Self-consistent thermodynamic description of silicate liquids, with application to shock melting of MgO periclase and MgSiO3 perovskite

Geophysical Journal International

Volumn 178, Issue 1, 2009, Pages 162-179

  de Koker, Nico ^a,c   Stixrude, Lars ^a,b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

^c UNIVERSITÄT BAYREUTH   (Germany)

Author keywords

Equations of state; High pressure behaviour; Mantle processes; Phase transitions; Physics of magma and magma bodies; Planetary interiors

Indexed keywords

CORE-MANTLE BOUNDARY; EQUATION OF STATE; HIGH PRESSURE; MAGMA; MAGNESIUM; MANTLE PROCESS; MELTING; PERICLASE; PEROVSKITE; PHASE TRANSITION; SILICATE MINERAL; THERMODYNAMIC PROPERTY;

EID: 67650248849     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2009.04142.x     Document Type: Article

References (147)

1. Agee, C.B. & Walker, D., 1988. Static compression and olivine flotation in ultrabasic silicate liquid, J. geophys. Res., 93, 3437-3449.
2. Agee, C.B. & Walker, D., 1993. Olivine flotation in mantle melt, Earth planet. Sci. Lett., 114, 315-324.
3. Aguado, A. & Madden, P.A., 2005. New insights into the melting behaviour of MgO from molecular dynamics simulations: The importance of premelting effects, Phys. Rev. Lett., 94, 068501.
4. 8 liquids to 25 GPa, J. geophys. Res., 113, B04203. doi: 10.1029/2007JB005010.
5. 3 perovskite and implications for melts in Earth's lowermost mantle, Geophys. Res. Lett., 31, L14612.
6. Alfe, D., 2005. Melting curve of MgO from first-principles simulations, Phys. Rev. Lett., 94, 235701.
7. Allen, M.P. & Tildesley, D.J., 1987. Computer Simulation of Liquids, 1st edn, Oxford University Press, Oxford.
8. Al'tshuler, L.V., Trunin, R.F. & Simakov, G.V., 1965. Shock wave compression of periclase and quartz and the composition of the Earth's lower mantle, Fizika zemli, 10, 1-6.
9. Anderson, O.L., 1995. Equations of State of Solids for Geophysics and Ceramic Science, Oxford University Press, New York.
10. Asimow, P.D., Hirschmann, M.M., Ghiorso, M.S., O'Hara, M.J. & Stolper, E.M., 1995. The effect of pressure-induced solid-solid transitions on decompression melting of the mantle, Geochim. Cosmochim. Acta, 59(21), 4489-4506.
11. 6, J. Geol., 60, 125-147.
12. Bacon, J.F., Hasapis, A.A. & Wholley, J.W., 1960. Viscosity and density of molten silica and high silica content glasses, Phys. Chem. Glass., 1, 90-98.
13. Belonoshko, A.B. & Dubrovinsky, L.S., 1996. Molecular dynamics of NaCl (B1 and B2) and MgO (B1) melting: Two-phase simulation, Am. Mineral., 81, 303-316.
14. Belonoshko, A.B. & Saxena, S.K., 1992. A unified equation of state for fluids of C - H - O - N - S - Ar composition and their mixtures up to very high temperatures and pressures, Geochim. Cosmochim. Acta, 56, 3611-3626.
15. Benz, W., Cameron, A.G.W. & Melosh, H.J., 1989. The origin of the moon and the single-impact hypothesis III, Icarus, 81, 113-131.
16. Birch, F., 1952. Elasticity and constitution of the Earth's interior, J. geophys. Res., 57(2), 227-286.
17. Birch, F., 1978. Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300K, J. geophys. Res., 83(B3), 1257-1268.
18. Bottinga, Y., 1985. On the isothermal compressibility of silicate liquids at high-pressure, Earth planet. Sci. Lett., 74, 350-360.
19. 2, Am. J. Sci., 37, 487-500.
20. Boyle, R., 1662. New Experiments Physico-Mechanical, Touching the Spring and Weight of the Air, and its Effects, H. Hall, Oxford.
21. Brodholt, J. & Wood, B., 1993. Simulations of the structure and thermodynamic proprieties of water at high pressures and temperatures, J. geophys. Res., 98(B1), 519-536.
