Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter April 30, 2016

Compressional and shear wave velocities for polycrystalline bcc-Fe up to 6.3 GPa and 800 K

Yuki Shibazaki, Keisuke Nishida, Yuji Higo, Mako Igarashi, Masaki Tahara, Tatsuya Sakamaki, Hidenori Terasaki, Yuta Shimoyama, Soma Kuwabara, Yusaku Takubo and Eiji Ohtani
From the journal American Mineralogist


The cores of the Earth and other differentiated bodies are believed to be comprised of iron and various amounts of light elements. Measuring the densities and sound velocities of iron and its alloys at high pressures and high temperatures is crucial for understanding the structure and composition of these cores. In this study, the sound velocities (vP and vS) and density measurements of body-centered cubic (bcc)-Fe were determined experimentally up to 6.3 GPa and 800 K using ultrasonic and X-ray diffraction methods. Based on the measured vP, vS, and density, we obtained the following parameters regarding the adiabatic bulk KS and shear G moduli of bcc-Fe: KS0 = 163.2(15) GPa, ∂KSP = 6.75(33), ∂KS/∂T = –0.038(3) GPa/K, G0 = 81.4(6) GPa, ∂GP = 1.66(14), and ∂G/∂T = –0.029(1) GPa/K. Moreover, we observed that the sound velocity–density relationship for bcc-Fe depended on temperature in the pressure and temperature ranges analyzed in this study and the effect of temperature on vS was stronger than that on vP at a constant density, e.g., 6.0% and 2.7% depression for vS and vP, respectively, from 300 to 800 K at 8000 kg/m3. Furthermore, the effects of temperature on both vP and vS at a constant density were much greater for bcc-Fe than for ε-FeSi (cubic B20 structure), according to previously obtained measurements, which may be attributable to differences in the degree of thermal pressure. These results suggest that the effects of temperature on the sound velocity–density relationship for Fe alloys strongly depend on their crystal structures and light element contents in the range of pressure and temperature studied.


We thank Y. Nakajima for useful suggestions and discussions. We also thank Y. Ito for chemical analysis. This work was supported by JSPS KAKENHI Grant Numbers 26887006 and 15K17784 for Y.S. and 22000002 for E.O. This work was carried out under the Visiting Researcher’s Program of Geodynamics Research Center, Ehime University (PRIUS). The synchrotron radiation experiments were performed at the BL04B1 beamline at the SPring-8 facility with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (proposal nos. 2014A1472 and 2014B1378).

References Cited

Adams, J.J., Agosta, D.S., Leisure, R.G., and Ledbetter, H. (2006) Elastic constants of monocrystal iron from 3 to 500 K. Journal of Applied Physics, 100, 113530.10.1063/1.2365714Search in Google Scholar

Anderson, O.L., Isaak, D.G., and Yamamoto, S. (1989) Anharmonicity and the equation of state for gold. Journal of Applied Physics, 65, 1534–1543.10.1063/1.342969Search in Google Scholar

Antonangeli, D., and Ohtani, E. (2015) Sound velocity of hcp-Fe at high pressure: experimental constraints, extrapolations and comparison with seismic models. Progress in Earth and Planetary Science, 2, 3, doi:10.1186/s40645-015-0034-9.10.1186/s40645-015-0034-9Search in Google Scholar

Antonangeli, D., Siebert, J., Badro, J., Farber, D.L., Fiquet, G., Morard, G., and Ryerson, F.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, 292–296.10.1016/j.epsl.2010.04.018Search in Google Scholar

Antonangeli, D., Komabayashi, T., Occelli, F., Borissenko, E., Walters, A.C., Fiquet, G., and Fei, Y. (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, 331-332, 210–214.10.1016/j.epsl.2012.03.024Search in Google Scholar

Antonangeli, D., Morard, G., Schmer, N.C., Komabayashi, T., Krisch, M., Fiquet, G., and Fei, Y. (2015) Toward a mineral physics reference model for the Moon’s core. Proceedings of the National Academy of Sciences, 112, 3916–3919.10.1073/pnas.1417490112Search in Google Scholar PubMed PubMed Central

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

Birch, F. (1952) Elasticity and constitution of the Earth’s interior. Journal of Geophysical Research, 52, 227–286.10.1029/SP026p0031Search in Google Scholar

Birch, F. (1961) Composition of the Earth’s mantle. Geophysical Journal of the Royal Astronomical Society, 4, 295–311.10.1029/SP026p0117Search in Google Scholar

Brown, J.M., and McQueen, R.G. (1986) Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa. Journal of Geophysical Research, 91, 7485–7494.10.1029/JB091iB07p07485Search in Google Scholar

