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Licensed Unlicensed Requires Authentication Published by De Gruyter September 20, 2020

Density and sound velocity of liquid Fe-S alloys at Earth’s outer core P-T conditions

  • Jie Fu ORCID logo , Lingzhi Cao , Xiangmei Duan and Anatoly B. Belonoshko
From the journal American Mineralogist

Abstract

Pressure-temperature-volume (P-T-V) data on liquid iron-sulfur (Fe-S) alloys at the Earth’s outer core conditions (~136 to 330 GPa, ~4000 to 7000 K) have been obtained by first-principles molecular dynamics simulations. We developed a thermal equation of state (EoS) composed of Murnaghan and Mie-Grüneisen-Debye expressions for liquid Fe-S alloys. The density and sound velocity are calculated and compared with Preliminary Reference Earth Model (PREM) to constrain the S concentration in the outer core. Since the temperature at the inner core boundary (TICB) has not been measured precisely (4850~7100 K), we deduce that the S concentration ranges from 10~14 wt% assuming S is the only light element. Our results also show that Fe-S alloys cannot satisfy the seismological density and sound velocity simultaneously and thus S element is not the only light element. Considering the geophysical and geochemical constraints, we propose that the outer core contains no more than 3.5 wt% S, 2.5 wt% O, or 3.8 wt% Si. In addition, the developed thermal EoS can be utilized to calculate the thermal properties of liquid Fe-S alloys, which may serve as the fundamental parameters to model the Earth’s outer core.

  1. Funding

    The authors acknowledge support from the National Natural Science Foundation of China (NSFC) (Grant No. 11804175 and 11874033) and the K.C. Wong Magna Foundation at Ningbo University. A.B. is thankful to the Swedish Research Council (VR) for financial support (grant 2017-03744). J.F. thanks Yunguo Li from University College of London for discussions. Computations were performed using the facilities at the Swedish National Infrastructure for Computing (SNIC) located at NSC in Linköping. The data can be obtained from the Mendeley data repository (https://data.mendeley.com/datasets/b8t6j2yd3k/1).

References cited

Alfè, D. (2009) Temperature of the inner-core boundary of the Earth: Melting of iron at high pressure from first-principles coexistence simulations. Physical Review B, 79, 1–4.10.1103/PhysRevB.79.060101Search in Google Scholar

Alfè, D., and Gillan, M.J. (1998) First-principles simulations of liquid Fe-S under Earth’s core conditions. Physical Review B, 58, 8248–8256.10.1103/PhysRevB.58.8248Search in Google Scholar

Alfè, D., Gillan, M.J., and Price, G.D. (2002a) Composition and temperature of the Earth’s core constrained by combining ab initio calculations and seismic data. Earth and Planetary Science Letters, 195, 91–98.10.1016/S0012-821X(01)00568-4Search in Google Scholar

Alfè, D., Price, G., and Gillan, M. (2002b) Iron under Earth’s core conditions: Liquid-state thermodynamics and high-pressure melting curve from ab initio calculations. Physical Review B, 65, 165118.10.1103/PhysRevB.65.165118Search in Google Scholar

Anderson, W.W., and Ahrens, T.J. (1994) An equation of state for liquid iron and implications for the Earth’s core. Journal of Geophysical Research, 99, 4273–4284.10.1029/93JB03158Search in Google Scholar

Anzellini, S., Dewaele, A., Mezouar, M., Loubeyre, P., and Morard, G. (2013) Melting of iron at Earth’s inner core boundary based on fast X-ray diffraction. Science, 340, 464–466.10.1126/science.1233514Search in Google Scholar PubMed

Badro, J., Fiquet, G., Guyot, F., Gregoryanz, E., Occelli, F., Antonangeli, D., and d’Astuto, M. (2007) Effect of light elements on the sound velocities in solid iron: Implications for the composition of Earth’s core. Earth and Planetary Science Letters, 254, 233–238.10.1016/j.epsl.2006.11.025Search in Google Scholar

Badro, J., Cote, A.S., and Brodholt, J.P. (2014) A seismologically consistent compositional model of Earth’s core. Proceedings of the National Academy of Sciences, 111, 7542–7545.10.1073/pnas.1316708111Search in Google Scholar PubMed PubMed Central

