An internal energy-dependent model for the Grüneisen parameter of silicate liquids
Abstract
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.
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 https://doi.org/10.22002/D1.1921. 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.Attached Files
Supplemental Material - 1-s2.0-S0016703721005949-mmc1.pdf
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Additional details
- Eprint ID
- 112181
- DOI
- 10.1016/j.gca.2021.10.005
- Resolver ID
- CaltechAUTHORS:20211202-191331622
- Office of Naval Research (ONR)
- N00014-20-1-2603
- Office of Naval Research (ONR)
- N00014-19-1-2081
- NSF
- EAR-1725349
- Resnick Sustainability Institute
- Created
-
2021-12-02Created from EPrint's datestamp field
- Updated
-
2022-01-22Created from EPrint's last_modified field
- Caltech groups
- Resnick Sustainability Institute, Division of Geological and Planetary Sciences
- Other Numbering System Name
- WAG
- Other Numbering System Identifier
- 1501