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9 - Elasticity at High Pressure with Implication for the Earth’s Inner Core

Published online by Cambridge University Press:  03 August 2023

Yingwei Fei
Affiliation:
Carnegie Institution of Washington, Washington DC
Michael J. Walter
Affiliation:
Carnegie Institution of Washington, Washington DC
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Summary

Elastic wave velocities and densities of iron and candidate iron alloys are important properties for understanding the seismological observations of Earth’s core. Several methods have been applied to measure the elastic wave velocities of iron and iron alloys at room temperature. Recently, measurements have been extended to simultaneous high-pressure and high-temperature conditions. Birch’s law, which is the linearity between density and compressional wave velocity (VP), is applicable to the experimental results of density and VP at high pressure and room temperature. The effect of temperature on Birch’s law is discussed, and it is not negligible at temperatures greater than 1,000–2,000 K. The VP and density of hcp Fe are extrapolated to pressure and temperature conditions of the inner core. VP of hcp Fe at 330–360 GPa is higher than the inner core seismic velocity, thus suggesting that iron should be alloyed with other elements so as to reduce not only its density, but also its velocity at inner core conditions. The VP of Fe–Si, Fe–H, and Fe–C alloys is slower than that of Fe at the pressure of the inner core. If the temperature effect on Birch’s law is taken into account, Si and H can be candidates for the major light elements in the inner core, while C, O, and S may not be included or exist as minor constituents.

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Publisher: Cambridge University Press
Print publication year: 2022

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References

Alfè, D., Gillan, M. J., Price, G. D. (2002). Composition and temperature of the Earth’s core constrained by combining ab initio calculations and seismic data. Earth and Planetary Science Letters, 195, 91–8.Google Scholar
Antonangeli, D., Komabayashi, T., Occelli, F. (2012). 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. Earth and Planetary Science Letters, 331332, 210214.Google Scholar
Antonangeli, D., Krisch, M., Fiquet, G., et al. (2004b). Elasticity of cobalt at high pressure studied by inelastic X-ray scattering. Physical Review Letters, 93(21), 215505.CrossRefGoogle ScholarPubMed
Antonangeli, D., Merkel, S., Farber, D. L. (2006). Elastic anisotropy in hcp metals at high pressure and the sound wave anisotropy of the Earth’s inner core. Geophysical Research Letters, 33, L24303.Google Scholar
Antonangeli, D., Morard, G., Paolasini, L. et al. (2018). 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. Earth and Planetary Science Letters, 482, 446453.CrossRefGoogle Scholar
Antonangeli, D., Occelli, F., Requardt, H. (2004a). Elastic anisotropy in textured hcp–iron to 112 GPa from sound wave propagation measurements. Earth and Planetary Science Letters, 225, 243251.CrossRefGoogle Scholar
Antonangeli, D., Ohtani, E. (2015). Sound velocity of hcp–Fe at high pressure: experimental constrants, extrapolations and comparison with seismic models. Progress in Earth and Planetary Science, 2, 3.Google Scholar
Antonangeli, D., Siebert, J., Aracne, C. M. (2011). Spin crossover in ferropericlase at high pressure: a seismologically transparent transition? Science, 331, 6467.CrossRefGoogle ScholarPubMed