Badro, J., Brodholt, J.P., Piet, H., Siebert, J., and Ryerson, F.J. (2015) Core formation and core composition from coupled geochemical and geophysical constraints. Proceedings of the National Academy of Sciences, 112, 12,310–12,314.10.1073/pnas.1505672112Search in Google Scholar PubMed PubMed Central

Bazhanova, Z.G., Roizen, V.V., and Oganov, A.R. (2017) High-pressure behavior of the Fe-S system and composition of the Earth’s inner core. Uspekhi Fizicheskih Nauk, 187, 1105–1113.10.3367/UFNe.2017.03.038079Search in Google Scholar

Belonoshko, A.B. (2010) Equation of state for ε-iron at high pressures and temperatures. Condensed Matter Physics, 13, 23,605–23,615.10.5488/CMP.13.23605Search in Google Scholar

Belonoshko, A.B., Ahuja, R., and Johansson, B. (2000) Quasi–ab initio molecular dynamic study of Fe melting. Physical Review Letters, 84, 3638–3641.10.1103/PhysRevLett.84.3638Search in Google Scholar PubMed

Belonoshko, A.B., Lukinov, T., Fu, J., Zhao, J., Davis, S., and Simak, S.I. (2017) Stabilization of body-centred cubic iron under inner-core conditions. Nature Geoscience, 10, 312.10.1038/ngeo2892Search in Google Scholar

Belonoshko, A.B., Fu, J., Bryk, T., Simak, S.I., and Mattesini, M. (2019) Low viscosity of the Earth’s inner core. Nature Communications, 10, 2483.10.1038/s41467-019-10346-2Search in Google Scholar PubMed PubMed Central

Birch, F. (1952) Elasticity and constitution of the Earth’s interior. Journal of Geophysical Research, 57, 227–286.10.1029/SP026p0031Search in Google Scholar

Blöchl, P.E. (1994) Projector augmented-wave method. Physical Review B, 50, 17,953–17,979.10.1103/PhysRevB.50.17953Search in Google Scholar

Boehler, R. (1993) Temperatures in the Earth’s core from melting-point measurements of iron at high-static pressures. Nature, 363, 534–536.10.1038/363534a0Search in Google Scholar

Bouchet, J., Mazevet, S., Morard, G., Guyot, F., and Musella, R. (2013) Ab initio equation of state of iron up to 1500 GPa. Physical Review B, 87, 1–8.10.1103/PhysRevB.87.094102Search in Google Scholar

Brown, J.M., and McQueen, R.G. (1986) Phase transitions, Gruneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa. Journal of Geophysical Research, 91, 7480–7494.10.1029/JB091iB07p07485Search in Google Scholar

Dewaele, A., Loubeyre, P., Occelli, F., Mezouar, M., Dorogokupets, P.I., and Torrent, M. (2006) Quasihydrostatic Equation of State of Iron above 2 Mbar. Physical Review Letters, 97, 215504.10.1103/PhysRevLett.97.215504Search in Google Scholar PubMed

Dziewonski, A.M., and Anderson, D.L. (1981) Preliminary Reference Earth Model. Physics of the Earth and Planetary Interiors, 25, 297–356.10.1016/0031-9201(81)90046-7Search in Google Scholar

Fei, Y., Li, J., Bertka, C.M., and Prewitt, C.T. (2000) Structure type and bulk modulus of Fe3S, a new iron-sulfur compound. American Mineralogist, 85, 1830–1833.10.2138/am-2000-11-1229Search in Google Scholar

Hirose, K., Labrosse, S., and Hernlund, J. (2013) Composition and state of the core. Annual Review of Earth and Planetary Sciences, 41, 657–691.10.1146/annurev-earth-050212-124007Search in Google Scholar

Hoover, W.G. (1985) Canonical dynamics: Equilibrium phase-space distributions. Physical Review A, 31, 1695–1697.10.1103/PhysRevA.31.1695Search in Google Scholar PubMed

