# High temperature ion-thermal behavior from average-atom calculations

## TL;DR

This paper develops a method to calculate ion-thermal behavior at high temperatures using average-atom models, reducing reliance on extensive molecular dynamics simulations, and applies it to carbon to analyze its equation of state.

## Contribution

It introduces a new functional form for free energy correction based on the Maxwell-Boltzmann distribution, with a single parameter calibrated by molecular dynamics.

## Key findings

- Ion displacement increases with temperature and compression.
- The effective density of potential modes is approximately 0.2 per atom.
- The method accurately predicts ion-thermal contributions across a wide range of conditions.

## Abstract

Atom-in-jellium calculations of the Einstein frequency were used to calculate the mean displacement of an ion over a wide range of compression and temperature. Expressed as a fraction of the Wigner-Seitz radius, the displacement is a measure of the asymptotic freedom of the ion at high temperature, and thus of the change in heat capacity from 6 to 3 quadratic degrees of freedom per atom. A functional form for free energy was proposed based on the Maxwell-Boltzmann distribution as a correction to the Debye free energy, with a single free parameter representing the effective density of potential modes to be saturated. This parameter was investigated using molecular dynamics simulations, and found to be ~0.2 per atom. In this way, the ion-thermal contribution can be calculated for a wide-range equation of state (EOS) without requiring a large number of molecular dynamics simulations. Example calculations were performed for carbon, including the sensitivity of key EOS loci to ionic freedom.