Self-consistent thermodynamic description of silicate liquids, with application to shock melting of MgO periclase and MgSiO 3 perovskite
dc.contributor.author | de Koker, Nico Pieter Jan | en_US |
dc.contributor.author | Stixrude, Lars | en_US |
dc.date.accessioned | 2010-06-01T22:04:43Z | |
dc.date.available | 2010-06-01T22:04:43Z | |
dc.date.issued | 2009-07 | en_US |
dc.identifier.citation | de Koker, Nico; Stixrude, Lars (2009). "Self-consistent thermodynamic description of silicate liquids, with application to shock melting of MgO periclase and MgSiO 3 perovskite." Geophysical Journal International 178(1): 162-179. <http://hdl.handle.net/2027.42/75103> | en_US |
dc.identifier.issn | 0956-540X | en_US |
dc.identifier.issn | 1365-246X | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/75103 | |
dc.description.abstract | We develop a self-consistent thermodynamic description of silicate liquids applicable across the entire mantle pressure and temperature regime. The description combines the finite strain free energy expansion with an account of the temperature dependence of liquid properties into a single fundamental relation, while honouring the expected limiting behaviour at large volume and high temperature. We find that the fundamental relation describes well previous experimental and theoretical results for liquid MgO, MgSiO 3 , Mg 2 SiO 4 and SiO 2 . We apply the description to calculate melting curves and Hugoniots of solid and liquid MgO and MgSiO 3 . For periclase, we find a melting temperature at the core–mantle boundary (CMB) of 7810 ± 160 K , with the solid Hugoniot crossing the melting curve at 375 GPa, 9580 K , and the liquid Hugoniot crossing at 470 GPa, 9870 K . For complete shock melting of periclase we predict a density increase of 0.14 g cm −3 and a sound speed decrease of 2.2 km s −1 . For perovskite, we find a melting temperature at the CMB of 5100 ± 100 K with the perovskite section of the enstatite Hugoniot crossing the melting curve at 150 GPa, 5190 K , and the liquid Hugoniot crossing at 220 GPa, 5520 K . For complete shock melting of perovskite along the enstatite principal Hugoniot, we predict a density increase of 0.10 g cm −3 , with a sound speed decrease of 2.6 km s −1 . | en_US |
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dc.format.extent | 3109 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.publisher | Blackwell Publishing Ltd | en_US |
dc.rights | Journal compilation © 2009 RAS | en_US |
dc.subject.other | Mantle Processes | en_US |
dc.subject.other | Equations of State | en_US |
dc.subject.other | High-pressure Behaviour | en_US |
dc.subject.other | Phase Transitions | en_US |
dc.subject.other | Planetary Interiors | en_US |
dc.subject.other | Physics of Magma and Magma Bodies | en_US |
dc.title | Self-consistent thermodynamic description of silicate liquids, with application to shock melting of MgO periclase and MgSiO 3 perovskite | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Geology and Earth Sciences | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Geological Sciences, University of Michigan, Ann Arbor, Michigan, USA. E-mail: nico.dekoker@uni-bayreuth.de | en_US |
dc.contributor.affiliationother | Department of Earth Sciences, University College London, UK | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/75103/1/j.1365-246X.2009.04142.x.pdf | |
dc.identifier.doi | 10.1111/j.1365-246X.2009.04142.x | en_US |
dc.identifier.source | Geophysical Journal International | en_US |
dc.identifier.citedreference | Agee, C.B. & Walker, D., 1988. Static compression and olivine flotation in ultrabasic silicate liquid, J. geophys. Res., 93, 3437 – 3449. | en_US |
dc.identifier.citedreference | Agee, C.B. & Walker, D., 1993. Olivine flotation in mantle melt, Earth planet. Sci. Lett., 114, 315 – 324. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Ai, Y. & Lange, R.A., 2008. New acoustic velocity measurements on CaO-MgO-Al 2 O 3 -SiO 2 liquids: Reevaluation of the volume and compressibility of CaMgSi 2 O 6 -CaAl 2 Si 2 O 8 liquids to 25 GPa, J. geophys. Res., 113, B04203, doi :. | en_US |
