Self-Consistent Thermodynamic Description of Silicate Liquids

Details Self-Consistent Thermodynamic Description of Silicate Liquids Self-Consistent Thermodynamic Description of Silicate Liquids

Dec 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agufmdi41a0344d&link_type=abstract

American Geophysical Union, Fall Meeting 2007, abstract #DI41A-0344

Physics

3611 Thermodynamics (0766, 1011, 8411), 3919 Equations Of State, 3924 High-Pressure Behavior, 5460 Physical Properties Of Materials, 8124 Earth'S Interior: Composition And State (1212, 7207, 7208, 8105)

Scientific paper

Describing the thermodynamic properties of dense liquids at extreme pressure and temperature is crucial to our understanding of planetary processes including deep melting, magma ocean dynamics and lunar formation. The functional form chosen to represent the equation of state should ideally depend on only a few parameters and correctly account for kinetic and electronic contributions to the free energy at extreme conditions. High pressure equation of state data for terrestrial liquids have mostly been fit to functional forms used for solids, such as the high temperature form of the Mie-Grüneisen equation, which assumes a constant thermal pressure coefficient (α KT). This approach is flawed since Maxwell relations require (∂ α KT / ∂ T)V = (∂ CV / ∂ V)T and we have found in first principles molecular dynamics studies of magnesiosilicate liquids at high pressure that the isochoric heat capacity (CV) varies significantly with volume. Moreover, the Mie-Grüneisen equation of state does not yield the correct (ideal gas) behavior in the limit of infinite temperature. Finally we have found that electronic contributions to thermodynamic properties are non-negligible. With these constraints in mind, we develop a number of approaches to expressing the Helmholtz potential over a large range of volume and temperature, including potential, kinetic and electronic contributions to the free energy. From these expressions for the fundamental relation, internally consistent equilibrium thermodynamic properties are derived by derivatives and Legendre transformations, which may be applied to the exploration of a large array of problems in planetary science.

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