Equation of state and thermodynamic properties of liquid Fe-O in the Earth’s outer core

Abstract

Equation of state (EoS) plays a crucial role in the prediction of the composition of the outer core. Here, we calculated pressure (P)-volume (V)-temperature (T) data of liquid iron-oxygen alloys (Fe-X wt.% O, X = 0, 2.8, 6.1, and 9.9) under the outer core conditions (∼136–330 GPa, 4000–6000 K) by first-principles molecular dynamics simulations. We established an EoS for liquid Fe-O alloys with parameters including P, T, V, and O concentrations. Consequently, thermodynamic properties of liquid Fe-O alloys such as density (ρ), thermal expansion coefficient, isothermal and adiabatic bulk modulus, and sound velocity (V_P) are calculated. To constrain the O content, we predicted the ρ-P and V_P-P profiles along the geotherm and compared them with data from the Preliminary Reference Earth Model (PREM). We conclude that the adiabatic T profile as a function of depth affects the prediction of O content dramatically. With several anchored T_ICB, the composition of Fe-6.1 wt.% O matches the PREM data with an acceptable range of error. But strictly speaking, the distribution in the outer core is probably uneven. In such case, we state that the O content in the outer core cannot be higher than approximately 6.1 wt.%.

Keywords

Equation of state / First-principles molecular dynamics / Liquid iron-oxygen alloys / Thermodynamic properties

References

D. Alfè. Temperature of the inner-core boundary of the Earth: Melting of iron at high pressure from first-principles coexistence simulations. Phys. Rev. B, 79 (6) (2009), Article 060101,

D. Alfè, G.D. Price, M.J. Gillan. Oxygen in the Earth’s core: a first-principles study. Phys. Earth Planet. In., 110 (3) (1999), pp. 191-210,

D. Alfè, G. Kresse, M.J. Gillan. Structure and dynamics of liquid iron under Earth’s core conditions. Phys. Rev. B, 61 (1) (2000), pp. 132-142,

D. Alfè, G.D. Price, M.J. Gillan. Thermodynamics of hexagonal-close-packed iron under Earth’s core conditions. Phys. Rev. B, 64 (4) (2001), Article 045123,

W.W. Anderson, T.J. Ahrens. An equation of state for liquid iron and implications for the Earth’s core. J. Geophys. Res.-Solid Earth, 99 (B3) (1994), pp. 4273-4284,

O.L. Anderson, D.G. Isaak. Another look at the core density deficit of Earth’s outer core. Phys. Earth Planet. In., 131 (1) (2002), pp. 19-27,

S. Anzellini, A. Dewaele, M. Mezouar, P. Loubeyre, G. Morard. Melting of iron at Earth’s inner core boundary based on fast X-ray diffraction. Science, 340 (6131) (2013), pp. 464-466,

Y. Asahara, D.J. Frost, D.C. Rubie. Partitioning of FeO between magnesiowüstite and liquid iron at high pressures and temperatures: Implications for the composition of the Earth’s outer core. Earth Planet. Sci. Lett., 257 (3) (2007), pp. 435-449,

J. Badro, A.S. Côté, J.P. Brodholt. A seismologically consistent compositional model of Earth’s core. Proc. Natl. Acad. Sci., 111 (21) (2014), pp. 7542-7545,

A.B. Belonoshko, R. Ahuja, B. Johansson. Quasi–Ab Initio molecular dynamic study of Fe melting. Phys. Rev. Lett., 84 (16) (2000), pp. 3638-3641,

F. Birch. Elasticity and constitution of the Earth’s interior. J. Geophys. Res., 57 (2) (1952), pp. 227-286,

P.E. Blöchl. Projector augmented-wave method. Phys. Rev. B, 50 (24) (1994), pp. 17953-17979,

R. Boehler. Temperatures in the Earth’s core from melting-point measurements of iron at high static pressures. Nature, 363 (6429) (1993), pp. 534-536,

