Equations of State and Their Applications in Geosciences

  • Tiziana Boffa Ballaran
Conference paper
Part of the NATO Science for Peace and Security Series B: Physics and Biophysics book series (NAPSB)


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.


Bulk Modulus Finite Strain Versus Data Pressure Determination Hencky Strain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Anderson, O. L., 1995, Equations of State of Solids for Geophysics and Ceramic Science. Oxford University Press, Oxford.Google Scholar
  2. 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.Google Scholar
  3. Angel, R. J., and Ross, N. L., 1996, Compression mechanism and equations of state. Phil. Trans. R. Soc. Lond., 354:1449–1459.ADSCrossRefGoogle Scholar
  4. 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.CrossRefGoogle Scholar
  5. 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.ADSzbMATHCrossRefGoogle Scholar
  6. Birch, F., 1947, Finite elastic strain of cubic crystals. Phys. Rev., 71:809–824.ADSzbMATHCrossRefGoogle Scholar
  7. Birch, F., 1952, Elasticity and constitution of the earth’s interior. J. Geophys. Res., 57:227–286.ADSCrossRefGoogle Scholar
  8. 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.Google Scholar
  9. Holzapfel, W. B., 2001, Equations of state for solids under strong compression. Z. Kristallogr., 216:473–488.CrossRefGoogle Scholar
  10. 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.CrossRefGoogle Scholar
  11. Love, A. E. H., 1927, A Treatise of the Mathematical Theory of Elasticity. Fourth edition, Cambridge University Press, Cambridge.zbMATHGoogle Scholar
  12. 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.ADSCrossRefGoogle Scholar
  13. 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.ADSCrossRefGoogle Scholar
  14. Murnaghan, F. D., 1951, Finite Deformation of an Elastic Solid. Wiley, New York.zbMATHGoogle Scholar
  15. 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.ADSCrossRefGoogle Scholar
  16. Poirier, J.-P., 2000, Introduction to the Physics of the Earth Interior. Second edition. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  17. Poirier, J. P., and Tarantola, A., 1998, A logarithmic equation of state, Phys. Earth Planet. Int., 109:1–8.ADSCrossRefGoogle Scholar
  18. 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.CrossRefGoogle Scholar
  19. 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.ADSCrossRefGoogle Scholar
  20. Stacey, F. D., Brennan, B. J., and Irvine, R. D., 1981, Finite strain theories and comparison with sismological data. Geophys Surv., 4:189–232.ADSCrossRefGoogle Scholar
  21. Vinet, P., Ferrante, J., Rose, J. H., and Smith, J. R., 1987, Compressibility of solids. J. Geophys. Res., 92:9319–9325.ADSCrossRefGoogle Scholar
  22. 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.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Bayerisches GeoinstitutUniversitaet BayreuthBayreuthGermany

Personalised recommendations