Theory and Practice - Thermodynamics, Equations of State, Elasticity, and Phase Transitions of Minerals at High Pressures and Temperatures

Treatise on Geophysics

Volumn 2, Issue , 2007, Pages 121-152

  Oganov, A R ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Elastic constants; Free energy; Geotherm; Gr neisen parameter; Intrinsic anharmonicity; Isosymmetric transitions; Landau theory; Partition function; Phase transformations; Phonon spectrum; Polytypsim; Quasiharmonic approximation; Seismic anisotropy; Spin transition

Indexed keywords

EID: 84882901500     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044452748-6.00033-X     Document Type: Chapter

References (133)

1. Ackland G.J., Reed S.K. Two-band second moment model and an interatomic potential for caesium. Physical Review 2003, B67:174108.
2. Adams D.M., Hatton P.D., Heath A.E., Russell D.R. X-ray diffraction measurements on potassium nitrate under high pressure using synchrotron radiation. Journal of Physics 1988, C21:505-515.
3. Al'tshuler L.V., Brusnikin S.E., Kuzmenkov E.A. Isotherms and Grüneisen functions of 25 metals. Journal of Applied Mechanics and Technical Physics 1987, 161:134-146.
4. Alexandrov K.S., Prodaivoda G.T. Elastic properties of minerals. Crystallografiya 1993, 38:214-234. (in Russian).
5. Alfè D., Gillan M.J., Price G.D. The melting curve of iron at the pressures of the Earth's core from ab initio calculations. Nature 1999, 401:462-464.
6. Alfè D., Gillan M.J., Price G.D. Composition and temperature of the Earth's core constrained by combining ab initio calculations and seismic data. Earth and Planetary Science Letters 2002, 195:91-98.
7. Allan D.R., Nelmes R.J. The structural pressure dependence of potassium titanyl phosphate (KTP) to 8GPa. Journal of Physics - Condensed Matter 1996, 8:2337-2363.
8. Allen M.P., Tildesley D.J. Computer Simulation of Liquids 1987, Clarendon Press, Oxford, 385pp.
9. Anderson D.L. Theory of the Earth 1989, Blackwell, Boston, 366pp.
10. Angel R.J. New phenomena in minerals at high pressures. Phase Transitions 1996, 59:105-119.
11. Angel R.J., Allan D.R., Milletich R., Finger L.W. The use of quartz as an internal pressure standard in high-pressure crystallography. Journal of Applied Crystallography 1997, 30:461-466.
12. 3. Physics and Chemistry of Minerals 2000, 27:719-731.
13. 1/c-C2/c phase transitions in clinopyroxenes: Influence of cation size and electronic structure. American Mineralogist 1998, 83:1176-1181.
14. Badro J., Fiquet G., Guyot F., et al. Iron partitioning in Earth's mantle: Toward a deep lower mantle discontinuity. Science 2003, 300:789-791.
15. Baroni S., de Gironcoli S., Dal Corso A., Gianozzi P. Phonons and related crystal properties from density-functional perturbation theory. Reviews of Modern Physics 2001, 73:515-562.
16. Baroni S., Gianozzi P., Testa A. Green-function approach to linear response in solids. Physical Review Letters 1987, 58:1861-1864.
17. Barron T.H.K., Klein M.L. Second-order elastic constants of a solid under stress. Proceedings of the Physical Society 1965, 85:523-532.
18. Belikov B.P., Aleksandrov K.S., Ryzhova T.V. Elastic Constants of Rock-Forming Minerals 1970, Nauka, Moscow, Russian, 276pp.
19. Binggeli N., Keskar N.R., Chelikowsky J.R. Pressure-induced amorphisation, elastic instability, and soft modes in α-quartz. Physical Review B 1994, 49:3075-3081.
20. Birch F. Elasticity and constitution of the Earth's interior. Journal of Geographical Research 1952, 57:227-286.
21. Birch F. Composition of the Earth's mantle. Geophysical Journal of the Royal Astronomical Society 1961, 4:295-311.
22. 3Si. Physical Review Letters 1966, 17:1216-1219.