22. Bukowinski, M.S.T., 1977. Theoretical equation of state for the inner core, Phys. Earth planet. Inter., 14(4), 333-344.
23. Callen, H.B., 1985. Thermodynamics and an Introduction to Thermostatistics, 2nd edn, John Wiley & Sons, New York.
24. Canup, R.M., 2004. Simulations of a late lunar-forming impact, Icarus, 168, 433-456.
25. Ceperley, D.M. & Alder, B.J., 1980. Ground-state of the electron-gas by a stochastic method, Phys. Rev. Lett., 45, 566-569.
26. Chandrasekhar, S., 1939. An Introduction to the Study of Stellar Structure, University of Chicago Press, Chicago.
27. Chen, G.Q., Ahrens, T.J. & Stolper, E.M., 2002. Shock-wave equation of state of molten and solid fayalite, Phys. Earth planet. Inter., 134, 35-52.
28. Clapeyron, B.P.E., 1834. Mémoire sur la puissance motrice de la chaleur, Journal de l'ecole polytechnique Paris, 14, 153-190.
29. Cohen, R.E. & Gong, Z., 1994. Melting and melt structure of MgO at high pressures, Phys. Rev. B, 50(17), 12301-12311.
30. Cohen, R.E. & Weitz, J.S., 1998. The melting curve and premelting of MgO, in Properties of Earth and Planetary Materials at High Pressure and Temperature, Geophysical Monograph, Vol. 101, pp. 185-196, eds Manghnani, M.H. & Yagi, T., American Geophysical Union, Washington, DC.
31. Cohen, R., Gülseren, O. & Hemley, R., 2000. Accuracy of equation-of-state formulations, Am. Mineral., 85, 338-344.
32. Courtial, P., Ohtani, E. & Dingwell, D.B., 1997. High-temperature densities of some mantle melts, Geochim. Cosmochim. Acta, 61(15), 3111-3119.
33. 4 liquid at high pressure, Geochim. Cosmochim. Acta, 72, 1427-1441. doi: 10.1016/j.gca.2007.12.019.
34. 2 and some geophysically relevant derived parameters for network liquids, Phys. Chem. Miner., 19, 445-453.
35. Dorogokupets, P.I., 2000. Thermodynamic functions at zero pressure and their relation to equations of state of minerals, Am. Mineral., 85, 329-337.
36. Dubrovinsky, L.S. & Saxena, S.K., 1997. Thermal expansion of periclase (MgO) and tungsten (W) to melting temperatures, Phys. Chem. Miner., 24, 547-550.
37. Duffy, T.S. & Ahrens, T.J., 1995. Compressional sound velocity, equation of state, and constitutive response of shock-compressed magnesium oxide., J. geophys. Res., 100(B1), 529-542.
38. Feynman, R.P., Metropolis, N. & Teller, E., 1949. Equations of state of elements based on the generalized Fermi-Thomas theory, Phys. Rev., 75, 1561-1572.
39. Flyvberg, H. & Petersen, H.G., 1989. Error-estimates on averages of correlated data, J. Chem. Phys., 91, 461-466.
40. Francis, G.P. & Payne, M.C., 1990. Finite basis set corrections to total energy pseudopotential calculations, J. Phys.-Conden. Matter, 2(19), 4395-4404.
41. Frenkel, D. & Smit, B., 1996. Understanding Molecular Simulation: From Algorithms to Applications, 1st edn, Academic Press, San Diego.
42. 2 in silicate liquids at elevated pressures and temperatures: A new experimental approach, Geochim. Cosmochim. Acta, 62(14), 2499-2508.
43. Garnero, E.J. & Helmberger, D.V., 1995. A very slow basal layer underlying large-scale low-velocity anomalies in the lower mantle beneath the pacific: Evidence from core phases, Phys. Earth planet. Inter., 91, 161-176.
44. Ghiorso, M.S., 2004. An equation of state for silicate melts. I. Formulation of a general model, Am. J. Sci., 304, 637-678.
45. Ghiorso, M.S. & Sack, R.O., 1995. Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures., Contrib. Mineral. Petrol., 119, 197-212.
46. Ghiorso, M.S., Hirschmann, M.M., Reiners, P.W. & Kress, V.C., 2002. The pMELTS: A revision of MELTS for improved calculation of phase relations and major element partitioning related to partial melting of the mantle to 3GPa, Geochem. Geophys. Geosyst., 3(5). doi: 10.1029/ 2001GC000217.
