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8 - Equations of State of Selected Solids for High-Pressure Research and Planetary Interior Density Models

Published online by Cambridge University Press:  03 August 2023

By
Yingwei Fei
Edited by
Yingwei Fei  and
Michael J. Walter
Yingwei Fei
Affiliation:
Carnegie Institution of Washington, Washington DC
Michael J. Walter
Affiliation:
Carnegie Institution of Washington, Washington DC
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Summary

Our ability to determine the density (specific volume) as a function of pressure and temperature has drastically improved in the last several decades, with the combination of synchrotron X-ray diffraction and high-pressure techniques such as laser-heated diamond-anvil cell and large-volume multi-anvil press. The improvements are in both pressure–temperature range and data quality, and obtaining high-resolution 2D angle-dispersive diffraction data at over a megabar pressure and above 2,500 K is now routine. In parallel, dynamic compression techniques, such as laser-driven shock wave and magnetically accelerated flyer plate-impact experiments, have provided new ways to measure density at extreme conditions. The combination of static and dynamic compression data allows us to examine internal consistency in pressure determination and establish reliable pressure scales. Internally consistent pressure scales for several pressure standards are emerging through extensive comparison of compression data over a large pressure range and simultaneous measurements of elasticity and density. A concerted effort is needed to further expand and improve measurements under simultaneous high pressure and temperature, particularly at temperatures above 2,500 K, in order to accurately model the thermal pressure. To decipher the compositions of the Earth’s interior based on density observations from seismology requires high accuracy in measuring the subtle compositional effects on the density of mantle and core materials. For a universal understanding of the thermal equations of state of solids, the emphasis should be on reconciling the static and dynamic data of well-studied materials that have substantial overlap in pressure–temperature ranges.

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Static and Dynamic High Pressure Mineral Physics , pp. 147 - 188
Publisher: Cambridge University Press
Print publication year: 2022

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References

Anderson, O. L., Isaak, D. G., Yamamoto, S. (1989). Anharmonicity and the equation of state for gold. Journal of Applied Physics, 65, 1534–1543.Google Scholar
Andrault, D., Bolfan-Casanova, N., Guignot, N. (2001). Equation of state of lower mantle (Al, Fe)-MgSiO3 perovskite. Earth and Planetary Science Letters, 193, 501–508.Google Scholar
Arimoto, T., Irifune, T., Nishi, M., Tange, Y., Kunimoto, T., Liu, Z. (2019). Phase relations of MgSiO3-FeSiO3 system up to 64 GPa and 2300 K using multianvil apparatus with sintered diamond anvils. Physics of the Earth and Planetary Interiors, 295, 106297.Google Scholar
Asanuma, H., Ohtani, E., Sakai, T., et al. (2011). 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. Earth and Planetary Science Letters, 310(1–2), 113–118.Google Scholar
Badro, J., Fiquet, G., Guyot, F., et al. (2003). Iron partitioning in Earth’s mantle: toward a deep lower mantle discontinuity. Science, 300, 789–791.Google Scholar
Badro, J., Rueff, J.-P., Vanko, G., Monaco, G., Fiquet, G., Guyot, F. (2004). Electronic transitions in perovskite: possible nonconvecting layers in the lower mantle. Science, 305, 383–386.Google Scholar
Birch, F. (1952). Elasticity and constitution of the Earth’s interior. Journal of Geophysical Research, 57, 227–286.Google Scholar
Birch, F. (1978). Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300 K. Journal of Geophysical Research, 83, 1257–1268.Google Scholar
Boffa Ballaran, T., Kurnosov, A., Glazyrin, K., et al. (2012). Effect of chemistry on the compressibility of silicate perovskite in the lower mantle. Earth and Planetary Science Letters, 333, 181–190.Google Scholar
Boness, D. A., Brown, J. M., McMahan, A. K. (1986). The electronic thermodynamics of iron under Earth core conditions. Physics of the Earth and Planetary Interiors, 42, 227–240.Google Scholar
Brown, J. M. (1999). The NaCl pressure standard. Journal of Applied Physics, 86(10), 5801–5808.Google Scholar