Antonangeli, D., Siebert, J., Badro, J. (2010). Composition of the Earth’s inner core from high-pressure sound velocity measurements in Fe–Ni–Si alloys. Earth and Planetary Science Letters, 295, 292296.Google Scholar
Anzellini, S., Dewaele, A., Mezouar, M., et al. (2013). Melting of iron at Earth’s inner core boundary based on fast X-ray diffraction. Science, 340, 464466.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, 789791.Google Scholar
Badro, J., Fiquet, G., Guyot, F. et al. (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, 233238.CrossRefGoogle Scholar
Badro, J., Rueff, J.-P., Vankó, G., et al. (2004). Electronic transitions in perovskite: possible nonconvecting layers in the lower mantle. Science, 305, 383386.Google Scholar
Barker, L. M., Hollenbach, R. E. (1972). Laser interferometer for measuring velocities of any reflecting of surface. Journal of Applied Physics, 43, 46694675.Google Scholar
Birch, F. (1952). Elasticity and constitution of the Earth’s interior. Journal of Geophysical Research, 57, 227286.Google Scholar
Birch, F. (1961). Composition of the Earth’s mantle. Geophysical Journal of the Royal Astronomical Society, 4(S0), 295311.Google Scholar
Brown, M. J., Shankland, T. J. (1981). Thermodynamic parameters in the Earth as determined from seismic profiles. Geophysical Journal of the Royal Astronomical Society, 66, 579596.CrossRefGoogle Scholar
Brown, M. J., McQueen, R. G. (1986). Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 440 GPa. Journal of Geophysical Research, 91(B7), 74857494.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 of the United States of America, 111(50), 1775517758.Google Scholar
Chigarev, N., Zinin, P., Ming, L.-C., et al. (2008). Laser generation and detection of longitudinal and shear acoustic waves in a diamond anvil cell. Applied Physics Letters, 93, 181905.Google Scholar
Cook, R. K. (1957). Variation of elastic constants and static strains with hydrostatic pressure: a method for calculation from ultrasonic measurements. Journal of the Acoustical Society of America, 29, 445449.CrossRefGoogle Scholar
Decremps, F., Antonangeli, A., Gauthier, M., et al. (2014). Sound velocity of iron up to 152 GPa by picosecond acoustics in diamond anvil cell. Geophysical Research Letters, 41, 14591464.CrossRefGoogle Scholar
Decremps, F., Gauthier, M., Ayrinhac, S., et al. (2015). Picosecond acoustics method for measuring the thermodynamical properties of solids and liquids at high pressure and high temperature. Ultrasonics, 56, 129140.Google Scholar
Dewaele, A., Loubeyre, P., Occelli, F., et al. (2006). Quasihydrostatic equation of state of iron above 2 Mbar. Physical Review Letters, 97, 215504.Google Scholar
Dorogokupets, P. I., Oganov, A. R. (2007). Ruby, metals, and MgO as alternative pressure scales: a semiempirical description of shock-wave, ultrasonic, X-ray, and thermochemical data at high temperatures and pressures. Physical Review B, 75, 024115.CrossRefGoogle Scholar
Duffy, T., Ahrens, T. J. (1995). Compressional sound velocity, equation of state, and constitutive response of shock-compressed magnesium oxide. Journal of Geophysical Research, 100, 529542.CrossRefGoogle Scholar
Dziewonski, A. M., Anderson, D. L. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25, 297356.CrossRefGoogle Scholar
Edmund, E., Antonangeli, D., Decremps, F., et al. (2019). Velocity-density systematics of Fe-5wt%Si: constraints on Si content in the Earth’s inner core. Journal of Geophysical Research, 124, 34363447.Google Scholar
Fei, Y., Murphy, C., Shibazaki, Y., et al. (2016). Thermal equation of state of hcp–iron: constraint on the density deficit of Earth’s solid inner core. Geophysical Research Letters, 43, 68376843.Google Scholar
