Physics and Chemistry of Minerals

, Volume 40, Issue 3, pp 207–227 | Cite as

An alternative use of Kieffer’s lattice dynamics model using vibrational density of states for constructing thermodynamic databases

  • Michael H. G. Jacobs
  • Rainer Schmid-Fetzer
  • Arie P. van den Berg
Original Paper

Abstract

We use Kieffer’s model to represent the vibrational density of states (VDoS) and thermodynamic properties of pure substances in pressure–temperature space. We show that this model can be simplified to a vibrational model in which the VDoS is represented by multiple Einstein frequencies without significant loss of accuracy in thermodynamic properties relative to experimental data. The resulting analytical expressions for thermodynamic properties, including the Gibbs energy, are mathematically simple and easily accommodated in existing computational software for making thermodynamic databases. We show for aluminium, platinum, orthoenstatite and forsterite that thermodynamic properties can be represented with comparable accuracy as with Kieffer’s model with the same number of fitting parameters as in the Mie–Grüneisen–Debye model. We demonstrate that the method enables to achieve thermodynamic properties with superior accuracy relative to the Mie–Grüneisen–Debye method. The method is versatile in the sense that it allows incorporating dispersion of Grüneisen parameters. It is possible to extend the formalism to include other physical effects, such as intrinsic anharmonicity in the same way as in vibrational models based on Kieffer’s formalism.

Keywords

Equation of state Vibrational density of states Aluminium Platinum Forsterite Orthoenstatite 

Notes

Acknowledgments

MHG Jacobs gratefully acknowledges financial support by the German Research Foundation (DFG) under Grant no. JA 1985/1. Collaboration between A. van den Berg and M. Jacobs has been supported through The Netherlands Research Center for Integrated Solid Earth Science (ISES) project ME-2.7. We wish to express our gratitude to M. Ghiorso and an anonymous reviewer for constructive suggestions which improved the quality of the manuscript significantly.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michael H. G. Jacobs
    • 1
  • Rainer Schmid-Fetzer
    • 1
  • Arie P. van den Berg
    • 2
  1. 1.Institute of MetallurgyClausthal University of TechnologyClausthal-ZellerfeldGermany
  2. 2.Department of Theoretical GeophysicsUtrecht UniversityUtrechtThe Netherlands

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