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High Pressure and High Temperature Equation-of-State of Gamma and Liquid Iron

Published online by Cambridge University Press:  10 February 2011

George Q. Chen  and
Thomas J. Ahrens
George Q. Chen
Affiliation:
Present address: The Santa Cruz Operations, Inc., 400 Encinal Street, POB 1900, Santa Cruz, CA 95061–1900
Thomas J. Ahrens
Affiliation:
Correspondent: Lindhurst Laboratory of Experimental Geophysics, Seismological Laboratory 252–21, California Institute of Technology, Pasadena, CA 91125, [email protected]
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Abstract

Shock-wave experiments on pure iron preheated to 1573 K were conducted in the 17–73 GPa range. The shock-wave equation of state of γ-iron at an initial temperature of 1573 K can be fit with us = 4.102 (0.015) km/s + 1.610(0.014) up with ρo = 7.413±0.012 Mg/m3 We obtain for γ-iron's bulk modulus and pressure derivative the values: 124.7±1.1 GPa and 5.44±0.06, respectively.

We present new data for sound velocities in the γ- and liquid-phases. In the γ-phase, to a first approximation, the longitudinal sound velocity is linear with respect to density: Vp = −3.13 (0.72) + 1.119(0.084) p(units for Vp and p are km/s and Mg/m3, respectively). Melting was observed in the highest pressure (about 70–73 GPa) experiments at a calculated shock temperature of 2775±160 K. This result is consistent with a previously calculated melting curve (for ε-iron) which is close to those measured by Boehler [1] and Saxena et al. [2]. The liquid iron sound velocity data yields a Grüneisen parameter value of 1.63±0.28 at 9.37±0.02 Mg/m3 at 71.6 GPa. The quantity γρ is 15.2±2.6 Mg/m3, which agrees with the uncertainty bounds of Brown and McQueen [3] (13.3–19.6 Mg/m3). Based on upward pressure and temperature extrapolation of the melting curve of γ-iron, the estimated inner core-outer core boundary temperature is 5500±400 K, the temperature at the core-mantle boundary on the outer core side is 3930±630 K.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 499: Symposium DD – High Pressure Materials Research , 1997 , 41
Copyright
Copyright © Materials Research Society 1998

