[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−xSix 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): -.