Carter, W. J., Marsh, S. P., Fritz, J. N., McQueen, R. G. (1971). The equation of state of selected materials for high-pressure references, in Lloyd, E. C., ed., Accurate Characterization of the High-Pressure Environment. National Bureau of Standards, Spec. Publ. 326, pp. 147–158.Google Scholar
Catalli, K., Shim, S. H., Prakapenka, V. B., et al. (2010). Spin state of ferric iron in MgSiO3 perovskite and its effect on elastic properties. Earth and Planetary Science Letters, 289, 68–75.Google Scholar
Catalli, K., Shim, S. H., Dera, P., et al. (2011). Effects of the Fe3+ spin transition on the properties of aluminous perovskite – new insights for lower-mantle seismic heterogeneities. Earth and Planetary Science Letters, 310, 293–302.Google Scholar
Chen, B., Gao, L., Lavina, B., et al. (2012). Magneto-elastic coupling in compressed Fe7C3 supports carbon in Earth’s inner core. Geophysical Research Letters, 39(18), L18301.Google Scholar
Chen, B., Li, Z., Zhang, D., et al. (2014). Hidden carbon in Earth’s inner core revealed by shear softening in dense Fe7C3. Proceedings of the National Academy of Sciences, 111(50), 17755–17758.Google Scholar
Chijioke, A. D., Nellis, W. J., Silvera, I. F. (2005). High-pressure equations of state of Al, Cu, Ta, and W. Journal of Applied Physics, 98(7), 073526.Google Scholar
Cohen, R. E., Gulseren, O., Hemley, R. J. (2000). Accuracy of equation of state formulations. American Mineralogist, 85(2), 338–344.Google Scholar
Coppari, F., Smith, R. F., Eggert, J. H., et al. (2013). Experimental evidence for a phase transition in magnesium oxide at exoplanet pressures. Nature Geoscience, 6, 926–929.Google Scholar
Decker, D. L. (1965). Equation of state of NaCl and its use as a pressure gauge in high‐pressure research. Journal of Applied Physics, 36(1), 157–161.Google Scholar
Desjarlais, M. P., Knudson, M. D., Cochrane, K. R. (2017). Extension of the Hugoniot and analytical release model of α-quartz to 0.2–3 TPa. Journal of Applied Physics, 122, 035903.Google Scholar
Dewaele, A. (2019). Equations of state of simple solids (including Pb, NaCl and LiF) compressed in helium or neon in the Mbar range. Minerals, 9, 684.Google Scholar
Dewaele, A., Datchi, F., Loubeyre, P., Mezouar, M. (2008b). High pressure–high temperature equations of state of neon and diamond. Physical Review B, 77(9), 094106.CrossRefGoogle Scholar
Dewaele, A., Loubeyre, P., Occelli, F., Marie, O., Mezouar, M. (2018). Toroidal diamond anvil cell for detailed measurements under extreme static pressure. Nature Communications, 9, 2913.Google Scholar
Dewaele, A., Loubeyre, P., Mezouar, M. (2004). Equations of state of six metals above 94 GPa. Physical Review B, 70(9), 094112.Google Scholar
Dewaele, A., Loubeyre, P., Occelli, F., Mezouar, M., Dorogokupets, P. I., Torrent, M. (2006). Quasihydrostatic equation of state of iron above 2 Mbar. Physical Review Letters, 97(21), 215504.Google Scholar
Dewaele, A., Torrent, M., Loubeyre, P., Mezouar, M. (2008a). Compression curves of transition metals in the Mbar range: Experiments and projector augmented‐wave calculations. Physical Review B, 78(10), 104102.Google Scholar
Dorfman, S. M., Prakapenka, V. B., Meng, Y., Duffy, T. S. (2012). Intercomparison of pressure standards (Au, Pt, Mo, MgO, NaCl and Ne) to 2.5 Mbar. Journal of Geophysical Research, 117, B08210.Google Scholar
Dorogokupets, P. I., Dewaele, A. (2007). Equations of state of MgO, Au, Pt, NaCl‐B1, and NaCl‐B2: internally consistent high‐temperature pressure scales. High Pressure Research, 27(4), 431–446.CrossRefGoogle Scholar
Dorogokupets, P. I., Oganov, A. R. (2006). Equations of state of Al, Au, Cu, Pt, Ta, and W and revised ruby pressure scale. Doklady Earth Sciences, 410(7), 1091–1095.Google Scholar
Dubrovinskaia, N., Dubrovinsky, L., Solopova, N. A., et al. (2016). Terapascal static pressure generation with ultrahigh yield strength nanodiamond. Science Advances, 2(7), e1600341.Google Scholar
Dubrovinsky, L., Dubrovinskaia, N., Prakapenka, V., Abakumov, A. M. (2012). Implementation of micro-ball nanodiamond anvils for high-pressure studies above 6 Mbar. Nature Communications, 3, 1163.Google Scholar
Dubrovinsky, L. S., Saxena, S. K., Tutti, F., Rekhi, S., Le Bihan, T. (2000). In situ X-ray study of thermal expansion and phase transition of iron at multimegabar pressure. Physical Review Letters, 84, 1720–1723.Google Scholar
Duffy, T. S., Ahrens, T. J. (1993). Thermal expansion of mantle and core materials at very high pressure. Geophysical Research Letters, 20, 1103–1106.Google Scholar
