Beyond the Mie-Grüneisen Approximation: Building a Better Thermal Equation of State for Silicate Liquids at Lower Mantle Pressures
Abstract
By shock compression, it is possible to directly measure density, temperature, and sound speed in silicate liquids at any mantle pressure (P). Likewise, all these properties can be computed in empirical or ab initio molecular dynamics (MD) simulations. To be of use in models of the evolution of early terrestrial magma oceans or for interpreting the state of the modern core mantle boundary, however, these properties must be systematically expressed by a thermal Equation of State (EoS). The functional form of such an EoS is still a matter of research. Data density and simulation quality are reaching the point that several of the assumptions made in these models can now be tested or generalized.
In particular, it is commonly assumed that the Grüneisen parameter (γ ) can be expressed simply as a one-parameter function of volume (V). This is called the Mie-Grüneisen approximation and is well-motivated for solid materials. For liquids it is questionable. Our increasingly precise measurements of γ using rarefaction overtake experiments remain consistent with the finite-difference value obtained by comparing cold solid and hot liquid Hugoniots. Nevertheless, a campaign of MD simulations have shown clear and systematic dependence of γ on internal energy (E) at constant V. We have abstracted a simple functional form γ(V, E) with only one extra parameter from these simulations and fit it to the combined sound-speed and shock velocity data set for the Diopside-Anorhite eutectic liquid composition. Together with a functional form for the heat capacity, CV, motivated by the same simulations and constrained by shock temperature data, we have a new and more predictive thermal EoS for this liquid in P-V-E-T space. We tested whether an enthalpy formulation is superior but it is neither simpler nor more complex so we continue to use the internal energy formulation. In this talk we will show the consequences of this new method of fitting and systematizing EoS data for questions of crystal/liquid buoyancy and magma ocean isentrope slopes.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFMMR22A..05A
- Keywords:
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- 3919 Equations of state;
- MINERAL PHYSICS;
- 3924 High-pressure behavior;
- MINERAL PHYSICS;
- 3939 Physical thermodynamics;
- MINERAL PHYSICS;
- 3994 Instruments and techniques;
- MINERAL PHYSICS