Equations of state for mixtures: results from density-functional (DFT) simulations compared to high accuracy validation experiments on Z

Abstract

We report a computational and validation study of equation of state (EOS) properties of liquid / dense plasma mixtures of Xe and ethane to explore and to illustrate the physics of the molecular scale mixing of light elements with heavy elements. Accurate EOS models are crucial to achieve high-fidelity hydrodynamics simulations of many high-energy density phenomena such as inertial confinement fusion, planet interiors, and planetary impact. While the EOS is often tabulated for separate species, the EOS for arbitrary mixtures is generally not available, requiring properties of the mixture to be approximated by combining physical properties of the pure systems. The main goal of this study is to assess how accurate this approximation is under shock conditions. Density functional theory molecular dynamics (DFT-MD) at elevated-temperature and pressure is used to assess the thermodynamics of the xenon-ethane and xenon-deuterium mixtures. The simulations are unbiased as to elemental species and therefore provide comparable accuracy when describing total energies, pressures, and other physical properties of mixtures as they do for pure systems. In addition, we have performed shock compression experiments using the Sandia Z-accelerator on pure xenon, ethane, and various mixture ratios thereof. The DFT-based simulation results for the principle Hugoniot compare well with the experimental points. The predictions of different EOS mixing models for Xe-D are considered, and we find that a mixing rule based on pressure equilibration performs reliably well.