Huang, H., Fei, Y., Cai, L., Jing, F., Hu, X., Xie, H., Zhang, L., and Gong, Z. (2011) Evidence for an oxygen-depleted liquid outer core of the Earth. Nature, 479, 513–516.10.1038/nature10621Search in Google Scholar PubMed

Huang, H., Wu, S., Hu, X., Wang, Q., Wang, X., and Fei, Y. (2013) Shock compression of Fe-FeS mixture up to 204 GPa. Geophysical Research Letters, 40, 687–691.10.1002/grl.50180Search in Google Scholar

Huang, H., Leng, C., Wang, Q., Yang, G., Hu, X., Wu, Y., Liu, X., and Fei, Y. (2018) Measurements of sound velocity of liquid Fe-11.8 wt% S up to 211.4 GPa and 6150 K. Journal of Geophysical Research: Solid Earth, 123, 4730–4739.10.1029/2017JB015269Search in Google Scholar

Huang, H., Leng, C., Wang, Q., Young, G., Liu, X., Wu, Y., Xu, F., and Fei, Y. (2019) Equation of state for shocked Fe-8.6 wt % Si up to 240 GPa and 4670 K. Journal of Geophysical Research: Solid Earth, 124, 8300–8312.10.1029/2019JB017983Search in Google Scholar

Ichikawa, H., Tschuchiya, T., and Tange, Y. (2014) The P-V-T equation of state and thermodynamic properties of liquid iron. Journal of Geophysical Research: Solid Earth, 119, 240–252.10.1002/2013JB010732Search in Google Scholar

Jing, Z., Wang, Y., Kono, Y., Yu, T., Sakamaki, T., Park, C., Rivers, M.L., Sutton, S.R., and Shen, G. (2014) Sound velocity of Fe-S liquids at high pressure: Implications for the Moon’s molten outer core. Earth and Planetary Science Letters, 396, 78–87.10.1016/j.epsl.2014.04.015Search in Google Scholar

Kawaguchi, S.I., Nakajima, Y., Hirose, K., Komabayashi, T., Ozawa, H., Tateno, S., Kuwayama, Y., Tsutsui, S., and Baron, A.Q.R. (2017) Sound velocity of liquid Fe-Ni-S at high pressure. Journal of Geophysical Research: Solid Earth, 122, 3624–3634.10.1002/2016JB013609Search in Google Scholar

Koči, L., Belonoshko, A.B., and Ahuja, R. (2007) Molecular dynamics calculation of liquid iron properties and adiabatic temperature gradient in the Earth’s outer core. Geophysical Journal International, 168, 890–894.10.1111/j.1365-246X.2006.03256.xSearch in Google Scholar

Kresse, G., and Furthmüller, J. (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B, 54, 11,169–11,186.Search in Google Scholar

Kresse, G., and Hafner, J. (1993) Ab initio molecular dynamics for liquid metals. Physical Review B, 47, 558–561.10.1016/0022-3093(95)00355-XSearch in Google Scholar

Kuskov, O.L., and Belashchenko, D.K. (2016) Thermodynamic properties of Fe-S alloys from molecular dynamics modeling: Implications for the lunar fluid core. Physics of the Earth and Planetary Interiors, 258, 43–50.10.1016/j.pepi.2016.07.006Search in Google Scholar

Laio, A., Bernard, S., Chiarotti, G.L., Scandolo, S., and Tosatti, E. (2000) Physics of Iron at Earth’s Core Conditions. Science, 287, 1027–1030.10.1126/science.287.5455.1027Search in Google Scholar PubMed

Lin, J.F., Sturhahn, W., Zhao, J., Shen, G., Mao, H.K., and Hemley, R.J. (2005) Sound velocities of hot dense iron: Birch’s Law revisited. Science, 308, 1892–1894.10.1126/science.1111724Search in Google Scholar PubMed

Litasov, K.D., and Shatskiy, A.F. (2016) Composition of the Earth’s core: A review. Russian Geology and Geophysics, 57, 22–46.10.1016/j.rgg.2016.01.003Search in Google Scholar

Mermin, N.D. (1965) Thermal properties of the inhomogeneous electron gas. Physical Review, 137, A1441–A1443.10.1103/PhysRev.137.A1441Search in Google Scholar

