Skip to main content
SpringerLink
Log in

Equations of State and Thermophysical Properties of Solids Under Pressure

  • Conference paper
High-Pressure Crystallography

Part of the book series: NATO Science Series ((NAII,volume 140))

Abstract

Equations of State (EOS) for a given thermodynamic system are usually considered to represent relations between the pressure, p, the volume, V, and the temperature, T, in the form p = p(V,T) or V = V(p,T). In most cases only the isothermal relations p = PT(V) or V = VT(p) are studied experimentally. Therefore in most cases only “parametric” EOS forms are discussed, in which the experimentally determined parameters for the volume V0(T), for the bulk modulus K0(T) and for its first and higher order pressure derivatives K′0 (T), K″0(T), ...., represent the values for ambient (zero) pressure at the given temperature T. Different isotherms are thereby represented usually by the same parametric EOS form with only different values for V0(T), K0(T), K′0(T), ....

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Falk, G. (1990) Physik - Zahl und Realität, Birkhäuser, Basel.

    Book  MATH  Google Scholar 

  2. Zharkov, V.N., and Kalinin, V.A. (1971) Equations of state forJonas at Hign rressure urtu Temperatures, Consultants Bureau, New York.

    Google Scholar 

  3. Stacey, F.D., Brennan, B.J., and Irvine, R.D. (1981) Finite strain theories and comparisons with seismological data, Geophysical Surveys 4, 189–232.

    Article  ADS  Google Scholar 

  4. Godwal, B.K., Sikka, S.K., and Chidambaram, R. (1983) Equations of state theories of condensed matter up to about 10 TPa, Phys. Rep. 102, 121–197.

    Article  ADS  Google Scholar 

  5. Eliezer, S., and Ricci, R.A. (1991) High-Pressure Equations of State: Theory and Applications, Elsevier Science Publishers, Amsterdam.

    Google Scholar 

  6. Anderson, O.L. (1995) Equations of State for Geophysics and Ceramic Science. Oxford University Press, New York.

    Google Scholar 

  7. Holzapfel, W.B. (1996) Physics of solids under strong compression, Rep. Prog. Phys. 49, 29–90.

    Article  ADS  Google Scholar 

  8. Holzapfel, W.B. (1998) Equations of state for solids under strong compression, High Press. Res. 16, 81–126.

    Article  ADS  Google Scholar 

  9. Poirier, J.-P. (1990) Introduction to the Physics of the Earth’s Interior, Cambridge University Press, Cambridge.

    Google Scholar 

  10. Holzapfel, W.B. (2001) Equations of state for solids under strong compression, Z. Kristallogr. 216, 473–488.

    Article  Google Scholar 

  11. Murnaghan, F.D. (1937) Finite deformations of an elastic solid, Am. J. Math. 59, 235–260.

    Article  MathSciNet  MATH  Google Scholar 

  12. Murnaghan, F.D. (1944) The compressibility of media under extreme pressure, Proc. Natl. Acad. Sci. USA 30, 244–247.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Freund, J., and Ingalls, R. (1989) Inverted isothermal equations of state and determination of Bo, B’o and B”o, J. Phys. Chem. Solids 50, 263–268.

    Article  ADS  Google Scholar 

  14. Baonza, V.G., Cäceres, M., and Nunez, J. (1995) Universal compressibility behaviour of dense phases, Phys. Rev. B 51, 28–37.

    Article  ADS  Google Scholar 

  15. Birch F. (1947) Finite elastic strain of cubic crystals, Phys. Rev. 71, 809–824.

    Article  ADS  MATH  Google Scholar 

  16. Vinet, P., Ferrante, J., Smith, J.R., and Rose, J.H. (1986) A universal equation of state for solids, J. Phys. Condens. Matter 19, L467-L473.

    Google Scholar 

  17. Slater, J.C., and Krutter, H.M. (1935) The Thomas-Fermi method for metals, Phys. Rev. 47, 559–568.

    Article  ADS  MATH  Google Scholar 

  18. Feynman, R.P., Metropolis, N., and Teller, E. (1949) Equation of state of elements based on the generalized Fermi-Thomas Theory, Phys. Rev. 75, 1561.

    Article  ADS  MATH  Google Scholar 

  19. Salpeter, E.E, and Zapolsky, H.S. (1967) Theoretical high-pressure equations of state including correlation energy, Phys. Rev. 158, 876–886.

    Article  ADS  Google Scholar 

  20. Landau, L.D., and Lifshitz, E.M. (1980) Statistical Physics. Part 1–3r ed., Pergamon Press, Oxford.

    Google Scholar 

  21. Stacey, F.D. (2000) The J-primed approach to high-pressure equations of state, Geophys. J. Int. 143, 621–628.

    Article  ADS  Google Scholar 

  22. Mie, G. (1903) Zur kinetischen Theorie der einatomigen Körper, Ann d. Phys. 11, 657–697.

    Article  ADS  MATH  Google Scholar 

  23. Jones, J.E. (1924) On the determination of molecular fields, Proc. Roy. Soc. (London) A106, 441–462.

    Article  ADS  Google Scholar 

  24. Born, M., and Mayer, J. (1932) Zur Gittertheorie der Ionenkristalle, Z. Physik 75, 1–18.

    Article  ADS  Google Scholar 

  25. Morse, Ph.M. (1929) Diatomic molecules according to the wave mechanics. II. vibrational levels, Phys. Rev. 34, 57–64.