Bundy, F.P. (1965) Pressure-temperature phase diagram of iron to 200 kbar, 900 °C. Journal of Applied Physics, 36, 616–620.10.1063/1.1714038Search in Google Scholar

Claussen, W.F. (1960) Detection of the α-γ iron phase transformation by differential thermal conductivity analysis. Review of Scientific Instruments, 31, 878–881.10.1063/1.1717076Search in Google Scholar

Decremps, F., Antonangeli, D., Gauthier, M., Ayrinhac, S., Morard, M., Le Marchand, G., Bergame, F., and Philippe, J. (2014) Sound velocity of iron up to 152 GPa by picosecond acoustics in diamond anvil cell. Geophysical Research Letters, 41, 1459–1464.10.1002/2013GL058859Search in Google Scholar

Dever, D.J. (1972) Temperature dependence of the elastic constants in αiron single crystals: relationship to spin order and diffusion anomalies. Journal of Applied Physics, 43, 3293–3301.10.1063/1.1661710Search in Google Scholar

Dumberry, M., and Rivoldini, A. (2015) Mercury’s inner core size and corecrystallization regime. Icarus, 248, 254–268.10.1016/j.icarus.2014.10.038Search in Google Scholar

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., Ricolleau, A., Frank, M., Mibe, K., Shen, G., and Prakapenka, V. (2007) Toward an internally consistent pressure scale. Proceedings of the National Academy of Sciences, 104, 9182–9186.10.1073/pnas.0609013104Search in Google Scholar PubMed PubMed Central

Fiquet, G., Badro, J., Guyot, F., Requardt, H., and Krisch, M. (2001) Sound velocities in iron to 110 gigapascals. Science, 291, 468–471.10.1126/science.291.5503.468Search in Google Scholar PubMed

Fiquet, G., Badro, J., Guyot, F., Bellin, Ch., Krisch, M., Antonangeli, D., Requardt, H., Mermet, A., Farber, D., Aracne-Ruddle, A., and Zhang, J. (2004) Application of inelastic X-ray scattering to the measurements of acoustic wave velocities in geophysical materials at very high pressure. Physics of the Earth and Planetary Interiors, 143–144, 5–18.10.1016/j.pepi.2003.10.005Search in Google Scholar

Fiquet, G., Badro, J., Gregoryanz, E., Fei, Y., and Occelli, F. (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, 125–129.10.1016/j.pepi.2008.05.016Search in Google Scholar

Gao, L., Chen, B., Wang, J., Alp, E.E., Zhao, J., Lerche, M., Sturhahn, W., Scott, H.P., Huang, F., Ding, Y., Sinogeikin, S.V., and others. (2008) Pressure-induced magnetic transition and sound velocities of Fe3C: Implications for carbon in the Earth’s inner core. Geophysical Research Letters, 35, L17306, doi:10.1029/2008GL034817.10.1029/2008GL034817Search in Google Scholar

Gao, L., Chen, B., Zhao, J., Alp, E.E., Sturhahn, W., and Li, J. (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, 213–220.10.1016/j.epsl.2011.06.037Search in Google Scholar

Guinan, M.W., and Beshers, D.N. (1968) Pressure derivatives of the elastic constants of α-iron to 10 kbs. Journal of Physics and Chemistry of Solids, 29, 541–549.10.1016/0022-3697(68)90131-5Search in Google Scholar

Guyot, F., Zhang, J., Martinez, I., Matas, J., Ricard, Y., and Javoy, M. (1997) P-V-T measurements of iron silicide (ε-FeSi): Implications for silicate-metal interactions in the early Earth. European Journal of Mineralogy, 9, 277–285.10.1127/ejm/9/2/0277Search in Google Scholar

Higo, Y., Kono, Y., Inoue, T., Irifune, T., and Funakoshi, K. (2009) A system for measuring elastic wave velocity under high pressure and high temperature using a combination of ultrasonic measurement and the multi-anvil apparatus at SPring-8. Journal of Synchrotron Radiation, 16, 762–768.10.1107/S0909049509034980Search in Google Scholar PubMed

Huang, E., Bassett, W.A., and Tao, P. (1987) Pressure-temperature-volume relationship for hexagonal close packed iron determined by synchrotron radiation. Journal of Geophysical Research, 92, 8129–8135.10.1029/JB092iB08p08129Search in Google Scholar

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

Isaak, D.G., and Masuda, K. (1995) Elastic and viscoelastic properties of α iron at high temperatures. Journal of Geophysical Research, 100, 17689–17698.10.1029/95JB01235Search in Google Scholar

Kamada, S., Ohtani, E., Fukui, H., Sakai, T., Terasaki, H., Takahashi, S., Shibazaki, Y., Tstsui, S., Baron, A.Q.R., Hirao, N., and Ohishi, Y. (2014) The sound velocity measurements of Fe3S. American Mineralogist, 99, 98–101.10.2138/am.2014.4463Search in Google Scholar