47. 3 liquid to 150GPa: An equation of state (EOS), tracer diffusivities, and a detailed analysis of changes in atomic coordination statistics as a function of temperature and pressure, EOS, Trans. Am. geophys. Un., 87(52), Fall Meeting Supplement, Abstract MR43B-1079.
48. Gomes Dacosta, P., Nielsen, O.H. & Kunc, K., 1986. Stress theorem in the determination of static equilibrium by the density functional method, J. Phys. C-Solid State Phys., 19(17), 3163-3172.
49. Halbach, H. & Chatterjee, N.D., 1982. An empirical Redlich-Kwong-type equation of state for water to and 100Kbar, Contrib. Mineral. Petrol., 79, 337-345.
50. 3 at lower mantle conditions and its geophysical implications, J. geophys. Res., 92(B11), 11437-11444.
51. Hicks, D.G., Boehly, T.R., Eggert, J.H., Miller, J.E., Celliers, P.M. & Collins, G.W., 2006. Dissociation of liquid silica at high pressures and temperatures, Phys. Rev. Lett., 97. doi: 10.1103/ PhysRevLett.97.025502.
52. Hofmeister, A.M., 1993. Interatomic potentials calculated from equations of state: Limitation of finite strain to moderate, Geophys. Res. Lett., 20(7), 635-638.
53. Hohenberg, P. & Kohn, W., 1964. Inhomogeneous electron gas, Phys. Rev. B., 136, B864.
54. 2O in the range 1bar to 50 kbar and 100-1600 °C, Contrib. Mineral. Petrol., 109, 265-273.
55. Hudon, P., Jung, I.-H. & Baker, D.R., 2002. Melting of β-quartz up to 2.0GPa and thermodynamic optimization of the silica liquidus up to 6.0GPa, Phys. Earth planet. Inter., 130, 159-174.
56. Isaak, D.G., Anderson, O.L. & Goto, T., 1989. Measured elastic moduli of single-crystal MgO up to 1800K, Phys. Chem. Miner., 16, 704-713.
57. Jeanloz, R., 1989. Shock wave equation of state and finite strain theory, J. geophys. Res., 94(B5), 5873-5886.
58. Karki, B.B., Wentzcovitch, R.M., De Gironcoli, S. & Baroni, S., 2000. High-pressure lattice dynamics and thermoelasticity of MgO, Phys. Rev. B, 61(13), 8793-8800.
59. 3 perovskite at high pressure, Phys. Rev. B, 62(22), 14750-14756.
60. Karki, B.B., Stixrude, L. & Wentzcovitch, R.M., 2001. High-pressure elastic properties of major materials of Earth's mantle from first principles, Rev. Geophys., 39, 507-534.
61. Karki, B.B., Bhattarai, D. & Stixrude, L., 2006. First principles calculations of the structural, dynamical and electronic properties of liquid MgO, Phys. Rev. B, 73, 174208.
62. Karki, B.B., Bhattarai, D. & Stixrude, L., 2007. First-principles simulations of liquid silica: Structural and dynamical behaviour at high pressure, Physical Review B, 76, 104205.
63. Kirkwood, J.G., 1933. Quantum statistics of almost classical assemblies, Phys. Rev., 44, 31-37.
64. 3 perovskite to 96GPa, evidence for a structural transition in lower mantle melts, Geophys. Res. Lett., 16(5), 421-424.
65. Knopoff, L. & Uffen, R.J., 1954. The densities of compounds at high pressures and the state of the Earth's interior, J. geophys. Res., 59, 471-484.
66. Kohn, W. & Sham, L.J., 1965. Self-consistent equations including exchange and correlation effects, Phys. Rev., 140, 1133.
67. Kresse, G. & Furthmüller, J., 1996. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Computat. Mater. Sci., 6, 15-50.
68. Kresse, G. & Hafner, J., 1994. Norm-conserving and ultrasoft pseudopotentials for first-row and transition-elements, J. Phys.-Conden. Matter, 6, 8245-8257.
69. 2 liquids from 700 to 1900K: Extension to crustal magmatic temperatures, Contrib. Mineral. Petrol., 130, 1-11.
70. 8 liquid with pressure, Am. Mineral., 88, 109-120.
71. 8 liquid to 6.5GPa, Am. Mineral., 92, 114-123.
