Thermodynamics of Crystalline States (eBook)

Thermodynamics of Crystalline States 3
Preface 5
Contents 7
Chapter 1: Introduction 11
1.1 Crystalline Phases 11
1.2 Structural Changes 14
1.3 Modulated Phases 16
1.4 Superconducting States in Metals 18
Exercises 1 18
Part I: Phonons and Order Variables 19
Chapter 2: Phonons 20
2.1 Normal Modes in a Simple Crystal 20
2.2 Quantized Normal Modes 23
2.3 Phonon Momentum 25
2.4 Thermal Equilibrium 27
2.5 Specific Heat 28
2.6 Approximate Models 30
2.6.1 Einstein´s Model 30
2.6.2 Debye´s Model 31
2.7 Phonon Statistics 1 32
2.8 Compressibility of a Crystal 34
Exercises 2 37
Chapter 3: Order Variables and Adiabatic Potentials 38
3.1 One-Dimensional Ionic Chains 38
3.2 Order Variables 41
3.2.1 Perovskite Crystals 42
3.2.2 Tris-Sarcosine Calcium Chloride 43
3.2.3 Potassium Dihydrogen Phosphate 44
3.3 Born-Oppenheimer´s Approximation 44
3.4 Lattice Periodicity and the Bloch Theorem 49
3.4.1 The Reciprocal Lattice 49
3.4.2 The Bloch Theorem 51
3.4.3 Lattice Symmetry 53
3.4.4 The Brillouin Zone 54
3.5 Phonon Scatterings 56
Exercises 3 57
Chapter 4: Statistical Theories of Binary Ordering 58
4.1 Probabilities in Binary Alloys 58
4.2 The Bragg-Williams Theory 60
4.3 Becker´s Interpretation 63
4.4 Ferromagnetic Order 65
4.5 Ferromagnetic Transitions in Applied Magnetic Fields 67
Exercises 4 69
Part II: Structural Phase Changes 70
Chapter 5: Pseudospin Clusters and Short-Range Correlations 71
5.1 Pseudospins for Binary Displacements 71
5.2 A Tunneling Model 74
5.3 Pseudospin Correlations 75
5.4 Condensates 76
5.5 Examples of Pseudospin Clusters 81
5.5.1 Cubic-to-Tetragonal Transition in SrTiO3 81
5.5.2 Monoclinic Crystals of Tris-Sarcosine Calcium Chloride 83
Exercises 5 85
Chapter 6: Critical Fluctuations 86
6.1 The Landau Theory of Binary Transitions 86
6.2 Adiabatic Fluctuations 90
6.3 Critical Anomalies 91
6.4 Observing Anomalies 93
6.5 Extrinsic Pinning 94
6.5.1 Pinning by Point Defects 95
6.5.2 Pinning by an Electric Field 95
6.5.3 Surface Pinning 96
Exercises 6 96
Chapter 7: Pseudospin Correlations 97
7.1 Propagation of a Collective Pseudospin Mode 97
7.2 Transverse Components and the Cnoidal Potential 101
7.3 The Lifshitz' Condition for Incommensurability 
102 
7.4 Pseudopotentials 105
Exercises 7 108
Chapter 8: The Soliton Theory 109
8.1 A Longitudinal Dispersive Mode of Collective Pseudospins 109
8.2 The Korteweg-deVries Equation 112
8.3 Solutions of the Korteweg-deVries Equation 115
8.4 Cnoidal Theorem and the Eckart Potential 118
8.5 Condensate Pinning by the Eckart Potentials 120
8.6 Remarks on the Soliton Potential 124
Exercises 8 124
Chapter 9: Soft Modes 128
9.1 The Lyddane-Sachs-Teller Relation 128
9.2 Soft Lattice Modes in Condensates 131
9.2.1 The Lattice Response to Collective Pseudospins 132
9.2.2 Temperature Dependence 136
9.2.3 Cochran´s Model 139
9.3 Central Peaks 140
9.4 A Change in Lattice Symmetry 142
Exercises 9 144
Chapter 10: Experimental Studies of Mesoscopic States 145
10.1 Diffuse X-Ray Diffraction 145
10.2 Neutron Inelastic Scatterings 150
10.3 Light Scattering Experiments 153
10.3.1 Brillouin Scatterings 154
10.3.2 Raman Scatterings 159
10.4 Magnetic Resonance 161
10.4.1 Principles of Magnetic Resonance and Relaxation 161
10.4.2 The Spin Hamiltonian 166
10.4.3 Hyperfine Interactions 168
10.4.4 Magnetic Resonance in Modulated Crystals 169
10.4.5 Examples of Transition Anomalies 172
10.4.5.1 Mn2+ Spectra in TSCC 172
10.4.5.2 Mn2+ Spectra in BCCD 173
10.4.5.3 VO2+ Spectra in BCCD 175
Part III: Superconducting States in Metals 176
Chapter 11: Electrons in Metals 177
11.1 Phonon Statistics 2 177
11.2 Conduction Electrons in Metals 180
11.2.1 The Pauli Principle 180
11.2.2 The Coulomb Interaction 182
11.2.3 The Lattice Potential 183
11.3 Many-Electron System 185
11.4 Fermi-Dirac Statistics for Conduction Electrons 188
Exercises 11 188
Chapter 12: Superconducting Phases 190
12.1 Superconducting States 190
12.1.1 Zero Electrical Resistance 190
12.1.2 The Meissner Effect 192
12.1.3 Normal and Superconducting Phases in Equilibrium 193
12.2 Long-Range Order in Superconducting States 195
12.3 Electromagnetic Properties of Superconductors 198
12.4 The Ginzburg-Landau Equation and the Coherence Length 204
Exercises 12 208
Chapter 13: Theories of Superconducting Transitions 210
13.1 The Fröhlich Condensate 210
13.2 The Cooper Pair 213
13.3 Critical Anomalies and the Superconducting Ground State 216
13.3.1 Critical Anomalies and Energy Gap in a Superconducting State 216
13.3.2 Order Variables in Superconducting States 218
13.3.3 BCS Ground States 223
13.3.4 Superconducting States at Finite Temperatures 227
Exercises 13 229
Appendix 230
References 232
Index 234