A new approach to the equation of state of silicate melts: An application of the theory of hard sphere mixtures

Geochimica et Cosmochimica Acta

Volumn 75, Issue 22, 2011, Pages 6780-6802

  Jing, Zhicheng ^a,b   Karato, Shun ichiro ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BULK MODULUS; COMPARATIVE STUDY; EQUATION OF STATE; EXPERIMENTAL DESIGN; MELTING; SILICATE MELT; SPHERE; TEMPERATURE EFFECT; THEORETICAL STUDY;

EID: 80054080306     PISSN: 00167037     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.gca.2011.09.004     Document Type: Article

References (105)

1. Agee C.B. Crystal-liquid density inversions in terrestrial and lunar magmas. Phys. Earth Planet. Inter. 1998, 107:63-74.
2. Agee C.B., Walker D. Olivin flotation in mantle melt. Earth Planet. Sci. Lett. 1993, 114:315-324.
3. 8 liquids to 25GPa. J. Geophys. Res. 2008, 113:B04203.
4. Andersen H.C., Weeks J.D., Chandler D. Relationship between the hard-sphere fluid and fluids with realistic repulsive forces. Phys. Rev. A 1971, 4:1597-1607.
5. Anderson D.L. Theory of the Earth 1989, Blackwell Scientific Publications.
6. Anderson D.L., Sammis C., Jordan T. Composition and evolution of the mantle and core. Science 1971, 171:1103-1112.
7. Anderson O.L. The determination of the volume dependence of the Grüneisen parameter γ. J. Geophys. Res. 1974, 79:1153-1155.
8. Anderson O.L. Equations of State of Solids for Geophysics and Ceramic Science 1995, Oxford University Press.
9. Anderson O.L., Nafe J.E. The bulk modulus-volume relationship for oxide compounds and related geophysical problems. J. Geophys. Res. 1965, 70:3951-3963.
10. Angel R.J. Equations of state of Plagioclase Feldspars. Contrib. Mineral. Petrol. 2004, 146:506-512.
11. Ashcroft N.W., Langreth D.C. Structure of binary liquid mixtures. I. Phys. Rev. 1967, 156:685-692.
12. Asimow P.D., Ahrens T.J. Shock compression of liquid silicates to 125GPa: the anorthite-diopside join. J. Geophys. Res. 2010, 115:B10209. 10.1029/2009JB007145.
13. Baidov V.V., Kunin L.L. Speed of ultrasound and compressibility of molten silica. Sov. Phys. - Dokl. 1968, 13:64-65.
14. Barrat J.-L., Hansen J.-P. Basic Concepts for Simple and Complex Liquids 2003, Cambridge University Press.
15. Bass J.D. Elasticity of minerals, glasses, and melts. Mineral Physics and Crystallography: A Handbook of Physical Constants 1995, 45-63. American Geophysical Union. T.J. Ahrens (Ed.).
16. Ben-Amotz D., Stell G. Hard sphere perturbation theory for fluids with soft-repulsive-core potentials. J. Chem. Phys. 2004, 120:4844-4851.
17. Birch F. Finite elastic strain of cubic crystals. Phys. Rev. 1947, 71:809-824.
18. Birch F. The velocity of compressional waves in rocks to 10kilobars, part 2. J. Geophys. Res. 1961, 66:2199-2224.
19. Blum L., Vericat F., Fawcett W.R. On the mean spherical approximation for hard ions and dipoles. J. Chem. Phys. 1992, 96:3039-3044.
20. Bockris J.O.M., Kojonen E. The compressibilities of certain molten alkali silicates and borates. J. Am. Ceram. Soc. 1960, 82:4493-4497.
21. Boehler R., Kennedy G.C. Pressure dependence of the thermodynamical Grüneisen parameter of liquids. J. Appl. Phys. 1977, 48:4183-4186.
22. Boehler R., Ramakrishnan J. Experimental results on the pressure dependence of the Grüneisen parameter: a review. J. Geophys. Res. 1980, 85:6996-7002.
23. Bottinga Y. On the isothermal compressibility of silicate liquids at high pressure. Earth Planet. Sci. Lett. 1985, 74:350-360.
24. Bottinga Y., Weill D.F. Densities of liquid silicate systems calculated from partial molar volumes of oxide components. Am. J. Sci. 1970, 269:169-182.