Fiquet, G., Badro, J., Gregoryanz, E., et al. (2009). Sound velocity in iron carbide (Fe3C) at high pressure: implications for the carbon content of the Earth’s inner core. Physics of the Earth and Planetary Interiors, 172, 125129.CrossRefGoogle Scholar
Fiquet, G., Badro, J., Guyot, F., et al. (2001). Sound velocities in iron to 110 gigapascals. Science, 291, 468471.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, 119, 28102827.CrossRefGoogle Scholar
Fukui, H., Katsura, T., Kuribayashi, T., et al. (2008). Precise determination of elastic constants by high-resolution inelastic X-ray scattering. Journal of Synchrotron Radiation, 15, 618623.CrossRefGoogle ScholarPubMed
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
Fukui, H., Yoneda, A., Nakatsuka, A. et al. (2016) Effect of cation substitution on bridgmanite elasticity: A key to interpret sesmic anomalies in the lower mantle. Scientific Reports, 6, 33337.Google Scholar
Gao, L., Chen, B., Wang, J., et al. (2008). Pressure-induced magnetic transition and sound velocities of Fe3C: implications for carbon in the Earth’s inner core. Geophysical Research Letters, 35, L17306.Google Scholar
Gao, L., Chen, B., Zhao, J., et al. (2011). Effect of temperature on sound velocities of compressed Fe3C, a candidate component of the Earth’s inner core. Earth and Planetary Science Letters, 309, 213220.CrossRefGoogle Scholar
Glazyrin, K., Pourovskii, L.V., Dubrovinsky, L., et al. (2013). Importance of correlation effects in hcp iron revealed by a pressure-induced electronic topological transition. Physical Review Letters, 110, 117206.Google Scholar
Gréaux, S., Irifune, T., Higo, Y., et al. (2019). Sound velocity of CaSiO3 perovskite suggests the presence of basaltic crust in the Earth’s lower mantle. Nature, 565, 218221.Google Scholar
Hamada, M., Kamada, S., Ohtani, E., et al. (2016). Magnetic and spin transitions in wüstite: a synchrotron Mössbauer spectroscopic study. Physical Review B, 93, 155165.CrossRefGoogle Scholar
Higo, Y., Inoue, T., Li, B., et al. (2006). The effect of iron on the elastic properties of ringwoodite at high pressure. Physics of the Earth and Planetary Interiors, 159, 276285.Google Scholar
Hirao, N., Kawaguchi-Imada, S., Hirose, K., et al. (2020). New developments in high-pressure X-ray diffraction beamline for diamond anvil cell at SPring-8. Matter and Radiation at Extremes, 5, 018403.CrossRefGoogle Scholar
Hirao, N., Kondo, T., Ohtani, E., et al. (2004). Compression of iron hydride to 80 GPa and hydrogen in the Earth’s core. Geophysical Research Letters, 31, L06616.Google Scholar
Holmes, N. C., Moriarty, J. A., Gathers, G. R., et al. (1989). The equation of state of platinum to 660 GPa (6.6 Mbar). Journal of Applied Physics, 66, 29622967.Google Scholar
Huang, H., Fei, Y., Cai, L., et al. (2011). Evidence for an oxygen-depleted liquid outer core of the Earth. Nature, 479, 513516.Google Scholar
Huang, H., Leng, C., Yang, G., et al. (2018). Measurements of sound velocity of liquid Fe-11.8 wt%S up to 211.4 GPa and 6150 K. Journal of Geophysical Research, 123, 47304739.Google Scholar
Jackson, J. M., Sturhahn, W., Shen, G., et al. (2005). A synchrotron Mössbauser spectroscopy study of (Mg,Fe)SiO3 perovskite up to 120 GPa. American Mineralogist, 90, 199205.Google Scholar
Jacobsen, S. D., Reichmann, H. J., Spetzler, H. A., et al. (2006). Structure and elasticity of single-crystal (Mg,Fe)O and a new method of generating shear waves for gigahertz ultrasonic interferometry. Journal of Geophysical Research, 107(B2), 2037.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 Publications, pp. 2748.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, 236242.Google Scholar
