Mineral Physics: Treatise on Geophysics

Cover......Page 1
Editor-in-Chief......Page 2
Volume Editors......Page 3
Preface......Page 4
2.01 Overview - Mineral Physics: Past,  Present, and Future......Page 7
References......Page 11
Introduction......Page 13
Overview......Page 14
Upper Mantle......Page 16
Transition Zone......Page 18
Lower Mantle......Page 21
Core......Page 23
Temperature......Page 25
Composition......Page 26
Phase......Page 27
Upper Mantle......Page 28
DPrime Layer......Page 29
Influence of Temperature......Page 30
Speculations on the Influence of Pressure......Page 31
References......Page 32
Introduction......Page 39
High-Pressure Technology......Page 40
Ab Initio Calculation......Page 42
Pressure Scale......Page 43
MgSiO3......Page 44
MgSiO3-FeSiO3......Page 45
MgSiO3-Al2O3......Page 46
MgO-FeO......Page 47
CaSiO3......Page 48
SiO2......Page 49
MgAl2O4, NaAlSiO4......Page 50
Phase D,\r delta-AlOOH......Page 51
Chemical Compositions and Density Calculations......Page 52
Pyrolite......Page 54
Harzburgite......Page 55
The 660km Discontinuity......Page 56
Middle Parts of the Lower Mantle......Page 57
Postperovskite Transition and the DPrime Layer......Page 59
Summary......Page 61
References......Page 62
Introduction......Page 69
Concentrations in the Primitive Upper Mantle and Bulk Silicate Earth......Page 70
Differentiation of the Silicate Earth and Formation of Deep-Mantle Reservoirs......Page 71
Crystal-Melt Partition Coefficients and Controlling Factors......Page 72
Crystallochemical control......Page 73
Effects of pressure, temperature, and composition......Page 74
Effects of Al content on large trivalent and tetravalent cations......Page 75
Crystal chemistry......Page 76
Substitution mechanisms in calcium silicate perovskite......Page 77
Effects of melt composition......Page 78
Comparison between CaTiO3 and CaSiO3 perovskites......Page 79
Ferropericlase......Page 80
A Primitive Majoritic or Perovskitic Reservoir?......Page 81
Recycled Lithosphere in the Deep Mantle?......Page 83
Water Solubility in Minerals from the Transition Zone......Page 84
Water and sharpness of the 410km discontinuity......Page 85
Water Solubility in Lower-Mantle Minerals......Page 88
Calcium silicate perovskite......Page 89
Conclusions......Page 90
References......Page 91
Introduction......Page 96
Anisotropy and Layering in the Inner Core......Page 97
Super-Rotation of the Inner Core......Page 99
The Structure of Iron in the Inner Core......Page 100
Thermodynamic Properties from Free Energies......Page 103
Heat capacity......Page 104
Grüneisen parameter......Page 105
Elasticity of Solid Iron......Page 106
Slip Systems in Iron......Page 107
Viscosity and the Inner Core......Page 109
The Temperature in the Earth’s Core......Page 111
Viscosity and Diffusion......Page 113
Evolution of the Core......Page 115
Bulk Composition......Page 116
Chemical potential calculations of FeX binary systems......Page 117
High-temperature elasticity of FeSi and FeS......Page 119
Summary......Page 121
References......Page 122
2.06 Theory and Practice - Thermodynamics, Equations of State, Elasticity, and Phase Transitions of Minerals at High Pressures and Temperatures......Page 126
Differential Relations......Page 127
Partition Function......Page 128
Harmonic Approximation......Page 129
Debye model......Page 130
General harmonic potential......Page 131
Quantum Effects in Thermodynamics......Page 132
Thermodynamic Perturbation Theory......Page 133
Beyond the QHA......Page 134
Mie-Grüneisen EOS......Page 136
Analytical static EOS......Page 137
EOS, internal strain, and phase transitions......Page 139
Elastic Constants......Page 140
Cauchy relations......Page 143
Birch’s law and effects of temperature on the elastic constants......Page 144
Classifications of Phase Transitions......Page 145
Landau Theory of First- and Second-Order Transitions......Page 146
Shortcomings of Landau Theory......Page 147
Ginzburg-Landau Theory......Page 148
Ising Spin Model......Page 149
Isosymmetric Transitions......Page 150
Pressure-Induced Amorphization......Page 151
Polytypism of MgSiO3 Post-Perovskite and Anisotropy of the Earth’s DPrime layer......Page 152
Spin Transition in (Mg, Fe)O Magnesiowüstite......Page 153
References......Page 154
Deep Earth Mineralogy and Mineral Physics......Page 158
Experimental Vibrational Spectroscopy of Mantle Minerals......Page 160
Mineral Lattice Dynamics Calculations......Page 161
Molecular Vibrations......Page 162
Vibrational Dispersion Relations......Page 164
Quantized Vibrations in Molecules and Crystals (Phonons)......Page 166