dc.identifier.citedreference | Akins, J.A., Luo, S.N., Asimow, P.D. & Ahrens, T.J., 2004. Shock-induced melting of MgSiO 3 perovskite and implications for melts in Earth's lowermost mantle, Geophys. Res. Lett., 31, L14612. | en_US |
dc.identifier.citedreference | Alfe, D., 2005. Melting curve of MgO from first-principles simulations, Phys. Rev. Lett., 94, 235701. | en_US |
dc.identifier.citedreference | Allen, M.P. & Tildesley, D.J., 1987. Computer Simulation of Liquids, 1st edn, Oxford University Press, Oxford. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Anderson, O.L., 1995. Equations of State of Solids for Geophysics and Ceramic Science, Oxford University Press, New York. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Atlas, L., 1952. The polymorphism of MgSiO 3 and solid-state equilibria of the system MgSiO 3 − CaMgSi 2 O 6, J. Geol., 60, 125 – 147. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Birch, F., 1952. Elasticity and constitution of the Earth's interior, J. geophys. Res., 57 ( 2 ), 227 – 286. | en_US |
dc.identifier.citedreference | Birch, F., 1978. Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300 K, J. geophys. Res., 83 ( B3 ), 1257 – 1268. | en_US |
dc.identifier.citedreference | Bottinga, Y., 1985. On the isothermal compressibility of silicate liquids at high-pressure, Earth planet. Sci. Lett., 74, 350 – 360. | en_US |
dc.identifier.citedreference | Bowen, N.L. & Andersen, O., 1914. The binary system MgO-SiO 2, Am. J. Sci., 37, 487 – 500. | en_US |
dc.identifier.citedreference | Boyle, R., 1662. New Experiments Physico-Mechanical, Touching the Spring and Weight of the Air, and its Effects, H. Hall, Oxford. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Bukowinski, M.S.T., 1977. Theoretical equation of state for the inner core, Phys. Earth planet. Inter., 14 ( 4 ), 333 – 344. | en_US |
dc.identifier.citedreference | Callen, H.B., 1985. Thermodynamics and an Introduction to Thermostatistics, 2nd edn, John Wiley & Sons, New York. | en_US |
dc.identifier.citedreference | Canup, R.M., 2004. Simulations of a late lunar-forming impact, Icarus, 168, 433 – 456. | en_US |
dc.identifier.citedreference | Ceperley, D.M. & Alder, B.J., 1980. Ground-state of the electron-gas by a stochastic method, Phys. Rev. Lett., 45, 566 – 569. | en_US |
dc.identifier.citedreference | Chandrasekhar, S., 1939. An Introduction to the Study of Stellar Structure, University of Chicago Press, Chicago. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Clapeyron, B.P.E., 1834. MÉmoire sur la puissance motrice de la chaleur, Journal de l'ecole polytechnique Paris, 14, 153 – 190. | en_US |
dc.identifier.citedreference | Cohen, R.E. & Gong, Z., 1994. Melting and melt structure of MgO at high pressures, Phys. Rev. B, 50 ( 17 ), 12 301 – 12 311. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Cohen, R., GÜlseren, O. & Hemley, R., 2000. Accuracy of equation-of-state formulations, Am. Mineral., 85, 338 – 344. | en_US |
dc.identifier.citedreference | Courtial, P., Ohtani, E. & Dingwell, D.B., 1997. High-temperature densities of some mantle melts, Geochim. Cosmochim. Acta, 61 ( 15 ), 3111 – 3119. | en_US |
dc.identifier.citedreference | De Koker, N.P., Stixrude, L. & Karki, B.B., 2008. Thermodynamics, structure, dynamics, and freezing of Mg 2 SiO 4 liquid at high pressure, Geochim. Cosmochim. Acta, 72, 1427 – 1441, doi :. | en_US |
dc.identifier.citedreference | Dingwell, D.B., Knoche, R. & Webb, S.L., 1993. A volume temperature relationship for liquid GeO 2 and some geophysically relevant derived parameters for network liquids, Phys. Chem. Miner., 19, 445 – 453. | en_US |