Kamada, S., Ohtani, E., Fukui, H., et al. (2014a). The sound velocity measurements of Fe3S. American Mineralogist, 99, 98101.CrossRefGoogle Scholar
Kamada, S., Ohtani, E., Terasaki, H., et al. (2014b). Equation of state of Fe3S at room temperature up to 2 megabars. Physics of the Earth and Planetary Interiors, 228, 106113.Google Scholar
Kamada, S., Suzuki, N., Maeda, F., et al. (2018). Electronic properties and compressional behavior of Fe–Si alloys at high pressure. American Mineralogist, 103, 19591965.Google Scholar
Kawaguchi, S. I., Nakajima, Y., Hirose, K., et al. (2017) Sound velocity of liquid Fe–Ni–S at high pressure. Journal of Geophysical Research, 122, 36243634.Google Scholar
Kennett, B. L. N., Engdahl, E. R. (1991). Traveltimes for global earthquake location and phase identification. Geophysical Journal International, 105(2), 429465.Google Scholar
Kennett, B. L. N., Engdahl, E. R., Buland, R. (1995). Constraints on seismic velocities in the Earth from traveltimes. Geophysical Journal International, 122(1), 108124.Google Scholar
Kono, Y., Irifune, T., Higo, Y., et al. (2010). P–V–T 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, 196211.Google Scholar
Kurnosov, A., Marquardt, H., Frost, D., et al. (2017). Evidence for a Fe3+-rich pyrolytic lower mantle from (Al,Fe)-bearing bridgmanite elasticity data. Nature, 543, 543546.Google Scholar
Kuwayama, Y., Morard, G., Nakajima, Y., et al. (2020). Equation of state of liquid iron under extreme conditions. Physical Review Letters, 124, 165701.Google Scholar
Li, B., Liebermann, R. C. (2014). Study of the Earth’s interior using measurements of sound velocities in minerals by ultrasonic interferometry. Physics of the Earth and Planetary Interiors, 233, 135153.CrossRefGoogle Scholar
Lifshitz, I. M. (1960). Anomalies of electron characteristics of a metal in the high pressure region. Soviet Physics JETP, 11(5), 11301135.Google Scholar
Li, J., Sturhahn, W., Jackson, J.M. (2006). Pressure effect on the electronic structure of iron in (Mg,Fe)(Si,Al)O3 perovskite: a combined synchrotron Mössbauer and X-ray emission spectroscopy study up to 100 GPa. Physics and Chemistry of Minerals, 33, 575585.Google Scholar
Li, Y., Vočadlo, L., Brodhol, J. P. (2018). The elastic properties of hcp–Fe alloys under the conditions of the Earth’s inner core. Earth and Planetary Science Letters, 493, 118–127. Physics of the Earth and Planetary Interiors, 233, 135-153.Google Scholar
Lin, J.-F., Campbell, A. J., Heinz, D. L., et al. (2003a). Static compression of iron–silicon alloys: implications for silicon in the Earth’s core. Journal of Geophysical Research, 108(B1), 2045.Google Scholar
Lin, J.-F., Fei, Y., Sturhahn, W., et al. (2004). Magnetic transition and sound velocities of Fe3S at high pressure: implications for Earth and planetary cores. Earth and Planetary Science Letters, 226, 3340.Google Scholar
Lin, J. F., Gavriliuk, A. G., Struzhkin, V. V., et al. (2006). Pressure-induced electronic spin transition of iron in magnesiowustite-(Mg.Fe)O. Physical Review B, 73, 113107.Google Scholar
Lin, J. F., Gavriliuk, A. G., Sturhahn, W. et al. (2009). Synchrotron Mossbauer spectroscopic study of ferropericlase at high pressures and temperatures. American Mineralogist, 94, 594599.Google Scholar
Lin, J. F., Struzhkin, V. V., Sturhahn, W., et al. (2003b). Sound velocities of iron–nickel and iron–silicon alloys at high pressures. Geophysical Research Letters, 30(21), 2112.CrossRefGoogle Scholar
Lin, J. F., Sturhahn, W., Zhao, J., et al. (2005). Sound velocities of hot dense iron: Birch’s law revisited. Science, 308, 18921894.Google Scholar