Duffy, T. S., Hemley, R. J., Mao, H.-K. (1995). Equation of state and shear strength at multimegabar pressures: magnesium oxide to 227 GPa. Physical Review Letters, 74, 1371–1374.Google Scholar
Dziewonski, A. M., Anderson, D. L. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25(4), 297–356.Google Scholar
Fan, D., Fu, S., Yang, J., Tkachev, S. N., Prakapenka, V. B., Lin, J. (2019). Elasticity of single-crystal periclase at high pressure and temperature: the effect of iron on the elasticity and seismic parameters of ferropericlase in the lower mantle. American Mineralogist, 104, 262–275.Google Scholar
Fat’yanov, O. V., Asimow, P. D., Ahrens, T. J. (2018). Thermodynamically complete equation of state of MgO from true radiative shock temperature measurements on samples preheated to 1850 K. Physical Review B, 97, 024106.Google Scholar
Fei, Y. (1999). Effects of temperature and composition on the bulk modulus of (Mg,Fe)O. American Mineralogist, 84, 272–276.Google Scholar
Fei, Y., Li, J., Hirose, K., et al. (2004). A critical evaluation of pressure scales at high temperatures by in situ X-ray diffraction measurements. Physics of the Earth and Planetary Interiors, 143–144, 515–526.Google Scholar
Fei, Y., Murphy, C., Shibazaki, Y., Shahar, A., Huang, H. (2016). Thermal equation of state of hcp-iron: constraint on the density deficit of Earth’s solid inner core. Geophysical Research Letters, 43, L069456.Google Scholar
Fei, Y., Ricolleau, A., Frank, M., Mibe, K., Shen, G., Prakapenka, V. B. (2007a). Toward an internally consistent pressure scale. Proceedings of the National Academy of Sciences, 104(22), 9182–9186.Google Scholar
Fei, Y., Seagle, C. T., Townsend, J. P., et al. (2021). Melting and density of MgSiO3 determined by shock compression of bridgmanite to 1254GPa. Nature Communications, 12, 876.Google Scholar
Fei, Y., Zhang, L., Corgne, A., et al. (2007b). Spin transition and equations of state of (Mg, Fe)O solid solutions. Geophysical Research Letters, 34, L17307.Google Scholar
Fiquet, G., Andrault, D., Dewaele, A., Charpin, T., Kunz, M., Hauesermann, D. (1998). P–V–T equation of state of MgSiO3 perovskite. Physics of the Earth and Planetary Interiors, 105, 21–31.Google Scholar
Fiquet, G., Dewaele, A., Andrault, D., Kunz, M., Le Bihan, T. (2000). Thermoelastic properties and crystal structure of MgSiO3 perovskite at lower mantle pressure and temperature conditions. Geophysical Research Letters, 27, 21–24.Google Scholar
Fischer, R. A., Campbell, A. J., Caracas, R., et al. (2014). Equations of state in the Fe–FeSi system at high pressures and temperatures. Journal of Geophysical Research: Solid Earth, 119, 2810–2827.Google Scholar
Fukui, H., Sakai, T., Sakamaki, T., et al. (2013). A compact system for generating extreme pressures and temperatures: an application of laser-heated diamond anvil cell to inelastic X-ray scattering. Review of Scientific Instruments, 84, 113902.Google Scholar
Greeff, C. W., Graf, M. J. (2004). Lattice dynamics and the high- pressure equation of state of Au. Physical Review B, 69(5), 054107.Google Scholar
Hemley, R. J., Zha, C.‐S., Jephcoat, A. P., Mao, H.‐K., Finger, L. W., Cox, D. E. (1989). X‐ray diffraction and equation of state of solid neon to 110 GPa. Physical Review B, 39(16), 11820–11827.Google Scholar
Hirao, N., Kawaguchi, S. I., Hirose, K., Shimizu, K., Ohtani, E., Ohishi, Y. (2020). New developments in high-pressure X-ray diffraction beamline for diamond anvil cell at SPring-8. Matter and Radiation at Extremes, 5, 018403.Google Scholar
Hirose, K., Sata, N., Komabayashi, T., Ohishi, Y. (2008). Simultaneous volume measurements of Au and MgO to 140 GPa and thermal equation of state of Au based on the MgO pressure scale. Physics of the Earth and Planetary Interiors, 167(3–4), 149–154.Google Scholar
Hixson, R. S., Fritz, J. N. (1992). Shock compression of tungsten and molybdenum. Journal of Applied Physics, 71, 1721–1728.Google Scholar
Holmes, N. C., Moriarty, J. A., Gathers, G. R., Nellis, W. J. (1989). The equation of state of platinum to 660 GPa (6.6 Mbar). Journal of Applied Physics, 66(7), 2962–2967.Google Scholar
Hu, X., Fei, Y., Yang, J., et al. (2019). Phase stability and thermal equation of state of iron carbide Fe3C to 245 GPa. Geophysical Research Letters, 46, L084545.Google Scholar
Huang, H., Wu, S., Hu, X., Wang, Q., Wang, X., Fei, Y. (2013). Shock compression of Fe‐FeS mixture up to 204 GPa. Geophysical Research Letters, 40, 687–691.Google Scholar
Huang, H., Leng, C., Wang, Q., et al. (2019). Equation of state for shocked Fe‐8.6 wt% Si up to 240 GPa and 4,670 K. Journal of Geophysical Research: Solid Earth, 124, B017983.Google Scholar
