Developments in Geochemistry 9

High-Pressure Geochemistryand mineral Physics

Basics for Planetologyand Geo-material Science

By

Sachinath Mitra

2004

ELSEVIER

Amsterdam - Boston - London - New York - Oxford - ParisSan Diego - San Francisco - Singapore — Sydney - Tokyo

Table of Contents

Preface vii

Acknowledgements ix

Section A: Preamble and Preview

Section B: The Earth and Planetary System

Chapter 1. (A) Cosmochemistry and Properties of Light ElementCompounds 17

1.1. Introduction 191.1.1. Range of pressure in the universe 211.1.2. The proto-solar nebula 21

1.2. Cosmochemistry 231.2.1. Data source 231.2.2. Chemical segregation in nebular condensation 241.2.3. The Solar System 24

1.2.3.1. Meteorites 251.2.3.2. Inner planets: major constituents and phases 30

1.3. Evolutionary history of the Solar System: terrestrial planetary formation . . . 311.3.1. Interplanetary flights of planetary materials 311.3.2. Primary chemical elements forUife 32

1.3.2.1. Microorganisms under pressure: clues to HPgenesis of life 34

1.3.2.2. Biogenesis 341.3.3. Primitive atmosphere 36

1.4. Charge density within planetary interiors 361.4.1. Electrons under pressure 37

1.5. Forces binding atoms 371.5.1. Van der Waals forces 38

1.5.1.1. Van der Waals compounds: new materials 381.5.2. Ionic compounds 41

1.5.2.1. Simple ionic model 411.5.2.2. Overlap- and self-energy: pair-potential 421.5.2.3. Ions in distorted lattice 421.5.2.4. Multipoles and polarization 43

1.5.3. Covalent and hydrogen bonding 43

xii Table of Contents

1.5.3.1. Pressure rupturing of the binding forces 441.6. Helioseismology and Jovian structures 441.7. Planetary constituents under pressure 45

1.7.1. Transition pressure 481.8. Hydrogen 48

1.8.1. Hydrogen molecular states 501.8.2. Vibrational properties 53

1.8.2.1. Vibrational excitations 541.8.2.2. Experiments (P>300 GPa) 551.8.2.3. Vibrons 551.8.2.4. Phonons 551.8.2.5. Rotons and librons 571.8.2.6. Hydrogen bridges 57

1.8.3. Quantum condensate, BEC 581.8.3.1. Proton quantum tunnelling 58

1.8.4. Insulator-metal transition 591.8.5. Solid hydrogen: frustrating metallic behaviour 60

1.8.5.1. Black hydrogen and metallization 611.8.5.2. >300 GPa 621.8.5.3. Effective charge: phase III 621.8.5.4. Solid hydrogen: alkali metal(?) at 340 GPa 63

1.8.6. Ortho- and para-hydrogen 631.8.6.1. Ortho-para conversion: quantum solid state 641.8.6.2. Conversion energy channels: EQQ 65

1.8.7. Hydrogen in Jupiter 661.8.8. H in terrestrial planets 67

1.8.8.1. Hydrogen in the Earth's minerals 671.8.8.2. Water in the Earth: D/H ratios 681.8.8.3. H/H2O in mantle phases 70

1.9. Water and ammonia in Uranus and Neptune 701.9.1. Electrical conductivity: "synthetic Uranus" 711.9.2. Metallicity(?) of water and ammonia 711.9.3. Water: structural order and anomalies 72

1.9.3.1. Proton (and oxygen) diffusion in water 731.9.4. Superionic solid state 73

1.9.4.1. Ammonia: superionic state 731.10. H2 mixtures and clathrates 74

1.10.1. H 2 -O 2 mixture: "Hard Spheres" 741.10.2. CH4-H2 and Ar-H2 systems: Laves phases 75

1.10.2.1. Laves phases 751.10.3. N2-CH4: Titan 76

1.11. H2O 761.11.1. Bonding: covalency 761.11.2. Hydrodynamics 78

Table of Contents xiii

1.11.3. H2O-ice structure: "ice rules" 781.11.3.1. Reflectance spectra 79

1.11.4. Entropy of ice 791.11.4.1. Ferroelectric alignment 801.11.4.2. Spin ice 82

1.11.5. Ice Ih, III, IV, V and VI: phase diagram 841.11.5.1. Ice VI in diamond 841.11.5.2. Ice /h: stability boundary 841.11.5.3. Proton ordering/disordering: new phase 851.11.5.4. Higher isomorphs: ices VII, VIII and X 861.11.5.5. Ice VII: as pressure medium 87

1.11.6. Supercooled water 881.11.6.1. Amorphous ice polymorphism: high-density

and low-density 891.11.6.2. Diffraction study 911.11.6.3. LDA ice, ice /j, and quenched water:

vibrational spectra 911.11.6.4. VHDAice 92

1.12. Deuterium at high pressure: Saturn's core 931.12.1. Deuterium in Mars 941.12.2. D/H ratios in minerals 95

1.12.2.1. D/H ratio in extraterrestrial and subsurface water 951.13. Alkali metals: Li to Cs ': 96

1.13.1. "Nearly-free electron" behaviour 971.13.2. Fermi pressure in.lithium isotopes 98

1.14. CO2 981.14.1. Stability of CO2 polymorphs: CO2-V quartz-like 991.14.2. H2O-CO2 mixture 99

1.15. Carbon in space and in the Earth f 1001.15.1. Fullerites and nano-crystallites 1021.15.2. Carbon polymorphs 1041.15.3. Carbon in the Earth 1041.15.4. Carbon in high P-T: stability 105

1.15.4.1. C, Si and Ge 1071.15.5. Carbon-bonding structure 1081.15.6. Graphite and diamond phases 109

1.15.6.1. Superhard graphite 1091.15.6.2. Resistivity and phase transition 1101.15.6.3. Pre-solar nano-diamonds 1101.15.6.4. Terrestrial occurrence I l l

1.15.7. Carbon isotopes 1141.15.7.1. Oxygen and carbon-12 (C-12) evolution

on the Earth '. 1151.15.7.2. 12C/13C ratios: interstellar 115

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1.15.7.3. Raman line: P, T calibration 1151.15.7.4. 14C diamond: elastic moduli 116

1.15.8. Optical behaviour of diamond: flow andpressure-luminescence 116

1.15.9. Carbon clusters 1181.15.9.1. Charged carbon clusters: low-F diamond 1181.15.9.2. C-nanotubes 1191.15.9.3. Fullerenes 119

1.15.10. Organic minerals in meteorites: shock loading 1241.15.10.1. Amino-acid racemization: chirality retention 1261.15.10.2. Vitrinite maturation 127

1.16. Nitrogen 1271.17. Sulphur 128

(B) Terrestrial Planets 1291.18. Early geochemical evolution 131

1.18.1. Chondritic character of terrestrial bodies 1311.18.1.1. Chemical differentiation: siderophile elements 132

1.19. Accretionary evolution of the Earth 1331.20. Compositional characteristics of the Earth 134

1.20.1. Magma ocean generation and crustal fractionation inearly Earth 1351.20.1.1. Early crust 136

1.21. Fluids within the Earth 1391.21.1. Water in the Earth 1391.21.2. Water in the magmatic processes 1411.21.3. Fluids in the. lower crust: granulites 1421.21.4. Mantle fluids 1421.21.5. Atmospheric noble gases in mantle melts 143

1.21.5.1. Inert gases: solar-like? 1441.21.5.2. AT, KrandXe 1441.21.5.3. Ar solubility 1441.21.5.4. The "missing xenon problem" 145