25. Brown J.M., Slutsky L.J., Nelson K.A., Cheng L.-T. Velocity of sound and equations of state for methanol and ethanol in a diamond-anvil cell. Science 1988, 241:65-67.
26. Caccamo C., Malescio G. Phase stability of dense charged hard sphere fluid mixtures. J. Chem. Phys. 1989, 90:1091-1098.
27. Chandler D. Structures of molecular liquids. Annu. Rev. Phys. Chem. 1978, 29:441-471.
28. Chen G.Q., Ahrens T.J., Stolper E.M. Shock-wave equation of state of molten and solid fayalite. Phys. Earth Planet. Inter. 2002, 134:35-52.
29. Chung D.H. Birch's law: why is it so good?. Science 1972, 177:261-263.
30. 4 liquid at high pressure. Geochim. Cosmochim. Acta 2008, 72:1427-1441.
31. Egelstaff P.A. An Introduction to the Liquid State 1994, Oxford University Press.
32. Fei Y. Thermal expansion. Mineral Physics and Crystallography: A Handbook of Physical Constants 1995, 29-41. American Geophysical Union. T.J. Ahrens (Ed.).
33. Fisher M., Levin Y. Criticality in ionic fluids: Deby-Huckel theory, Bjerrum, and beyond. Phys. Rev. Lett. 1993, 71:3826-3829.
34. Funamori N., Yamamoto S., Yagi T., Kikegawa T. Exploratory studies of silicate melt structure at high pressures and temperatures by in situ X-ray diffraction. J. Geophys. Res. 2004, 109:B03203. 10.1029/2003JB002650.
35. 25MgO NMR study. Am. Mineral. 1998, 83:1022-1029.
36. Ghiorso M.S. An equation of state for silicate melts. I. Formulation of a general model. Am. J. Sci. 2004, 304(8-9):637-678.
37. Ghiorso M.S. An equation of state for silicate melts. III. Analysis of stoichiometric liquids at elevated pressure: shock compression data, molecular dynamics simulations and mineral fusion curves. Am. J. Sci. 2004, 304(8-9):752-810.
38. Ghiorso M.S. An equation of state for silicate melts. IV. Calibration of a multicomponent mixing model to 40GPa. Am. J. Sci. 2004, 304(8-9):811-838.
39. Ghiorso M.S., Sack R.O. Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibra in magmatic systems at elevated temperatures and pressures. Contrib. Mineral. Petrol. 1995, 119:197-212.
40. 5Pa. Am. J. Sci. 2004, 304(8-9):679-751.
41. Ghiorso M.S., Hirschmann M.M., Reiners P.W., Kress V.C. The pMELTS: a revision of MELTS for improved calculations of phase relations and major element partitioning related to partial melting of the mantle to 3GPa. Geochem. Geophys. Geosyst. 2002, 3. 10.1029/2001GC000217.
42. Guillot B., Guissani Y. Towards a theory of coexistence and criticality in real molten salts. Mol. Phys. 1996, 1996:37-86.
43. Guillot B., Sarda P. The effect of compression on noble gas solubility in silicate melts and consequences for degassing at mid-ocean ridges. Geochim. Cosmochim. Acta 2006, 70:1215-1230.
44. Hansen J.-P., McDonald I.R. Theory of Simple Liquids 2006, Academic Press.
45. Hansen-Goos H., Roth R. A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres. J. Chem. Phys. 2006, 124:154506.
46. Henderson D. The theory of liquids and dense gases. Annu. Rev. Phys. Chem. 1964, 15:31-62.
47. 3 orthoenstatite up to 8.5GPa. Am. Mineral. 1994, 79:405-410.
48. Isaak D.G., Ohno I., Lee P.C. The elastic constants of monoclinic single-crystal chrome-diopside to 1300K. Phys. Chem. Miner. 2006, 32:691-699.
49. Itami T., Shimoji M. Hard-sphere model of fused salts. J. C. S. Faraday II 1980, 76:1347-1353.
50. Karki B.B., Bhattarai D., Stixrude L. First-principles calculations of the structural, dynamical, and electronic properties of liquid MgO. Phys. Rev. B 2006, 73:174208.
51. Karki B.B., Bhattarai D., Stixrude L. First-principles simulations of liquid silica: structural and dynamical behavior at high pressure. Phys. Rev. B 2007, 76:104205.
