Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T12:27:59.748Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermodynamics from first principles: temperature and composition of the Earth’s core

Published online by Cambridge University Press:  05 July 2018

D. Alfé ,
M. J. Gillan  and
G. D. Price
D. Alfé*
Affiliation:
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, UK
M. J. Gillan
Affiliation:
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
G. D. Price
Affiliation:
Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, UK
*
* E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We summarize the main ideas used to determine the thermodynamic properties of pure systems and binary alloys from first principles calculations. These are based on the ab initio calculations of free energies. As an application we present the study of iron and iron alloys under Earth,s core conditions. In particular, we report the whole melting curve of iron under these conditions, and we put constraints on the composition of the core. We found that iron melts at 6350士600 K at the pressure corresponding to the boundary between the solid inner core and the liquid outer core (ICB). We show that the core could not have been formed from a binary mixture of Fe with S, Si or O and we propose a ternary or quaternary mixture with 8—10% of S/Si in both liquid and solid and an additional ~8% of oxygen in the liquid. Based on this proposed composition we calculate the shift of melting temperature with respect to the melting temperature of pure Fe of ~—700 K, so that our best estimate for the temperature of the Earth's core at ICB is 5650±600 K.

Keywords

thermodynamicsfirst principles calculationsEarth’s coreironinner core boundary (ICB).
Type
Research Article
Information
Mineralogical Magazine , Volume 67 , Issue 1 , February 2003 , pp. 113 - 123
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alfé, D. and Gillan, M.J. (1998) First-principles simulations of liquid Fe-S under Earth's core conditions Physical Review B, 58, 8248—8256.CrossRefGoogle Scholar
Alfé, D. (1998) Program available at http://chianti.geol. ucl.ac.uk/〜darioGoogle Scholar
Alfé, D. Gillan M.J. and Price, G.D. (1999a) The melting curve of iron at the pressures of the Earth's core from ab initio calculations. Nature, 401, 462—464.CrossRefGoogle Scholar
Alfé, D. Price, G.D. and Gillan, M.J. (1999b) Oxygen in the Earth's core: a first-principles study. Physics o f the Earth and Planetary Interiors, 110, 191—210.CrossRefGoogle Scholar
Alfé, D.(1999c) Ab initio molecular dynamics, a simple algorithm for charge extrapolation. Computer Physics Communications, 118, 31—33.CrossRefGoogle Scholar
Alfé, D. de Wijs, G.A., Kresse, G. and Gillan, M.J. (2000a) Recent developments in ab initio thermo dynamics. International Journal o f Quantum Chemistry, 77, 871—879.3.0.CO;2-3>CrossRefGoogle Scholar
Alfé, D. Kresse, G. and Gillan, M.J. (2000b) Structure and dynamics of liquid iron under Earth's core conditions. Physical Review B, 61, 132—142.CrossRefGoogle Scholar
Alfé, D. Gillan, M.J. and Price, G.D. (2000c) Constraints on the composition of the Earth's core from ab initio calculations. Nature, 405, 172—175.CrossRefGoogle Scholar
Alfé, D. Gillan, M.J. and Price, G.D. (2000d) Thermodynamic stability of Fe/O solid solution at inner-core conditions. Geophysical Research Letters, 27, 2417—2420.CrossRefGoogle Scholar
Alfé, D. Gillan, M.J. and Price, G.D. (2001) Thermodynamics of hexagonal-close-packed iron under Earth's core conditions. Physical Review B , 61, 045123, 1—16.Google Scholar
Alfé, D. Gillan, M.J. and Price, G.D. (2002a) Iron under Earth's core conditions: Liquid-state thermodynamics and high-pressure melting curve from ab initio calculations. Physical Review B , 65, 165118, 1—11.CrossRefGoogle Scholar