1.22. Potassium budget in the Earth's mantle 1451.22.1. K-feldspar/Hollandite 1451.22.2. Phlogopite 1461.22.3. Clinopyroxene 1461.22.4. K2O in mantle solidus: seismic attenuation 146

1.23. Mantle isotopes 1471.23.1. Sm-Nd ratios 1471.23.2. Eu anomaly 1481.23.3. Sr, Nd and Hf 1481.23.4. Osmium , 1481.23.5. l87Re and 187Os 1481.23.6. U-Pb and Re-Os ratio 149

Table of Contents xv

1.23.7. Isotopes in MORB and hotspots 1501.23.8. Isotopes in UHP rocks 151

1.23.8.1. l8O isotopes: non-equilibration 1521.23.8.2. 818O: an example for isotope separation 152

1.24. ^e/^He reservoirs 154(C) Heavy Element Compounds 155

1.25. Ferrous metals in rocky planets 1571.26. Element distribution in mineral system 157

1.26.1. Partitioning of elements 1581.26.1.1. Siderophile elements 1581.26.1.2. Incompatible elements 159

1.27. Transition metals in magmas: CFSE 1601.27.1. Principles of metal distribution in magmatic differentiation 1611.27.2. Transition-element partitioning in mineral systems 163

1.27.2.1. Ni2+ and Co2+: pressure partitioning 1641.27.2.2. Cr3+, Ni2+, Fe3 +and Ti4 +ions 1651.27.2.3. Cr2+, Ni2+ and Co3 + ions 1651.27.2.4. Ni-Co partitioning 1661.27.2.5. Plutonic rocks and metal concentration 1671.27.2.6. Highly siderophile elements 168

1.28. Ca-Al and Mg-Si proportionation in the mantle 1701.28.1. Critical ratios 171

1.29. Core differentiation/heterogeneous accretion ; 1721.29.1. 182W fractionation and Hf/W ratio 173

1.29.1.1. Hf/W in early history 1731.29.2. Core:Re/Os 175

1.30. 40K in the core 175

Chapter 2. Petro-Tectonic Features of Terrestrial Planets 1772.1. Introduction 1772.2. The Earth models 178

2.2.1. The PREM model 1782.2.2. Seismological models 180

2.2.2.1. Elastic constants 1812.2.3. Petrological models 181

2.2.3.1. Pyrolite model 1842.2.3.2. Piclogite model 184

2.2.4. Convection model 1852.2.4.1. Mantle convection at Archean-Proterozoic transition . . . 1872.2.4.2. Mantle Raleigh number and flush instability

at late Archean 1882.3. Physical parameters 188

2.3.1. Parameter changes with depths 1892.3.1.1. Lithosphere 190

xvi Table of Contents

2.3.2. Parameterized PREM model: EOS 1922.4. Seismic model: discontinuities 193

2.4.1. Seismic discontinuities: Moho to the D" zone 1942.5. Thermal structures of the Earth's mantle 195

2.5.1. Temperature-depth relation 1962.5.1.1. Heat sources and heat flow 199

2.5.2. Thermal anomalies 2002.5.2.1. Upper mantle 2002.5.2.2. Lower mantle 2002.5.2.3. Thermal structure of the core and CMB 201

2.5.3. Adiabatic gradient 2022.5.3.1. Deviations from adiabaticity 2032.5.3.2. Heat flow and plate tectonics 203

2.6. Elastic parameters of the Earth's interior 2032.6.1. Stress and strain 204

2.6.1.1. Strain tensor 2052.6.1.2. Zero-pressure bulk modulus, Ko: Eulerian strain 205

2.6.2. Seismic waves 2062.6.2.1. P- and S-waves in seismic discontinuities

and in the core 2072.6.2.2. Minor discontinuities (reflective) 2082.6.2.3. Wave velocities in the lower crust 2082.6.2.4. Wave velocities in lower mantle: T effects 2092.6.2.5. Crustal plates and earthquakes 2102.6.2.6. Strain transients and earthquakes, co- and

post-seismic 2122.6.2.7. Precursors to earthquakes 215

2.6.3. Acoustic and ultrasonic wave-velocities 2172.6.3.1. Ultrasonic velocities and Q in porous rocks 217

2.6.4. Subcrustal stress fields: ore localization 2182.6A.I. Gravitational field models: degree harmonics

and mantle flow 2182.6.5. Tools for sub-surface studies 219

2.6.5.1. GPS in tectonic studies 2192.6.5.2. Mars global surveyor (MGS) 220

2.7. The crust and cratons ("keels") 2212.7.1. Continental lithosphere 2212.7.2. Subcontinental mantle 2212.7.3. Plate tectonics, magmatism and hotspots 222

2.8. The mantle 2232.8.1. Geochemistry 223

2.8.1.1. Mantle end members 2242.8.2. Petro-tectonics 2252.8.3. Xenoliths 226

Table of Contents xvii

2.8.4. Deep-mantle flow and Wilson cycle: American Cordillera 2262.8.5. Diversification of rock types 226

2.8.5.1. Petrogeny's residua system 2262.8.5.2. Effusive rocks 2272.8.5.3. Calc-alkaline magmatism: LIL enrichment

and "Pb paradox" 2282.9. Earth's rheology and dynamism 229

2.9.1. Lithospheric rheology and dynamism 2292.9.2. Mantle rheology 231

2.9.2.1. Decompression and magma fragmentation 2312.9.3. Seismic tomography: Iceland hotspot and Nazca plate 231

2.9.3.1. Anomalous low-velocity zone 2322.10. Convergent plate boundaries 233

2.10.1. Subducting slabs 2332.10.1.1. Slab tomography: volatiles and partial melting 2352.10.1.2. Deflections of seismic discontinuities:

NW Pacific subduction 2352.10.1.3. Deep-focus earthquakes: fossil slab at

transition zone 2362.10.2. Subducting mafic, ultramafic rocks and sediments 237

2.10.2.1. Subduction of oceanic lithosphere: upper tolower mantle 237

2.10.2.2. Mid-oceanic ridge basalt 2392.10.3. Mantle wedge 241

2.10.3.1. Arc magmatism: alkali and H2O activity 2422.10.4. Hotspots and mantle plumes: OIB versus MORB 243

2.10.4.1. Iceland mantle plume 2432.10.4.2. Plumes and underplating 2442.10.4.3. Megaplumes •• 244

2.11. Upper mantle 2442.11.1. Upper-mantle anisotropy 2462.11.2. Mantle minerals versus discontinuities 247

2.11.2.1. Upper mantle 2492.11.2.2. 400, 520 and 670 km discontinuities 2492.11.2.3. Ca-phases in mantle discontinuities 250

2.11.3. Mantle melting and extraction 2502.11.3.1. Deep-mantle melting: melt sinking 2512.11.3.2. Depletion and mixing: non-Newtonian

high-viscosity blobs 2512.11.4. Peridotite mineralogy at depths 252

2.11.4.1. Mantle silicate framework 2532.12. Lower mantle 256

2.12.1. Phases 2562.12.2. Solidus in the lower mantle 258

xviii Table of Contents

2.12.3. Fe, Si enrichment in the lower mantle 2582.12.3.1. Effects of Fe 2592.12.3.2. P- and S-velocities and shear modulus 260

2.13. Core-mantle boundary 2602.13.1. Minerals at CMB 2612.13.2. Hotspots and CMB 2622.13.3. Anisotropic structures at CMB 263

2.13.3.1. Seismic anisotropy in D" layer 2632.13.3.2. Anisotropy caused by paleo-slabs 2662.13.3.3. Carribbean and Pacific evidence 266