Vibrational Frequency Shifts at High P and T; Quasi-Harmonic Model and Phonon Anharmonicity......Page 167
Mineral Thermodynamic Quantities from Vibrational Spectra......Page 170
Theoretical Calculations of Mantle Mineral Lattice Vibrations......Page 171
Diamond and (Mg,  Fe)O Magnesiowuumulstite......Page 173
(Mg,\rFe)SiO3 Perovskite, Post-Perovskite, and CaSiO3 Perovskite......Page 176
Stishovite and Post-Stishovite SiO2 Polymorphs......Page 182
(Mg,Fe)2SiO4 Olivine, beta- and gamma-(Mg,Fe)2SiO4, and (Mg,Fe)SiO3 Pyroxe\rnes......Page 185
MgSiO3 Ilmenite and Majoritic Garnets......Page 187
OH in Mantle Minerals......Page 189
References......Page 190
2.08 Theory and Practice - Multianvil Cells and High-Pressure Experimental Methods......Page 202
Glossary......Page 203
Precompression......Page 204
Massive support......Page 205
Conceptual Advantages of the MAAs over the Opposed-Type Apparatus......Page 206
Multianvil Apparatus......Page 207
Cubic anvil apparatus......Page 208
Octahedral anvil apparatus......Page 209
Combination of multianvil systems......Page 210
Anvil Materials......Page 211
Pressure Media and Gasket Materials......Page 213
Fixed Points for Pressure Calibration......Page 214
Heating Assemblies and Temperature Measurement......Page 215
Quench Experiment......Page 217
Crystal Growth at High Pressure and High Temperature......Page 218
Electrical Conductivity Measurement......Page 219
Multianvil System Interfaced with SR......Page 221
Experimental Procedures for In Situ X-Ray Diffraction Study......Page 223
Pressure standard materials and the pressure scales......Page 224
Comparison of the pressure scales......Page 225
Application to Phase Equilibrium Studies......Page 226
Viscosity Measurement by X-Ray Radiography......Page 228
Pressure Generation Using Sintered Diamond Anvil......Page 229
New Applications and Future Perspectives......Page 230
References......Page 232
Relevant Website......Page 235
Diamond-Anvil Cell as a Window to the Earth’s Interior......Page 236
Comprehensive High P-T Mineral Properties......Page 237
Anvils and Axial Windows......Page 239
Gasket and Side Window......Page 241
Samples and Pressure Media......Page 242
DAC Body......Page 243
Compression Mechanism......Page 244
Pressure Calibration......Page 245
Resistive Heating......Page 246
Laser Heating......Page 247
Cryogenic......Page 248
Temperature Measurement......Page 249
Optical Probes......Page 250
Optical Absorption......Page 251
Raman Spectroscopy......Page 252
Brillouin Spectroscopy and Impulsive Stimulated Light Scattering Spectroscopy......Page 253
Fluorescence Spectroscopy......Page 254
Axial XRD......Page 255
Radial XRD......Page 256
X-Ray Absorption Spectroscopy (XAS)......Page 258
X-Ray Emission Spectroscopy (XES)......Page 259
Inelastic X-Ray Scattering - Near-Edge Spectroscopy......Page 261
Nuclear Resonant X-Ray Spectroscopy......Page 262
Nonresonant Phonon Inelastic X-Ray Scattering......Page 264
References......Page 265
Introduction......Page 273
Static Compression......Page 274
Diamond Anvil Cell......Page 275
Ultrasonic Methods......Page 278
Ultrasonic Wave Transmission Techniques......Page 279
Ultrasonic echo methods......Page 280
High-Pressure Ultrasonics......Page 282
Vibrational Resonance......Page 284
Brillouin Scattering......Page 285
Impulsive Stimulated Scattering......Page 287
Nuclear Resonant Inelastic X-Ray Scattering (NRIXS)......Page 288
Inelastic X-Ray Scattering from Phonons......Page 289
Shock Waves......Page 290
Other Techniques......Page 291
References......Page 292
2.11 Theory and Practice - Measuring High-Pressure Electronic and Magnetic Properties......Page 296
Glossary......Page 297
Conventional bonding classification......Page 299
Bonding under high P-T conditions......Page 300
Electronic Structure......Page 301
Magnetic Properties......Page 302
Dielectric Functions......Page 303
KK analysis......Page 304
Crystal field transitions......Page 305
Overview of Experimental Techniques......Page 306
Optical absorption and reflectivity......Page 307
IR spectroscopy......Page 309
Raman scattering......Page 311
Brillouin and Rayleigh scattering......Page 312
Nonlinear optical methods......Page 313
Mössbauer Spectroscopy......Page 314
Neutron diffraction......Page 315
X-ray absorption spectroscopy......Page 316
X-ray emission spectroscopy......Page 317
X-ray inelastic near-edge spectroscopy......Page 318
X-ray magnetic circular dichroism......Page 319
Resonant inelastic X-ray spectroscopy......Page 320
Nuclear resonance forward scattering......Page 321
Phonon inelastic X-ray scattering......Page 322