J.M. Brown, R.G. McQueen. Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa. J. Geophys. Res.-Solid Earth, 91 (B7) (1986), pp. 7485-7494,

A. Dewaele, P. Loubeyre, F. Occelli, M. Mezouar, P.I. Dorogokupets, M. Torrent. Quasihydrostatic equation of state of Iron above 2 Mbar. Physical Rev. Lett., 97 (21) (2006), Article 215504,

P.I. Dorogokupets, A.M. Dymshits, K.D. Litasov, T.S. Sokolova. Thermodynamics and equations of state of iron to 350 GPa and 6000 K. Sci. Rep., 7 (1) (2017), p. 41863,

L.S. Dubrovinsky, S.K. Saxena, F. Tutti, S. Rekhi, T. LeBehan. In situ X-Ray study of thermal expansion and phase transition of iron at multimegabar pressure. Phys. Rev. Lett., 84 (8) (2000), pp. 1720-1723,

A.M. Dziewonski, D.L. Anderson. Preliminary reference Earth model. Phys. Earth Planet. In., 25 (4) (1981), pp. 297-356,

D.J. Frost, Y. Asahara, D.C. Rubie, N. Miyajima, L.S. Dubrovinsky, C. Holzapfel, et al.. Partitioning of oxygen between the Earth’s mantle and core. J. Geophys. Res.-Solid Earth, 115 (B2) (2010),

J. Fu, L. Cao, X. Duan, A.B. Belonoshko. Density and sound velocity of liquid Fe-S alloys at Earth’s outer core P-T conditions. Am. Mineral., 105 (9) (2020), pp. 1349-1354,

F. González-Cataldo, B. Militzer. Ab initio determination of iron melting at terapascal pressures and Super-Earths core crystallization. Phys. Rev. Res., 5 (3) (2023), Article 033194,

V.J. Hillgren, C.K. Gessmann, J. Li. An experimental perspective on the light element in Earth’s core. Origin of the Earth and Moon, 30 (2000), pp. 245-263

K. Hirose, S. Labrosse, J. Hernlund. Composition and state of the core. Annu. Rev. Earth Planet. Sci., 41 (1) (2013), pp. 657-691,

K. Hirose, B. Wood, L. Vočadlo. Light elements in the Earth’s core. Nat. Rev. Earth Environ., 2 (9) (2021), pp. 645-658,

W.G. Hoover. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A, 31 (3) (1985), pp. 1695-1697,

H. Huang, X. Hu, F. Jing, L. Cai, Q. Shen, Z. Gong, H. Liu. Melting behavior of Fe-O-S at high pressure: A discussion on the melting depression induced by O and S. J. Geophys. Res.-Solid Earth, 115 (B5) (2010),

H. Huang, Y. Fei, L. Cai, F. Jing, X. Hu, H. Xie, et al.. Evidence for an oxygen-depleted liquid outer core of the Earth. Nature, 479 (7374) (2011), pp. 513-516,

H. Ichikawa, T. Tsuchiya. Atomic transport property of Fe–O liquid alloys in the Earth’s outer core P, T condition. Transp. Propert. Earth’s Core, 247 (2015), pp. 27-35,

H. Ichikawa, T. Tsuchiya, Y. Tange. The P-V-T equation of state and thermodynamic properties of liquid iron. J. Geophys. Res.-Solid Earth, 119 (1) (2014), pp. 240-252,

T. Komabayashi. Thermodynamics of melting relations in the system Fe-FeO at high pressure: Implications for oxygen in the Earth’s core. J. Geophys. Res.-Solid Earth, 119 (5) (2014), pp. 4164-4177,

G. Kresse. Ab initio molecular dynamics for liquid metals. J. Non Cryst. Solids, 192–193 (1995), pp. 222-229,

G. Kresse, J. Furthmüller. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B, 54 (16) (1996), pp. 11169-11186,

Y. Kuwayama, G. Morard, Y. Nakajima, K. Hirose, A.Q.R. Baron, S.I. Kawaguchi, et al.. Equation of state of liquid iron under extreme conditions. Phys. Rev. Lett., 124 (16) (2020), Article 165701,