dc.identifier.citedreference | Dorogokupets, P.I., 2000. Thermodynamic functions at zero pressure and their relation to equations of state of minerals, Am. Mineral., 85, 329 – 337. | en_US |
dc.identifier.citedreference | Dubrovinsky, L.S. & Saxena, S.K., 1997. Thermal expansion of periclase (MgO) and tungsten (W) to melting temperatures, Phys. Chem. Miner., 24, 547 – 550. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Flyvberg, H. & Petersen, H.G., 1989. Error-estimates on averages of correlated data, J. Chem. Phys., 91, 461 – 466. | en_US |
dc.identifier.citedreference | Francis, G.P. & Payne, M.C., 1990. Finite basis set corrections to total energy pseudopotential calculations, J. Phys.-Conden. Matter, 2 ( 19 ), 4395 – 4404. | en_US |
dc.identifier.citedreference | Frenkel, D. & Smit, B., 1996. Understanding Molecular Simulation: From Algorithms to Applications, 1st edn, Academic Press, San Diego. | en_US |
dc.identifier.citedreference | Gaetani, G.A., Asimow, P.D. & Stolper, E.M., 1998. Determination of the partial molar volume of SiO 2 in silicate liquids at elevated pressures and temperatures: a new experimental approach, Geochim. Cosmochim. Acta, 62 ( 14 ), 2499 – 2508. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Ghiorso, M.S., 2004. An equation of state for silicate melts. I. Formulation of a general model, Am. J. Sci., 304, 637 – 678. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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 3 GPa, Geochem. Geophys. Geosyst., 3 ( 5 ), doi :. | en_US |
dc.identifier.citedreference | Ghiorso, M.S., Nevins, D. & Spera, F.J., 2006. Molecular dynamics studies of MgSiO 3 liquid to 150 GPa: 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Halbach, H. & Chatterjee, N.D., 1982. An empirical Redlich-Kwong-type equation of state for water to and 100 Kbar, Contrib. Mineral. Petrol., 79, 337 – 345. | en_US |
dc.identifier.citedreference | Heinz, D.L. & Jeanloz, R., 1987. Measurement of the melting curve of Mg 0.9 Fe 0.1 SiO 3 at lower mantle conditions and its geophysical implications, J. geophys. Res., 92 ( B11 ), 11 437 – 11 444. | en_US |
dc.identifier.citedreference | 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 :. | en_US |
dc.identifier.citedreference | Hofmeister, A.M., 1993. Interatomic potentials calculated from equations of state: limitation of finite strain to moderate, Geophys. Res. Lett., 20 ( 7 ), 635 – 638. | en_US |
dc.identifier.citedreference | Hohenberg, P. & Kohn, W., 1964. Inhomogeneous electron gas, Phys. Rev. B., 136, B864. | en_US |
dc.identifier.citedreference | Holland, T. & Powell, R., 1991. A compensated-Redlich–Kwong (CORK) equation for volumes and fugacities of CO 2 and H 2 O in the range 1 bar to 50 kbar and 100–, Contrib. Mineral. Petrol., 109, 265 – 273. | en_US |
dc.identifier.citedreference | Hudon, P., Jung, I.-H. & Baker, D.R., 2002. Melting of Β-quartz up to 2.0 GPa and thermodynamic optimization of the silica liquidus up to 6.0 GPa, Phys. Earth planet. Inter., 130, 159 – 174. | en_US |
dc.identifier.citedreference | Isaak, D.G., Anderson, O.L. & Goto, T., 1989. Measured elastic moduli of single-crystal MgO up to 1800 K, Phys. Chem. Miner., 16, 704 – 713. | en_US |
dc.identifier.citedreference | Jeanloz, R., 1989. Shock wave equation of state and finite strain theory, J. geophys. Res., 94 ( B5 ), 5873 – 5886. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Karki, B.B., Wentzcovitch, R.M., de Gironcoli, S. & Baroni, S., 2000. Ab initio lattice dynamics of MgSiO 3 perovskite at high pressure, Phys. Rev. B, 62 ( 22 ), 14750 – 14756. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Kirkwood, J.G., 1933. Quantum statistics of almost classical assemblies, Phys. Rev., 44, 31 – 37. | en_US |