72. 2 liquids-new measurements and derived partial molar properties, Geochim. Cosmochim. Acta, 51, 2931-2946.
73. 3-bearing silicate liquids, Contrib. Mineral. Petrol., 110, 311-320.
74. 2, Phys. Rev. B, 70, 165108.
75. Luo, S.-N., Ahrens, T.J., Çaǧin, T., Strachan, A., Goddard, III, W.A. & Swift, D.C., 2003. Maximum superheating and undercooling: Systematics, molecular dynamics simulations, and dynamic experiments, Phys. Rev. B, 68(13), 134206.
76. 3 glass, enstatite, olivine, and quartz: Optical emission, temperatures, and melting, J. geophys. Res., 109, B05205.
77. Lupis, C.H.P., 1983. Chemical Thermodynamics of Materials, Prentice-Hall Inc., New York.
78. Marsh, S.P., 1980. LASL Shock Hugoniot Data, University of California Press, Berkeley, CA.
79. Marshak, R.E. & Bethe, H.A., 1940. The generalized Thomas-Fermi method as applied to stars, Astrophys. J., 91, 239-243.
80. 4 at high temperatures and pressure in the range 0-150GPa from molecular dynamics simulation, EOS, Trans. Am. geophys. Un., 87(52), Fall Meeting Supplement, Abstract MR43B-1080.
81. Matsui, M., 1989. Molecular dynamics study of the structural and thermodynamic properties of MgO crystal with quantum correction, J. Chem. Phys., 91, 489-494.
82. Matsukage, K.N., Jing, Z. & Karato, S., 2005. Density of hydrous silicate melt at the conditions of Earth's deep upper mantle, Nature, 438, 488-491.
83. McKenzie, D. & Bickle, M.J., 1988. The volume and composition of melt generated by extension of the lithosphere, J. Petrol., 29(3), 625-679.
84. McQuarrie, D.A., 1984. Statistical Mechanics, University Science Books, Sausalito, CA.
85. Mermin, N.D., 1965. Thermal properties of inhomogeneous electron gas, Phys. Rev., 137, 1441.
86. Miller, G.H., Stolper, E.M. & Ahrens, T.J., 1991a. The equation of state of a molten komatiite. 1. Shock wave compression to 36GPa, J. geophys. Res., 96(B7), 11849-11864.
87. Miller, G.H., Stolper, E.M. & Ahrens, T.J., 1991b. The equation of state of a molten komatiite. 2. Application to komatiite petrogenesis and the hadean mantle, J. geophys. Res., 96 (B7), 11849-11864.
88. More, R.M., Warren, K.H., Young, D.A. & Zimmerman, G.B., 1988. A new quitidian equation of state (QEOS) for hot dense matter, Phys. Fluids, 31(10), 3059-3078.
89. 4 liquid at ultra-high pressures from shock measurements to 200GPa on forsterite and wadsleyite, J. geophys. Res., 112 (B06208). doi: 10.1029/2006JB004364.
90. 3 system at high pressure: Thermodynamic properties of perovskite, post-perovskite, and melt from global inversion of shock and static compression data, J. geophys. Res., 114, B01203. doi: 10.1029/2008JB005900.
91. Navrotsky, A., Ziegler, D., Oestrike, R. & Maniar, P., 1989. Calorimetry of silicate melts at 1773K-measurement of enthalpies of fusion and of mixing in the systems diopside-anorthite-albite and anorthite-forsterite, Contrib. Mineral. Petrol., 101, 122-130.
92. Nosé, S., 1984. A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys., 81, 511-519.
93. Oganov, A.R. & Dorogokupets, P.I., 2003. All-electron and pseudopotential study of MgO: Equation of state, anharmonicity, and stability, Phys. Rev. B, 67. doi: 10.1103/PhysRevB.67.224110.
94. 3 perovskite at pressures and temperatures of the Earth's mantle., Nature, 411, 934-937.
95. Ohtani, E., 1988. Chemical stratification of the mantle formed by melting in the early stage of the terrestrial evolution, Tectonophysics, 154, 201-210.
96. Ohtani, E. & Sawamoto, H., 1987. Melting experiment on a model chondritic mantle composition at 25GPa, Geophys. Res. Lett., 14(7), 733-736.
