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

Zhou, Yacong (Brooke) and Goddard, William A. and Asimow, Paul D. (2022) An internal energy-dependent model for the Grüneisen parameter of silicate liquids. Geochimica et Cosmochimica Acta, 316 . pp. 59-68. ISSN 0016-7037. doi:10.1016/j.gca.2021.10.005.

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We investigated the accuracy of the Mie-Grüneisen approximation, which treats the Grüneisen parameter (γ) 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 simulations to ensure that it reproduces pressure, heat capacity, and 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 at numerous N-V-E state points. To first order, the results show the expected volume-dependence for silicate liquids, with increasing as volume decreases. However, there are also significant and systematic variations of with internal energy (E) at constant volume. We propose a simple model form that captures the volume and E dependence of with only one more free parameter than a typical Mie-Grüneisen 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.

Item Type:Article
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URLURL TypeDescription ItemData
Zhou, Yacong (Brooke)0000-0001-9496-9565
Goddard, William A.0000-0003-0097-5716
Asimow, Paul D.0000-0001-6025-8925
Additional Information:© 2021 Elsevier. Received 22 March 2021; accepted in revised form 4 October 2021; available online 13 October 2021. This work is funded by the Office of Naval Research, award numbers N00014-20–1-2603 (to PDA) and N00014-19–1-2081 (to WAG), and by the National Science Foundation, award number 1725349. The computations presented here were conducted in the Resnick High Performance Center, a facility supported by Resnick Sustainability Institute at the California Institute of Technology. Research Data associated with this article (the V-P-E simulation points shown in Fig. 1, Fig. 3) can be accessed at the CaltechDATA repository at The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Group:Resnick Sustainability Institute
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-20-1-2603
Office of Naval Research (ONR)N00014-19-1-2081
Resnick Sustainability InstituteUNSPECIFIED
Subject Keywords:Molecular dynamics; Silicate liquids; Grüneisen parameter; Equation of state
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Record Number:CaltechAUTHORS:20211202-191331622
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Official Citation:Yacong (Brooke) Zhou, William A. Goddard, Paul D. Asimow, An internal energy-dependent model for the Grüneisen parameter of silicate liquids, Geochimica et Cosmochimica Acta, Volume 316, 2022, Pages 59-68, ISSN 0016-7037,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112181
Deposited By: George Porter
Deposited On:02 Dec 2021 21:31
Last Modified:22 Jan 2022 00:02

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