dc.identifier.citedreference | Knittle, E. & Jeanloz, R., 1989. Melting curve of (Mg, Fe)SiO 3 perovskite to 96 GPa, evidence for a structural transition in lower mantle melts, Geophys. Res. Lett., 16 ( 5 ), 421 – 424. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Kohn, W. & Sham, L.J., 1965. Self-consistent equations including exchange and correlation effects, Phys. Rev., 140, 1133. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Kresse, G. & Hafner, J., 1994. Norm-conserving and ultrasoft pseudopotentials for first-row and transition-elements, J. Phys.-Conden. Matter, 6, 8245 – 8257. | en_US |
dc.identifier.citedreference | Lange, R.A., 1997. A revised model for the density and thermal expansivity of K 2 O − Na 2 O − CaO − MgO − Al 2 O 3 − SiO 2 liquids from 700 to 1900 K: extension to crustal magmatic temperatures, Contrib. Mineral. Petrol., 130, 1 – 11. | en_US |
dc.identifier.citedreference | Lange, R.A., 2003. The fusion curve of albite revisited and the compressibility of NaAlSi 3 O 8 liquid with pressure, Am. Mineral., 88, 109 – 120. | en_US |
dc.identifier.citedreference | Lange, R.A., 2007. The density and compressibility of KAlSi 3 O 8 liquid to 6.5 GPa, Am. Mineral., 92, 114 – 123. | en_US |
dc.identifier.citedreference | Lange, R.A. & Carmichael, I.S.E., 1987. Densities of Na 2 O − K 2 O − CaO − MgO − FeO − Fe 2 O 3 − Al 2 O 3 -TiO 2 − SiO 2 liquids—new measurements and derived partial molar properties, Geochim. Cosmochim. Acta, 51, 2931 – 2946. | en_US |
dc.identifier.citedreference | Lange, R.A. & Navrotsky, A., 1992. Heat capacities of Fe 2 O 3 -bearing silicate liquids, Contrib. Mineral. Petrol., 110, 311 – 320. | en_US |
dc.identifier.citedreference | Laudernet, Y., ClÉrouin, J. & Mazevet, S., 2004. Ab initio simulations of the electrical and optical properties of shock-compressed SiO 2, Phys. Rev. B, 70, 165108. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Luo, S.N., Akins, J.A., Ahrens, T.J. & Asimow, P.D., 2004. Shock-compressed MgSiO 3 glass, enstatite, olivine, and quartz: optical emission, temperatures, and melting, J. geophys. Res., 109, B05205. | en_US |
dc.identifier.citedreference | Lupis, C.H.P., 1983. Chemical Thermodynamics of Materials, Prentice-Hall Inc., New York. | en_US |
dc.identifier.citedreference | Marsh, S.P., 1980. LASL Shock Hugoniot Data, University of California Press, Berkeley, CA. | en_US |
dc.identifier.citedreference | Marshak, R.E. & Bethe, H.A., 1940. The generalized Thomas–Fermi method as applied to stars, Astrophys. J., 91, 239 – 243. | en_US |
dc.identifier.citedreference | Martin, B., Spera, F.J. & Nevins, D., 2006. Thermodynamic and structural properties of liquid Mg 2 SiO 4 at high temperatures and pressure in the range 0–150 GPa from molecular dynamics simulation, EOS, Trans. Am. geophys. Un., 87 ( 52 ), Fall Meeting Supplement, Abstract MR43B–1080. | en_US |
dc.identifier.citedreference | Matsui, M., 1989. Molecular dynamics study of the structural and thermodynamic properties of MgO crystal with quantum correction, J. Chem. Phys., 91, 489 – 494. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | McKenzie, D. & Bickle, M.J., 1988. The volume and composition of melt generated by extension of the lithosphere, J. Petrol., 29 ( 3 ), 625 – 679. | en_US |
dc.identifier.citedreference | McQuarrie, D.A., 1984. Statistical Mechanics, University Science Books, Sausalito, CA. | en_US |
dc.identifier.citedreference | Mermin, N.D., 1965. Thermal properties of inhomogeneous electron gas, Phys. Rev., 137, 1441. | en_US |
dc.identifier.citedreference | Miller, G.H., Stolper, E.M. & Ahrens, T.J., 1991a. The equation of state of a molten komatiite. 1. Shock wave compression to 36 GPa, J. geophys. Res., 96 ( B7 ), 11 849 – 11 864. | en_US |
dc.identifier.citedreference | 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 ), 11 849 – 11 864. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Mosenfelder, J.L., Asimow, P.D. & Ahrens, T.J., 2007. Thermodynamic properties of Mg 2 SiO 4 liquid at ultra-high pressures from shock measurements to 200 GPa on forsterite and wadsleyite, J. geophys. Res., 112 ( B06208 ), doi :. | en_US |
