Thermodynamic Properties of Solids

Thermodynamic Properties of Solids: Experiment and Modeling......Page 1
Contents......Page 9
Preface......Page 17
List of Contributors......Page 19
Abbreviations......Page 21
1.1 Introduction......Page 23
1.2 Spectroscopic Techniques and Semiempirical Theoretical Methods......Page 24
1.4 First-Principles Quantum Mechanical Methods......Page 25
References......Page 26
2 Optical Spectroscopy Methods and High-Pressure–High-Temperature Studies......Page 29
2.1.1 Semiconductors......Page 31
2.1.2.1 Maxwell Equations......Page 32
2.1.2.2 Mechanical Equations......Page 33
2.1.2.3 Lorentz Approach......Page 34
2.1.2.4 Effective Charge/Force Constant......Page 35
2.1.2.5 Combined Electrical/Mechanical Equations: Dispersion of Polaritons Modes......Page 36
2.1.3.1 IR Spectroscopies: A Direct Light/Optical-Mode Interaction [4, 5, 11]......Page 37
2.1.3.2 Raman Scattering: An Indirect Light/Optical-Mode Interaction [13, 14]......Page 38
2.1.3.3 Brillouin Scattering: An Indirect Light/Acoustical-Mode Interaction......Page 41
2.1.4.1 Multioscillator System......Page 42
2.1.4.2 Multilayer System [12]......Page 43
2.1.4.3 Multicomponent System (Composite) [22]......Page 44
2.1.5.1 Raman Scattering......Page 45
2.1.5.3 Brillouin Scattering......Page 46
2.2.1 A Specific Impact/Identity in the Field......Page 47
2.2.1.1 Solid-State Physics......Page 48
2.2.1.2 Earth Sciences......Page 50
2.2.2.1 Temperature and Emissivity......Page 51
2.2.2.2 High-Pressure Optical Cells, Diamond–Anvil Cells......Page 53
2.2.2.3 High-Temperature Instrumentation......Page 56
2.2.2.4 Brillouin Devices......Page 59
2.2.2.5 Raman Devices......Page 60
2.2.2.6 Infrared Devices: Emissivity Measurements (Temperature and Pressure)......Page 64
2.2.3.1 General Presentation......Page 66
2.2.3.2 Examples......Page 69
2.2.4.1 Pressure Aspect......Page 77
2.2.4.2 Temperature Aspect......Page 80
2.3.1.1 Natural Development of Existing Setups......Page 85
2.3.1.2 Innovative Combinations of X-ray and Vibrational Spectroscopies......Page 86
2.3.2.1 Phonons (Zone-Center): A Natural .Mesoscope. into the Alloy Disorder......Page 87
2.3.2.2 Elucidation of the Mechanism of the Pressure-Induced Phase Transformations......Page 90
2.3.2.3 Glasses......Page 91
References......Page 92
3.1 Introduction......Page 97
3.2.1 Theoretical Formalisms......Page 99
3.3 Computational Techniques......Page 102
3.4 Thermodynamic Properties of Solids......Page 104
3.5 Theory of Inelastic Neutron Scattering......Page 106
3.5.1 Inelastic Neutron Scattering from Single Crystals: Phonon Dispersion Relations......Page 107
3.5.2 Inelastic Neutron Scattering from Powder Samples: Phonon Density of States......Page 108
3.6 Experimental Techniques for Inelastic Neutron Scattering......Page 110
3.6.1.1 Phonon Density of States......Page 111
3.6.2 Measurements Using Time-of-Flight Technique......Page 113
3.6.2.1 Phonon Density of States......Page 114
3.7 Molecular Dynamics Simulation......Page 115
3.8.1 Phonon Density of States......Page 117
3.8.2 Raman and Infrared Modes, and Phonon Dispersion Relation......Page 119
3.8.3 Elastic Constants, Gibbs Free Energies, and Phase Stability......Page 122
3.8.3.1 Zircon Structured Compound......Page 123
3.8.4 Negative Thermal Expansion from Inelastic Neutron Scattering and Lattice Dynamics......Page 124
3.8.4.1 Negative Thermal Expansion Calculation......Page 126
3.8.4.2 Thermal Expansion from Experimental High-Pressure Inelastic Neutron Scattering......Page 127
3.8.5 Thermodynamic Properties......Page 128
3.8.6 Phase Transitions in Magnesium Silicate, MgSiO3......Page 129
3.8.7 Fast Ion Diffusion in Li2O and U2O......Page 133
3.9 Conclusions......Page 136
References......Page 137
4.1 Introduction......Page 145
4.2.1 Scattering Kinematics and Dynamical Structure Factor......Page 147
4.2.2 IXS Cross Section......Page 149
4.3 Instrumental Principles......Page 152
4.4 IXS in the Low-Q Limit......Page 155
4.4.1 Scattering from (Quasi)Longitudinal Phonons......Page 156
4.4.2 Scattering from Quasitransverse Phonons......Page 158
4.4.3 The Aggregate Elasticity of Polycrystalline Materials......Page 160
4.4.4 Effects of Texture......Page 162
