Introduction to the Physics of the Earths Interior

Table of Contents......Page 6
Preface to the first edition......Page 10
Preface to the second edition......Page 13
Introduction to the first edition......Page 15
1.1 Extensive and intensive conjugate quantities......Page 18
1.2 Thermodynamic potentials......Page 20
1.3 Maxwell’s relations. Stiffnesses and compliances......Page 22
2.1 Background of linear elasticity......Page 25
2.2 Elastic constants and moduli......Page 27
2.3.2 Isothermal and adiabatic moduli......Page 34
2.3.3 Thermal pressure......Page 39
3.2.1 Dispersion curve of an infinite lattice......Page 41
3.2.2 Density of states of a finite lattice......Page 47
3.3.1 Debye’s frequency......Page 50
3.3.2 Vibrational energy and Debye temperature......Page 52
3.3.3 Specific heat......Page 53
3.3.4 Validity of Debye’s approximation......Page 55
3.4 Mie–Grüneisen equation of state......Page 58
3.5 The Grüneisen parameters......Page 60
3.6.1 Generalities......Page 71
3.6.2 Thermal expansion......Page 72
4.1 Generalities......Page 77
4.2 Murnaghan’s integrated linear equation of state......Page 78
4.3.1 Finite strain......Page 80
4.3.2 Second-order Birch—Murnaghan equation of state......Page 84
4.3.3 Third-order Birch—Murnaghan equation of state......Page 86
4.4.1 The Hencky finite strain......Page 88
4.4.2 The logarithmic EOS......Page 90
4.5.1 EOS derived from the Mie potential......Page 91
4.5.2 The Vinet equation of state......Page 92
4.6.1 Generalities......Page 93
4.6.2 Bulk-velocity—density systematics......Page 96
4.7 Thermal equations of state......Page 104
4.8.1 Generalities......Page 108
4.8.2 The Rankine—Hugoniot equations......Page 110
4.8.3 Reduction of the Hugoniot data to isothermal equation of state......Page 114
4.9.1 Thomas—Fermi equation of state......Page 116
4.9.2 Ab-initio quantum mechanical equations of state......Page 121
5.1 Generalities......Page 124
5.2.2 Volume and entropy of melting......Page 129
5.2.3 Metastable melting......Page 132
5.3.1 Simon equation......Page 134
5.3.2 Kraut—Kennedy equation......Page 135
5.4.1 Shear instability models......Page 137
5.4.2 Vibrational instability: Lindemann law......Page 139
5.4.3 Lennard-Jones and Devonshire model......Page 146
5.4.4 Dislocation-mediated melting......Page 153
5.4.5 Summary......Page 157
5.5 Melting of lower-mantle minerals......Page 158
5.5.2 Melting of MgO and magnesiowüstite......Page 159
5.6 Phase diagram and melting of iron......Page 160
6.1 Generalities......Page 170
6.2 Mechanisms of diffusion in solids......Page 176
6.3 Viscosity of solids......Page 188
6.4 Diffusion and viscosity in liquid metals......Page 198
6.5.1 Generalities on the electronic structure of solids......Page 203
6.5.2 Mechanisms of electrical conduction......Page 208
6.5.3 Electrical conductivity of mantle minerals......Page 217
6.5.4 Electrical conductivity of the fluid core......Page 226
6.6 Thermal conduction......Page 227
7.1 Generalities......Page 235
7.2.1 Density distribution in the Earth......Page 237
7.2.2 The PREM model......Page 241
7.3.1 Sources of heat......Page 244
7.3.2 Heat transfer by convection......Page 245
7.3.3 Convection patterns in the mantle......Page 250
7.3.4 Geotherms......Page 255
7.4.1 Phase transitions of the mantle minerals......Page 258
7.4.2 Mantle and core models......Page 273
Appendix PREM model (1s) for the mantle and core......Page 286
Bibliography......Page 289
D......Page 323
L......Page 324
S......Page 325
W......Page 326