dc.identifier.citedreference | Mosenfelder, J.L., Asimow, P.D., Frost, D.J., Rubie, D.C. & Ahrens, T.J., 2009. The MgSiO 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 :. | en_US |
dc.identifier.citedreference | Navrotsky, A., Ziegler, D., Oestrike, R. & Maniar, P., 1989. Calorimetry of silicate melts at 1773 K—measurement of enthalpies of fusion and of mixing in the systems diopside-anorthite-albite and anorthite-forsterite, Contrib. Mineral. Petrol., 101, 122 – 130. | en_US |
dc.identifier.citedreference | NosÉ, S., 1984. A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys., 81, 511 – 519. | en_US |
dc.identifier.citedreference | 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 :. | en_US |
dc.identifier.citedreference | Oganov, A.R., Brodholt, J.P. & Price, G.D., 2001. The elastic constants of MgSiO 3 perovskite at pressures and temperatures of the Earth's mantle., Nature, 411, 934 – 937. | en_US |
dc.identifier.citedreference | Ohtani, E., 1988. Chemical stratification of the mantle formed by melting in the early stage of the terrestrial evolution, Tectonophysics, 154, 201 – 210. | en_US |
dc.identifier.citedreference | Ohtani, E. & Sawamoto, H., 1987. Melting experiment on a model chondritic mantle composition at 25 GPa, Geophys. Res. Lett., 14 ( 7 ), 733 – 736. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Pavese, A., 2002. Pressure-volume-temperature equations of state: a comparative study based on numerical simulations, Phys. Chem. Miner., 29, 43 – 51. | en_US |
dc.identifier.citedreference | Phillips, A.C., 1994. The Physics of Stars, John Wiley & Sons, Chichester. | en_US |
dc.identifier.citedreference | Pitzer, K.S. & Sterner, S.M., 1994. Equations of state valid continuously from zero to extreme pressures for H 2 O and CO 2, J. Chem. Phys., 101 ( 4 ), 3111 – 3116. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Revenaugh, J. & Sipkin, S.A., 1994. Seismic evidence for silicate melt atop the 410 km mantle discontinuity, Nature, 369 ( 6480 ), 474 – 476. | en_US |
dc.identifier.citedreference | Richet, P. & Bottinga, Y., 1986. Thermochemical properties of silicate glasses and liquids: a review, Rev. Geophys., 24 ( 1 ), 1 – 25. | en_US |
dc.identifier.citedreference | Rigden, S.M., Ahrens, T.J. & Stolper, E.M., 1984. Densities of liquid silicates at high pressures, Science, 226 ( 4678 ), 1071 – 1074. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Rivers, M.L. & Carmichael, I.S.E., 1987. Ultrasonic studies of silicate melts, J. geophys. Res., 92, 9247 – 9270. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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 :. | en_US |
dc.identifier.citedreference | Sakamaki, T., Suzuki, A. & Ohtani, E., 2006. Stability of hydrous melt at the base of the Earth's upper mantle, Nature, 439, 192 – 194. | en_US |
dc.identifier.citedreference | Shen, G. & Lazor, P., 1995. Measurement of melting temperatures of some minerals under lower mantle pressures, J. geophys. Res., 100 ( B9 ), 17 699 – 17 713. | en_US |
dc.identifier.citedreference | Slater, J.C. & Krutter, H.M., 1935. Thomas-Fermi method for metals, Phys. Rev., 47, 559 – 568. | en_US |
dc.identifier.citedreference | Solomatov, V.S. & Stevenson, D.J., 1993. Nonfractional crystallization of a terrestrial magma ocean, J. geophys. Res., 98 ( E3 ), 5391 – 5406. | en_US |
dc.identifier.citedreference | Song, T.R.A., Helmberger, D.V. & Grand, S.P., 1994. Low-velocity zone atop the 410 km seismic discontinuity in the northwestern United States, Nature, 427 ( 6974 ), 530 – 533. | en_US |
dc.identifier.citedreference | Span, R. & Wagner, W., 1997. On the extrapolation behaviour of empirical equations of state, Int. J. Thermophys., 18 ( 6 ), 1415 – 1443. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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 ), 19 311 – 19 325. | en_US |