2.14. Reaction between mantle and liquid-core 2672.14.1. Ultra-low-velocity zone 269

2.15. The Earth's magnetism and orbital obliquity 2702.15.1. Mantle plume and geomagnetic reversals 270

2.16. Mars 2712.16.1. Crust and mantle 2712.16.2. SNC and LHB: ALH 84001 2722.16.3. Martian mantle composition 272

2.16.3.1. Mantle geochemistry: SNC 2752.16.3.2. Mantle-phase stability: MB versus KLB 2762.16.3.3. Fe-rich Martian mantle: density increase 2772.16.3.4. Olivine-spinel phase transition 2792.16.3.5. Mantle-flow: viscosity 2792.16.3.6. Magmatic water in Mars 279

2.16.4. Magnetism 2802.16.4.1. i Core formation and magnetism 280

2.17. Venus 2802.17.1. Gabbro —» eclogite transition in Venus 281

2.18. Mercury 2812.19. Galilean satellites 2822.20. Interplanetary flights of planetary materials 282

Chapter 3. Structural Types of Major Phases: AB, AB2, A2B3, ABX3,ABX4, AB2X4 and A2B2X7 283

3.1. AB structures 2833.1.1. NaCl (Bl): alkali halides 286

3.1.1.1. Exciton in alkali halides 2873.1.1.2. NaCl structure at lower mantle 289

3.1.2. CsCl (B2) structure 2913.1.2.1. Cs-halide (B2), Csl: metallization 2913.1.2.2. Convergence with rare gas: solid Xe 291

3.1.3. NiAs (B8) structure 2933.1.3.1. Chemical bonding 2933.1.3.2. Hexagonal close packing and c/a ratio 294

Table of Contents xix

3.2. AB2 structure 2943.2.1. SiO2 polymorphs 296

3.2.1.1. Si-coordination 2973.2.1.2. Polarization and chirality 297

3.2.2. TiO2 2983.2.2.1. Cotunnite type: hardest polymorph 3003.2.2.2. Crystallographic shear (cs) planes 300

3.2.3. Post-stishovite phase 3003.2.3.1. Stishovite(TiO2) —» a-PbO2 structural transformation . . . 3013.2.3.2. Baddeleyite-type structure 301

3.3. A2B3 structure 3023.3.1. Fe2O3 303

3.3.1.1. Structural and spin transition 3043.3.1.2. X-ray emission spectra 305

3.3.2. A12O3 3063.3.2.1. Quadrupole polarizability 307

3.4. ABX3 3073.4.1. Perovskite-ilmenite 3073.4.2. Ilmenite structure: stability 308

3.4.2.1. Polymorphism of FeTiO3: LiNbO3 structure 3093.4.3. Ilmenite solution in olivine: Alpe Arami massif 309

3.5. ABX4 3093.5.1. Berlinite/scheelite structure: AW04 3103.5.2. Berlinite and crystobalite: A1PO4 310

3.5.2.1. GaPO4 and AlAsO4 3133.6. A2BX4 structure 313

3.6.1. Tetragonal structure: K2NiO4 3133.6.2. Spinel structure \ 315

3.7. A2B2X7 : 3163.7.1. Pyrochlore structure 316

3.7.1.1. Frustration and magnetic "spin ice" 3163.7.1.2. Tl2Mn207: GMR 317

Section C: Basics for Pressures Studies

Chapter 4. Principles of Techniques 3214.1. Introduction 321

4.1.1. Insulator-metal transition 3224.1.1.1. Mott insulators 326

4.1.2. High-pressure techniques 3264.1.2.1. Synchrotron source 3294.1.2.2. Synchrotron radiation 329

xx Table of Contents

4.1.2.3. Multi-anvil and DAC 3304.1.2.4. Measurement techniques 332

4.2. Diamond-anvil cell 3334.2.1. Properties of the gaskets 3334.2.2. Pressure medium and calibration 334

4.2.2.1. Quasi-hydrostatic stress 3364.2.2.2. Shear stress (a) 336

4.2.3. Reference-phase transitions 3374.2.3.1. CaO-MgO-SiO2 system 337

4.2.4. Temperature control 3384.2.4.1. Cryogenic methods 3384.2.4.2. Laser heating 338

4.2.5. Ruby (Al2O3:Cr3+) calibration 3384.2.6. Diamond window 340

4.3. Hydrothermal diamond-anvil cell 3404.3.1. Pressure calibration 340

4.4. Diffraction and spectroscopic techniques in pressure studies 3414.4.1. Optical spectroscopy 341

4.4.1.1. Crystal-field under pressure: theory 3424A.I.2. Transition-metal compounds: ionic model 3464.4.1.3. Pressure on crystal-field parameters 3484.4.1.4. Racah parameters and band shifts 3494.4.1.5. Examples: Cr3+-bearing minerals 3504.4.1.6. Intervalence charge transfer 3524.4.1.7. O —» M charge transfer 3524.4.1.8. , M-M bonding and Cr dimerization 3534.4.1.9. Crystal-field effect on transition pressure 3534.4.1.10. Exchange-coupled pair bands 3544.4.1.11. CFSE and elastic property change: Fe2+ : 355

4.4.2. Volume compressibility and crystal-field splitting 3554.4.3. Vibrational spectroscopy 356

4.4.3.1. Soft modes 3584.4.3.2. Pressure relationship 3594.4.3.3. Infrared 3604.4.3.4. Raman spectroscopy 3624.4.3.5. Second-order Raman scattering: disordering 3664.4.3.6. Non-linear optical methods 3674.4.3.7. Brillouin scattering 367

4.4.4. Ultrasound spectroscopy 3694.4.4.1. Instrumentation 371

4.4.5. Fluorescence spectroscopy 3714.4.5.1. Experiments 3724.4.5.2. Side-band fluorescence ultrasonic technique 372

4.4.6. Photoluminescence spectroscopy 374

Table of Contents xxi

4.4.6.1. Photo-emission method 3754.4.7. X-ray diffraction 375

4.4.7.1. Radial X-ray diffraction (RXD): deviatoric stress 3774.4.7.2. Density determination 3804.4.7.3. High-pressure XRD (powder) study: An example

of MgSiO3 ilmenite 3804.4.8. Mossbauer spectroscopy 380

4.4.8.1. Pressure dependence of isomer shift (So) 3824.4.8.2. Quadrupole splitting (A£Q) 383

4.4.9. NMR spectroscopy 3844.4.9.1. Pressure effects on proton NMR spectra 385

4.4.10. Thermoluminescence 3864.4.10.1. ZnS phosphor 3874.4.10.2. Trap depths 387

4.5. Computational simulations 3874.5.1. Introduction 387

4.5.1.1. Ab initio methods 3884.5.1.2. First-principles approximations 3884.5.1.3. Density functional theory: Kohn-Sham equations 390

4.5.2. LCAO model 3914.5.2.1. Molecular dynamics simulation 3924.5.2.2. Inter-atomic potential 3934.5.2.3. Tight-binding total-energy model : 3934.5.2.4. Potential-induced breathing model 3944.5.2.5. Variationally induced breathing model: MgO 394

4.5.3. Electronic approximations: "Muffin tin", KSS and Bloch'stheorem 3954.5.3.1. Double exchange (DE) model 396

4.5.4. LMTO method vs. APW and KKR 3984.5.4.1. Average pair correlation function for NN geometry:

SiO2 glass 3984.6. Shock pressure studies 398

Chapter 5. (Crystalline) Materials Under High Pressure 4015.1. Material properties : 401