52. 3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contrib. Mineral. Petrol. 1991, 108:82-92.
53. 2. Geochim. Cosmochim. Acta 1988, 52:283-293.
54. 2 and F on the density and viscosity of silicate melts. Volatiles in Magmas 1994, vol. 30:331-369. Mineralogical Society of America.
55. 2 liquids from 700 to 1900K: extension to crustal magmatic temperatures. Contrib. Mineral. Petrol. 1997, 130:1-11.
56. 2 liquids: new measurements and derived partial molar properties. Geochim. Cosmochim. Acta 1987, 51:2931-2946.
57. Lange R.A., Carmichael I.S.E. Thermodynamic properties of silicate liquids with emphasis on density thermal expansion and compressibility. Modern methods of igneous petrology; understanding magmatic processes, 1990, vol. 24:25-64. Mineralogical Society of America.
58. 3-bearing silicate liquids. Contrib. Mineral. Petrol. 1992, 110:311-320.
59. Lebowitz J.L. Exact solution of generalized Percus-Yevick equation for a mixture of hard spheres. Phys. Rev. 1964, 133:A895-A899.
60. Lebowitz J.L., Helfand E., Praestgaard E. Scaled particle theory of fluid mixtures. J. Chem. Phys. 1965, 43:774-779.
61. Lee S.K., Cody G.D., Fei Y., Mysen B.O. Nature of polymerization and properties of silicate melts and glasses at high pressure. Geochim. Cosmochim. Acta 2004, 68:4189-4200.
62. Levien L., Weidner D.J., Prewitt C.T. Elasticity of diopside. Phys. Chem. Miner. 1979, 4:105-113.
63. Liebermann R.C., Ringwood A.E. Birch's law and polymorphic phase transformations. J. Geophys. Res. 1973, 78:6926-6932.
64. Longuet-Higgins H.C., Widom B. A rigid sphere model for the melting of argon. Mol. Phys. 1964, 8:549-553.
65. Mansoori G.A., Carnahan N.F., Starling K.E., Leland T.W. Equilibrium thermodynamic properties of the mixture of hard spheres. J. Chem. Phys. 1971, 54:1523-1525.
66. March N.H., Tosi M.P. Introduction to Liquid State Physics 2002, World Scientific Publishing Co. Pte. Ltd.
67. McBroom R.B., McQuarrie D.A. Mean field theory of fused salts. J. Phys. Chem. 1983, 87:3171-3173.
68. McMillan P.F., Wolf G.H. Vibrational spectroscopy of silicate liquids. Structure, Dynamics and Properties of Silicate Melts 1994, vol. 32:247-315. Mineralogical Society of America.
69. Miller G.H., Stolper E.M., Ahrens T.J. The equation of state of a molten komatiite 1. Shock wave compression to 36GPa. J. Geophys. Res. 1991, 96:11831-11848.
70. 3 system at high pressure: Thermodynamic properties of perovskite, postperovskite, and melt from global inversion of shock and static compression data. J. Geophys. Res. 2009, 114:B01203. 10.1029/2008JB005900.
71. Mysen B.O., Richet P. Silicate Glasses and Melts: Properties and Structure 2005, Elsevier.
72. Ohtani E., Maeda M. Density of basaltic melt at high pressure and stability of the melt at the base of the lower mantle. Earth Planet. Sci. Lett. 2001, 193:69-75.
73. Poirier J.-P. Introduction to the Physics of the Earth's Interior 2000, Cambridge University Press.
74. Reiss H., Frisch H.L., Lebowitz J.L. Statistical mechanics of rigid spheres. J. Chem. Phys. 1959, 31:369-380.
75. Richet P., Neuville D.R. Thermodynamics of silicate melts: configurational properties. Adv. Phys. Geochem. 1992, 10:132-161.
76. Rigden S.M., Ahrens T.J., Stolper E.M. Shock compression of molten silicate: results for a model basaltic composition. J. Geophys. Res. 1988, 93:367-382.
77. Rigden S.M., Ahrens T.J., Stolper E.M. High-pressure equation of state of molten anorthite and diopside. J. Geophys. Res. 1989, 94:9508-9522.
