# Equation of state and shock compression of warm dense sodium - a first-principles study

## TL;DR

This study combines first-principles methods to accurately determine sodium's equation of state across wide conditions, revealing ionization effects and benchmarking existing models for shock compression behavior.

## Contribution

It presents a coherent EOS for sodium using PIMC and DFT-MD, identifying ionization-induced compression maxima and providing benchmark data for popular EOS models.

## Key findings

- Identified two compression maxima due to K-shell and L-shell ionization.
- Provided benchmark EOS data for sodium over wide density-temperature ranges.
- Showed radiation effects dominate at very high temperatures, affecting shock compression.

## Abstract

As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially-ionized states [B. Militzer and K. P. Driver, Phys. Rev. Lett. 115, 176403 (2015)] at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide density-temperature range of $1.93-11.60$ g/cm$^{3}$ and $10^3-1.29\times10^8$ K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that are consistent with DFT-MD at intermediate temperatures of $2\times10^6$ K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to $K$-shell and $L$-shell ionization. Our Hugoniot curves provide a benchmark for widely-used EOS models, SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 10$^7$ K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. We also compute the temperature-density dependence of thermal and pressure ionization processes.