Kantor, A.P., Kantor, I.Y., Kurnosov, A.V., Kuznetsov, A.Y., Dubrovinskaia, N.A., Krisch, M., Bossak, A.A., Dmitriev, V.P., Urusov, V.S., and Dubrovinsky, L.S. (2007) Sound wave velocities of fcc Fe-Ni alloy at high pressure and temperature by mean of inelastic X-ray scattering. Physics of the Earth and Planetary Interiors, 164, 83–89.10.1016/j.pepi.2007.06.006Search in Google Scholar

Klotz, S., and Braden, M. (2000) Phonon dispersion of bcc iron to 10 GPa. Physical Review Letters, 85, 3209–3212.10.1103/PhysRevLett.85.3209Search in Google Scholar PubMed

Leese, J., and Lord, A.E. Jr. (1968) Elastic stiffness coefficients of single-crystal iron from room temperature to 500 °C. Journal of Applied Physics, 30, 3986–3988.10.1063/1.1656884Search in Google Scholar

Li, Y., and Fei, Y. (2014) Experimental constraints on core composition. In R.W. Carlson, Ed., The Mantle and Core, 2nd ed., 3, p. 527–557. Treatise on Geochemistry, Elsevior, U.K.10.1016/B978-0-08-095975-7.00214-XSearch in Google Scholar

Lin, J.-F., Struzhkin, V.V., Sturhahn, W., Huang, E., Zhao, J., Hu, M.Y., Alp, E.E., Mao, H.-K., Boctor, N., and Hemley, R.J. (2003) Sound velocities of iron-nickel and iron-silicon alloys at high pressures. Geophysical Research Letters, 30, 2112, doi:10.1029/2003GL018405.10.1029/2003GL018405Search in Google Scholar

Lin, J.-F., Fei, Y., Sturhahn, W., Zhao, J., Mao, H.-K., and Hemley, R.J. (2004) Magnetic transition and sound velocities of Fe3S at high pressure: Implications for Earth and planetary cores. Earth and Planetary Science Letters, 226, 33–40.10.1016/j.epsl.2004.07.018Search in Google Scholar

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., Sharygin, I.S., Dorogokupets, P.I., Shatskiy, A., Gavryushkin, P.N., Sokolova, T.S., Ohtani, E., Lie, J., and Funakoshi, K. (2013) Thermal equation of state and thermodynamic properties of iron carbide Fe3C to 31 GPa and 1473 K. Journal of Geophysical Research, 118, 1–11.10.1002/2013JB010270Search in Google Scholar

Liu, L.-G., and Bassett, W.A. (1975) The melting of iron up to 200 kbar. Journal of Geophysical Research, 80, 3777–3782.10.1029/JB080i026p03777Search in Google Scholar

Liu, J., Lin, J.-F., Alatas, A., and Bi, W. (2014) Sound velocities of bcc-Fe and Fe0.85Si0.15 alloy at high pressure and temperature. Physics of the Earth and Planetary Interiors, 233, 24–32.10.1016/j.pepi.2014.05.008Search in Google Scholar

Lord, O.T., Walter, M.J., Dobson, D.P., Armstrong, L., Clark, S.M., and Kleppe, A. (2010) The FeSi phase diagram to 150 GPa. Journal of Geophysical Research, 115, B06208, doi:10.1029/2009JB006528.10.1029/2009JB006528Search in Google Scholar

Mao, H.-K., Bassett, W.A., and Takahashi, T. (1967) Effect of pressure on crystal structure and lattice parameters of iron up to 300 kbar. Journal of Applied Physics, 38, 272–276.10.1063/1.1708965Search in Google Scholar

Mao, H.-K., Xu, J., Struzhkin, V.V., Shu, J., Hemley, R.J., Sturhahn, W., Hu, M.Y., Alp, E.E., Vočadlo, L., Alfè, D., and others. (2001) Phonon density of states of iron up to 153 gigapascals. Science, 292, 914–916.10.1126/science.1057670Search in Google Scholar

Mao, Z., Lin, J.-F., Liu, J., Alatas, A., Gao, L., Zhao, J., and Mao, H.-K. (2012) Sound velocities of Fe and Fe-Si alloy in the Earth’s core. Proceedings of the National Academy of Sciences, 109, 10239–10244.10.1073/pnas.1207086109Search in Google Scholar

Martorell, B., Vočadlo, L., Brodholt, J., and Wood, I.G. (2013) Strong premelting effect in the elastic properties of hcp-Fe under inner-core conditions. Science, 342, 466–468.10.1126/science.1243651Search in Google Scholar