5.1.1. Thermodynamics, equilibrium and time interval 4045.1.2. Many-body systems and broken symmetry 404

5.1.2.1. Crystalline symmetries: 5-fold symmetry,icosahedra and quasi-crystals 404

5.1.2.2. Broken symmetry 4055.1.2.3. Electron excitations and band gaps 4065.1.2.4. Dielectric properties 4075.1.2.5. Electronic and magnetic behaviour '. 4075.1.2.6. Ionicity in bonding: Madelung forces 408

xxii Table of Contents

5.1.3. Covalent bonding and hardness 4095.1.3.1. Hardness and bulk moduli 4095.1.3.2. Phonon-s and band states 409

5.1.4. Elasticity 4105.1.4.1. Elastic anisotropy 411

5.1.5. Elastic constants: crystal systems 4125.1.5.1. Cauchy relation and its violations 415

5.1.6. Born's stability criteria: fij, B2 and fi3 4165.1.7. Thermoelasticity 418

5.2. Atomic vibrations in crystals: phonon-s 4195.2.1. Elastic waves in crystals 420

5.2.1.1. Shock waves 4205.2.1.2. Shock velocity and particle velocity 4215.2.1.3. Shock-induced transitions 423

5.3. Inelastic and non-hydrostatic states 4245.3.1. Stress states 424

5.3.1.1. Non-hydrostatic stress 4255.3.2. Crystallographic shear 426

5.3.2.1. Shear and deformational twinning 4275.3.3. Strain anisotropy in crystalline mass: e.g., hep iron 427

5.4. Spontaneous strain 4285.4.1. Spontaneous strain and order parameter 429

5.5. Strain tensor 4315.6. Bulk modulus of ionic compounds 432

5.6.1. Molar volume 4325.6.2. Shear modulus: mantle perovskite 432

5.7. Magnetic features 4335.7.1. Ferromagnetism 433

5.7.1.1. Curie temperature 4335.7.2. Ferrimagnetism 4345.7.3. Spin states of iron 434

5.7.3.1. Electronic/magnetic ordering: examples 4355.7.3.2. Magnetic collapse: oxides and perovskites 4355.7.3.3. Magnetism in phase stability 4365.7.3.4. Magnetic frustration 437

5.8. Polyhedral changes 4375.8.1. Elasticity of MgO6 and SiO6 octahedra: MgSiO3 ilmenite 4405.8.2. Anisotropic deformation: decompression 4415.8.3. Radius ratio and coordination changes 4425.8.4. Five-fold coordination: silicon and titanium 4435.8.5. Thermal expansivity and deformation equivalence {alp) 4465.8.6. Volume compressibility: negative 448

5.8.6.1. Relative compressibilities 4495.8.7. Thermodynamic parameters and EOS 449

Table of Contents xxiii

5.8.7.1. P-V-T data and EOS 4495.8.7.2. Birch EOS 4505.8.7.3. Equations of state: density ratio 451

5.8.8. Bulk moduli: isothermal and isentropic 4535.8.8.1. K of mineral mixture: Reuss bound and

Voigt bound 4545.8.8.2. Crystal-field spectra 454

5.8.9. Velocity-volume relationship 4555.8.10. Velocity-density relationship: rules 4555.8.11. Stretch densification 4565.8.12. Compressibility and Si-O-Si bending 457

5.8.12.1. Ionic compressibilities 4575.9. Free and thermal energies: phase boundaries 458

5.9.1. Free energy 4595.9.1.1. Free energy change and phase boundary 4605.9.1.2. Volume change and AH 4615.9.1.3. Activation volume and activation enthalpy 4615.9.1.4. Communal entropy: fluid 4625.9.1.5. Heat capacity, entropy and phase boundaries 464

5.9.2. Thermal-expansion coefficient 4665.9.2.1. a values: spectroscopic vs. volumetric 467

5.9.3. Griineisen parameter (y) 4695.9.3.1. Mode Griineisen (M-G) parameter 4695.9.3.2. Thermal Griineisen parameter (yth) 4695.9.3.3. Density "and Griineisen parameter 4705.9.3.4. Debye model 4715.9.3.5. Anderson-Gruneisen parameter 4715.9.3.6. Vinet equation 4715.9.3.7. Holzapfel equation '}. 4725.9.3.8. Logarithmic equation 4725.9.3.9. Microscopic and macroscopic 472

5.9.4. Thermal expansion and crystal-field changes 4735.9.5. Radiative-heat transport 4735.9.6. Thermal pressure: Eularian strain 474

5.9.6.1. Thermal pressure as a function of volume 4755.10. Phase transitions 475

5.10.1. Mixed and quasi-stable phases 4765.10.2. Lattice disorder 4805.10.3. Silicon: (3-tin — hep 4805.10.4. Cation distribution and order-disorder 4805.10.5. Incommensurate phases 4815.10.6. Order of transition: first order and second order 4815.10.7. Order parameters 4825.10.8. Superlattice ordering 482

xxiv Table of Contents

5.10.9. Structural changes 4825.10.10. Phase changes: principles and types 483

5.10.10.1. Thermal transformations 4845.10.10.2. Soft modes 4845.10.10.3. Order parameter (17). Free energy and transition

temperature 4845.10.10.4. Landau theory 4865.10.10.5. Landau order parameter 4885.10.10.6. Origin of doubled-well potential, V(TJ) 4895.10.10.7. Rigid-unit mode: "split atoms" and energy spectra 489

5.10.11. Pressure-induced order-disorder 4905.10.11.1. Fe-Mg ordering in silicates 4915.10.11.2. Structural disordering and twinning 4925.10.11.3. Free energy and order parameter (Q) 4935.10.11.4. Order parameter (Q) and strain (e) in

phase transition 4945.10.12. Isosymmetric transitions 494

5.10.12.1. Energetics of iso-symmetric transition 4955.10.13. Growth rates 495

5.11. Charge distribution in ionic solids: valence and core states 4965.11.1. Ionic solid under compression: MgO 498

5.11.1.1. Band-gap change: implication in lower mantle 4985.11.2. High-spin-low-spin transition 499

5.11.2.1. Energy change in spin transition 4995.11.2.2. Spin-pairing in the lower mantle ". 503

5.11.3. Pressure dissolution and substitution 5045.12. Amorphization 505

5.12.1. Pressure-induced amorphization 5055.12.1.1. Metastability and reversible amorphization 5075.12.1.2. Non-hydrostatic pressure and amorphization 507

5.12.2. Disordering and amorphization: Raman scattering 5085.12.2.1. Non-bonded atoms and steric hindrances 5085.12.2.2. Memory glass: A1PO4 509

5.12.3. Solid-liquid (melt) stability boundary 5095.12.3.1. Law of melting: Lindemann 509

Section D: Mineral Systems

Chapter 6. MgO-FeO-SiO2 (MFS) System: Olivines and Pyroxenes 5156.1. Introduction 515

6.1.1. Stability of binary oxides and ternary phases 5186.1.2. MgO-FeO-SiO2: thermodynamic data and phase equilibria

in the mantle 520

Table of Contents xxv

6.2. MFS system in Mars 5236.3. Mg-olivines 524

6.3.1. Olivines in the mantle: pyrolite model..- 5256.3.1.1. Mg2SiO4-Fe2SiO4 system: binary loop in

the mantle 5276.3.1.2. Fe-Mg in a-/3 phases: ordering 5306.3.1.3. Thermal properties of MgO-SiO2 system 531