Mori, Y., Ozawa, H., Hirose, K., Sinmyo, R., Tateno, S., Morard, G., and Ohishi, Y. (2017) Melting experiments on Fe–Fe3S system to 254 GPa. Earth and Planetary Science Letters, 464, 135–141.10.1016/j.epsl.2017.02.021Search in Google Scholar

Murnaghan, F.D. (1944) The compressibility of media under extreme pressures. Proceedings of the National Academy of Sciences, 30, 244–247.10.1073/pnas.30.9.244Search in Google Scholar PubMed PubMed Central

Nosé, S. (1984) A molecular dynamics method for simulations in the canonical ensemble. Molecular Physics, 52, 255–268.10.1080/00268978400101201Search in Google Scholar

Perdew, J.P., Burke, K., and Ernzerhof, M. (1996) Generalized Gradient Approximation made simple. Physical Review Letters, 77, 3865–3868.10.1103/PhysRevLett.77.3865Search in Google Scholar

Poirier, J.P. (1994) Light elements in the Earth’s outer core: A critical review. Physics of the Earth and Planetary Interiors, 85, 319–337.10.1016/0031-9201(94)90120-1Search in Google Scholar

Sanloup, C., Guyot, F., Gillet, P., and Fei, Y. (2002) Physical properties of liquid Fe alloys at high pressure and their bearings on the nature of metallic planetary cores. Journal of Geophysical Research: Solid Earth, 107, ECV 4-1–ECV 4-9.10.1029/2001JB000808Search in Google Scholar

Seagle, C.T., Campbell, A.J., Heinz, D.L., Shen, G., and Prakapenka, V.B. (2006) Thermal equation of state of Fe3S and implications for sulfur in Earth’s core. Journal of Geophysical Research: Solid Earth, 111, 1–7.10.1029/2005JB004091Search in Google Scholar

Stixrude, L., Wasserman, E., and Cohen, R.E. (1997) Composition and temperature of Earth’s inner core. Journal of Geophysical Research: Solid Earth, 102, 24,729–24,739.10.1029/97JB02125Search in Google Scholar

Umemoto, K., and Hirose, K. (2015) Liquid iron-hydrogen alloys at outer core conditions by first-principles calculations. Geophysical Research Letters, 42, 7513–7520.10.1002/2015GL065899Search in Google Scholar

Umemoto, K., and Hirose, K. (2020) Chemical compositions of the outer core examined by first principles calculations. Earth and Planetary Science Letters, 531, 116009.10.1016/j.epsl.2019.116009Search in Google Scholar

Umemoto, K., Hirose, K., Imada, S., Nakajima, Y., Komabayashi, T., Tsutsui, S., and Baron, A.Q.R. (2014) Liquid iron-sulfur alloys at outer core conditions by first-principles calculations. Geophysical Research Letters, 41, 6712–6717.10.1002/2014GL061233Search in Google Scholar

Vočadlo, L., Alfè, D., Gillan, M.J., and Price, G.D. (2003) The properties of iron under core conditions from first principles calculations. Physics of the Earth and Planetary Interiors, 140, 101–125.10.1016/j.pepi.2003.08.001Search in Google Scholar

Wagle, F., and Steinle-Neumann, G. (2019) Liquid iron equation of state to the terapascal regime from ab initio simulations. Journal of Geophysical Research: Solid Earth, 124, 3350–3364.10.1029/2018JB016994Search in Google Scholar

Wasserman, E., Stixrude, L., and Cohen, R.E. (1996) Thermal properties of iron at high pressures and temperatures. Physical Review B, 53, 8296–8309.10.1103/PhysRevB.53.8296Search in Google Scholar

Zhang, Y., Sekine, T., He, H., Yu, Y., Liu, F., and Zhang, M. (2016) Experimental constraints on light elements in the Earth’s outer core. Scientific Reports, 6, 22473.10.1038/srep22473Search in Google Scholar PubMed PubMed Central

Received: 2019-10-29
Accepted: 2020-02-23
Published Online: 2020-09-20
Published in Print: 2020-09-25

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