97. Panero, W.R. & Stixrude, L., 2004. Hydrogen incorporation in stishovite at high pressure and symmetric hydrogen bonding in δ-AlOOH, Earth planet. Sci. Lett., 221, 421-431.
98. Pavese, A., 2002. Pressure-volume-temperature equations of state: A comparative study based on numerical simulations, Phys. Chem. Miner., 29, 43-51.
99. Phillips, A.C., 1994. The Physics of Stars, John Wiley & Sons, Chichester.
100. 2, J. Chem. Phys., 101(4), 3111-3116.
101. Redlich, O. & Kwong, J.N.S., 1949. On the thermodynamics of solutions. 5. An equation of state-fugacities of gaseous solutions., Chemical Reviews, 44(1), 233-244.
102. Revenaugh, J. & Meyer, R., 1997. Seismic evidence of partial melt within a possibly ubiquitous low-velocity layer at the base of the mantle, Science, 277, 670-673.
103. Revenaugh, J. & Sipkin, S.A., 1994. Seismic evidence for silicate melt atop the 410km mantle discontinuity, Nature, 369 (6480), 474-476.
104. Richet, P. & Bottinga, Y., 1986. Thermochemical properties of silicate glasses and liquids: A review, Rev. Geophys., 24(1), 1-25.
105. Rigden, S.M., Ahrens, T.J. & Stolper, E.M., 1984. Densities of liquid silicates at high pressures, Science, 226(4678), 1071-1074.
106. Rigden, S.M., Ahrens, T.J. & Stolper, E.M., 1988. Shock compression of molten silicate: Results for a model basaltic composition, J. geophys. Res., 93(B1), 367-382.
107. Rigden, S.M., Ahrens, T.J. & Stolper, E.M., 1989. High-pressure equation of state of molten anorthite and diopside, J. geophys. Res., 94(B7), 9508-9522.
108. Riley, B., 1966. The determination of melting points at temperatures above 2000° celcius, Revue International des hautes Temperatures et des Refractaires, 3(3), 327-336.
109. Rivers, M.L. & Carmichael, I.S.E., 1987. Ultrasonic studies of silicate melts, J. geophys. Res., 92, 9247-9270.
110. Rosenfeld, Y. & Tarazona, P., 1998. Density functional theory and the asymptotic high density expansion of the free energy of classical solids and fluids, Mol. Phys., 95(2), 141-150.
111. Saika-Voivod, I., Sciortino, F. & Poole, P.H., 2001. Computer simulations of liquid silica: Equation of state and liquid-liquid phase transition, Phys. Rev. E, 63. doi: 10.1103/PhysRevE.63.011202.
112. Sakamaki, T., Suzuki, A. & Ohtani, E., 2006. Stability of hydrous melt at the base of the Earth's upper mantle, Nature, 439, 192-194.
113. Shen, G. & Lazor, P., 1995. Measurement of melting temperatures of some minerals under lower mantle pressures, J. geophys. Res., 100(B9), 17699-17713.
114. Slater, J.C. & Krutter, H.M., 1935. Thomas-Fermi method for metals, Phys. Rev., 47, 559-568.
115. Solomatov, V.S. & Stevenson, D.J., 1993. Nonfractional crystallization of a terrestrial magma ocean, J. geophys. Res., 98(E3), 5391-5406.
116. Song, T.R.A., Helmberger, D.V. & Grand, S.P., 1994. Low-velocity zone atop the 410km seismic discontinuity in the northwestern United States, Nature, 427(6974), 530-533.
117. Span, R. & Wagner, W., 1997. On the extrapolation behaviour of empirical equations of state, Int. J. Thermophys., 18(6), 1415-1443.
118. Stebbins, J.F., Carmichael, I.S.E. & Moret, L.K., 1984. Heat-capacities and entropies of silicate liquids and glasses, Contrib. Mineral. Petrol., 86, 131-148.
119. Stixrude, L. & Bukowinski, M.S.T., 1990a. Fundamental thermodynamic relations and silicate melting with implications for the constitution of the D'', J. geophys. Res., 95(B12), 19311-19325.
120. Stixrude, L. & Bukowinski, M.S.T., 1990b. A novel topological compression mechanism in a covalent liquid, Science, 250, 541-543.
121. 3 liquid in the Earth's lower mantle, Science, 310, 297-299.