Irifune, T., Shinmei, T., McCammon, C. A., Miyajima, N., Rubie, D. C., Frost, D. J. (2010). Iron partitioning and density changes of pyrolite in Earth’s lower mantle. Science, 327, 193–195.Google Scholar
Ishii, T., Yamazaki, D., Tsujino, N., et al. (2017). Pressure generation to 65 GPa in a Kawai-type multi-anvil apparatus with tungsten carbide anvils. High Pressure Research, 37(4), 507–515.Google Scholar
Ito, E., Yamazaki, D., Yoshino, T., et al. (2010). Pressure generation and investigation of the post-perovskite transformation in MgGeO3 by squeezing the Kawai-cell equipped with sintered diamond anvils. Earth and Planetary Science Letters, 293, 84–89.Google Scholar
Jackson, I., Niesler, H. (1982). The elasticity of periclase to 3 GPa and some geophysical implications, in Akimoto, S., Manghnani, M. H., eds., High Pressure Research in Geophysics. Center for Academic Publishing, pp. 93–113.Google Scholar
Jacobsen, S. D., Holl, C. M., Adams, K. A., et al. (2008). Compression of single-crystal magnesium oxide to 118 GPa and a ruby pressure gauge for helium pressure media. American Mineralogist, 93, 1823–1828.Google Scholar
Jamieson, J. C., Fritz, J. N., Manghnani, M. H. (1982). Pressure measurement at high temperature in X‐ray diffraction studies: gold as a primary standard, in Akimoto, S., Manghnani, M. H., eds., High Pressure Research in Geophysics. Center for Academic Publishing, pp. 27–48.Google Scholar
Jenei, Z., O’Bannon, E. F., Weir, S. T., Cynn, H., Lipp, M. J., Evans, W. J. (2018). Single crystal toroidal diamond anvils for high pressure experiments beyond 5 megabar. Nature Communications, 9, 3563.Google Scholar
Kamada, S., Ohtani, E., Terasaki, H., et al. (2012). Melting relationships in the Fe–Fe3S system up to the outer core conditions. Earth and Planetary Science Letters, 359–360, 23–33.Google Scholar
Kamada, S., Ohtani, E., Terasaki, H., et al. (2014). Equation of state of Fe3S at room temperature up to 2 megabars. Physics of the Earth and Planetary Interiors, 228, 106–113.Google Scholar
Kamada, S., Fukui, H., Yoneda, A., et al. (2019). Elastic constants of single-crystal Pt measured up to 20 GPa based on inelastic X-ray scattering: Implication for the establishment of an equation of state. Comptes Rendus Geoscience, 351(2–3), 236–242.Google Scholar
Katsura, T., Funakoshi, K., Kubo, A., et al. (2004). A large-volume high P-T apparatus for in situ X-ray observation, “SPEEDMkII”. Physics of the Earth and Planetary Interiors, 143–144, 497–506.Google Scholar
Katsura, T., Yokoshi, S., Kawabe, K., et al. (2009). P–V–T relations of MgSiO3 perovskite determined by in situ X-ray diffraction using a large-volume high-pressure apparatus. Geophysical Research Letters, 36, L01305.Google Scholar
Katsura, T., Yoneda, A., Yamazaki, D., Yoshino, T., Ito, E. (2010). Adiabatic temperature profile in the mantle. Physics of the Earth and Planetary Interiors, 183, 212–218.Google Scholar
Kawai, N., Togaya, M., Onodera, A. (1973). A new device for high pressure vessels. Proceedings of the Japan Academy, 49, 623–626.Google Scholar
Kennedy, G., Keeler, R. (1972). Compressibility, in Gray, D. E., ed., American Institute of Physics Handbook, 3rd edition. McGraw-Hill, pp. 4–39.Google Scholar
Knudson, M. D., Desjarlais, M. P. (2013). Adiabatic release measurements in α-quartz between 300 and 1200 GPa: characterization of α-quartz as a shock standard in the multimegabar regime. Physical Review B, 88, 184107.Google Scholar
Kohler, U., Johannsen, P. G., Holzapfel, W. B. (1997). Equation-of-estate data for CsCl-type alkali halides. Journal of Physics: Condensed Matter, 9, 5581–5592.Google Scholar
Komabayashi, T., Hirose, K., Nagaya, Y., Sugimura, E., Ohishi, Y. (2010). High temperature compression of ferropericlase and the effect of temperature on iron spin transition. Earth and Planetary Science Letters, 297, 691–699.Google Scholar
Kono, Y., Irifune, T., Higo, Y., Inoue, T., Barnhoorn, A. (2010). PVT relation of MgO derived by simultaneous elastic wave velocity and in situ X‐ray measurements: a new pressure scale for the mantle transition region. Physics of the Earth and Planetary Interiors, 183(1–2), 196–211.Google Scholar
Kuramochi, K., Ishimatsu, N., Sakai, T., Kawamura, N., Irifune, T. (2020). An application of NPD to double-stage diamond anvil cells: XAS spectra of rhenium metal under high pressures above 300 GPa. High Pressure Research, 40(1), 119–129.Google Scholar