Alfé, D. Gillan, M.J. and Price, G.D. (2002b) Composition and temperature of the Earth's core constrained by combining ab initio calculations and seismic data. Earth and Planetary Science Letters, 195, 91—98.CrossRefGoogle Scholar
Alfé, D. Price, G.D. and Gillan, M.J. (2002c) Complementary approaches to the ab initio calculation of melting properties. Journal o f Chemical Physics , 116, 6170—6177.CrossRefGoogle Scholar
Alfé, D. Price, G.D. and Gillan, M.J. (2002d) Ab initio chemical potentials of solid and liquid solutions and the chemistry of the Earth's core. Journal of Chemical Physics , 116, 7127—7136.CrossRefGoogle Scholar
Belonoshko, A.B., Ahuja, R. and Johansson, B. (2000) Quasi-Ab Initio Molecular Dynamic Study of Fe Melting Physical Review Letters, 84, 3638—3641.CrossRefGoogle ScholarPubMed
Birch, F. (1952) Elasticity and composition of the Earth's interior. Journal of Geophysical Research , 57, 227—286.CrossRefGoogle Scholar
Birch, F. (1964) Density and composition of mantle and core. Journal o f Geophysics Research , 69, 4377—4388.CrossRefGoogle Scholar
Blochl, P.E. (1994) Projector augmented-wave method Physical Review B, 50, 17953—17979.CrossRefGoogle ScholarPubMed
Boehler, R. (1993) Temperatures in the earth's core from melting-point measurements of iron at high static pressures Nature, 363, 534—536.CrossRefGoogle Scholar
Brown, J.M. and McQueen, R.G. (1986) Phase-transitions, Griineisen-parameter, and elasticity for shocked iron between 77-Gpa and 400-Gpa Journal o f Geophysical Research, 91, 7485—7494.CrossRefGoogle Scholar
Car, R. and Parrinello, M. (1985) Unified Approach for Molecular Dynamics and Density-Functional Theory. Physical Review Letters , 55, 2471—2475.CrossRefGoogle ScholarPubMed
Chandler, D. (1987) Introduction to Modern Statistical Mechanics. Oxford University Press, Oxford, UK.Google Scholar
de Wijs, G.A., Kresse, G. and Gillan, M.J. (1998) First-order phase transitions by first-principles free-energy calculations: The melting of Al. Physical Review B , 57, 8223—8234.CrossRefGoogle Scholar
Errandonea, D., Schwager, B., Ditz, R., Gessmann, C., Boehler, R. and Ross, M. (2001) Systematics of transition-metal melting Physical Review B, 63, 132104, 1—4.CrossRefGoogle Scholar
Frenkel, D. and Smit, B. (1996) Understanding Molecular Simulation, Academic Press, New York.Google Scholar
Jephcoat, A. and Olson, P. (1987) Is the inner core ofthe Earth pure iron? Nature, 325, 332—335.CrossRefGoogle Scholar
Johnson, K., Zollweg, J.A. and Gubbins, E. (1993) The Lennard-Jones equation of state revisited. Molecular Physics, 78, 591—618.CrossRefGoogle Scholar
Karki, B.B., Wentzcovitch, R.M., de Gironcoli, S. and Baroni, S. (2000) Ab initio lattice dynamics of MgSi〇3 perovskite at high pressure. Physical Review B , 62, 14750—14756.CrossRefGoogle Scholar
Kern, G., Kresse, G. and Hafner, J. (1999) Ab initio calculation of the lattice dynamics and phase diagram of boron nitride. Physical Review B , 59, 8551—8559.CrossRefGoogle Scholar
Kresse, G., Furthmuller, J. and Hafner, J. (1995) Ab-initio force-constant approach to phonon dispersion relations of diamond and graphite. Europhysics Letters , 32, 729—734.CrossRefGoogle Scholar
Kresse, G. and Furthmuller, J. (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B , 54, 11169—11186.CrossRefGoogle ScholarPubMed
Kresse, G. and Joubert, D. (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Physical Review B , 59, 1758—1775.CrossRefGoogle Scholar
Laio, A., Bernard, S., Chiarotti, G.L., Scandolo, S. and Tosatti, E. (2000) Physics of iron at Earth's core conditions Science, 287, 1027—1030.CrossRefGoogle ScholarPubMed
Lichtenstein, A.I., Jones, R.O., de Gironcoli, S. and Baroni, S. (2000) Anisotropic thermal expansion in silicates: A density functional study of beta-eucryptite and related materials. Physical Review B, 62, 11487—11493.CrossRefGoogle Scholar
Loper, D.E. (1978) The gravitationally powered dynamo Geophysical Journal o f the Royal Astronomical Society, 54, 389—404.CrossRefGoogle Scholar
Masters, T.G. and Shearer, P.M. (1990) Summary of seismological constraints on the structure ofthe earth core. Journal o f Geophysical Research , 95, 21691—21695.CrossRefGoogle Scholar
Parr, R.G. and Yang, W. (1989) Density-Functional Theory of Atoms and Molecules. Oxford University Press, Oxford, UK.Google Scholar
Pickett, W.E. (1989) Pseudopotential methods in condensed matter applications. Computer Physics Reports, 9, 115—197.CrossRefGoogle Scholar
Poirier, J.-P. (1994) Light elements in the Earth's outer core: a critical review Physics of the Earth and Planetary Interiors, 85, 319—337.CrossRefGoogle Scholar
Ringwood, A.E. (1977) On the h; 135.composition of the core and implications for the origin of the Earth Geochimica et Cosmochimica Acta, 11, 111 — 135.Google Scholar
Saxena, S.K., Shen, G. and Lazor, P. (1994) Temperatures in earths core based on melting and phase-transformation experiments on iron Science, 264, 405—407.CrossRefGoogle Scholar
Shen, G., Mao, H., Hemley, R.J., Duffy, T.S. and Rivers, M.L. (1998) Melting and crystal structure of iron at high pressures and temperatures Geophysical Research Letters, 25, 373—376.CrossRefGoogle Scholar
Soderlind, P., Moriarty, J.A. and Wills, J.M. (1996) First-principles theory of iron up to earth-core pressures: Structural, vibrational and elastic properties Physical Review B, 53, 14063—14072.CrossRefGoogle ScholarPubMed
Stixrude, L., Cohen, R.E. and Singh, D.J. (1994) Iron at high pressure: Linearized-augmented-plane-wave computations in the generalized-gradient approximation Physical Review B, 50, 6442—6445.CrossRefGoogle ScholarPubMed
Stixrude, L., Wasserman, E. and Cohen, R.E. (1997) Composition and temperature of the Earth's inner core Journal o f Geophysical Research, 102, 24729—24739.CrossRefGoogle Scholar
Sugino, O. and Car, R. (1995) Ab initio molecular dynamics study of first-order phase transitions: melting of silicon Physical Review Letters, 74, 1823—1826.CrossRefGoogle ScholarPubMed
Vanderbilt, D. (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Physical Review, 41, 7892—7895.CrossRefGoogle Scholar
Vocadlo, L., de Wijs, G.A., Kresse, G., Gillan, M.J. and Price, G.D. (1997) First-principles calculations on crystalline and liquid iron at Earth's core conditions Faraday Discussions, 106, 205—217.CrossRefGoogle Scholar
Vocadlo, L. and Alfé, D. (2002) Ab initio melting curve of the fcc phase of aluminum. Physical Review B, 65, 214105, 1—12.CrossRefGoogle Scholar
Vocadlo, L., Alfé, D., Brodholt, J.P., Price, G.D. and Gillan, M.J. (2000) Ab initio free energy calculations on the polymorphs of iron at core conditions Physics o f the Earth and Planetary Interiors, 117, 123—137.CrossRefGoogle Scholar
Wang, Y. and Perdew, J. (1991) Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling. Physical Review B , 44, 13298—13307.CrossRefGoogle ScholarPubMed
Wei, S.H. and Krakauer, H. (1985) Local-density-functional calculation of the pressure-induced metallization of BaSe and BaTe. Physical Review Letters , 55, 1200—1203.CrossRefGoogle ScholarPubMed
Williams, Q., Jeanloz, R., Bass, J.D., Svendesen, B. and Ahrens, T.J. (1987) The melting curve of iron to 250 gigapascals — a constraint on the temperature at earths center Science, 286, 181—182.CrossRefGoogle Scholar
Yoo, C.S., Holmes, N.C., Ross, M., Webb, D.J. and Pike, C. (1993) Shock temperatures and melting of iron at Earth core conditions Physical Review Letters, 70, 3931—3934.CrossRefGoogle ScholarPubMed