Volume 33 Issue 6
Nov 2019
Turn off MathJax
Article Contents
LI Peiyun, HUANG Haijun, LI Yanli. First-Principles Calculations of the Equation of State and Sound Velocity of Fe-3.24%Si: Implications for the Composition of Earth’s Inner Core[J]. Chinese Journal of High Pressure Physics, 2019, 33(6): 060101. doi: 10.11858/gywlxb.20190781
Citation: LI Peiyun, HUANG Haijun, LI Yanli. First-Principles Calculations of the Equation of State and Sound Velocity of Fe-3.24%Si: Implications for the Composition of Earth’s Inner Core[J]. Chinese Journal of High Pressure Physics, 2019, 33(6): 060101. doi: 10.11858/gywlxb.20190781

First-Principles Calculations of the Equation of State and Sound Velocity of Fe-3.24%Si: Implications for the Composition of Earth’s Inner Core

doi: 10.11858/gywlxb.20190781
  • Received Date: 22 May 2019
  • Rev Recd Date: 26 Jun 2019
  • Issue Publish Date: 25 Sep 2019
  • Silicon (Si) is considered as one major light element in Earth’s inner core, but its content is still controversy. In order to constrain its content in the inner core, using first-principles calculation method, we constructed four different supercells of Fe-3.24%Si and investigated the effects of cell size and spin on geometry optimization. It is found that the spin doesn’t affect the equation of state of Fe-3.24%Si above 100 GPa, and below 100 GPa, the calculated results with the spin are closer to the experimental data. Based on the equation of state, the sound velocity at 0 K and the corresponding thermodynamic parameters, the density and sound velocity of Fe-3.24%Si are obtained under the conditions of the inner core. The density of Fe-3.24%Si is lower than that of pure iron and slightly higher than that of the inner core. The sound velocities of longitudinal wave and shear wave for Fe-3.24%Si are very close to that of pure iron, but both are significantly higher than that of the inner core. Therefore, we could exclude the possibility that Earth’s inner core contains a large amount of Si.

     