23. Born M., Huang K. Dynamical Theory of Crystal Lattices 1954, Oxford University Press, Oxford, 420pp.
24. Bowley R., Sánchez M. Introductory Statistical Mechanics 1999, Oxford University Press, Oxford, 352pp. 2nd edn.
25. Bruce A.D., Cowley R.A. Structural Phase Transitions 1981, Taylor and Francis, London, 326pp.
26. Buerger M.J. Polymorphism and phase transformations. Fortschritte Der Mineralogie 1961, 39:9-24.
27. Bukowinski M.S.T. Quantum geophysics. Annual Reviews of Earth and Planetary Science 1994, 22:167-205.
28. Burdett J.K. Chemical Bonding in Solids 1995, Oxford University Press, New York, 319pp.
29. 6. Inorganic Chemistry 1998, 37:1486-1492.
30. Carpenter M.A., Salje E.K.H. Elastic anomalies in minerals due to structural phase transitions. Eurpoean Journal of Mineralogy 1998, 10:693-812.
31. Carpenter M.A., Salje E.K.H. Strain and Elasticity at Structural Phase Transitions in Minerals. Reviews in Mineralogy and Geochemistry 2000, 39:35-64.
32. Carpenter M.A., Salje E.K.H., Graeme-Barber A. Spontaneous strain as a determinant of thermodynamic properties for phase transitions in minerals. European Journal of Mineralogy 1998, 10:621-691.
33. Catti M. Crystal elasticity and inner strain - A computational model. Acta Crystallographica 1989, A45:20-25.
34. Chandler D. Introduction to Modern Statistical Mechanics 1987, Oxford University Press, NY, 274pp.
35. Christy A.G. Multistage diffusionless pathways for reconstructive phase transitions: application to binary compounds and calcium carbonate. Acta Crystallographica B 1993, 49:987-996.
36. Christy A.G. Isosymmetric structural phase transitions: Phenomenology and examples. Acta Crystallographica B 1995, 51:753-757.
37. Cohen R.E., Gulseren O., Hemley R.J. Accuracy of equation-of-state formulations. American Mineralogist 2000, 85:338-344.
38. Cowley R.A. Acoustic phonon instabilities and structural phase transitions. Physical Review 1976, B13:4877-4885.
39. Dove M. Structure and Dynamics 2003, Oxford University Press, Oxford.
40. Dove M.T. Introduction to Lattice Dynamics 1993, Cambridge University Press, Cambridge, 258pp.
41. Dove M.T. Theory of displacive phase transitions in minerals. American Mineralogist 1997, 82:213-244.
42. Fedorov F.I. Theory of Elastic Waves In Crystals 1968, Plenum, New York, 375pp.
43. Gale J.D. Analytical free energy minimization of silica polymorphs. Journal of Physical Chemistry B 1998, 102:5423-5431.
44. Garber J.A., Granato A.V. Theory of the temperature dependence of second-order elastic constants in cubic materials. Physical Review B 1975, 11:3990-3997.
45. 4C1 order-disorder transition at high pressures. Physical Review B 1971, 3:1634-1637.
46. Garnero E.J., Maupin V., Lay T., Fouch M.J. Variable azimuthal anisotropy in Earth's lowermost mantle. Science 2004, 306:259-261.
47. Gillet P., Matas J., Guyot F., Ricard Y. Thermodynamic properties of minerals at high pressures and temperatures from vibrational spectroscopic data. Miscroscopic Properties and Processes in Minerals, NATO Science Series, v. C543 1999, 71-92. Kluwer, Dordrecht. K. Wright, R. Catlow (Eds.).
48. Haines J., Leger J.M., Schulte O. High-pressure isosymmetric phase transition in orthorhombic lead fluoride. Physical Review B 1998, 57:7551-7555.
49. Hama J., Suito K. The search for a universal equation of state correct up to very high pressures. Journal of Physics - Condensed Matter 1996, 8:67-81.
50. Harris M.J., Dove M.T. Lattice melting at structural phase transitions. Modern Physics Letters 1995, 9:67-85.
51. 3(II) phase transition. Physical Review B 1981, 23:368-374.