Electrical conductivity......Page 323
Magnetic susceptibility......Page 324
Nuclear magnetic resonance......Page 325
de Haas-van Alphen......Page 326
Magnesiowüstite......Page 327
Silicate Perovskite and Post-Perovskite......Page 329
Volatiles......Page 330
Iron and Iron Alloys......Page 331
References......Page 332
Introduction......Page 341
Importance of High-Pressure Rheology Measurements......Page 342
Lateral variation of asthenosphere viscosity......Page 343
Stress Measurement......Page 344
New High-Pressure Deformation Devices......Page 347
The Instruments of Flow......Page 349
Dislocations, Slip Systems,\rand Texture......Page 350
Polycrystalline Materials......Page 352
Activation Volume of Olivine......Page 355
High-Pressure Phases......Page 356
References......Page 357
Introduction......Page 361
First-Principles Techniques......Page 363
Density Functional Theory......Page 364
PPs and basis sets......Page 365
Ultrasoft (Vanderbilt) PPs......Page 366
QMC methods......Page 367
Crystal structures and phase transitions......Page 369
Elastic constants......Page 370
Finite Temperature......Page 371
Molecular dynamics......Page 372
Thermodynamic Properties......Page 373
The Helmholtz free energy: Low-temperature and the quasi-harmonic approximation......Page 374
Calculation of phonon frequencies......Page 375
The Helmholtz free energy: High-temperature and thermodynamic integration......Page 377
Melting......Page 379
Solutions......Page 382
First-principles calculations of chemical potentials......Page 383
Solid-liquid equilibrium......Page 384
Shift of freezing point......Page 385
Conclusions......Page 386
References......Page 387
Introduction......Page 390
Thermodynamics......Page 391
Kinetics......Page 393
Line Defects - Structure and Dynamics......Page 395
Planar Defects - Structure and Energy......Page 397
Mechanisms of Deformation and Constitutive Equations......Page 399
Grain-boundary diffusion......Page 400
Dislocation creep......Page 401
Grain-boundary sliding and migration......Page 403
Low-temperature plasticity......Page 404
Role of melt in rock deformation......Page 406
Role of water in rock deformation......Page 408
Upper-Mantle Viscosity......Page 411
Western US Mantle Viscosity Profile......Page 412
Concluding Remarks......Page 413
References......Page 414
Role of Melts in Earth Differentiation......Page 419
Volcanic Ascent and Eruption......Page 420
Structural Relaxation......Page 421
Phenomenology of the Glass Transition......Page 422
Methods of Investigation......Page 423
Tracer Diffusivities: Self-Diffusivities and Chemical Diffusion......Page 424
Intrinsic versus Extrinsic Diffusivities......Page 425
Methods of Investigation......Page 426
Temperature Dependence of Newtonian Viscosity......Page 427
Compositional Dependence of Newtonian Viscosity......Page 428
Non-Newtonian Rheology in Silicate Melts......Page 430
Concluding Statements......Page 431
References......Page 434
Introduction......Page 437
Elasticity and Hooke’s Law......Page 443
Plane Waves and Christoffel’s Equation......Page 448
Measurement of Elastic Constants......Page 453
Effective Elastic Constants for Crystalline Aggregates......Page 456
Seismic Properties of Polycrystalline Aggregates at High Pressure and Temperature......Page 458
Upper mantle......Page 461
Transition zone......Page 463
Lower mantle......Page 465
Inner core......Page 468
Olivine the Most Studied Mineral: State of the Art - Temperature, Pressure, Water, Melt,\r ETC......Page 472
Seismic Anisotropy and Melt......Page 477
References......Page 482
nomenclature......Page 492
Phenomenological Description of Viscoelasticity......Page 495
Stress-induced rearrangement of point defects......Page 498
The vibrating-string model of dislocation damping......Page 499
The role of kinks in dislocation mobility: migration of geometrical kinks......Page 500
The role of kinks in dislocation mobility: formation and migration of kink pairs......Page 501
Role of water in nominally anhydrous minerals......Page 503
Effects of elastic and thermoelastic heterogeneity in polycrystals and composites......Page 504
Elastically accommodated grain-boundary sliding......Page 505
Diffusionally accommodated grain-boundary sliding......Page 506
Stress-induced variation of the proportions of coexisting phases......Page 507
Anelastic Relaxation Associated with Stress-Induced Fluid Flow......Page 508
Laboratory measurements on single crystals and coarse-grained rocks......Page 511
Grain-boundary migration in b.c.c. and f.c.c. Fe?......Page 512
Grain-boundary sliding......Page 513
