Physics and Chemistry of Minerals

, Volume 44, Issue 1, pp 43–62 | Cite as

Phase diagrams, thermodynamic properties and sound velocities derived from a multiple Einstein method using vibrational densities of states: an application to MgO–SiO2

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


In a previous paper, we showed a technique that simplifies Kieffer’s lattice vibrational method by representing the vibrational density of states with multiple Einstein frequencies. Here, we show that this technique can be applied to construct a thermodynamic database that accurately represents thermodynamic properties and phase diagrams for substances in the system MgO–SiO2. We extended our technique to derive shear moduli of the relevant phases in this system in pressure–temperature space. For the construction of the database, we used recently measured calorimetric and volumetric data. We show that incorporating vibrational densities of states predicted from ab initio methods into our models enables discrimination between different experimental data sets for heat capacity. We show a general technique to optimize the number of Einstein frequencies in the VDoS, such that thermodynamic properties are affected insignificantly. This technique allows constructing clones of databases from which we demonstrate that the VDoS has a significant effect on heat capacity and entropy, and an insignificant effect on volume properties.


Equation of state Vibrational density of states Pressure scale Elasticity Anharmonicity 



MHG Jacobs gratefully acknowledges financial support by the German Research Foundation (DFG) under Grant No. JA 1985/1-2. 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 thank M. Ghiorso and M. Tirone for thoughtful suggestions and ideas, which significantly improved the quality of the manuscript.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Michael H. G. Jacobs
    • 1
    Email author
  • 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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