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References

REFERENCES

[1] Boehler, R., Temperatures in the Earth's core from melting-point measurements of iron at high pressures, Nature, 363, 534–536, 1993.Google Scholar
[2] Saxena, S.K., Shen, G. and Lazor, P., Experimental evidence for a new iron phase and implications for Earth's core, Science, 260, 1312–1314, 1993.Google Scholar
[3] Brown, J.M. and McQueen, R.G., Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa, J. Geophys. Res., 91, 7485–7494, 1986.Google Scholar
[4] Williams, Q., Jeanloz, R., Bass, J., Svendsen, B. and Ahrens, T.J., The melting curve of iron to 250 Gigapascals: A constraint on the temperature at Earth's center, Science, 236, 181–182, 1987.Google Scholar
[5] Barker, L.M. and Hollenbach, R.E., Shock wave study of the α-ε transition in iron, J. Appl. Phys., 45, 4872–4887, 1974.Google Scholar
[6] Chen, G.Q. and Ahrens, T.J., Radio Frequency Heating Coils for Shock Wave Experiments, in 1997 Fall Meeting Symposium Proceedings, submitted, 1998.Google Scholar
[7] Rigden, S.M., Ahrens, T.J. and Stolper, E.M., Shock compression of molten silicates: Results for a model basaltic composition, J. Geophys. Res., 93, 367–382, 1988.Google Scholar
[8] Miller, G.H., Ahrens, T.J. and Stolper, E.M., The equation of state of molybdenum at 1400°C, J. Appl. Phys., 63, 4469–4475, 1988.Google Scholar
[9] Duffy, T.S. and Ahrens, T.J., Dynamic response of molybdenum shock compressed at 1400°C, J. Appl. Phys., 76, 835–842, 1994.Google Scholar
[10] Touloukin, Y.S. (Ed.), Thermophysical Properties of Matter, The TPRC Data Series, Thermal Expansion: Metallic Solids, 12, 1970.Google Scholar
[11] Mitchell, A.C. and Nellis, W.J., Shock compression of aluminum, copper, and tantalum, J. Appl. Phys., 52, 3363–3374, 1981.Google Scholar
[12] Marsh, S.P. (Ed.), LASL Shock Hugoniot Data, pp. 1–658, University of California Press, Berkeley, 1980.Google Scholar
[14] Ruoff, A.L., Linear shock-velocity-particle-velocity relationship, J. Appl. Phys., 38, 4976–4980, 1967.Google Scholar
[15] Barker, L.M. and Hollenbach, R.E., Laser interferometer for measuring high velocities of any reflecting surface, J. Appl. Phys., 43, 4669–4675, 1972.Google Scholar
[16] Barker, L.M. and Hollenbach, R.E., Shock-wave studies of PMMA, fused silica, and sapphire, J. Appl. phys., 41, 4208–4226, 1970.Google Scholar
[17] Duffy, T.S., 1992. Elastic properties of metals and minerals under shock compression, Ph.D. thesis, 298 pp., California Institute of Technology, Pasadena, CA.Google Scholar
[18] Lide, D.R., Handbook of Chemistry and Physics, Vol. 74th Edition, edited by 4–70, CRC Press, Boca Raton, Florida, 1993–1994.Google Scholar
[19] Nasch, P.M., Manghnani, M.H. and Secco, R.A., Sound-velocity measurements in liquid-iron by ultrasonic interferometry, J. Geophys. Res., 99, 4285–4291, 1994.Google Scholar
[20] Yoo, C.S., Akella, J., Campbell, A.J., Mao, H.K. and Hemley, R.J., Phase diagram of iron by in-situ x-ray diffraction: implications for Earth's core, Science, 270, 1473–1475, 1995.Google Scholar
[21] Boehler, R., Besson, J.M., Nicol, M., Nielsen, M., Itie, J.P., Weill, G., Johnson, S. and Grey, F., X-ray diffraction of γ-iron at high temperatures and pressures, J. Appl. Phys., 65, 1795–1797, 1989.Google Scholar
[22] Belonoshko, A.B., Atomic simulation of shock wave-induced melting in argon, Science, 275, 955–957, 1997.Google Scholar
[23] Saxena, S.K., Dubrovinsky, L.S., Häggkvist, P., Cerenius, Y., Shen, G. and Mao, H.K., Synchrotron X-ray study of iron at high-pressure and temperature, Science, 269, 1703–1704, 1995.Google Scholar
[24] Huang, E., Bassett, W.A. and Tao, P., Pressure-temperature-volume relation for hexagonal close packed iron determined by synchrotron radiation, J. Geophys. Res., 92, 8129–8235, 1987.Google Scholar
[25] Boehler, R. and Ramakrishnan, J., Experimental results on the pressure dependence of the Grüneisen parameter: a review, J. Geophys. Res., 85, 6996–7002, 1980.Google Scholar
[26] McQueen, R.G., Marsh, S.P., Taylor, J.W., Fritz, J.N. and Carter, W.J., The equation of state of solids from shock wave studies, in: High-Velocity Impact Phenomena, edited by Kinslow, R., pp. 249–419, Academic Press, New York, 1970.Google Scholar
[27] Robie, R.A., Hemingway, B.S. and Fisher, J.R., Thermodynamic properties of minerals and related substances at 298.15K and 1 bar (105 pascals) pressure and at higher temperatures, U.G.S.G. Bulletin, 1452, 456, 1979.Google Scholar
[28] Touloukian, Y.S., Kirby, R.K., Taylor, R.E. and Desai, P.D., Thermal expansion of metallic elements and alloys, 208–218 pp., Plenum, New York, 1970.Google Scholar
[29] Saxena, S.K., Dubrovinsky, L.S. and Häggkvist, P., X-ray evidence for the new phase beta-iron at high-temperature and high-pressure, Geophys. Res. Lett., 23, 2441–2444, 1996.Google Scholar
[30] Brown, J.M. and McQueen, R.G., The equation of state for iron and the earth's core, in: High Pressure Research in Geophysics, edited by Akimoto, S. and Manghnani, M. H., pp. 611–622, Academic Press, New York, 1982.Google Scholar
[31] Holland, K.G., 1997. Phase Changes and Transport Properties of Geophysical Materials under Shock Loading, Ph.D. thesis, California Institute of Technology, Pasadena, California.Google Scholar
[32] Boness, D.A., Brown, J.M. and Shaner, J.W., Rarefaction velocities in shocked lead, in: Shock Waves in Condensed Matter -1987, edited by Schmidt, S. C. and Holmes, N. C., pp. 115–118, North-Holland, New York, 1988.Google Scholar
[33] Anderson, W.W. and Ahrens, T.J., An equation of state for liquid iron and implications for the Earth's core, J. Geophys. Res., 99, 4273–4284, 1994.Google Scholar
[34] Hixson, R.S., Winkler, M.A. and Hodgdon, M.L., Sound speed and thermophysical properties of iron and nickel, Phys. Rev. B, 42, 6485–6491, 1990.Google Scholar
[35] Falzone, A.J. and Stacey, F.D., Second-order elasticity theory: explanation for the high Poisson's ratio of the inner core, Phys. Earth Planet. Int., 21, 371–377, 1980.Google Scholar