Lin, J. F., Tsuchiya, T. (2008). Spin transition of iron in the Earth’s lower mantle. Physics of the Earth and Planetary Interiors, 170, 248259.CrossRefGoogle Scholar
Liu, J., Lin, J. F., Alatas, A., et al. (2014). Sound velocities of bcc–Fe and Fe0.85Si0.15 alloy at high pressure and temperature. Physics of the Earth and Planetary Interiors, 233, 2432.Google Scholar
Liu, J., Lin, J.-F., Alatas, A., et al. (2016). Seismic parameters of hcp–Fe alloyed with Ni and Si in the Earth’s inner core. Journal of Geophysical Research, 121, 610623.CrossRefGoogle Scholar
Maeda, F., Kamada, S., Ohtani, E., et al. (2017). Spin state and electronic environment of iron in basaltic glass in the lower mantle. American Mineralogist, 102, 21062112.Google Scholar
Mao, H. K., Shu, J., Shen, G., et al. (1998). Elasticity and rheology of iron above 220 GPa and the nature of the Earth’s inner core. Nature, 396, 741743.Google Scholar
Mao, H. K., Wu, Y., Shu, J. F., et al. (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(B13), 2173721742.Google Scholar
Mao, H. K., Xu, J., Struzhkin, V. V., et al. (2001). Phonon density of states of iron up to 153 gigapascals. Science, 292, 914916.Google Scholar
Mao, W. L., Sturhahn, W., Heinz, D. L., et al. (2004). Nuclear resonant X-ray scattering of iron hydride at high pressure. Geophysical Research Letters, 31, L15618.Google Scholar
Mao, Z., Lin, J. F., Liu, J. et al. (2012). Sound velocities of Fe and Fe–Si alloy in the Earth’s core. Proceedings of the National Academy of Sciences of the United States of America, 109(26), 1023910244.Google Scholar
Martorell, B., Vočadlo, L., Brodholt, J., et al. (2013). Strong premelting effect in the elastic properties of hcp–Fe under inner-core conditions. Science, 342, 466468.Google Scholar
Martorell, B., Wood, I. G., Vočadlo, L. (2016). The elastic properties of hcp–Fe1-xSix at Earth’s inner-core conditions. Earth and Planetary Science Letters, 451, 8996.Google Scholar
Masters, G., Gubbins, D. (2003). On the resolution of density within the Earth. Physics of the Earth and Planetary Interiors, 140, 159167.Google Scholar
McDonough, M. F. (2017). Earth’s core, in White, W., eds., Encyclopedia of Geochemistry. Encyclpedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-319-39193-9_258-1.Google Scholar
Merkel, S., Miyajima, N., Antonangeli, D., et al. (2006). Lattice preferred orientation and stress in polyscrytalline hcp–Co plastically deformed under high pressure. Journal of Applied Physics, 100, 023510.Google Scholar
Merkel, S., Shu, J., Gillet, P., et al. (2005). X-ray diffraction study of the single-crystal elastic moduli of ε–Fe up to 30 GPa. Journal of Geophysical Research, 110, B05201.Google Scholar
Merkel, S., Tomé, C., Wenk, H.-R. (2009). Modeling analysis of the influence of plasticity on high pressure deformation of hcp–Co. Physical Review B, 79, 064110.Google Scholar
Mitsui, T., Hirao, N., Ohishi, Y., et al. (2009). Development of an energy-domain 57Fe–Mössbauer spectrometer using synchrotron radiation and its application to ultrahigh-pressure studies with a diamond anvil cell. Journal of Synchrotron Radiation, 16, 723729.Google Scholar
Morrison, R. A., Jackson, J. M., Struhahn, W., et al. (2018). Equations of state and anisotropy of Fe–Ni–Si alloys. Journal of Geophysical Research, 123, 46474675.Google Scholar
Morrison, R. A., Jackson, J. M., Struhahn, W., et al. (2019). High pressure thermoelasticity and sound velocities of Fe–Ni–Si alloys. Physics of the Earth and Planetary Interiors, 294, 106268.Google Scholar
Murakami, M., Ohishi, Y., Hirao, N., et al. (2012). A perovskitic lower mantle inferred from high-pressure, high-temperature sound velocity data. Nature, 485, 9094.Google Scholar
