Constructing high-pressure thermodynamic models: problems and possible solutions
Abstract
Conventional thermodynamic databases (e.g. Fabrichnaya et al. 2004, Holland and Powell 1998, 2011) consist of expressions for the Gibbs energy at ambient pressure, extended to higher pressures through the integration of some EOS (Equation Of State). While this is simple and straight-forward, such thermodynamic models are prone to produce manifestly unphysical predictions of negative thermal expansion and even negative heat capacity at high pressure. It has been shown (Brosh et al. 2007) that these errors arise not only from problems the EOS itself but also from incompatibilities between the EOS and the models used for extrapolations of the heat capacity at ambient pressure. One solution is a radical restructuring of thermodynamic databases. Instead of modelling the Gibbs energy, new databases can be based on modelling the Helmholtz energy using Debye-Mie-Grüneisen EOS. This approach is very successful for modelling solid substances (Jacobs 2009, 2010, Dorogokupets et al. 2007, 2012) but the Debye-Mie-Grüneisen equations of state are not easily applicable to liquids. Other difficulties stem from the treatment of the predicted mechanical instability above the normal melting point. However, the most severe difficulty with the utilization of the Debye-Mie-Grüneisen approach is that it is incompatible with the current ambient-pressure thermodynamic databases and one will not be able to use them as a basis for high pressure modelling. Another approach (Brosh et al. 2007) is based on an interpolation of the thermophysical properties between the ambient pressure models given in conventional databases and the Debye-Mie-Grüneisen model at extreme pressures. This avoids most of the spurious anomalies of conventional models. The limitations of the interpolation scheme are the inclusion of several model parameters whose physical essence is not well-defined and an underestimation of the heat capacity at high pressures. In this presentation, the predictions of the interpolation scheme are compared with those of more physical Debye-Mie-Grüneisen models for several substances: Al, Fe and MgO. The utility of the interpolation scheme in calculating phase equilibria and thermophysical properties from ambient to earth-core pressures is illustrated by calculations on the Fe-Ni-C alloy system.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFM.V13A2582B
- Keywords:
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- 1012 GEOCHEMISTRY Reactions and phase equilibria;
- 1009 GEOCHEMISTRY Geochemical modeling;
- 1011 GEOCHEMISTRY Thermodynamics