An internal energy-dependent model for the Gruneisen parameter of silicate liquids

YC Zhou and WA Goddard and PD Asimow, GEOCHIMICA ET COSMOCHIMICA ACTA, 316, 59-68 (2022).

DOI: 10.1016/j.gca.2021.10.005

We investigated the accuracy of the Mie-Gruneisen approximation, which treats the Gruneisen parameter (y) as a one -parameter function of volume, for use in describing the thermal equation of state of a silicate liquid. For this study, we focused on a single composition: the diopside-anorthite eutectic, an Fe-free basalt analog that has been extensively studied by shock wave experiments. We tuned an empirical force-field to a small set of ab initio N -V-T molecular dynamics simula-tions to ensure that it reproduces pressure, heat capacity, and y at high and low pressures. We then used empirical force-field molecular dynamics simulations in a larger system and for longer run times to ensure accurate extraction of y at numerous N- V-E state points. To first order, the results show the expected volume-dependence for silicate liquids, with y increasing as volume decreases. However, there are also significant and systematic variations of y with internal energy (E) at constant volume. We propose a simple model form that captures the volume and E dependence of y with only one more free parameter than a typical Mie-Gruneisen formulation. We demonstrate the utility of this new model for well-constrained fitting to sparse shock wave experiment data below 200 GPa, obtaining a marked improvement in the ability to simultaneously fit the pre-heated liquid Hugoniot and points substantially offset from this Hugoniot. (C) 2021 Elsevier Ltd. All rights reserved.

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