  • loading
  • [1]
    RINGWOOD A E. On the chemical evolution and densities of the planets [J]. Geochimica et Cosmochimica Acta, 1959, 15(4): 257–283. doi: 10.1016/0016-7037(59)90062-6
    [2]
    BIRCH F. Density and composition of mantle and core [J]. Journal of Geophysical Research, 1964, 69(20): 4377–4388. doi: 10.1029/JZ069i020p04377
    [3]
    TAKAFUJI N, HIROSE K, MITOME M, et al. Solubilities of O and Si in liquid iron in equilibrium with (Mg, Fe)SiO3 perovskite and the light elements in the core [J]. Geophysical Research Letters, 2005, 32(6).
    [4]
    FISCHER R A, CAMPBELL A J, REAMAN D M, et al. Phase relations in the Fe-FeSi system at high pressures and temperatures [J]. Earth and Planetary Science Letters, 2013, 373: 54–64. doi: 10.1016/j.jpgl.2013.04.035
    [5]
    FISCHER R A, CAMPBELL A J, CARACAS R, et al. Equations of state in the Fe-FeSi system at high pressures and temperatures [J]. Journal of Geophysical Research: Solid Earth, 2014, 119(4): 2810–2827. doi: 10.1002/2013JB010898
    [6]
    TATENO S, KUWAYAMA Y, HIROSE K, et al. The structure of Fe-Si alloy in Earth’s inner core [J]. Earth and Planetary Science Letters, 2015, 418: 11–19. doi: 10.1016/j.jpgl.2015.02.008
    [7]
    OZAWA H, HIROSE K, YONEMITSU K, et al. High-pressure melting experiments on Fe-Si alloys and implications for silicon as a light element in the core [J]. Earth and Planetary Science Letters, 2016, 456: 47–54. doi: 10.1016/j.jpgl.2016.08.042
    [8]
    KNITTLE E, JEANLOZ R. Earth’s core-mantle boundary: results of experiments at high pressures and temperatures [J]. Science, 1991, 251(5000): 1438–1443. doi: 10.1126/science.251.5000.1438
    [9]
    DUBROVINSKY L, DUBROVINSKAIA N, LANGENHORST F, et al. Iron-silica interaction at extreme conditions and the electrically conducting layer at the base of Earth’s mantle [J]. Nature, 2003, 422(6927): 58. doi: 10.1038/nature01422
    [10]
    LIN J F, CAMPBELL A J, HEINZ D L, et al. Static compression of iron-silicon alloys: implications for silicon in the Earth’s core [J]. Journal of Geophysical Research: Solid Earth, 2003, 108(B1).
    [11]
    ASANUMA H, OHTANI E, SAKAI T, et al. Static compression of Fe0.83Ni0.09Si0.08 alloy to 374 GPa and Fe0.93Si0.07 alloy to 252 GPa: implications for the Earth’s inner core [J]. Earth and Planetary Science Letters, 2011, 310(1/2): 113–118. doi: 10.1016/j.jpgl.2011.06.034
    [12]
    BADRO J, FIQUET G, GUYOT F, et al. Effect of light elements on the sound velocities in solid iron: implications for the composition of Earth’s core [J]. Earth and Planetary Science Letters, 2007, 254(1/2): 233–238.
    [13]
    ANTONANGELI D, SIEBERT J, BADRO J, et al. Composition of the Earth’s inner core from high-pressure sound velocity measurements in Fe-Ni-Si alloys [J]. Earth and Planetary Science Letters, 2010, 295(1/2): 292–296.
    [14]
    MAO Z, LIN J F, LIU J, et al. Sound velocities of Fe and Fe-Si alloy in the Earth’s core [J]. Proceedings of the National Academy of Sciences, 2012, 109(26): 10239–10244. doi: 10.1073/pnas.1207086109
    [15]
    LIU J, LIN J F, ALATAS A, et al. Seismic parameters of hcp-Fe alloyed with Ni and Si in the Earth’s inner core [J]. Journal of Geophysical Research: Solid Earth, 2016, 121(2): 610–623. doi: 10.1002/2015JB012625
    [16]
    SAKAIRI T, SAKAMAKI T, OHTANI E, et al. Sound velocity measurements of hcp Fe-Si alloy at high pressure and high temperature by inelastic X-ray scattering [J]. American Mineralogist, 2018, 103(1): 85–90. doi: 10.2138/am-2018-6072
    [17]
    ANTONANGELI D, MORARD G, PAOLASINI L, et al. Sound velocities and density measurements of solid hcp-Fe and hcp-Fe-Si (9 wt.%) alloy at high pressure: constraints on the Si abundance in the Earth’s inner core [J]. Earth and Planetary Science Letters, 2018, 482: 446–453. doi: 10.1016/j.jpgl.2017.11.043
    [18]
    TSUCHIYA T, FUJIBUCHI M. Effects of Si on the elastic property of Fe at Earth’s inner core pressures: first principles study [J]. Physics of the Earth and Planetary Interiors, 2009, 174(1): 212–219.
    [19]
    CÔTÉ A S, VOČADLO L, DOBSON D P, et al. Ab initio lattice dynamics calculations on the combined effect of temperature and silicon on the stability of different iron phases in the Earth’s inner core [J]. Physics of the Earth and Planetary Interiors, 2010, 178(1/2): 2–7.
    [20]
    MARTORELL B, WOOD I G, BRODHOLT J, et al. The elastic properties of hcp-Fe1− xSi x at Earth’s inner-core conditions [J]. Earth and Planetary Science Letters, 2016, 451: 89–96. doi: 10.1016/j.jpgl.2016.07.018
    [21]
    HOHENBERG P, KOHN W. Inhomogeneous electron gas [J]. Physical Review, 1964, 136(3B): B864. doi: 10.1103/PhysRev.136.B864
    [22]
    PERDEW J P. Exchange and correlation in atoms, molecules, and solids: the density functional picture [M]//Electron Correlations and Materials Properties. Boston: Springer, 1999: 287–298.
    [23]
    GROSS E K U, DREIZLER R M. Density functional theory: an approach to the quantum many-body problem [M]. Berlin: Springer, 1990.
    [24]
    KOHN W, SHAM L J. Quantum density oscillations in an inhomogeneous electron gas [J]. Physical Review, 1965, 137(6A): A1697. doi: 10.1103/PhysRev.137.A1697
    [25]
    LANGRETH D C, PERDEW J P. Theory of nonuniform electronic systems. I. analysis of the gradient approximation and a generalization that works [J]. Physical Review B, 1980, 21(12): 5469. doi: 10.1103/PhysRevB.21.5469
    [26]
    PERDEW J P, CHEVARY J A, VOSKO S H, et al. Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation [J]. Physical Review B, 1992, 46(11): 6671. doi: 10.1103/PhysRevB.46.6671
    [27]
    SEGALL M D, LINDAN P J D, PROBERT M J, et al. First-principles simulation: ideas, illustrations and the CASTEP code [J]. Journal of Physics: Condensed Matter, 2002, 14(11): 2717. doi: 10.1088/0953-8984/14/11/301
    [28]
    VOIGT W. The relation between the two elastic moduli of isotropic materials [J]. Annals of Physics (Leipzig), 1889, 33: 573.
    [29]
    REUSS A. Calculation of the flow limits of mixed crystals on the basis of the plasticity of monocrystals [J]. Zeitschrift für Angewandte Mathematik und Mechanik, 1929, 9: 49–58. doi: 10.1002/zamm.19290090104
    [30]
    HILL R. The elastic behaviour of a crystalline aggregate [J]. Proceedings of the Physical Society Section A, 1952, 65(5): 349. doi: 10.1088/0370-1298/65/5/307
    [31]
    WANG C S, KLEIN B M, KRAKAUER H. Theory of magnetic and structural ordering in iron [J]. Physical Review Letters, 1985, 54(16): 1852. doi: 10.1103/PhysRevLett.54.1852
    [32]
    ASADA T, TERAKURA K. Cohesive properties of iron obtained by use of the generalized gradient approximation [J]. Physical Review B, 1992, 46(20): 13599. doi: 10.1103/PhysRevB.46.13599
    [33]
    COHEN R E, MUKHERJEE S. Non-collinear magnetism in iron at high pressures [J]. Physics of the Earth and Planetary Interiors, 2004, 143: 445–453.
    [34]
    BROWN J M, FRITZ J N, HIXSON R S. Hugoniot data for iron [J]. Journal of Applied Physics, 2000, 88(9): 5496–5498. doi: 10.1063/1.1319320
    [35]
    冯磊. 高压下温度对Fe-8.6Si声速的影响 [D]. 武汉: 武汉理工大学, 2017: 72–83.