6.3.2. Nucleation rates 5326.3.3. Elasticity 533

6.3.3.1. San Carlos olivine 5346.3.3.2. Mode-Griineisen parameter 537

6.3.4. (Mn, Fe, Co) olivines: compressibility 5376.3.5. Post-spinel transitions: phase-boundary study 5386.3.6. OH~ ions 539

6.3.6.1. OH-bearing planar defects 5406.3.7. Inter-diffusion and activation volume, V* 5426.3.8. Seismic and acoustic velocities: VP and Vs 542

6.3.8.1. a-P system 5436.3.8.2. Fe/Mg in velocity relation 545

6.3.9. Minor element partitioning in a —> j3 transformation 5466.3.9.1. Cr3+ and Al3+ in wadsleyite 5476.3.9.2. Ti4+ in olivine/wadsleyite 5486.3.9.3. Cr2+ in olivine structure 548

6.3.10. Partition coefficients: olivine-melt 5486.3.10.1. Al3+ partitioning: Onuma diagram 549

6.3.11. Compressibility and amorphization 5516.4. /3-Mg2SiO4 (wadsleyite) 554

6.4.1. Single-crystal elasticity 5546.4.2. Hydrous wadsleyite, 0-Mg2_xSiH2;cO4 (0.00 < x < 0.25) 557

6.4.2.1. H2O in a-j8 transition 5606.4.2.2. Mg-vacant structural module 5626.4.2.3. Fe in wadsleyite II 5636.4.2.4. Fe3+ in protonation 563

6.5. Olivine —• spinel transition: CFS 5646.5.1. Oxygen sublattice transformation (hep —> fee):

partial dislocations 5656.5.2. Olivine-spinel compressibility 5666.5.3. y-Mg2SiO4 (ringwoodite and inverse ringwoodite) 567

6.5.3.1. Under pressure 5686.5.3.2. Thermodynamics 5706.5.3.3. Symmetry analysis 571

6.5.4. Olivine-(enstatite)-spinel nucleation in subducting lithosphere 5736.5.4.1. Hydrous ringwoodite (y-Mg2SiO4) : 573

6.6. Fe2SiO4 systems 574

xxvi Table of Contents

6.6.1. y-Fe2SiO4 spinel 5756.6.1.1. Fe2SiO4-Fe3O4 system 575

6.6.2. Cr2SiO4 : Cr2+ orthosilicates 5766.6.2.1. XRD and electronic spectroscopy 5766.6.2.2. M-M bonding and Cr dimerization 5776.6.2.3. Compressional anisotropy 577

6.6.3. Ni2Si04: deformation 5776.6.4. Mg2GeO4 olivine 577

6.7. Pyroxenes 5786.7.1. Structural chains and angles 5816.7.2. MgSiO3-FeSiO3 system 581

6.7.2.1. MgSiO3 orthopyroxene 5826.7.2.2. Orthoenstitite-clinoenstatite: LCLEN —* HCLEN 5856.7.2.3. Aluminous orthopyroxene: elasticity and

velocities 5886.7.2.4. MD simulation 5896.7.2.5. Ab initio simulation: Hartree-Fock 590

6.7.3. Clinopyroxene 5906.7.3.1. C2lc clinoenstatite 5916.7.3.2. Diopside-hedenbergite join 5926.7.3.3. Enstatite-diopside-jadeite join: garnet 5996.7.3.4. Clinopyroxene and anorthite 6026.7.3.5. Potassium in clinopyroxene 6026.7.3.6. Pyroxene-garnet transition: Martian mantle 6036.7.3.7. FeSiO3: clinoferrosilite 6066.7.3.8. Na-pyroxene 610

6.7.4. Akermanite, CaMgSi2O7: incommensurate to normalphase transition 612

Chapter 7. (K2O, Na2O, CaO)-Al2O3-SiO2 System 6137.1. KAlSi3O8-NaAlSi3O8-CaAlSi3O8 felspars 613

7.1.1. Bulk moduli 6157.1.2. Compressibilities: M - 0 and (T-O-T) 617

7.1.2.1. Unit strains in felspars 6197.2. KAlSi3Og system 620

7.2.1. Stability 6217.2.2. Phase relations 6227.2.3. Displacive-phase transition 623

7.3. Hollandite-type compounds 6237.3.1. Pb-hollandite 624

7.4. Anorthoclase (KAlSi3O8-NaAlSi3O8) 6257.4.1. Phase relations 625

7.5. Plagioclase felspars (NaAlSi3O8-CaAl2Si2O8) 6267.5.1. Albite, NaAlSi3O8 626

Table of Contents xxvii

7.5.1.1. Al-Si order-disorder 6277.5.1.2. Low albite: <A1-O-Si) change 628

7.5.2. Anorthite, CaAl2Si2O8 6297.5.2.1. Al-Si order-disorder 6307.5.2.2. Structure 6317.5.2.3. Phase diagram 6327.5.2.4. P\ «-> / I transition: non-ferroic displacive 6347.5.2.5. Amorphization 6357.5.2.6. Shock transition to glass: Raman results 635

7.5.3. P i <- / I 29Si MAS-NMR spectroscopic study 6367.6. Reedmergnerite, NaBSiO8 637

Chapter 8. Al2O3-SiO2 and (CaO-MgO)-Al2O3-SiO2 Systems 6398.1. Al2O3-SiO2 system 639

8.1.1. Sillimanite and andalusite 6418.1.2. Kyanite 642

8.1.2.1. Bulk modulus 6458.1.2.2. dP/dr slope and stability 646

8.2 CaO-MgO-Al2O3-SiO2 (CMAS) system 6468.2.1. Thermodynamic equilibria parameters of CMAS system 6488.2.2. Garnet structure 649

8.2.2.1. Andradite 6528.2.2.2. Pyrope Mg3 Al2(Si04)3 652

8.2.3. Pyrope —> ilmenite —» perovskite transformation: Al-content 6548.2.4. Almandine (Fe3Al2Si3Oi2) break-down 6548.2.5. Factors for garnet compression 6558.2.6. Bulk moduli 6568.2.7. Thermal expansion 6578.2.8. YAG .'r 6588.2.9. Mg-Cr-garnet i 658

8.2.9.1. Cr, Al fractionation in garnets 6608.2.10. Tetragonal garnets 661

8.2.10.1. Majorite garnet 6628.2.10.2. Compressibility 6688.2.10.3. Bulk modulus 6688.2.10.4. Vibrational modes: IAxla 669

8.2.11. Ca-garnets 6698.2.12. Andradite-skiagite solid solution 6708.2.13. Calderite garnet, Mn3Fe2

+Si3O12 671

Chapter 9. AB2X4 Structure 673(A) Oxide Spinels 675

9.1. Introduction : 6779.1.1. Normal/inverse spinels 679

xxviii Table of Contents

9.1.2. CFSE in spinels 6809.1.3. JT effect 6819.1.4. Crystal structure 681

9.1.4.1. Compressibility 6829.1.5. High-pressure studies 683

9.1.5.1. Compressibility 6839.1.5.2. Polyhedral bulk moduli, K 685

9.2. MgAl2O4 spinel 6859.2.1. Spectral models 687

9.2.1.1. Cr3+ in MgAl2O4 6889.2.2. (MgAl2O4)^ (Fe3O4), -x solid solution 6889.2.3. Order-disorder (OD): cation partitioning 6889.2.4. Magnetic behaviour: Ms 689

