critical indices 404

The renormalization-group and ε-expansion method 406

The isotropic model 413

45．Critical Behavior of Anisotropic Systems 415

Universal classes 415

Cubic anisotropy 417

Examples of systems with multicomponent order parameters 419

46．Fluctuation-Induced Break-Down to First-Order Phase Transitions 423

The absence of stable fixed points 423

First-order transitions in magnetic systems 424

47．Fluctuations in the Vicinity of Multicritical Points 426

Systems with coupled order parameters.Bicritical and tetracritical points 426

Lifschitz point 434

References 437

Appendix 439

Index 441