Murphy, C.A., Jackson, J.M., and Sturhahn, W. (2013) Experimental constraints on the thermodynamics and sound velocities of hcp-Fe to core pressures. Journal of Geophysical Research, 118, 1999–2016.10.1002/jgrb.50166Search in Google Scholar

Ohtani, E., Shibazaki, Y., Sakai, T., Mibe, K., Fukui, H., Kamada, S., Sakamaki, T., Seto, T., Tsutsui, S., and Baron, A.Q.R. (2013) Sound velocity of hexagonal close-packed iron up to core pressures. Geophysical Research Letters, 40, 1–6.10.1002/grl.50992Search 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

Quareni, F., and Mulargia, F. (1988) The validity of the common approximate expressions for the Grüneisen parameter. Geophysical Journal, 93, 505–519.10.1111/j.1365-246X.1988.tb03877.xSearch in Google Scholar

Rotter, C.A., and Smith, C.S. (1966) Ultrasonic equation of state of iron: I. low pressure, room temperature. Journal of Physics and Chemistry of Solids, 27, 267–276.10.1016/0022-3697(66)90032-1Search in Google Scholar

Santamaría-Pérez, D., and Boehler, R. (2008) FeSi melting curve up to 70 GPa. Earth and Planetary Science Letters, 265, 743–747.10.1016/j.epsl.2007.11.008Search 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, 111, B06209, doi:10.1029/2005JB004091.10.1029/2005JB004091Search in Google Scholar

Sha, X., and Cohen, R.E. (2010) Elastic isotropy of ε-Fe under Earth’s core conditions. Geophysical Research Letters, 37, L10302, doi:10.1029/2009GL042224.10.1029/2009GL042224Search in Google Scholar

Shibazaki, Y., Ohtani, E., Fukui, H., Sakai, T., Kamada, S., Ishikawa, D., Tsutsui, S., Baron, A.Q.R., Nishitani, N., Hirao, N., and Takemura, K. (2012) Sound velocity measurements in dhcp-FeH up to 70 GPa with inelastic X-ray scattering: Implications for the composition of the Earth’s core. Earth and Planetary Science Letters, 313-314, 79–85.10.1016/j.epsl.2011.11.002Search in Google Scholar

Takahashi, T., Bassett, W.A., and Mao, H.-K. (1968) Isothermal compression of the alloys of iron up to 300 kilobars at room temperature: Iron-nickel alloys. Journal of Geophysical Research, 73, 4717–4725.10.1029/JB073i014p04717Search in Google Scholar

Tange, Y., Nishihara, Y., and Tsuchiya, T. (2009) 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, doi:10.1029/2008JB005813.10.1029/2008JB005813Search in Google Scholar

Vočadlo, L., Dobson, D.P., and 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, 534–538.10.1016/j.epsl.2009.10.015Search in Google Scholar

Wakabayashi, D., and Funamori, N. (2015) Solving the problem of inconsistency in reported equations of state for h-BN. High Pressure Research, 35, 123–129.10.1080/08957959.2015.1028931Search in Google Scholar

Whitaker, M.L., Liu, W., Liu, Q., Wang, L., and Li, B. (2009) Thermoelasticity of ε-FeSi to 8 GPa and 1273 K. American Mineralogist, 94, 1039–1044.10.2138/am.2009.3166Search in Google Scholar

Wilburn, D.R., and Bassett, W.A. (1978) Hydrostatic compression of iron and related compounds: an overview. American Mineralogist, 63, 591–596.Search in Google Scholar

Yamazaki, D., Ito, E., Yoshino, T., Yoneda, A., Guo, X., Zhang, B., Sun, W., Shimojuku, A., Tsujino, N., Kunimoto, T., Higo, Y., and Funakoshi, K. (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, doi:10.1029/2012GL053540.10.1029/2012GL053540Search in Google Scholar

Zaresky, J., and Stassis, C. (1987) Lattice dynamics of γ-Fe. Physical Review B, 35, 4500–4502.10.1103/PhysRevB.35.4500Search in Google Scholar PubMed

Zhang, J., and Guyot, F. (1999) Thermal equation of state of iron and Fe0.91Si0.09. Physics and Chemistry of Minerals, 26, 206–211.10.1007/s002690050178Search in Google Scholar

Zharkov, V.N., Gudkova, T.V., and Molodensky, S.M. (2009) On models of Mars’ interior and amplitudes of forced nutations: 1. the effects of deviation of Mars from its equilibrium state on the flattening of the core-mantle boundary. Physics of the Earth and Planetary Interiors, 172, 324–334.10.1016/j.pepi.2008.10.009Search in Google Scholar

Received: 2015-8-29
Accepted: 2015-12-24
Published Online: 2016-4-30
Published in Print: 2016-5-1

© 2016 by Walter de Gruyter Berlin/Boston

Scroll Up Arrow