Lai, X., Zhu, F., Liu, J., et al. (2018). The high-pressure anisotropic thermoelastic properties of a potential inner core carbon-bearing phase, Fe7C3, by single-crystal X-ray diffraction. American Mineralogist, 103, 1568–1574.Google Scholar
Li, B., Woody, K., Kung, J. (2006). Elasticity of MgO to 11 GPa with an independent absolute pressure scale: Implications for pressure calibration. Journal of Geophysical Research, 111, B11206.Google Scholar
Li, J., Fei, Y. (2014). Experimental constraints on core composition, in Carlson, R. W., ed., Treatise on Geochemistry. Elsevier, pp. 527–557.Google Scholar
Li, J., Fei, Y., Mao, H. K., Hirose, K., Shieh, S. R. (2001). Sulfur in the Earth’s inner core. Earth and Planetary Science Letters, 193, 509–514.Google Scholar
Li, J., Mao, H. K., Fei, Y., Gregoryanz, E., Eremets, M., Zha, C. S. (2002). Compression of Fe3C to 30 GPa at room temperature. Physics and Chemistry of Minerals, 29, 166–169.Google Scholar
Li, J., Struzhkin, V. V., Mao, H. -K., et al. (2004). Electronic spin state of iron in lower mantle perovskite. Proceedings of the National Academy of Sciences, 101, 14027–14030.Google Scholar
Li, X., Jeanloz, R. (1987). Measurement of the B1–B2 transition pressure in NaCl at high temperatures. Physical Review B: Condensed Matter and Materials Physics, 36(1), 474–479.Google Scholar
Lin, J. F., Gavriliuk, A. G., Struzhkin, V. V., et al. (2006). Pressure-induced electronic spin transition of iron in magnesiowüstite-(Mg,Fe)O. Physical Review B, 73, 113107.Google Scholar
Lin, J. F., Struzhkin, V. V., Jacobsen, S. D., et al. (2005). Spin transition of iron in magnesiowüstite in the Earth’s lower mantle. Nature, 436, 377–380.Google Scholar
Litasov, K. D., Dorogokupets, P. I., Ohtani, E., et al. (2013a). Thermal equation of state and thermodynamic properties of molybdenum at high pressures. Journal of Applied Physics, 113, 093507.Google Scholar
Litasov, K. D., Gavryushkin, P. N., Dorogokupets, P. I., et al. (2013b). Thermal equation of state to 33.5 GPa and 1673 K and thermodynamic properties of tungsten. Journal of Applied Physics, 113, 133505.Google Scholar
Litasov, K. D., Sharygin, I. S., Dorogokupets, P. I., et al. (2013c). Thermal equation of state and thermodynamic properties of iron carbide Fe3C to 31 GPa and 1473 K. Journal of Geophysical Research, 118, 5274–5284.Google Scholar
Liu, Z., Irifune, T., Nishi, M., Tange, Y., Arimoto, T., Shinmei, T. (2016). Phase relations in the system MgSiO3–Al2O3 up to 52 GPa and 2000 K. Physics of the Earth and Planetary Interiors, 257, 18–27.Google Scholar
Lundin, S., Catalli, K., Santillan, J., et al. (2008). Effect of Fe on the equation of state of mantle silicate perovskite over 1 Mbar. Physics of the Earth and Planetary Interiors, 168, 97–102.Google Scholar
Mao, H. K., Hemley, R. J., Fei, Y., et al. (1991). Effect of pressure, temperature, and composition on the lattice parameters and density of three (Fe, Mg)SiO3 perovskites up to 30 GPa. Journal of Geophysical Research, 96, 8069–8079.Google Scholar
Mao, Z., Lin, J. F., Liu, J., Prakapenka, V. B. (2011). Thermal equation of state of lower-mantle ferropericlase across the spin crossover. Geophysical Research Letters, 38, L23308.Google Scholar
Mao, Z., Lin, J. F., Yang, J., Inoue, T., Prakapenka, V. B. (2015). Effects of the Fe3+ spin transition on the equation of state of bridgmanite. Geophysical Research Letters, 42, 4335–4342.Google Scholar
Mao, Z., Wang, F., Lin, J.-F., et al. (2017). Equation of state and hyperfine parameters of high-spin bridgmanite in the Earth’s lower mantle by synchrotron X-ray diffraction and Mössbauer spectroscopy. American Mineralogist, 102, 357–368.Google Scholar
Mao, H. K., Wu, Y., Chen, L. C., Shu, J. F., Jephcoat, A. P. (1990). Static compression of iron to 300 GPa and Fe0.8Ni0.2 Alloy to 260 GPa: implications for composition of the core. Journal of Geophysical Research, 95, 21737–21742.Google Scholar
Mao, H. K., Xu, J., Bell, P. M. (1986). Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions. Journal of Geophysical Research: Solid Earth, 91(B5), 4673–4676.Google Scholar
Matsui, M., Higo, Y., Okamoto, Y., Irifune, T., Funakoshi, K.‐I. (2012). Simultaneous sound velocity and density measurements of NaCl at high temperatures and pressures: Application as a primary pressure standard. American Mineralogist, 97(10), 1670–1675.Google Scholar
Matsui, M., Ito, E., Katsura, T., et al. (2009). The temperature–pressure–volume equation of state of platinum. Journal of Applied Physics, 105(1), 013505.Google Scholar
Matsui, M., Parker, S. C., Leslie, M. (2000). The MD simulation of the equation of state of MgO: application as a pressure calibration standard at high temperature and high pressure, American Mineralogist, 85, 312–316.Google Scholar
McCoy, C. A., Knudson, M. D., Root, S. (2017). Absolute measurement of the Hugoniot and sound velocity of liquid copper at multimegabar pressures. Physical Review B, 96, 174109.Google Scholar
McDonough, W. F., Sun, S.-S. (1995). The composition of the Earth. Chemical Geology, 120, 223–253.Google Scholar
Meng, Y., Shen, G., Mao, H. K. (2006). Double-sided laser heating system at HPCAT for in situ X-ray diffraction at high pressures and high temperatures. Journal of Physics: Condensed Matter, 18, S1097–S1103.Google Scholar
Meng, Y., Weidner, D. J., Fei, Y. (1993). Deviatoric stress in a quasi-hydrostatic diamond anvil cell: Effect on the volume-based pressure calibration. Geophysical Research Letters, 20, 1147–1150.Google Scholar
Murakami, M., Takata, N. (2019). Absolute primary pressure scale to 120 GPa: toward a pressure benchmark for Earth’s lower mantle. Journal of Geophysical Research, 124, 6581–6588.Google Scholar
Nellis, W. J., Moriarty, J. A., Mitchell, A. C., et al. (1988). Metals physics at ultrahigh pressure: aluminum, copper, and lead as prototypes. Physical Review Letters, 60, 1414–1417.Google Scholar
Nishio-Hamane, D., Yagi, T. (2009). Equations of state for postperovskite phases in the MgSiO3–FeSiO3–FeAlO3 system. Physics of the Earth and Planetary Interiors, 175, 145–150.Google Scholar
Noguchi, M., Komabayashi, T., Hirose, K., Ohishi, Y. (2013). High‐temperature compression experiments of CaSiO3 perovskite to lowermost mantle conditions and its thermal equation of state. Physics and Chemistry of Minerals, 40, 81–91.Google Scholar
Ohishi, Y., Hirao, N., Sata, N., Hirose, K., Takata, M. (2008). Highly intense monochro- matic X-ray diffraction facility for high-pressure research at SPring-8. High Pressure Research, 28, 163–173.Google Scholar
Ono, S. (2010). The equation of state of B2‐type NaCl. Journal of Physics: Conference Series, 215, 012196.Google Scholar
Ono, S., Brodholt, J. P., Price, G. D. (2011). Elastic, thermal and structural properties of platinum. Journal of Physics and Chemistry of Solids, 72(3), 169–175.Google Scholar
Ono, S., Kikegawa, T., Ohishi, Y. (2006). Structural property of CsCl‐type sodium chloride under pressure, Solid State Communications, 137(10), 517–521.Google Scholar
Prakapenka, V. B., Kubo, A., Kuznetsov, A., et al. (2008). Advanced flat top laser heating system for high pressure research at GSECARS: application to the melting behavior of germanium. High Pressure Research, 28, 225–235.Google Scholar
Prescher, C., Dubrovinsky, L., Bykova, E., et al. (2015). High Poisson’s ratio of Earth’s inner core explained by carbon alloying. Nature Geoscience, 8(3), 220–223.Google Scholar
Rech, G. L., Zorzi, J. E., Perottoni, C. A. (2019). Equation of state of hexagonal-close-packed rhenium in the terapascal regime. Physical Review B, 100, 174107.Google Scholar
Ricolleau, A., Fei, Y., Cottrell, E., et al. (2009). Density profile of pyrolite under the lower mantle conditions. Geophysical Research Letters, 36, L06302.Google Scholar
Root, S., Townsend, J. P., Davies, E., et al. (2018). The principal Hugoniot of forsterite to 950 GPa. Journal Geophysical Research Letters, 45, 3865–3872.Google Scholar
Sakai, T., Ohtani, E., Hirao, N., Ohishi, Y. (2011), Equation of state of the NaCl‐B2 phase up to 304 GPa. Journal of Applied Physics, 109(8), 084912.Google Scholar
Sakai, T., Takahashi, S., Nishitani, N., Mashini, I., Ohtani, E., Hirao, N. (2014). Equation of state of pure iron and Fe0.9Ni0.1 alloy up to 3 Mbar. Physics of the Earth and Planetary Interiors, 228, 114–126.Google Scholar
Sata, N., Hirose, K., Shen, G., Nakajima, Y., Ohishi, Y., Hirao, N. (2010). Compression of FeSi, Fe3C, Fe095O, and FeS under the core pressures and implication for light element in the Earth’s core. Journal of Geophysical Research, 115, B09204.Google Scholar
Sata, N., Shen, G., Rivers, M. L., Sutton, S. R. (2002). Pressure‐volume equation of state of the high‐pressure B2 phase of NaCl. Physical Review B, 65(10), 104114.Google Scholar
Schultz, E., Mezouar, M., Crichton, W., et al. (2005). Double-sided laser heating system for in situ high pressure and high temperature monochromatic X-ray diffraction at the ESRF. High Pressure Research, 25, 71–83.Google Scholar