dc.identifier.citedreference | Stixrude, L. & Bukowinski, M.S.T., 1990b. A novel topological compression mechanism in a covalent liquid, Science, 250, 541 – 543. | en_US |
dc.identifier.citedreference | Stixrude, L. & Karki, B.B., 2005. Structure and freezing of MgSiO 3 liquid in the Earth's lower mantle, Science, 310, 297 – 299. | en_US |
dc.identifier.citedreference | Stixrude, L. & Lithgow-Bertelloni, C., 2005. Thermodynamics of mantle minerals — I. Physical properties., Geophys. J. Int., 162, 610 – 632. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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 :. | en_US |
dc.identifier.citedreference | Sun, N., 2008. Magma in earth's lower mantle: first principle molecular dynamics simulations of silicate liquids, PhD thesis, University of Michigan. | en_US |
dc.identifier.citedreference | Suzuki, A. & Ohtani, E., 2003. Density of peridotite melts at high pressure, Phys. Chem. Miner., 30, 449 – 456. | en_US |
dc.identifier.citedreference | Svendsen, B. & Ahrens, T.J., 1987. Shock-induced temperatures of MgO, Geophys. J. R. astr. Soc., 91, 667 – 691. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Tangeman, J.A., Phillips, B.L., Navrotsky, A., Weber, J.K.R., Hixson, A.D. & Key, T.S., 2001. Vitreous forsterite (Mg 2 SiO 4 ): synthesis, structure, and thermochemistry, Geophys. Res. Lett., 28, 2517 – 2520. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Trave, A., Tangney, P., Scandolo, S., Pasquarello, A. & Car, R., 2002. Pressure-induced structural changes in liquid SiO 2 from ab initio simulations, Phys. Rev. Lett., 89 ( 24 ), 245504. | en_US |
dc.identifier.citedreference | Tsuchiya, T., Tsuchiya, J., Umemoto, K. & Wentzcovitch, R.M., 2004. Phase transition in MgSiO 3 in Earth's lower mantle, Earth planet. Sci. Lett., 224, 241 – 248. | en_US |
dc.identifier.citedreference | van der Waals, J.D., 1873. Over de Continuiteit van den Gas- en Vloeistoftoestand, A.W. Sijthoff, Leiden. | en_US |
dc.identifier.citedreference | Vassiliou, M.S. & Ahrens, T.J., 1981. Hugoniot equation of state of periclase to 200 GPa, Geophys. Res. Lett., 8 ( 7 ), 729 – 732. | en_US |
dc.identifier.citedreference | Vočadlo, L. & Price, G.D., 1996. The melting of MgO - computer calculations via molecular dynamics, Phys. Chem. Miner., 23, 42 – 49. | en_US |
dc.identifier.citedreference | Wan, J.T.K., Duffy, T.S., Scandolo, S. & Car, R., 2007. First-principles study of density, viscosity, and diffusion coefficients of liquid MgSiO 3 at conditions of the Earth's deep mantle, J. geophys. Res., 112, B03208. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Wigner, E., 1932. On the quantum correction for thermodynamic equilibrium, Phys. Rev., 40, 749 – 759. | en_US |
dc.identifier.citedreference | Williams, Q. & Garnero, E.J., 1996. Seismic evidence for partial melt at the base of Earth's mantle, Science, 273, 1528 – 1530. | en_US |
dc.identifier.citedreference | Williams, Q. & Jeanloz, R., 1988. Spectroscopic evidence for pressure-induced coordination changes in silicate glasses and melts, Science, 239, 902 – 905. | en_US |
dc.identifier.citedreference | Wolf, G.H. & Jeanloz, R., 1984. Lindemann melting law - anharmonic correction and test of its validity for minerals, J. geophys. Res., 89, 7821 – 7835. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Zerr, A. & Boehler, R., 1993. Melting of (Mg,Fe)SiO 3 -perovskite to 625 Kilobars: Indication of a high melting temperature in the lower mantle, Science, 262, 553 – 555. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Zhang, L. & Fei, Y., 2008. Melting behaviour of (Mg,Fe)O solid solutions at high pressure, Geophys. Res. Lett., 35, doi :. | en_US |
dc.identifier.citedreference | Zhang, J., Liebermann, R.C., Gasparik, T. & Herzberg, C.T., 1993. Melting and subsolidus relations of SiO 2 at 9 − 14 GPa, J. geophys. Res., 98 ( B11 ), 19 785 – 19 793. | en_US |
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