    FENG L. Effect of temperature on Fe-8.6Si sound velocity at high pressure [D]. Wuhan: Wuhan University of Technology, 2017: 72–83.
    [36]
    经福谦. 实验物态方程导引 [M]. 2版. 北京: 科学出版社, 1999: 188–197.

    JING F Q. Introduction to experimental equation of state [M]. 2nd ed. Beijing: Science Press, 1999: 188–197.
    [37]
    BROWN J M, MCQUEEN R G. Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa [J]. Journal of Geophysical Research: Solid Earth, 1986, 91(B7): 7485–7494. doi: 10.1029/JB091iB07p07485
    [38]
    BONESS D A, BROWN J M, MCMAHAN A K. The electronic thermodynamics of iron under Earth core conditions [J]. Physics of the Earth and Planetary Interiors, 1986, 42(4): 227–240. doi: 10.1016/0031-9201(86)90025-7
    [39]
    FEI Y, MURPHY C, SHIBAZAKI Y, et al. Thermal equation of state of hcp-iron: constraint on the density deficit of Earth’s solid inner core [J]. Geophysical Research Letters, 2016, 43(13): 6837–6843. doi: 10.1002/2016GL069456
    [40]
    ANDERSON O L. The power balance at the core-mantle boundary [J]. Physics of the Earth and Planetary Interiors, 2002, 131(1): 1–17. doi: 10.1016/S0031-9201(02)00009-2
    [41]
    BIRCH F. Elasticity and constitution of the Earth’s interior [J]. Journal of Geophysical Research, 1952, 57(2): 227–286. doi: 10.1029/JZ057i002p00227
    [42]
    HIROSE K, LABROSSE S, HERNLUND J. Composition and state of the core [J]. Annual Review of Earth and Planetary Sciences, 2013, 41: 657–691. doi: 10.1146/annurev-earth-050212-124007
    [43]
    ZHANG Y, SEKINE T, LIN J F, et al. Shock compression and melting of an Fe-Ni-Si alloy: implications for the temperature profile of the Earth’s core and the heat flux across the core-mantle boundary [J]. Journal of Geophysical Research: Solid Earth, 2018, 123(2): 1314–1327. doi: 10.1002/2017JB014723
    [44]
    ANTONANGELI D, KOMABAYASHI T, OCCELLI F, et al. Simultaneous sound velocity and density measurements of hcp iron up to 93 GPa and 1100 K: an experimental test of the Birch’s law at high temperature [J]. Earth and Planetary Science Letters, 2012, 331: 210–214.
    [45]
    ANTONANGELI D, OHTANI E. Sound velocity of hcp-Fe at high pressure: experimental constraints, extrapolations and comparison with seismic models [J]. Progress in Earth and Planetary Science, 2015, 2(1): 3. doi: 10.1186/s40645-015-0034-9
    [46]
    LIN J F, STURHAHN W, ZHAO J, et al. Sound velocities of hot dense iron: Birch’s law revisited [J]. Science, 2005, 308(5730): 1892–1894. doi: 10.1126/science.1111724
    [47]
    SAKAMAKI T, OHTANI E, FUKUI H, et al. Constraints on Earth’s inner core composition inferred from measurements of the sound velocity of hcp-iron in extreme conditions [J]. Science Advances, 2016, 2(2): e1500802. doi: 10.1126/sciadv.1500802
    [48]
    CHEN B, LAI X, LI J, et al. Experimental constraints on the sound velocities of cementite Fe3C to core pressures [J]. Earth and Planetary Science Letters, 2018, 494: 164–171. doi: 10.1016/j.jpgl.2018.05.002
    [49]
    GAO L, CHEN B, WANG J, et al. Pressure-induced magnetic transition and sound velocities of Fe3C: implications for carbon in the Earth’s inner core [J]. Geophysical Research Letters, 2008, 35(17).
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(5)

    Article Metrics

    Article views(10180) PDF downloads(74) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return