Murphy, C. A., Jackson, J. M., Sturhahn, W. (2013). Experimental constraints on the thermodynamics and sound velocities of hcp–Fe to core pressures. Journal of Geophysical Research, 118, 19992016.Google Scholar
Nguyen, J. H., Holmes, N. C. (2004). Melting of iron at the physical conditions of the Earth’s core. Nature, 427, 339342.CrossRefGoogle ScholarPubMed
Nishida, K., Kono, Y., Terasaki, H., et al. (2013). Sound velocity measurements in liquid Fe–S at high pressure: implications for Earth’s and lunar cores. Earth and Planetary Science Letters, 362, 182186.Google Scholar
Ohtani, E., Shibazaki, Y., Sakai, T., et al. (2013). Sound velocity of hexagonal close-packed iron up to core pressures. Geophysical Research Letters, 40, 50895094.Google Scholar
Ozawa, H., Takahashi, F., Hirose, K., et al. (2011). Phase transition of FeO and stratification in Earth’s outer core. Science, 334, 792794.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, 319337.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, 220223.Google Scholar
Sakai, T., Takahashi, S., Nishitani, N., et al. (2014). Equation of state of pure iron and Fe0.9Ni0.1 alloy up to 3 Mbar. Physics of the Earth and Planetary Interiors, 228, 114126.Google Scholar
Sakairi, T., Sakamaki, T., Ohtani, E., et al. (2018). Sound velocity measurements of hcp Fe–Si alloy at high pressure and high temperature by inelastic X-ray scattering. American Mineralogist, 103, 8590.Google Scholar
Sakaiya, T., Takahashi, H., Kondo, T., et al. (2014). Sound velocity and density measurements of liquid iron up to 800 GPa: a universal relation between Birch’s law coefficients for solid and liquid metals. Earth and Planetary Science Letters, 392, 8085.Google Scholar
Sakamaki, T., Ohtani, E., Fukui, H., et al. (2016). Constraints on Earth’s inner core composition inferred from measurements of the sound velocity of hcp–iron in extreme conditions. Science Advances, 2(2), e1500802.Google Scholar
Scott, H. P., Williams, Q., Knittle, E. (2001). Stability and equation of state of Fe3C to 73 GPa: implications for carbon in the Earth’s core. Geophysical Research Letters, 28(9), 18751878.Google Scholar
Seagle, C. T., Campbell, A. J., Heinz, D. L., et al. (2006). Thermal equation of state of Fe3S and implications for sulfur in Earth’s core. Journal of Geophysical Research, 111, B06209.Google Scholar
Shibazaki, Y., Ohtani, E., Fukui, H., et al. (2012). Sound velocity measurements in dhcp–FeH up to 70 GPa with inelastic X-ray scattering: implications for the composition of the Earth’s cores. Earth and Planetary Science Letters, 313314, 7985.Google Scholar
Singh, A. K. (1993). The lattice strains in a specimen (cubic system) compressed nonhydrostatically in an opposed anvil device. Journal of Applied Physics, 73(9), 42784286.Google Scholar
Singh, A. K., Balasingh, C. (1994). The lattice strains in a specimen (hexagonal system) compressed nonhydrostatically in an opposed anvil high pressure setup. Journal of Applied Physics, 75(10), 49564962.Google Scholar
Singh, A. K., Balasingh, C., Mao, H. K., et al. (1998). Analysis of lattice strains measured under nonhydrostatic pressure. Journal of Applied Physics, 83(12), 75677575.Google Scholar
Sinmyo, R., Glazyrin, K., McCammon, C., et al. (2014). The influence of solid solution on elastic wave velocity determination in (Mg,Fe)O using nuclear inelastic scattering. Physics of the Earth and Planetary Interiors, 229, 1623.Google Scholar
Sinogeikin, S. V., Bass, J. D. (2000). Single-crystal elasticity of pyrope and MgO to 20 GPa by Brillouin scattering in the diamond cell. Physics of the Earth and Planetary Interiors, 120, 4362.CrossRefGoogle Scholar