Shen, G., Mao, H. K. (2017). High-pressure studies with X-rays using diamond anvil cells. Reports on Progress in Physics, 80, 1–53.Google Scholar
Shen, G., Rivers, M. L., Wang, Y., Sutton, S. R. (2001). A laser heated diamond cell system at the Advanced Photon Source for in situ X-ray measurements at high pressure and temperature. Review of Scientific Instruments, 72, 1273–1282.Google Scholar
Shim, S. H., Duffy, T. S., Shen, G. (2000). The stability and P–V–T equation of state of CaSiO3 perovskite in the Earth’s lower mantle. Journal of Geophysical Research, 105, 25955–25968.Google Scholar
Shim, S. H., Duffy, T. S., Takemura, K. (2002). Equation of state of gold and its application to the phase boundaries near 660 km depth in Earth’s mantle. Earth and Planetary Science Letters, 203(2), 729–739,Google Scholar
Solomatova, N. V., Jackson, J. M., Sturhahn, W., et al. (2016). Equation of state and spin crossover of (Mg, Fe)O at high pressure, with implications for explaining topographic relief at the core-mantle boundary. American Mineralogist, 101, 1084–1093.Google Scholar
Speziale, S., Zha, C.‐S., Duffy, T. S., Hemley, R. J., Mao, H.‐K. (2001). Quasi‐hydrostatic compression of magnesium oxide to 52 GPa: implications for the pressure–volume–temperature equation of state. Journal of Geophysical Research, 106(B1), 515–528.Google Scholar
Sun, N., Mao, Z., Yan, S., Wu, X., Prakapenka, V. B., Lin, J.-F. (2016). Confirming a pyrolitic lower mantle using self-consistent pressure scales and new constraints on CaSiO3 perovskite. Journal of Geophysical Research, 121, 4876–4894.Google Scholar
Sun, N., Wei, W., Han, S., et al. (2018). Phase transition and thermal equation of state of (Fe,Al)‐bridgmanite and post‐perovskite: implication for the chemical heterogeneity at the lowermost mantle. Earth and Planetary Science Letters, 490, 161–169.Google Scholar
Takahashi, S., Ohtani, E., Ikuta, D., et al. (2019). Thermal equation of state of Fe3C to 327 GPa and carbon in the core. Minerals, 9, 744.Google Scholar
Takemura, K., Dewaele, A. (2008). Isothermal equation of state for gold with a He‐pressure medium. Physical Review B, 78(10), 104119.Google Scholar
Takemura, K., Watanuki, T., Ohwada, K., Machida, A., Ohmura, A., Aoki, K. (2010). Powder X‐ray diffraction study of Ne up to 240 GPa. Journal of Physics: Conference Series, 215, 012017.Google Scholar
Tange, Y., Irifune, T., Funakoshi, K. (2008). Pressure generation to 80 GPa using multianvil apparatus with sintered diamond anvils. High Pressure Research, 28, 245–254.Google Scholar
Tange, Y., Kuwayama, Y., Irifune, T., Funakoshi, K., Ohishi, Y. (2012). P–V–T equation of state of MgSiO3 perovskite based on the MgO pressure scale: a comprehensive reference for mineralogy of the lower mantle. Journal of Geophysical Research, 117, L08988.Google Scholar
Tange, Y., Nishihara, Y., Tsuchiya, T. (2009b). Unified analyses for P‐V‐T equation of state of MgO: a solution for pressure‐scale problems in high P–T experiments. Journal of Geophysical Research, 114, B03208.Google Scholar
Tange, Y., Takahashi, E., Nishihara, Y., Funakoshi, K., Sata, N. (2009a). Phase relations in the system MgO-FeO-SiO2 to 50 GPa and 2000 °C: an application of experimental techniques using multianvil apparatus with sintered diamond anvils. Journal of Geophysical Research, 114, B02214.Google Scholar
Tateno, S., Kuwayama, Y., Hirose, K., Ohishi, Y. (2015). The structure of Fe–Si alloy in Earth’s inner core. Earth and Planetary Science Letters, 418, 11–19.Google Scholar
Thompson, S., Komabayashi, T., Breton, H., et al. (2020). Compression experiments to 126 GPa and 2500 K and thermal equation of state of Fe3S: implications for sulphur in the Earth’s core. Earth and Planetary Science Letters, 534, 116080.Google Scholar
Tomlinson, K., Seagle, C. T., Huang, H., Smith, G. E., Taylor, J. L., Paguio, R. R. (2018). Enhanced dual confocal measurement system. Fusion Science and Technology, 73, 139–148.Google Scholar
Tsuchiya, T. (2003). First‐principles prediction of the P–V–T equation of state of gold and the 660‐km discontinuity in Earth’s mantle. Journal of Geophysical Research, 108(B10), 2462.Google Scholar
Ueda, Y., Matsui, M., Yokoyama, A., Tange, Y., Funakoshi, K. (2008). Temperature–pressure–volume equation of state of the B2 phase of sodium chloride. Journal of Applied Physics, 103(11), 113513.Google Scholar
Utsumi, W., Funakoshi, K., Katayama, Y., Yamakata, M., Okata, T., Shimomura, O. (2002). High-pressure science with a multi-anvil apparatus at SPring-8. Journal of Physics: Condensed Matter, 14, 10497–10504.Google Scholar