122. Stixrude, L. & Lithgow-Bertelloni, C., 2005. Thermodynamics of mantle minerals -I. Physical properties., Geophys. J. Int., 162, 610-632.
123. Stolper, E.M., Walker, D., Hager, B.H. & Hays, J.F., 1981. Melt segregation from partially molten source regions-the importance of melt density and source region size, J. geophys. Res., 86, 6261-6271.
124. Strachan, A., Çaǧin, T. & Goddard III, W.A., 2001. Reply to comment on 'phase diagram of MgO from density-functional theory and molecular-dynamics simulations', Phys. Rev. B, 63. doi: 10.1103/ PhysRevB.63.096102
125. Sun, N., 2008. Magma in earth's lower mantle: First principle molecular dynamics simulations of silicate liquids, PhD thesis, University of Michigan.
126. Suzuki, A. & Ohtani, E., 2003. Density of peridotite melts at high pressure, Phys. Chem. Miner., 30, 449-456.
127. Svendsen, B. & Ahrens, T.J., 1987. Shock-induced temperatures of MgO, Geophys. J. R. astr. Soc., 91, 667-691.
128. Sweeney, J.S. & Heinz, D.L., 1998. Laser-heating through a diamond-anvil cell: Melting at high pressures, in Properties of Earth and Planetary Materials at High Pressure and Temperature, Geophysical Monograph, Vol. 101, pp. 197-213, eds Manghnani, M.H. & Yagi, T., American Geophysical Union, Washington, DC.
129. 4): Synthesis, structure, and thermochemistry, Geophys. Res. Lett., 28, 2517-2520.
130. Tomlinson, J.W., Heynes, M.S.R. & Bockris, J.O., 1958. The structure of liquid silicates. Part 2. Molar volumes and expansivities, Trans. Faraday Soc., 54, 1822-1833.
131. Touloukian, Y.S., Kirby, R.K., Taylor, E.R. & Lee, T.Y.R., 1977. Thermophysical Properties of Matter-The TPRC Data Series, Vol. 13: Thermal Expansion-Nonmetallic Solids., IFI/Plenum, New York.
132. 2 from ab initio simulations, Phys. Rev. Lett., 89 (24), 245504.
133. 3 in Earth's lower mantle, Earth planet. Sci. Lett., 224, 241-248.
134. van der Waals, J.D., 1873. Over de Continuiteit van den Gas- en Vloeistoftoestand, A.W. Sijthoff, Leiden.
135. Vassiliou, M.S. & Ahrens, T.J., 1981. Hugoniot equation of state of periclase to 200GPa, Geophys. Res. Lett., 8(7), 729-732.
136. Vočadlo, L. & Price, G.D., 1996. The melting of MgO - computer calculations via molecular dynamics, Phys. Chem. Miner., 23, 42-49.
137. 3 at conditions of the Earth's deep mantle, J. geophys. Res., 112, B03208.
138. Watt, J.P., Davies, G.F. & O'Connel, R.J., 1976. The elastic properties of composite materials, Rev. Geophyis. Space Phys., 14(4), 541-563.
139. Wigner, E., 1932. On the quantum correction for thermodynamic equilibrium, Phys. Rev., 40, 749-759.
140. Williams, Q. & Garnero, E.J., 1996. Seismic evidence for partial melt at the base of Earth's mantle, Science, 273, 1528-1530.
141. Williams, Q. & Jeanloz, R., 1988. Spectroscopic evidence for pressure-induced coordination changes in silicate glasses and melts, Science, 239, 902-905.
142. Wolf, G.H. & Jeanloz, R., 1984. Lindemann melting law - anharmonic correction and test of its validity for minerals, J. geophys. Res., 89, 7821-7835.
143. Young, D.A. & Corey, E.M., 1995. A new global equation of state model for hot, dense matter, J. Appl. Phys., 78(6), 3748-3755.
144. 3 -perovskite to 625Kilobars: Indication of a high melting temperature in the lower mantle, Science, 262, 553-555.
145. Zerr, A. & Boehler, R., 1994. Constraints on the melting temperature of the lower mantle from high-pressure experiments on MgO and magnesiowüstite, Nature, 371, 506-508.
146. Zhang, L. & Fei, Y., 2008. Melting behaviour of (Mg,Fe)O solid solutions at high pressure, Geophys. Res. Lett., 35. doi: 10.1029/ 2008GL03458.
147. 2 at 9 -14GPa, J. geophys. Res., 98(B11), 19785-19793.