Abstract
This lecture is an attempt to give an overview of the equations of state (EoS) commonly used to fit P–V data in geosciences and to discuss their assumptions. It is limited to static data (i.e. data obtained by squeezing a sample between pistons or anvils and measuring the associated change in volume). The various details of how to determine the parameters of an EoS from experimental data and of the best fitting procedure are discussed extensively in Angel (2000) and will be the subject of a workshop.
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Anderson, O. L., 1995, Equations of State of Solids for Geophysics and Ceramic Science. Oxford University Press, Oxford.
Angel, R. J., 2000, Equations of state. In R. M. Hazen and R. T. Downs (eds.), High-pressure and high-temperature crystal chemistry, MSA Rev. Mineral., 41:35–60.
Angel, R. J., and Ross, N. L., 1996, Compression mechanism and equations of state. Phil. Trans. R. Soc. Lond., 354:1449–1459.
Angel, R. J., Allan, D. R., Miletich, R., and Finger, L. W., 1997, The use of quartz as an internal pressure standard in high pressure crystallography. J. Appl. Crystallogr., 30:461–466.
Birch, F., 1938, The effect of pressure upon the elastic parameters of isotropic solids, according to Murnaghan’s theory of finite strain. J. Appl. Phys., 9:279–288.
Birch, F., 1947, Finite elastic strain of cubic crystals. Phys. Rev., 71:809–824.
Birch, F., 1952, Elasticity and constitution of the earth’s interior. J. Geophys. Res., 57:227–286.
Duffy, T. S., and Wang, Y., 1998, Pressure-volume-temperature equations of state. In R. J Hemley. (ed.), Ultrahigh-pressure mineralogy: physics and chemistry of the Earth’s deep interior, MSA Rev. Mineral., 37:425–457.
Holzapfel, W. B., 2001, Equations of state for solids under strong compression. Z. Kristallogr., 216:473–488.
Jacobsen, S. D., Holl, C. M., Adams, K. A., Fischer, R. A., Martin, E. S., Bina, C. R., Lin, J.-F., Prakapenka, V. B., Kubo, A., and Dera P., 2008, Compression of single-crystal magnesium oxide to 118 Gpa and a ruby pressure gauge for helium pressure media. Am. Mineral., 93:1823–1828.
Love, A. E. H., 1927, A Treatise of the Mathematical Theory of Elasticity. Fourth edition, Cambridge University Press, Cambridge.
Mao, H.-K., Bell, P. M., Shaner, J., and Steinberg, D., 1978, Specific volume measurements of Cu, Mo, Pd and Au and calibration of the ruby R 1 fluorescence pressure gauge from 0.06 to 1 Mbar. J. Appl. Phys., 49:3276–3283.
Mao, H.-K., Xu, J., and Bell, P. M., 1986, Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions.J. Geophys. Res., 91:4673–4676.
Murnaghan, F. D., 1951, Finite Deformation of an Elastic Solid. Wiley, New York.
Ono, S., Kikegawa, T., and Iizuka, T., 2004, The equation of state of orthorhombic perovskite in a peridotitic mantle composition to 80 GPa: implications for chemical composition of the lower mantle. Phys. Earth Planet. Int., 145:9–17.
Poirier, J.-P., 2000, Introduction to the Physics of the Earth Interior. Second edition. Cambridge University Press, Cambridge.
Poirier, J. P., and Tarantola, A., 1998, A logarithmic equation of state, Phys. Earth Planet. Int., 109:1–8.
Rekhi, S., Dubrovinsky, L. S., and Saxena, S. K., 1999, Temperature-induced ruby fluorescence shifts up to a pressure of 15 GPa in an externally heated diamond anvil cell. High Temp. – High Press., 31:299–305.
Saikia, A., Boffa Ballaran, T., and Frost, D. J., 2008, The effect of Fe and Al substitution on the compressibility of MgSiO3 perovskite determined through single–crystal X-ray diffraction. Phys. Earth Planet. Int., 173:153–161.
Stacey, F. D., Brennan, B. J., and Irvine, R. D., 1981, Finite strain theories and comparison with sismological data. Geophys Surv., 4:189–232.
Vinet, P., Ferrante, J., Rose, J. H., and Smith, J. R., 1987, Compressibility of solids. J. Geophys. Res., 92:9319–9325.
Vinet, P., Rose, J. H., Ferrante, J., and Smith, J. R., 1989, Universal features of the equation of state of solids. J. Phys: Condens. Matter, 1:1941–1963.
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Ballaran, T.B. (2010). Equations of State and Their Applications in Geosciences. In: Boldyreva, E., Dera, P. (eds) High-Pressure Crystallography. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9258-8_12
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DOI: https://doi.org/10.1007/978-90-481-9258-8_12
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