52. Hemmati M., Czizmeshya A., Wolf G.H., Poole P.H., Shao J., Angell C.A. Crystalline-amorphous transition in silicate perovskites. Physical Review B 1995, 51:14841-14848.
53. Holzapfel W.B. Physics of solids under strong compression. Reports on Progress in Physics 1996, 59:29-90.
54. Holzapfel W.B. Equations of state for solids under strong compression. Zeitschrift Fur Kristallographie 2001, 216:473-488.
55. Iannuzzi M., Laio A., Parrinello M. Efficient exploration of reactive potential energy surfaces using Car-Parrinello molecular dynamics. Physical Review Letters 2003, 90. (art. no. 238302).
56. International Tables for Crystallography, Vol. A., Space-Group Symmetry 1994, Kluwer, Dordrecht. T. Hahn (Ed.).
57. Ito E., Katsura T. A temperature profile of the mantle transition zone. Geophysical Research Letters 1989, 16:425-428.
58. Jaeger G. The Ehrenfest classification of phase transitions: Introduction and evolution. Archives of Histology and Exact Science 1998, 53:51-81.
59. Kantorovich L.N. Thermoelastic properties of perfect crystals with nonprimitive lattices: 1: General theory. Physical Review B 1995, 51:3520-3534.
60. Karki BB (1997) High-Pressure Structure and Elasticity of the Major Silicate and Oxide Minerals of the Earth's Lower Mantle, 170 pp. PhD Thesis, University of Edinburgh.
61. Karki B.B., Wentzcovitch R.M., de Gironcoli S., Baroni S. First-principles determination of elastic anisotropy and wave velocities of MgO at lower mantle conditions. Science 1999, 286:1705-1707.
62. 3 perovskite at high pressure. Physical Review B 2000, 62:14750-14756.
63. 5 Polymorphs. Reviews in Mineralogy 1990, 22:406.
64. 4. Physical Review B 1994, 50:9072-9078.
65. Kieffer S.W. Thermodynamics and lattice vibrations of minerals. 1: Mineral heat capacities and their relationship to simple lattice vibrational models. Reviews of Geophysics and Space Physics 1979, 17:1-19.
66. Kunc K., Loa I., Syassen K. Equation of state and phonon frequency calculations of diamond at high pressures. Physical Review B 2003, 68. (art. 094107).
67. Laio A., Parrinello M. Escaping free-energy minima. Proceedings of the National Academy of Sciences 2002, 99:12562-12566.
68. Landau L.D., Lifshitz E.M. Part I. (Course of Theoretical Physics, v. 5). Statistical Physics 1980, Butterworth and Heinemann, Oxford, 544pp. 3rd edn.
69. Legrand B. Relations entre la structure èlectronique et la facilitè de glissement dans les métaux hexagonaux compacts. Philosophical Magazine 1984, 49:171-184.
70. Lin J.F., Struzhkin V.V., Jacobsen S.D., et al. Spin transition of iron in magnesiowusite in Earth's lower mantle. Nature 2005, 436:377-380.
71. Liu L.-G., Bassett W.A. Elements, Oxides, and Silicates. High-Pressure Phases with Implications for the Earth's Interior 1986, Oxford University Press, New York, 250pp.
72. Loubeyre P., LeToullec R., Hausermann D., et al. X-ray diffraction and equation of state of hydrogen at megabar pressures. Nature 1996, 383:702-704.
73. Matsui M. Molecular dynamics study of the structural and thermodynamic properties of MgO crystal with quantum correction. Journal of Chemical Physics 1989, 91:489-494.
74. 2 α-Quartz: An anisotropic amorphous solid. Physical Review Letters 1991, 68:83-85.
75. Mishima O., Calvert L.D., Whalley E. Melting of ice I at 77K and 10kbar: A new method for making amorphous solids. Nature 1984, 310:393-394.
76. Montagner J.-P., Nataf H.-C. A simple method for inverting the azimuthal anisotropy of surface waves. Journal of Geophysical Research 1986, 91:511-520.
77. Montroll E.W. Frequency spectrum of crystalline solids. Journal of Chemical Physics 1942, 10:218-229.
78. Montroll E.W. Frequency spectrum of crystalline solids. II: General theory and applications to simple cubic lattices. Journal of Chemical Physics 1943, 10:481-495.