A. Laio, S. Bernard, G.L. Chiarotti, S. Scandolo, E. Tosatti. Physics of iron at Earth’s core conditions. Science, 287 (5455) (2000), pp. 1027-1030,

N.D. Mermin. Thermal properties of the inhomogeneous electron gas. Phys. Rev., 137 (5A) (1965), pp. A1441-A1443,

G. Morard, Y. Nakajima, D. Andrault, D. Antonangeli, A.L. Auzende, E. Boulard, et al.. Structure and density of Fe-C Liquid alloys under high pressure. J. Geophys. Res.-Solid Earth, 122 (10) (2017), pp. 7813-7823,

F.D. Murnaghan. The compressibility of media under extreme pressures. Proc. Natl. Acad. Sci., 30 (9) (1944), pp. 244-247,

S. Nosé. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys., 81 (1) (1984), pp. 511-519,

J.P. Perdew, K. Burke, M. Ernzerhof. Generalized gradient approximation made simple. Phys. Rev. Lett., 77 (18) (1996), pp. 3865-3868,

J.-P. Poirier. Light elements in the Earth’s outer core: A critical review. Phys. Earth Planet. In., 85 (3–4) (1994), pp. 319-337,

C.T. Seagle, A.J. Campbell, D.L. Heinz, G. Shen, V.B. Prakapenka. Thermal equation of state of Fe3S and implications for sulfur in Earth’s core. J. Geophys. Res.-Solid Earth, 111 (B6) (2006),

X. Sha, R.E. Cohen. First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures. Phys. Rev. B, 81 (9) (2010), Article 094105,

T. Uchida, Y. Wang, M.L. Rivers, S.R. Sutton. Stability field and thermal equation of state of ε-iron determined by synchrotron X-ray diffraction in a multianvil apparatus. J. Geophys. Res.- Solid Earth, 106 (B10) (2001), pp. 21799-21810,

K. Umemoto, K. Hirose. Liquid iron-hydrogen alloys at outer core conditions by first-principles calculations. Geophys. Res. Lett., 42 (18) (2015), pp. 7513-7520,

K. Umemoto, K. Hirose. Chemical compositions of the outer core examined by first principles calculations. Earth Planet. Sci. Lett., 531 (2020), Article 116009,

K. Umemoto, K. Hirose, S. Imada, Y. Nakajima, T. Komabayashi, S. Tsutsui, A.Q.R. Baron. Liquid iron-sulfur alloys at outer core conditions by first-principles calculations. Geophys. Res. Lett., 41 (19) (2014), pp. 6712-6717,

L. Vočadlo, D. Alfè, M.J. Gillan, G.D. Price. The properties of iron under core conditions from first principles calculations. Phys. Earth Planet. In., 140 (1–3) (2003), pp. 101-125,

L. Vočadlo, D.P. Dobson, I.G. Wood. Ab initio calculations of the elasticity of hcp-Fe as a function of temperature at inner-core pressure. Earth Planet. Sci. Lett., 288 (3–4) (2009), pp. 534-538,

D. Yamazaki, E. Ito, T. Yoshino, A. Yoneda, X. Guo, B. Zhang, et al.. P-V-T equation of state for ε-iron up to 80 GPa and 1900 K using the Kawai-type high pressure apparatus equipped with sintered diamond anvils. Geophys. Res. Lett., 39 (20) (2012),

G. Young, L. Fan, B. Zhao, X. Chen, X. Liu, H. Huang. Equation of state for Fe-9.0 wt% O up to 246 GPa: Implications for oxygen in the earth’s outer core. J. Geophys. Res.-Solid Earth, 126 (2) (2021),

Y. Zhang, T. Sekine, H. He, Y. Yu, F. Liu, M. Zhang. Experimental constraints on light elements in the Earth’s outer core. Sci. Rep., 6 (1) (2016), p. 22473,