9.3. Magnetite, Fe3O4 6909.3.1. h-Fe3O4 693

9.3.1.1. EOS and molar volume 6949.3.1.2. Neel temperature, TN 695

9.3.2. Pressure dependence of u and a 6969.3.3. Polyhedral bulk modulus, K 6979.3.4. Ca-ferrite structure 697

9.3.4.1. CaMn2O4 and Mn3O4 6989.3.5. Fe3O4, MgAl2O4 and y-Ni2SiO4 spinels 698

9.3.5.1. MgAl2O4 and MgO: elastic constantsand sound velocities 699

9.3.6. Electrical resistivity 7009.3.7. >y-Fe2O3 701

9.4. Cr-spinels, MCr264 (M = Mg, Mn, Zn): decomposition 7019.4.1. Oxidation of Cr-spinel 7029.4.2. OD in Cr-spinels 703

9.4.2.1. Thermopower (Q) and conductivity 7039.4.3. Defects and electrical behaviour 704

9.4.3.1. Shocked chromite 7059.4.4. Chromite: post-spinel orthorhombic polymorph 706

9.4.4.1. Chromite: Raman bands 706(B) Sulfide Spinels 7079.4.5. ZnCr2S4 spinel 709

Chapter 10. ABX3, Perovskite-Ilmenite Structure 71110.1 Introduction 711

10.1.1. Magnetic ordering 71310.1.2. Perovskite and mantle convection 71310.1.3. Layered mantle 71410.1.4. Outlook 714

Table of Contents xxix

10.1.5. Structure and types of perovskites 71410.1.5.1. Defects in oxide perovskites 71810.1.5.2. Fe2O3 perovskite: TM and "magnetic hardening" 720

10.1.6. MgSiO3 Perovskite 72010.1.6.1. Atomistic simulation: MEG 72110.1.6.2. Phonon spectrum 721

10.1.7. Perovskite melting and bouyancy 72610.2 MgO-(FeO)-SiO2 system: perovskites 727

10.2.1. Tolerence factor, t 72710.2.2. Silicate perovskites 729

10.2.2.1. Orthorhombic- tetragonal -cubic transitions 72910.2.2.2. Ferroelectricity 73010.2.2.3. MgSiO3-FeSiO3 perovskites 73110.2.2.4. Shear moduli: ultrasonic interferometry 73110.2.2.5. Vibrational modes 732

10.2.3. Elasticity: modelling 73410.2.3.1. Wave velocities: anisotropy 736

10.2.4. Thermoelasticity and expansivity 73710.2.4.1. Bulk modulus and EOS 73710.2.4.2. Lattice compressiblity and KT 739

10.2.5. XRD results 74010.2.6. (Mg,Fe)SiO3-perovskite 740

10.2.6.1. Iron in perovskite 74110.2.6.2. Fe2+ in perovskites: A-site occupancy 74310.2.6.3. Temperature-dependent electron delocalization 74610.2.6.4. Defect equilibria and M3+: physical properties 748

10.2.7. Glassy phase 74910.3. Transformations 749

10.3.1. Activation energy .•; 74910.3.2. Perovskite breakdown: volume change 75010.3.3. Vibrational models: intrinsic anharmonic effects 75010.3.4. Raman study 750

10.3.4.1. Soft-mode transition 75110.3.5. Ilmenite structure (R3) 752

10.3.5.1. MgSiO3 ilmenite 75210.4. CaO-SiO2 system 755

10.4.1. CaSiO3 perovskite 75510.4.1.1. LAPW calculations: phonon spectrum

and transition temperature 75610.4.1.2. Density and acoustic velocity 757

10.4.2. Pseudo-wollastonite 75710.4.3. CaSiO3-CaTiO3 join 758

10.5. MgO(CaO)-SiO2(GeO2)-Al2O3 system 75810.5.1. Ca-Al perovskite 759

xxx Table of Contents

10.5.2. Ca-Ge perovskites 76010.5.2.1. IR modes: Ca translation 760

10.6. Alkaline-earth perovskites 76110.6.1. Li(Nb,Ta)O3 ferroelectrics 761

10.6.1.1. Ferroelectric and para-electric structures 76310.6.2. RE orthoferrites 764

10.6.2.1. (Sr/Ca) FeO3 perovskite 76510.7. Titanate perovskites and ilmenites 765

10.7.1. CaTiO3-FeTiO3 join 76610.7.2. MgTiO3-FeTiO3 join 768

10.7.2.1. MgTiO3, geikielite 77110.7.2.2. High-temperature phase transition

(without order-disorder) 77410.7.2.3. FeTiO3 structure 77410.7.2.4. Shocked FeTiO3-ilmenite: Mossbauer study 778

10.7.3. Xenoliths in Kimberlites 78010.7.4. BaTiO3 781

10.7.4.1. Ferroelectricity and ferroelasticity 78410.7.4.2. Linearized augmented plane wave (LAPW)

calculations: surface effects 78610.7.4.3. Multiple-site model for perovskite ferroelectrics 78610.7.4.4. Ferroelectric instability: "rattling-ion" model 787

10.7.5. PbTiO3 78810.7.6 Other titanates 789

10.7.6.1. MgTi2O5 karrooite: order-disorder 78910.7.7. Ti/Nb perovskites : 790

10.8. Mn-oxide perovskites 79110.8.1. "Ruddlestone-Popper" series 792

Chapter 11. Silicate Melts and Rocks 79311.1. Introduction 793

11.1.1. Magmatic melt under pressure 79511.2. Alumino-silicate melts .. > 796

11.2.1. CaO-Al2O3-SiO2 melts: compressibilities 79611.2.2. Na2O-Al2O3-SiO2 melts: Ab5ONTS5o 797

11.3. Viscosity: controlling factors 79811.3.1. Diffusivity: Stokes-Einstein equation 79811.3.2. Temperature dependence: Arrhenian approximation 79811.3.3. Alkali oxides 79911.3.4. Water effect 79911.3.5. Pressure effects on viscosity 79911.3.6. Silicate polymerization 80011.3.7. Density and viscosity determination •. 801

Table of Contents xxxi

11.3.8. Melt percolation 80111.3.9. Crystal-melt phase equilibria 802

11.3.9.1. / O , , /H 2 O and aHiO 80211.4. H2O in silicate melts 803

11.4.1. K2O-SiO2-H2O system 80311.5. REE patterns 804

11.5.1. Fe3+ in glass 80411.5.2. Partition coefficient in melt/solid 804

11.6. Rocks under pressure 80611.6.1. Transformation under shock: pseudotachylites 80611.6.2. Terrigenous and pelagic sediments under subduction 806

11.6.2.1. Density change and buoyancy 80711.6.2.2. Potassium mobility in subduction pressures 80911.6.2.3. Lead paradox 80911.6.2.4. Subducting slabs 810

11.6.3. Ultra-high-pressure metamorphism 81011.6.3.1. Coesite-diamond 81011.6.3.2. Crustal metamorphic regimes 81111.6.3.3. Hot and cold eclogites: collision/subduction zones 81111.6.3.4. Dabie-Sulu collision zone 81211.6.3.5. Alpe Arami UHP lherzolite 81311.6.3.6. Exsolutions in VHP minerals 815

11.6.4. Basalts and eclogites 81611.6.4.1. Dehydration melting of metabasalt

at 0.8-3,2 GPa 81711.6.5. MORB 81811.6.6. Komatiite, picrite and lherzolite: CaO-MgO(FeO)-SiO2

systems 81911.6.7. Garnet peridotites: "forbidden zone" 820

11.6.7.1. Exsolutions 82111.6.7.2. Emplacement of garnet peridotites 821

Chapter 12. Simple Oxides and Carbonates 82312.1 Dioxides: SiO2 823

12.1.1. a-Quartz: structural change : 82612.1.1.1. Fracture strength 828

12.1.2. Stishovite 82812.1.2.1. Structure 82912.1.2.2. SiO6: densities 83012.1.2.3. Elastic moduli 83012.1.2.4. Compressibility 831