79. 3. Science 2004, 304:855-858.
80. Nye J.F. Physical Properties of Crystals. Their Representation by Tensors and Matrices 1998, Oxford University Press, Oxford, 329pp.
81. Oganov A.R., Dorogokupets P.I. All-electron and pseudopotential study of MgO: Equation of state, anharmonicity, and stability. Physical Review B 2003, 67. (art. 224110).
82. Oganov A.R., Dorogokupets P.I. Intrinsic anharmonicity in thermodynamics and equations of state of solids. Journal of Physics - Condensed Matter 2004, 16:1351-1360.
83. Oganov AR (2002) Computer Simulation Studies of Minerals, 290 pp. PhD Thesis, University of London.
84. 3 perovskite. Physics of the Earth and Planetary Interiors 2000, 122:277-288.
85. 3 perovskite at pressures and temperatures of the Earth's mantle. Nature 2001, 411:934-937.
86. Oganov A.R., Brodholt J.P., Price G.D. Ab initio theory of thermoelasticity and phase transitions in minerals. EMU Notes in Mineralogy, Vol. 4: Energy Modeling in Minerals 2002, 83-170. Springer, Bolin. C.M. Gramaccioli (Ed.).
87. Oganov A.R., Gillan M.J., Price G.D. Ab initio lattice dynamics and structural stability of MgO. Journal of Chemical Physics 2003, 118:10174-10182.
88. Oganov A.R., Gillan M.J., Price G.D. Structural stability of silica at high pressures and temperatures. Physical Review 2005, B71. (art. 064104).
89. 3 post-perovskite phase. Nature 2005, 438:1142-1144.
90. 3 in Earth's D″ layer. Nature 2004, 430:445-448.
91. Oganov A.R., Ono S. The high-pressure phase of alumina and implications for Earth's D″ layer. Proceedings of the National Academy of Sciences 2005, 102:10828-10831.
92. 3 perovskite at high pressures and temperatures. Journals of Chemical Physics 2005, 122. (art. 124501).
93. 5 polymorphs. Acta Crystallographica 2001, A57:548-557.
94. Parker S.C., Price G.D. Computer modelling of phase transitions in minerals. Advances in Solid State Chemistry 1989, 1:295-327.
95. Poirier J.P. Equations of state. Miscroscopic Properties and Processes in Minerals, NATO Science Series, v. C543 1999, 19-42. Kluwer, Dordrecht. K. Wright, R. Catlow (Eds.).
96. Poirier J.-P. Introduction to the Physics of the Earth's Interior 2000, Cambridge University Press, Cambridge, 326pp. 2nd edn.
97. Poirier J.-P., Price G.D. Primary slip system of ε-iron and anisotropy of the Earth's inner core. Physics of the Earth and Planetary Interiors 1999, 110:147-156.
98. Price G.D., Yeomans J. The application of the ANNNI model to polytypic behavior. Acta Crystallographica B 1984, 40:448-454.
99. Price G.D. Polytypism and the factors determining the stability of spinelloid structures. Physics and Chemistry of Minerals 1983, 10:77-83.
100. Rao C.N.R., Rao K.J. Phase Transitions in Solids: An Approach to the Study of the Chemistry and Physics of Solids 1978, McGraw-Hill, NY, 330pp.
101. Redfern S.A.T. Order-disorder phase transitions. Reviews in Mineralogy and Geochemistry 2000, 39:105-133.
102. Richet P., Gillet P. Pressure-induced amorphisation of minerals: A review. European Journal of Mineralogy 1997, 9:907-933.
103. Ringwood A.E. Phase transformations and their bearing on the constitution and dynamics of the mantle. Geochimica et Cosmochimica Acta 1991, 55:2083-2110.
104. Robie R.A., Edwards J.L. Some Debye temperatures from single crystal elastic constant data. Journal of Applied Physics 1966, 37:2659-2663.
105. Rydberg V.R. Graphische Darstellungeiniger bandenspektroskopischer Ergebnisse. Journal of Applied Physics 1932, 73:376-385.