Viscoelastic Relaxation in Cracked and Water-Saturated Crystalline Rocks......Page 515
Vibrating string model......Page 516
Kink model......Page 517
The Role of Water in Seismic Wave Dispersion and Attenuation......Page 518
Migration of Transformational Twin Boundaries as a Relaxation Mechanism in the Lower Mantle?......Page 519
Summary and Outlook......Page 520
References......Page 521
Melting of (Mg,\r Fe)SiO3-Perovskite......Page 525
Melting of MgO......Page 526
Partial Melting in the Lower Mantle......Page 528
f.c.c.-h.c.p. Transition......Page 529
Iron Melting below 100GPa......Page 530
Diamond-Cell Measurements of Iron and Transition Metals......Page 531
Local Structures of Icosahedral Short-Range Order in Transition Metal Melts......Page 533
Shock Melting......Page 534
Theoretical Calculations of the Iron Melting Curve......Page 535
Viscosity of Iron at Earth Core Conditions......Page 536
References......Page 537
2.19 Properties of Rocks and Minerals - Thermal Conductivity of the Earth......Page 540
nomenclature......Page 541
Types of Thermal Transport and Justification for Omitting Metals......Page 542
Scope of the Present Chapter......Page 543
Acoustic models of lattice heat transport......Page 544
The damped harmonic oscillator (DHO) - phonon gas model......Page 546
Distinguishing direct from diffusive radiative transport on the basis of frequency-dependent attenuation......Page 547
Spectroscopic models for diffusive radiative transport inside the Earth......Page 549
An approximate formula that connects krad with concentration......Page 551
Conventional Techniques Involving Multiple Physical Contacts......Page 552
Methods Using a Single Physical Contact......Page 553
Contact-Free, Laser-Flash Analys\ris......Page 554
Ambient conditions......Page 556
Elevated temperature......Page 561
Laser-Flash Data on Various Minerals......Page 563
Effect of chemical composition and hydration on room temperature values......Page 564
Comparison of the Room Temperature Lattice Contribution to Theoretical Models and Estimation of D and k for Some High-Pressure Phases......Page 565
Ambient conditions and compositional dependence......Page 566
Elevated temperature......Page 567
Lattice Thermal Conductivity and Its Temperature Dependence......Page 568
Calculation of the Effective Thermal Conductivity for Diffusive Radiative Transfer......Page 569
References......Page 570
2.20 Properties of Rocks and Minerals - Magnetic Properties of Rocks and Minerals......Page 575
Introduction......Page 576
Exchange Interactions and Magnetic Structure in Fe-Bearing Oxides......Page 577
Theory......Page 580
Application to magnetic nanoparticles......Page 582
Application to coupled magnetic and chemical ordering in solid solutions......Page 583
Amplitude and phase of a TEM image......Page 587
Calculation of the mean inner potential......Page 589
Formation of an electron hologram......Page 590
Processing of the electron hologram......Page 591
Removing the mean inner potential contribution......Page 592
Quantification of the magnetic induction......Page 593
Electron holography of isolated magnetite crystals......Page 594
Electron holography of chains of closely spaced magnetite crystals......Page 597
Electron holography of two-dimensional magnetite nanoparticle arrays......Page 599
Exchange interactions across antiphase boundaries in ilmenite-hematite......Page 602
Magnetism at the Micrometer Length Scale......Page 604
The micromagnetic energy......Page 605
Discretization of the micromagnetic energy......Page 606
Finite element discretization......Page 607
Equilibrium domain states in isolated magnetite particles......Page 608
Temperature dependence of domain states in isolated particles......Page 610
Field dependence of domain states......Page 612
Magnetostatic interactions between particles......Page 613
Magnetism at the Macroscopic Length Scale......Page 614
First-order reversal curves and the FORC distribution......Page 615
Extended FORCs and the reversible ridge......Page 616
SP particles......Page 617
SD particles......Page 618
Mean-Field Interactions and FORC Diagrams......Page 619
Practical Applications of FORC Diagrams......Page 620
Summary......Page 621
References......Page 622
nomenclature......Page 627
Point Defects and Conductivity......Page 628
Effects of Temperature and Pressure......Page 629
Point Defects in Olivine......Page 630
Electrical Conductivity and Anisotropy of Olivine......Page 631
Anhydrous Materials......Page 633
Effects of Hydrogen......Page 634
Mixing Relationships......Page 635
Application to MT Studies......Page 636
References......Page 637