12.1.3. Fluorite (CaCl2) structure 83212.1.3.1. EOS 83412.1.3.2. Theoretical models 837

xxxii Table of Contents

12.1.3.3. Columbite (a-PbO2) structure: MD simulation 83912.1.3.4. Seismic velocities: discontinuities 840

12.1.4. Cristobalite 84012.1.4.1. Structure: phase transition 84012.1.4.2. Phase transition: symmetry change 84312.1.4.3. Cristobalite III 84412.1.4.4. Raman study: I —• II transition 844

12.1.5. a-quartz, coesite, stishovite and cristobalite 84612.1.5.1. Coesite to quartz transformation kinetics 847

12.1.6. Instability and ferroelastic transition 84812.1.6.1. A new phase 849

12.1.7. Amorphization experiments 84912.1.7.1. a —• c growth rate: magma viscosity 85012.1.7.2. SiO2 glass 850

12.2. ZrO2-SiO2: shocked 85312.3. TiO2 85412.4. Simple monoxides 854

12.4.1. MgO, FeO, CoO, MnO and NiO 85412.4.1.1. MgO and CoO 85412.4.1.2. MnO and FeO 85512.4.1.3. Normal and inverse NiAs structures 85712.4.1.4. FeO in D" zone 85712.4.1.5. MgO 85712.4.1.6. Elasticity 86112.4.1.7. B1-B2 phase transition .- 86212.4.1.8.. Elastic constants 862

12.4.2. FeO at high P-T 86212.4.2.1. Magnetic-phase transition 86612.4.2.2. NiAs phase 867

12.4.3. Fe / ) 86912.4.3.1. Wustite (Fei_xO) 87112.4.3.2. Fe-FeO system 87212.4.3.3. Fe-FeO + diluting elements: solid solution under P .... 873

12.5. Carbonates 87412.5.1. CaCO3 calcite —» aragonite polymorphism 874

12.5.1.1. Calcite, CaCO3 87612.5.1.2. Compressibility and bulk modulus 87712.5.1.3. Oxy-anion-cation packing 878

12.5.2. Mg-carbonates 88012.5.2.1. Dolomite stability at depths 882

12.6. Other carbonates 88312.7. CaO-MgO-SiO2-CO2 system 883

12.7.1. CaO-MgO-SiO2-CO2-H2O system: XCo2 883

Table of Contents xxxiii

Chapter 13. Hydrous Minerals 88513.1. Water in primary minerals 885

13.1.1. Introduction . . . . . . . : 88513.1.2. Hydrous minerals under pressure 888

13.1.2.1. Water in subducting slabs 88913.1.3. H(D)-0 bonds in hydroxides 893

13.1.3.1. OH bonds: dv/dP 89313.2. Geophysical effects of water 894

13.2.1. Creep rate 89513.2.2. Electrical conductivity 895

13.3. H2O in the mantle and magmatic melt 89513.3.1. H2O in plagioclase crystallization 896

13.4. MgO-SiO2-H2O ternary system 89713.4.1. DHMS phases 898

13.4.1.1. MgO-SiO2 + volatiles (H2O, F2, Cl2) system 90013.4.1.2. Halogens in DHMS phases 902

13.4.2. NMR spectroscopic study 90213.4.3. Choke point 90313.4.4. Serpentine and phase A 904

13.4.4.1. Serpentine, Mg3SiO5(OH)4 90413.4.4.2. Phase A (Mg7Si2O8(OH)6) 90413.4.4.3. Chrysotile transformations 90713.4.4.4. Talc and phase A 90813.4.4.5. Discussion 90813.4.4.6. 10-A phase, Mg3Si4O10(OH)2,nH20 90913.4.4.7. 3.65-A phase 909

13.4.5. Anhy-B 90913.4.5.1. Octahedral sites: M3 site 91113.4.5.2. Phase B \ 91113.4.5.3. NMR study ': 912

13.4.6. Phase D (MgSi2H2O6) 91713.4.6.1. Structure 91913.4.6.2. Density and bulk modulus 92113.4.6.3. Anisotropic compressibility 922

13.4.7. Phase E (Mg2.08Si,.6H3.2O6) ) . . . . ' . 92213.4.7.1. Related phases 92413.4.7.2. Phase F(?) 925

13.4.8. Phase G and other MSH phases : 92513.5. Humite group minerals 925

13.5.1. Clinohumite and chondrodite 92513.5.2. Elastic properties 92613.5.3. Clinohumite-OH and chondrodite-OH 927

13.6. MgO-Na2O-SiO2-H2O system: hydrated aenigmatites : 92713.6.1. Hydrated-Na-aenigmatite: crystal structure 928

xxxiv Table of Contents

13.7. CaO-Al2O3-SiO2-H2O system 92813.7.1. Zoisite and clinozoisite, Ca2Al2 (Al,_pFep) (O/OH/Si2O7/SiO4) . . . 928

13.7.1.1. Compressibility 93013.7.1.2. Thermal expansivity 93113.7.1.3. &KT/bT and Anderson-Griineisen parameter 93213.7.1.4. Stability 93213.7.1.5. Zoisite and lawsonite 93313.7.1.6. Subducting andesitic rocks 935

13.8. CaO-Al2O3-SiO2-H2O system 93513.8.1. Amphiboles 935

13.8.1.1. Kaersutitic amphibole: oxidation-hydrogenationreactions 936

13.8.1.2. Kaersutite in SNC meteorites: Martian H2O 93813.8.2. High Fe3+ content and the aHiO 93913.8.3. Lawsonite, CaAl2Si2OrH2O 940

13.8.3.1. Ko and a values 94213.8.3.2. Compressibility 94313.8.3.3. IR study: Griineisen parameter and thermal

expansion 94413.9. MgO-Al2O3-SiO2-H2O system 946

13.9.1. Muscovite 94713.9.1.1. Phlogopite 94713.9.1.2. Phase X 948

13.10. K2O-MgO-Al2O3-SiO2-H2O system 94813.10.1. Cold geotherms 948

13.11. Al2O3-SiO2-H2O (ASH) system 94913.11.1. AlSiO3OH, "phase egg" 950

13.11.1.1. Discussion 95313.11.1.2. Phase egg in subduction zone 954

13.12. Clay minerals 95413.12.1. Structural disorder 95513.12.2. 19- and 15-A hydrate 95513.12.3. Interlayer cations 95613.12.4. Kaolinite: Raman study 95613.12.5. Chlorite 957

13.13. Hydrous oxides 95713.13.1. Hydrous silica: Shergotty and LM 95713.13.2. AIO(OH), diaspore 95813.13.3. Mg(OH)2, brucite 959

13.13.3.1. XRD study 96113.13.3.2. IR study 96213.13.3.3. Raman study 963

13.14. Portlandite (Ca(OH)2) 965

Table of Contents xxxv

Chapter 14. Iron and Siderophile Elements: The Earth's Core 96714.1. Introduction 967

14.1.1. Theories of iron under pressure 96814.1.1.1. Energy bands and electron transitions at core 96914.1.1.2. Phase predictions from theoretical calculations 97014.1.1.3. First-principles approximation: bcc and hep 971

14.1.2. fee and hep phases 97214.1.2.1. P -p relationship 975

14.2. Iron core 97714.2.1. Core iron 97814.2.2. Anisotropy 97814.2.3. EOS and melting 97914.2.4. Density deficit 98014.2.5. Iron phases 983