    Article  ADS  MATH  Google Scholar 

  26. Rydberg, R. (1932) Graphische Darstellung einiger bandenspektroskopischer Ergebnisse, Z Physik 73, 376–385.

    Article  ADS  Google Scholar 

  27. 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.

    Article  ADS  Google Scholar 

  28. Holzapfel, W.B. (1991) Equations of state for strong compression, High Press. Res. 7, 290–293.

    Article  ADS  Google Scholar 

  29. Holzapfel, W.B. (2002) Equations of state for regular solids, High Press. Res. 22, 209–216.

    Article  Google Scholar 

  30. Holzapfel, W.B., Hartwig, M., and Reiss, G. (2001) Equations of state for rare gas solids under strong compression, J Low Temp. Phys. 122, 401–412.

    Article  ADS  Google Scholar 

  31. Holzapfel, W.B. (2003) Comment on „Energy and pressure versus volume: Equation of state motivated by the stabilized jellium model”, Phys. Rev. B67, 026102/1–3.

    Google Scholar 

  32. Köhler, U., Johannsen, P.G., and Holzapfel, W.B. (1997) Equation of state data for CsCl-type alkali halides, J Phys.: Condens. Matter 9, 5581–5592.

    Article  ADS  Google Scholar 

  33. Holzapfel, W.B. (1994) Approximate equations of state for solids from limited data sets, J. Phys. Chem. Solids 55, 711–719.

    Article  ADS  Google Scholar 

  34. Einstein, A. (1907) Die Plancksche Theorie der Strahlung and die Theorie der spezifischen Wärme, Ann d. Phys. 22, 180–194.

    ADS  MATH  Google Scholar 

  35. Grüneisen, E. (1912) Theorie des festen Zustandes einatomiger Elemente, Ann. d. Phys. IV, 257–306.

    Article  ADS  Google Scholar 

  36. Debye, P. (1912) Zur Theorie der spezifischen Wärme, Ann. d. Phys. 39, 789–839.

    Article  ADS  MATH  Google Scholar 

  37. Kieffer, S.W. (1979) Thermodynamics and lattice vibrations of minerals. 3. Lattice dynamics and an approximation for minerals with application to simple substances and framework silicates, Rev. Geophys. Space Phys. 17, 35–59.

    Article  ADS  Google Scholar 

  38. Gillet, Ph., Guyot, F., and Malezieux, J-M. (1998) High-pressure, high-temperature Raman spectroscopy of Ca2Ge04 (olivine form): some insight on anharmonicity, Phys. Earth Planet. Inter. 58, 141–154.

    Article  ADS  Google Scholar 

  39. Holzapfel, W.B., Hartwig, M., and Sievers, W. (2001) Equations of state for Cu, Ag, and Au for wide ranges in temperature and pressure up to 500 GPa and Above, J. Phys. Chem. Ref Data 30, 515–529.

    Article  ADS  Google Scholar 

  40. Holzapfel, W.B. (2002) Anharmonicity in the EOS of Cu, Ag, and Au, J. Phys.: Condens. Matter 14, 10525–10531.

    Article  ADS  Google Scholar 

  41. Table 5.1 and discussion on p. 140 in ref. 2.

    Google Scholar 

  42. Segeletes, S.B. (1998) Army Research Laboratory, Aberdeen, USA, report number: ARL-TR-1758.

    Google Scholar 

  43. Barton, M.A., and Stacey, F.D. (1985) The Grüneisen parameter at high pressure: A molecular dynamic study, Phys. Earth Planet. Inter. 39, 167–177.

    Article  ADS  Google Scholar 

  44. Ponkratz, U., and Holzapfel, W.B. (2003) (to be presented) at the ALRAPT conference, Bordeaux.

    Google Scholar 

  45. Oganov, A.R., Brodholt, J.P., and Price, G.D. (2000) Comparative study of quasiharmonic lattice dynamics, molecular dynamics and Debye model applied to MgSiO3 perovskite, Phys. Earth Planet. Inter. 122, 277–288.

    Article  ADS  Google Scholar 

  46. Karasevskyy, A.I., and Holzapfel, W.B. (2003) Equations of states and thermodynamic properties of rare gas solids under pressure calculated with a self-consistent statistical method, Phys. Rev. B. (to be published).

    Google Scholar 

  47. The webpage www.EOSdata.de is presently in preparation to provide these codes and any question concerning their application should be directed to holzapfel@physik.upb.de

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, University Paderborn, 33095, Paderborn, Germany

    Wilfried B. Holzapfel

Authors
  1. Wilfried B. Holzapfel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Chemistry, Adam Mickiewicz University, Poznań, Poland

    Andrzej Katrusiak

  2. Department of Chemistry, University College London, UK

    Paul McMillan

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media New York

About this paper

Cite this paper

Holzapfel, W.B. (2004). Equations of State and Thermophysical Properties of Solids Under Pressure. In: Katrusiak, A., McMillan, P. (eds) High-Pressure Crystallography. NATO Science Series, vol 140. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2102-2_14

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-2102-2_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1954-8

  • Online ISBN: 978-1-4020-2102-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation