Elastic Properties and Equations of State

Title Page
......Page 3
Copyright
......Page 4
Contents
......Page 5
Preface
......Page 7
JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES......Page 9
PROPOSED DENSITY DISTRIBUTION......Page 18
SUMMARY......Page 24
SCIENTIFIC NOTES AND NEWS......Page 27
1. INTRODUCTION......Page 29
2. EQUATIONS FOR SMALL STRAINS SUPERPOSED ON AN ARBITARY HYDROSTATIC COMPRESSION......Page 30
3. SPECIAL FORM OF POTENTIAL ENERGY FUNCTION......Page 34
4. COMPARISON WITH EXPERIMENT......Page 35
ABSTRACT......Page 39
INTRODUCTION......Page 40
ACKNOWLEDGMENTS......Page 46
EQUILIBRIUM OF A HOMOGENEOUS LAYER......Page 47
EVALUATION OF THE PARAMETERS......Page 49
EQUATIONS OF STATE......Page 51
COMPARISON WITH MEASUREMENTS OF COMPRESSION......Page 54
THERMAL EXPANSION AND GRtJNEISEN'S RATIO......Page 60
ISOTHERMAL AND ADIABATIC COMPRESSIBILITIES......Page 66
CHANGE OF COMPRESSIBILITY WITH TEMPERATURE......Page 67
SPECI FIC HEATS......Page 68
DISCUSSION OF THE INDIVIDUAL LAYERS......Page 69
CHEMICAL COMPOSITION......Page 82
CONCLUSION......Page 93
References......Page 94
The Velocity of Compressional Waves in Rocks to 10 Kilobars, Part 2¹......Page 99
REFERENCES......Page 121
I. Introduction......Page 125
2. Density distributions for the mantle......Page 128
3. The nature of the transition layer......Page 135
4. Core......Page 138
References......Page 140
1. INTRODUCTION......Page 142
2. THE PRECISION OF ULTRASONIC VELOCITY MEASUREMENTS......Page 143
3. THE POLYNOMIAL COMPRESSION EQUATION......Page 144
5. THE ADIABATIC-ISOTHERMALTRANSFORMATIONS......Page 146
6. COMPARISON OF PREDICTED AND EXPERIMENTAL COMPRESSION......Page 147
7. ESTIMATING COMPRESSION FROM THERMAL EXPANSIVITY DATA......Page 153
8. DISCUSSION......Page 154
REFERENCES......Page 159
INTRODUCTION......Page 161
THE BULK MODULUS OF IONIC CRYSTALS......Page 162
THE EFFECT OF PRESSURE ON BULK MODULUS......Page 165
THE EFFECT OF TEMPERATURE ON THE BULK MODULUS......Page 166
THE EFFECT OF POROSITY......Page 168
DISCUSSIONS AND CONCLUSIONS......Page 169
REFERENCES......Page 172
I. INTRODUCTION......Page 174
III. THE BULK-MODULES TEMPERATURE EQUATION......Page 175
APPENDIX......Page 177
Notation and basic relationships......Page 179
1. Introduction......Page 180
2. Birch's hypothesis......Page 181
3. Isothermal-adiabatic transformations......Page 183
4. Effect of temperature......Page 185
5. The equation of state......Page 187
6. Effect of composition and phase......Page 191
7. Density distributions for the mantle......Page 195
8. Summary......Page 198
References......Page 199
DESCRIPTION OF INSTRUMENT......Page 201
ALIGNMENT PROCEDURES......Page 203
EXPERIMENTAL RESULTS......Page 204
ACKNOWLEDGMENTS......Page 206
INTRODUCTION......Page 207
SHOCK-WAVE PROPERTIES AND EXPERIMENTALMETHODS......Page 209
McQUEEN, MARSH, AND FRITZ......Page 210
HUGONIOT EQUATION OF STATE......Page 211
ZERO-PRESSURE BULK COMPRESSIBILITY......Page 213
EFFECT OF PHASE CHANGES ON HUGONIOTS......Page 216
THERMODYNAMIC CALCULATION......Page 224
TRANSFORMATIONS OF HIGH-PRESSURE SHOCKWAVEDATA TO A HIGH-DENSITYMETASTABLE HUGONIOT......Page 225
SUMMARY......Page 242
REFERENCES......Page 243
INTRODUCTION......Page 245
EQUATIONS USED FOR TABLE 1 AND THEIR SOURCES......Page 247
EFFECT OF TEMPERATURE ON THE ELASTIC CONSTANTS......Page 256
PRESSURE DERIVATIVES OF CONSTANTS: EFFECTSOF ANISOTROPY AND POROSITY......Page 259
PATTERNS RELATING ELASTIC PROPERTIES......Page 265
REFERENCES......Page 272
APPENDIX......Page 277
INTRODUCTION......Page 279
EXPERIMENTAL RESULTS......Page 280
REFERENCES......Page 289
The Bulk Modulus-Volume Relationship for Oxides *? 2......Page 291
REFERENCES......Page 296
INTRODUCTION......Page 298
EXPERIMENTAL TECHNIQUE......Page 299
REFERENCES......Page 312
Velocity-Density Systematics: Derivation from Debye Theory andthe Effect of Ionic Size......Page 313
ISOSTRUCTURAL LINES ON A VELOCITY-DENSITYPLOT......Page 314
APPLICATION TO IONIC SIZE EFFECTS......Page 315
REFERENCES......Page 320
1. INTRODUCTION......Page 322
II. EQUILIBRIUM PROPERTIES O F ALKALI-HALIDECRYSTALS IN NaCl STRUCTURE......Page 323
III. CsCl STRUCTURE; POLYMORPHIC TRANSITION ATHIGH PRESSURES......Page 325
IV. ALKALINE-EARTH-DIHALIDE CRYSTALS......Page 327
Introduction......Page 329
2. Experimental procedure......Page 330
3. Elasticity data......Page 332
4. Discussion......Page 334
5. Future work......Page 341
References......Page 342
VELOCITY-DENSITY SYSTEMATICS
......Page 343
COMPOSITION OF THE MANTLE......Page 345
REFERENCES......Page 348
1. Introduction......Page 349
3. Results......Page 350
4. Discussion......Page 352
References......Page 355
1. Introduction ? Geophysical significance of the Gruneisen parameter......Page 357
2. Griineisen's ratio for a simple cubic lattice with nearest-neighbour central forces......Page 358
3. Calculations for other crystal structures and noncentral forces......Page 360
4. Temperature dependence of Griineisen's ratio......Page 361
6. Pressure dependence of y at high pressures......Page 362
7. Application to the earth......Page 363
References......Page 364
Abstract.......Page 366
References......Page 368
I. Introduction......Page 369
2. Theory and Calculation Procedure......Page 370
3. Experimental Procedure......Page 372
4. Experimental Results......Page 373
5 . Discussion......Page 379
REFERENCES......Page 383
1. Introduction......Page 384
2. Garnet Specimen......Page 385
3. Results......Page 386
4. Discussions......Page 388
REFERENCES......Page 390
INTRODUCTION......Page 392
GENERAL CONSIDERATIONS......Page 393
STATISTICAL TREATMENT......Page 394
SCATTERING THEORY TREATMENT......Page 395
BOUNDING METHODS......Page 396
RESULTS FOR SPECIFIC GEOMETRIES......Page 400
POLYCRYSTALS......Page 404
NONLINEAR COMPOSITES......Page 407
DETERMINATION OF COMPONENT PROPERTIES......Page 408
APPENDIX 1: Kroner's [1967] RESULTFOR EQUAL SHEAR MODULI......Page 410
REFERENCES......Page 411
Procedures......Page 415
Discussion......Page 417
References......Page 420
Abstract.......Page 422
Limitations For Microcrystals......Page 423
Sample......Page 424
Elastic Constants......Page 425
Comparison With Previous Work......Page 432
References......Page 433
INTRODUCTION AND BACKGROUND......Page 435
EXPERIMENTAL PROCEDURES FOR SHOCK EXPERIMENTSON PYRRHOTITE SINGLE CRYSTALS......Page 436
EXPERIMENTAL RESULTS FOR PYRRHOTITE......Page 438
REDUCTION OF PYRITE SHOCK DATA......Page 441
CONSTRAINTS ON THE SULFUR CONTENT OF THE CORE......Page 445
DISCUSSION......Page 446
REFERENCES......Page 447
Results......Page 449
References......Page 452
1. Introduction......Page 454
2. Phases of Iron at High Pressure and Temper......Page 455
3. Equation of State for s-Iron......Page 458
4. State of the Earth's Core......Page 459
5. Discussion......Page 463
6. Conclusion......Page 464
REFERENCES......Page 465
EXPERIMENTAL TECHNIQUES......Page 467
RESULTS......Page 468
COMPARISON WITH PREVIOUS RESULTS......Page 471
REFERENCES......Page 473
Introduction......Page 474
X-Ray Diffraction Techniques......Page 475
Results......Page 476
Error Analysis......Page 477
General......Page 479
References......Page 481
1. Introduction......Page 483
2. Seismological models for the lower mantle andtheir extrapolation to zero pressure......Page 484
3. Perovskite + magnesiowustite models for thelower mantle......Page 485
4. Qualifications of the applicability of the model......Page 491
5. Comparison with other studies involving perovskite+ magnesiowiistite model mantles......Page 492
6. Conclusions......Page 493
References......Page 494
INTRODUCTION......Page 496
MULTIVARIANT PHASE TRANSITIONS......Page 497
UNIVARIANT TRANSITIONS......Page 505
CHEMICAL TRANSITIONS......Page 506
CONCLUSIONS......Page 508
REFERENCES......Page 509
Measurements and Results......Page 511
Discussion......Page 514
References......Page 520
Results and Discussion......Page 521
References......Page 523
Structural Properties and Calculation Methods......Page 525
Results and Discussion......Page 526
References......Page 528
Thermal expansion of silicate perovskite and stratification of the Earth's mantle......Page 529
INTRODUCTION......Page 532
EXPERIMENTAL PROCEDURE......Page 533
EQUATION-OF-STATE FITTING PROCEDURE......Page 534
RESULTS FOR α IRON AND α-ξ TRANSITION......Page 535
RESULTS FOR S IRON......Page 536
DISCUSSION......Page 537
CONCLUSIONS......Page 538
REFERENCES......Page 539
Introduction......Page 540
Experimental Method......Page 541
Results......Page 544
Discussion......Page 547
REFERENCES......Page 548
BIBLIOGRAPHY......Page 550