78. Rivers M.L., Carmichael I.S.E. Ultrasonic studies of silicate melts. J. Geophys. Res. 1987, 92(B9):9247-9270.
79. Rosenfeld Y. Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas. J. Chem. Phys. 1993, 98:8126-8148.
80. Rowlinson J.S. The statistical mechanics of systems with steep intermolecular potentials. Mol. Phys. 1964, 8:107-115.
81. Schilling F.R., Sinogeikin S.V., Hauser M., Bass J.D. Elastic properties of model basaltic melt compositions at high temperatures. J. Geophys. Res. 2003, 108(B6):2304. 10.1029/2001JB000517.
82. Secco R.A., Manghnani M.H., Liu T.-C. The bulk modulus-attenuation-viscosity systematics of diopside-anorthite melts. Geophys. Res. Lett. 1991, 18:93-96.
83. Shankland T.J. Velocity-density systematics: derivation from Debye theory and the effect of ionic size. J. Geophys. Res. 1972, 77:3750-3758.
84. 3 glasses under high pressure. J. Phys.: Condens. Matter 2006, 18:6531-6544.
85. Smyth J.R., McCormick T.C. Crystallographic data for minerals. Mineral Physics and Crystallography: A Handbook of Physical Constants 1995, American Geophysical Union. T.J. Ahrens (Ed.).
86. Stebbins J.F. Dynamics and structure of silicate and oxide melts: nuclear magnetic resonance studies. Structure, dynamics and properties of silicate melts 1995, vol. 32:191-246. Mineralogical Society of America.
87. Stillinger F.H. Compressibility of simple fused salts. J. Chem. Phys. 1961, 35:1581-1583.
88. 3 liquid in Earth's lower mantle. Science 2005, 310:297-299.
89. Stixrude L., Lithgow-Bertelloni C. Thermodynamics of mantle minerals - I. Physical properties. Geophys. J. Int. 2005, 162:610-632.
90. Stixrude L., de Koker N.P., Sun N., Mookherjee M., Karki B.B. Thermodynamics of silicate liquids in the deep Earth. Earth Planet. Sci. Lett. 2009, 278:226-232.
91. Suski L., Tomczyk P. Application of hard-sphere theory to the compressibilities of some fused-salt binary mixtures. J. Chem. Thermodyn. 1981, 13:803-814.
92. Suzuki A., Ohtani E. Density of peridotite melts at high pressure. Phys. Chem. Miner. 2003, 30:449-456.
93. Suzuki A., Ohtani E., Kato T. Density and thermal expansion of a peridotite melt at high pressure. Phys. Earth Planet. Inter. 1998, 107:53-61.
94. 8 liquid. Am. Mineral. 2007, 92:1573-1585.
95. Thiele E. Equation of state for hard spheres. J. Chem. Phys. 1963, 39:474-479.
96. Tomczyk P. Compressibility of simple molten salts. J. Phys. Chem. 1977, 81:183-184.
97. Vinet P., Ferrante J., Smith J.R., Rose J.H. A universal equation of state for solids. J. Phys. C: Solid State Phys. 1986, 19:L467-L473.
98. Wang H. Elasticity of Silicate Glasses 1989, M.S., University of Illinois at Urbana.
99. 2 system. Geochim. Cosmochim. Acta 1996, 60(1):75-86.
100. Wertheim Exact solution of the Percus-Yevick integral equation for hard spheres. Phys. Rev. Lett. 1963, 10:321-323.
101. Wolf G.H., McMillan P.F. Pressure effects on silicate melt structure and properties. Structure, Dynamics and Properties of Silicate Melts 1995, vol. 32:505-561. Mineralogical Society of America.
102. Xue X., Stebbins J.F., Kanzaki M., Tronnes R.G. Silicon coordination and speciation changes in a silicate liquid at high pressures. Science 1989, 245:962-964.
103. Yamada A., Inoue T., Urakawa S., Funakoshi K.-i., Funamori N., Kikegawa T., Ohfuji H., Irifune T. In situ X-ray experiment on the structure of hydrous Mg-silicate melt under high pressure and high temperature. Geophys. Res. Lett. 2007, 34:L10303. 10.1029/2006GL028823.
104. Zhou Y., Stell G. Criticality of charged systems. II. The binary mixture of hard spheres and ions. J. Chem. Phys. 1995, 102:5796-5802.
105. Zhou Y., Yeh S., Stell G. Criticality of charged systems. I. The restricted primitive model. J. Chem. Phys. 1995, 102:5785-5795.