Vinet, P., Ferrante, J., Smith, J. R., Rose, J. H. (1986). A universal equation of state for solids. Journal of Physics C: Solid State Physics, 19(20), L467–L473.Google Scholar
Walker, D., Carpenter, M. A., Hitch, C. M. (1990). Some simplifications to multianvil devices for high pressure experiments. American Mineralogist, 75, 1020–1028.Google Scholar
Walter, M., Kubo, A., Yoshino, T., Brodholt, J., Koga, K. T., Ohishi, Y. (2004). Phase relations and equation-of-state of aluminous Mg–silicate perovskite and implications for Earth’s lower mantle. Earth and Planetary Science Letters, 222, 501–516.Google Scholar
Walter, M., Trønnes, R. G., Armstrong, L. S., Lord, O., Caldwell, W. A., Clark, A. M. (2006). Subsolidus phase relations and perovskite compressibility in the system MgO–AlO1.5–SiO2 with implications for Earth’s lower mantle. Earth and Planetary Science Letters, 248, 77–89.Google Scholar
Wang, Y., Ahuja, R., Johansson, B. (2002). Reduction of shock-wave data with mean-field potential approach. Journal of Applied Physics, 92, 6616.Google Scholar
Weir, C. E., Lippincott, E. R., Valkenburg, A. V., Bunting, E. N. (1959). Infrared studies in the 1-to 15-micron ragion to 30,000 atmospheres. Journal of Research NBS, 63A(1), 55–62.Google Scholar
Wolf, A. S., Jackson, J. M., Dera, P., Prakapenka, V. B. (2015). The thermal equation of state of (Mg, Fe)SiO3 bridgmanite (perovskite) and implications for lower mantle structures. Journal of Geophysical Research, 120, 7460–7489.Google Scholar
Wu, Z., Wentzcovitch, R. M., Umemoto, K., Li, B., Hirose, K., Zheng, J.-C. (2008). Pressure–volume–temperature relations in MgO: an ultra- high pressure-temperature scale for planetary sciences applications. Journal of Geophysical Research, 113, B06204.Google Scholar
Yamazaki, D., Ito, E. (2020). High pressure generation in the Kawai-type multianvil apparatus equipped with sintered diamond anvils. High Pressure Research, 40, 3–11.Google Scholar
Yamazaki, D., Ito, E., Yoshino, T., (2012). P–V–T equation of state for ɛ-iron up to 80 GPa and 1900 K using the Kawai-type high pressure apparatus equipped with sintered diamond anvils. Geophysical Research Letters, 39, L20308.Google Scholar
Yamazaki, D., Ito, E., Yoshino, Y., et al. (2014). Over 1 Mbar generation in the Kawai-type multianvil apparatus and its application to compression of (Mg0.92Fe0.08)SiO3 perovskite and stishovite. Physics of the Earth and Planetary Interiors, 228, 262–267.Google Scholar
Yamazaki, D., Ito, E., Yoshino, T., et al. (2019). High-pressure generation in the Kawai-type multianvil apparatus equipped with tungsten-carbide anvils and sintered- diamond anvils, and X-ray observation on CaSnO3 and (Mg,Fe)SiO3. Comptes Rendus Geoscience, 351(2–3), 253–259.Google Scholar
Yang, J., Fei, Y., Hu, X., Greenberg, E., Prakapenka, V. B. (2019). Effect of carbon on the volume of solid iron at high pressure: implications for carbon substitution in iron structures and carbon content in the Earth’s inner core. Minerals, 9, 720.Google Scholar
Ye, Y., Prakapenka, V., Meng, Y., Shim, S.-H. (2017). Intercomparison of the gold, platinum, and MgO pressure scales up to 140 GPa and 2500 K. Journal of Geophysical Research, 122, 3450–3464.Google Scholar
Ye, Y., Shim, S. H., Prakapenka, V., Meng, Y. (2018). Equation of state of solid Ne inter-calibrated with the MgO, Au, Pt, NaCl-B2, and ruby pressure scales up to 130 GPa. High Pressure Research, 38, 377–395.Google Scholar
Yokoo, M., Kawai, N., Nakamura, K. G., Kondo, K. (2009). Ultrahigh-pressure scales for gold and platinum at pressures up to 550 GPa. Physical Review B, 80, 104114.Google Scholar
Zha, C.‐S., Mao, H.‐K., Hemley, R. J. (2000). Elasticity of MgO and a primary pressure scale to 55 GPa. Proceedings of the National Academy of Sciences, 97(25), 13,494–13,499.Google Scholar
Zha, C.‐S., Mibe, K., Bassett, W. A., Tschauner, O., Mao, H.‐K., Hemley, R. J. (2008). P–V–T equation of state of platinum to 80 GPa and 1900 K from internal resistive heating/X‐ray diffraction measurements. Journal of Applied Physics, 103(5), 054908.Google Scholar
Zhang, Y., Sekine, T., He, H., Yu, Y., Liu, F., Zhang, M. (2016). Experimental constraints on light elements in the Earth’s outer core. Scientific Reports, 6(1), 22473.Google Scholar
Zhang, Y., Sekine, T., Lin, J. F., et al. (2018). 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. Journal of Geophysical Research, 123, 1314–1327.Google Scholar

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