14.2.5.1. Stability of bcc and fee phases 98514.2.5.2. J3-Fe (dhep) phase 98614.2.5.3. e —• Pbcm iron transformation 98814.2.5.4. Stability 99014.2.5.5. Thermal Griineisen parameter 99014.2.5.6. Vibrational modes 991

14.2.6. Phase boundaries and the triple points 99214.2.6.1. a-e-y triple point and e - y transition 99214.2.6.2. E -7 - I triple point 99514.2.6.3. Liquid iron: structural change under P 995

14.2.7. Elasticity and rheology 99614.2.7.1. Experimental 99614.2.7.2. Shear viscosity 998

14.2.8. Rigid core: slichter modes of translational motion 99914.2.9. Outer core \ 99914.2.10. Inner core 1000

14.2.10.1. Heat sources 100114.2.10.2. Rotation 100114.2.10.3. Crystalline structure: elastic/seismic behaviour 100214.2.10.4. Anisotropism: axial angle 100414.2.10.5. Discontinuities 100814.2.10.6. Geodynamo: convection and aw-dynamo 100914.2.10.7. Geomagnetic-field propagation 101014.2.10.8. Magnetic field, heat flow and plate tectonics 1011

14.3. e-Fe and paramagnetism 101114.3.1. Hugoniot temperature 1012

14.4. Iron and tungsten: yield strengths 101214.5. Fe-Ni alloy 101314.6. Fe-Si alloy : 101514.7. Fe-H system 1016

xxxvi Table of Contents

14.8. Sulphur in the core 101714.8.1. Oxygen and sulphur solution in iron 1017

14.8.1.1. S, Se and Te 101814.9. Iron sulphides 1018

14.9.1. FeS: five polymorphs 101914.9.1.1. FeS III, monoclinic 101914.9.1.2. FeS IV, hexagonal (2a,c) 102014.9.1.3. FeS V: hexagonal (a,c) 102214.9.1.4. Spin state of ferrous iron 102314.9.1.5. R (Fe-S) change and spin splitting 1026

14.9.2. FeS: Martian CMB and core 102814.9.3. Fe-FeS system: eutectic points 1028

14.9.3.1. Fe3S2, Fe3S, Fe2S 102814.9.4. FeS2 1029

14.9.4.1. FeS2, pyrite 102914.9.4.2. Pyrrhotite: magnetic transition 1030

14.10. Fe3S2 103014.11. Mn-S system 1031

14.11.1. a-MnS 103114.11.2. MnS2 103114.11.3. (Fe,Mg)S and (Fe,Mn)S 1032

14.12. Pressure behaviour of FeS vs. FeO 103314.13. Fe(Ni)-Cu-S compounds 1033

14.13.1. Nickel sulphides 103314.13.2. Cubanite, CuFe2S3 1034

14.14. Phosphates '. 103514.14.1. Berlinite; A1PO4: memory glass (?) 103514.14.2. Farringtonite-Mg3 (PO4)2-II 103714.14.3. Apatite (Ca5(PO4)3, (F,Cl,OH))-monazite topotaxy: REE 103814.14.4. Bearthite (Ca2Al(PO4)2OH) 1038

Section E: Transport Properties at Deep Depths & Related CondensedMatter Phenomena

Chapter 15. Transport Properties in Deep Depths and RelatedCondensed-Matter Phenomena 1041

15.1. Transport properties under pressure 104115.1.1. Introduction 104115.1.2. Electrical conductivity 1042

15.1.2.1. Electrical conductivity and activation energy 104415.1.2.2. Techniques employed 104515.1.2.3. Conductivity of minerals 1045

15.2. Electron/hole transfer and magnetic behaviour 1047

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15.2.1. Polarons: small and large 104815.2.2. Ferroelectricity: regimes and local well potential 1049

15.3. Insulator to superconductivity : 105015.3.1. Superconductivity and magnetism: "co-habitation" 1051

15.3.1.1. "Magnetic glue" and failed spin: ghost magnetism 105215.3.2. Novel physics: paramagnetic Meissner effect 1053

15.3.2.1. Mesoscopic magnetism: frustration andsuperconducting loop 1053

15.3.3. Double exchange in magnetic transition 105415.3.4. "Skutterudites" and chalcogenides: "holey" and

"unholey" semiconductors 105515.4. RE-Mn perovskite 1056

15.4.1. La1_^CaIMnO3 105615.4.1.1. Resistivity and magnetism under pressure 105715.4.1.2. CMR: R E ^ ^ M n O s 1059

15.4.2. Pressure on polarons, activation energy and chargecarrier mobility 106115.4.2.1. Electron-lattice coupling 1062

15.4.3. LaMnO3 perovskite 106315.4.3.1. M-I cohabitation 1063

15.5. La^SrJVInO;, 106415.6. Pr-manganates 1066

15.6.1. Pr,_/:aJvInO3 106715.6.2. (La^Pr^i-^AJVInO:?: short- and

long-range order 106715.7. Fe3+ in perovskite and conductivity 106715.8. A12O3 content and conductivity 106815.9. Conductive TiO2, SiO2, FeO, Fe2O3 and Fe3O4 106915.10. Thermal conductivity, K 1071

15.10.1. K at mantle depths 107215.10.1.1. Radiative and lattice contribution 1073

15.10.2. K at D" zone 107415.10.3. K and convective power of core 107715.10.4. K under shock pressure 1077

15.11. Ferroelectric transitions 107715.11.1. Ferroelectric phenomena in large planets 1078

15.12. Non-elastic transport properties 107815.12.1. Power law: fractal distribution 107915.12.2. Diffusion: self and co-operative 1080

15.13. Defects, dislocations and deformation 108015.13.1. Defects 108015.13.2. Dislocations 108115.13.3. Dislocation recovery 108115.13.4. Deformation 1082

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15.13.4.1. Olivine deformation 108315.13.4.2. Deformation: single crystal to polycrystalline

mass 108415.14. Diffusion, creep and viscoplastic deformation 1084

15.14.1. Diffusion 108415.14.1.1. Mg, Fe diffusion: olivine, pyroxene and garnet 108515.14.1.2. Grain-boundary diffusion 1085

15.14.2. Creep 108615.14.2.1. Creep rate 108615.14.2.2. Dislocation (power-law) creep —• diffusion creep 108715.14.2.3. Dislocation creep and spinel deformation 108915.14.2.4. Slip systems 109015.14.2.5. Creep, diffusion rate and conduction 1090

15.14.3. Diffusivity and viscosity: Stokes-Einstein diffusivity 109115.14.3.1. Silicate melts: O, Si diffusion 1091

15.14.4. Intrinsic and extrinsic regimes 109215.15. Cation (Mg, Fe and Ni) diffusion in olivine: a —• (3-7 transition 1093

15.15.1. a <=> P <=> 7 transitions and upper-mantle rheology 109415.15.2. Chemical diffusion in the slab and transition zone 1095

15.15.2.1. Homogenization rate in mantle 109615.15.2.2. Diffusion in lower mantle: MgO

(Ita and Cohen, 1998) 109615.15.3. Rheology of lower mantle: strain rate 1097

15.16. Transformational plasticity: partial dislocation, martensiticor synchro-shear mechanism 1098

15.17. Oxygen fugacity in the Earth's dynamics 109915.17.1. Solid-state diffusion: / O 2 1099

15.17.1.1. Olivine/iron buffer 109915.17.1.2. Ferric iron and redox zone: crustal recycling 110015.17.1.3. Core-mantle partitioning 1100

References 1103

Glossary 1205

Subject Index 1223