4.5 IXS in the High-Q Limit: The Phonon Density of States......Page 163
4.5.1 Magnesium Oxide......Page 165
4.5.2 Boron Nitride [78]......Page 167
4.5.3 Clathrate Ba8Si46 [90]......Page 170
4.6 IXS in the Intermediate Q-Range......Page 171
4.7 Concluding Remarks......Page 175
References......Page 177
5.1 Introduction......Page 181
5.2.1 Adiabatic Heat Capacity Calorimetry......Page 182
5.2.2 Adiabatic Scanning Calorimetry......Page 184
5.2.4 Laser-Flash Calorimetry......Page 187
5.2.5 Temperature Jump Calorimetry......Page 189
5.3 Thermodynamic Relation Between Cp and Cv......Page 190
5.4.1.1 Classical Theory of Lattice Heat Capacity......Page 192
5.4.1.2 Einstein.s Model of Lattice Heat Capacity......Page 193
5.4.1.3 Debye.s Model of Lattice Heat Capacity......Page 195
5.4.1.4 Anharmonic Term of Lattice Heat Capacity......Page 197
5.4.2.1 Electronic Heat Capacity (Ce,c)......Page 198
5.4.2.2 Schottky-type Heat Capacity (Ce,sh)......Page 199
5.4.2.3 Magnetic Heat Capacity (Cm)......Page 200
5.5.1.1 Heat Capacity Data at Low Temperatures......Page 201
5.5.1.2 Heat Capacity Data of Metal Oxides with Fluorite-Type Crystal Structure......Page 202
5.5.1.3 Heat Capacity Data of Negative Thermal Expansion Materials ZrW2O8......Page 203
5.5.2 Kopp–Neumann Law......Page 206
5.5.3 Estimation of Heat Capacity Data from Thermal Expansion Coefficient......Page 207
5.5.5 Volumetric Interpolation Schemes......Page 208
5.6.1.1 Order–Disorder Phase Transition due to Atomic Configuration......Page 210
5.6.1.2 Order–Disorder Phase Transition due to Orientation in ZrW2O8......Page 211
5.6.2 Magnetic Order–Disorder Phase Transition......Page 213
5.7.1.1 Adiabatic Heat Capacity Calorimetry......Page 214
5.7.3 Estimation of Normal Heat Capacity......Page 215
5.7.3.5 Metal Oxides with Fluorite-Type Crystal Structure at High Temperatures......Page 216
5.7.4.2 Order–Disorder Phase Transition due to Orientation in ZrW2O8......Page 217
References......Page 218
6.1 Introduction......Page 219
6.2 Strain Analysis......Page 221
6.3 Thermodynamics of Thermal Expansion......Page 223
6.4 Origin of Thermal Expansion......Page 225
6.5 Techniques for Measurement of Thermal Expansion......Page 227
6.5.1 Dilatometer......Page 228
6.5.2 Interferometer......Page 229
6.5.4 Diffraction Methods......Page 230
6.6 X-Ray Diffraction in Thermal Expansion......Page 231
6.7 Positive and Negative Thermal Expansions......Page 235
6.8.1 Melting Points......Page 237
6.8.2 Bond Strengths......Page 238
6.8.4 Defects and Impurities or Alloy Formation......Page 239
6.9 Structure and Thermal Expansion......Page 240
6.10.1 Fluorite-Type AO2 Compounds......Page 243
6.10.1.1 Isovalent Substituted AO2 Lattices......Page 244
6.10.1.2 Aliovalent Substituted AO2 Lattice......Page 250
6.10.2 Framework Materials......Page 254
6.10.2.1 Cristobalite-Type APO4 (A =Al3+, Ga3+, and B3+)......Page 255
6.10.2.2 Molybdates and Tungstates......Page 261
6.10.3.1 CaMoO4 and CaWO4......Page 272
6.10.3.2 LuPO4, LuVO4, and GdVO4 (Zircon Type)......Page 275
References......Page 281
7.2 First-Principles Theory......Page 291
7.2.1 Density-Functional Theory: Hohenberg–Kohn Theorems and Kohn–Sham Equation......Page 292
7.2.2 Exchange-Correlation Functional......Page 293
7.2.4 Linearized Muffin-Tin Orbitals Method......Page 294
7.2.5 Hellman–Feynman Theorem and Geometry Optimization......Page 295
7.3 Structural Phase Transition from First Principles......Page 296
7.4 Alkali Metals......Page 297
7.5 Alkaline Earth Metals......Page 299
7.6 Transition Metals......Page 302
7.7 Group III Elements......Page 304
7.8 Group IV Elements......Page 305
7.9 Group V Elements......Page 307
7.10 Overview......Page 308
References......Page 309
8.1 Introduction......Page 313
8.2 Phonons......Page 314
8.3 Density-Functional Perturbation Theory......Page 318
8.3.1 Perturbation Expansion......Page 319
8.3.3 Mixed Perturbations......Page 321
8.4 Infrared and Raman Spectra......Page 322
8.4.1 Infrared......Page 323
8.4.2 Raman......Page 325
8.5 Thermodynamical Properties......Page 328
8.6.1 Polymeric Nitrogen......Page 329
8.6.2 Ice X......Page 331
8.7 Conclusions......Page 334
References......Page 335
Index......Page 339