106. Schilling F.R., Sinogeikin S.V., Bass J.D. Single-crystal elastic properties of lawsonite and their variation with temperature. Physics of the Earth and Planetary Interiors 2003, 136:107-118.
107. Seitz F. Modern Theory of Solids 1949, GITTI, Moscow, (Russian translation) 736pp.
108. Shannon R.D., Prewitt C.T. Effective ionic radii in oxides and fluorides. Acta Crystallographia B 1969, 25:925-946.
109. Sharma S.M., Sikka S.K. Pressure-induced amorphization of materials. Progress in Materials Science 1996, 40:1-77.
110. Sirotin Y.I., Shaskolskaya M.P. Fundamentals of Crystal Physics 1975, Nauka, Moscow, (in Russian) 680pp.
111. Sposito G. Landau's choice of the critical-point exponent β. American Journal of Physics 1974, 42:1119-1121.
112. Sturhahn W., Jackson J.M., Lin J.-F. The spin state of iron in minerals of Earth's lower mantle. Geophysical Research Letters 2005, 32:L12307.
113. Sutton A.P. Electronic Structure of Materials 1993, Oxford University Press, Oxford, 260pp.
114. Terhune R.W., Kushida T., Ford G.W. Soft acoustic modes in trigonal crystals. Physical Review 1985, B32:8416-8419.
115. Tröster A., Schranz W., Miletich R. How to couple Landau theory to an equation of state. Physical Review Letters 2002, 88. art. 055503.
116. Tse J.S., Klug D.D. Anisotropy in the structure of pressure-induced disordered solids. Physical Review Letters 1993, 70:174-177.
117. 3 perovskite in the earth's lower mantle. Earth and Planetary Science Letters 2004, 224:241-248.
118. 3 in the cores of gas giants and terrestrial exoplanets. Science 2006, 311:983-986.
119. Vinet P., Ferrante J., Smith J.R., Rose J.H. A universal equation of state for solids. Journal of Physics 1986, C19:L467-L473.
120. Vinet P., Rose J.H., Ferrante J., Smith J.R. Universal features of the equation of state of solids. Journal of Physics - Condensed Matter 1989, 1:1941-1963.
121. Vočadlo L., Price G.D., Poirier J.-P. Grüneisen parameters and isothermal equations of state. American Mineralogist 2000, 85:390-395.
122. Vorob'ev V.S. On model description of the crystalline and liquid states. Teplofizika Vysokih Temperatur (High-Temperature Thermophysics) 1996, 34:397-406. (in Russian).
123. Wallace D.C. Thermodynamics of Crystals 1998, Dover Publications, New York, 484pp.
124. Wang Y., Li J., Yip S., Phillpot S., Wolf D. Mechanical instabilities of homogeneous crystals. Physical Review B 1995, 52:12627-12635.
125. Wang Y., Yip S., Phillpot S., Wolf D. Crystal instabilities at finite strain. Physical Review Letters 1993, 71:4182-4185.
126. Warren M.C., Dove M.T., Myers E.R., et al. Monte Carlo methods for the study of cation ordering in minerals. Mineralogical Magazine 2001, 65:221-248.
127. Watt J.P., Davies G.F., O'Connell R.J. The elastic properties of composite materials. Reviews of Geophysics and Space Physics 1976, 14:541-563.
128. Welch D.O., Dienes G.J., Paskin A. A molecular dynamical study of the equation of state of solids at high temperature and pressure. Journal of Physics and Chemistry of Solids 1978, 39:589-603.
129. Wilson K.G. The renormalization group and related phenomena. Reviews of Modern Physics 1983, 55:583-600.
130. Wookey J., Kendall J.-M., Rümpker G. Lowermost mantle anisotropy beneath the north Pacific from differential S-ScS splitting. Geophysical Journal International 2005, 161:829-838.
131. Yeomans J.M. Statistical Mechanics of Phase Transitions 1992, Oxford University Press, Oxford, 168pp.
132. Zhang L., Ahsbahs H., Kutoglu A., Hafner S.S. Compressibility of grunerite. American Mineralogist 1992, 77:480-483.
133. Zharkov V.N., Kalinin V.A. Equations of state of solids at high pressures and temperatures 1971, Consultants Bureau, New York, 257pp.