Spetzler, H., Shen, A., Chen, G., et al. (1996). Ultrasonic measurements in a diamond anvil cell. Physics of the Earth and Planetary Interiors, 98, 93–9.Google Scholar
Speziale, S., Marquardt, H., Duffy, T. S. (2014). Brillouin scattering and its application in geosciences. Reviews in Mineralogy & Geochemistry, 78, 543603.Google Scholar
Takahashi, S., Ohtani, E., Ikuta, D., et al. (2019b) Thermal equation of state of Fe3C to 327 GPa and carbon in the core. Minerals, 9(12), 744.Google Scholar
Takahashi, S., Ohtani, E., Sakamaki, T., et al. (2019a). Sound velocity of Fe3C at high pressure and high temperature determined by inelastic X-ray scattering. Comptes Rendus Geoscience, 351, 190196.Google Scholar
Tanaka, R., Sakamaki, T., Ohtani, E., et al. (2020). The sound velocity of wüstite at high pressures: implications for low-velocity anomalies at the base of the lower mantle. Progress in Earth and Planetary Science, 7, 23.Google Scholar
Tateno, S., Hirose, K., Ohishi, Y., et al. (2010). The structure of iron in Earth’s inner core. Science, 330, 359361.Google Scholar
Tateno, S., Kuwayma, Y., Hirose, K., et al. (2015). The structure of Fe–Si alloy in Earth’s inner core. Earth and Planetary Science Letters, 418, 1119.Google Scholar
Thomson, A. R., Crchton, W. A., Brodholt, J. P., et al. (2019). Seismic velocities of CaSiO3 perovskite can explain LLSVPs in Earth’s lower mantle. Nature, 572, 643647.Google Scholar
Vočadlo, L., Dobson, D. P., Wood, I. G. (2009). Ab initio calculations of the elasticity of hcp–Fe as a function of temperature at inner-core pressure. Earth and Planetary Science Letters, 288, 534538.Google Scholar
Wakamatsu, T., Ohta, K., Yagi, T. (2018). Measurements of sound velocity in iron–nickel alloys by femtosecond laser pulses in a diamond anvil cell. Physics and Chemistry of Minerals, 45, 589595.Google Scholar
Weidner, D. J., Swyler, K., Carleton, H. R. (1975). Elasticity of microcrystals. Geophysical Research Letters, 2(5), 189192.Google Scholar
Yamazaki, D., Ito, E., Yoshino, T., et al. (2012). 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. Geophysical Research Letters, 39, L20308.Google Scholar
Yokoo, M., Kawai, N., Nakamura, K. G., et al. (2009). Ultrahigh-pressure scales for gold and platinum at pressures up to 550 GPa. Physical Review B, 80, 104114.Google Scholar
Yoneda, A., Fukui, H., Gomi, H., et al. (2017). Single crystal elasticity of gold up to ~20 GPa: bulk modulus anomaly and implication for a primary pressure scale. Japanese Journal of Applied Physics, 56, 095801.Google Scholar
Yoneda, A., Kobayashi, S., Kamada, S. (2019). GHz ultrasonic velocity measurement in diamond anvil cell. Review of High Pressure Science and Technology, 29(2), 144155.Google Scholar
Yoshino, T., Kamada, S., Zhao, C., et al. (2016). Electrical conductivity model of Al-bearing bridgmanite with implications for the electrical structure of the Earth’s lower mantle. Earth and Planetary Science Letters, 434, 208219.Google Scholar
Zha, C. S., Duffy, T.S., Downs, R. T., et al. (1996). Sound velocity and elasticity of single-crystal forsterite to 16 GPa. Journal of Geophysical Research, 101(B8), 1753517545.Google Scholar
Zha, C. S., Hemley, R. J., Mao, H. K., et al. (1994). Acoustic velocities and refractive index of SiO2 glass to 57.5 GPa by Brillouin scattering. Physical Review B, 50(18), 1310513112.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 of the United States of America, 97(25), 1349413499.Google Scholar

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Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

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