# Finite element simulation of the liquid-liquid transition to metallic hydrogen

## TL;DR

This paper presents a finite element simulation of the liquid-liquid transition to metallic hydrogen, confirming experimental signatures and suggesting complex transition dynamics, while proposing experiments to distinguish optical property changes.

## Contribution

The study introduces a detailed finite element model that accurately simulates laser-heated hydrogen and analyzes the phase transition signatures, highlighting the need for large latent heat values and complex transition dynamics.

## Key findings

- Simulated heating curves match experimental plateaus indicating phase transition.
- Large latent heat values are required to explain observed signatures.
- Proposed experiments can differentiate between metallic transition and bandgap closure.

## Abstract

Hydrogen at high temperature and pressure undergoes a phase transition from a liquid molecular phase to a conductive atomic state, or liquid metallic hydrogen, sometimes referred to as the plasma phase transition (PPT). The PPT phase line was observed in a recent experiment studying laser-pulse heated hydrogen in a diamond anvil cell in the pressure range $\sim 100 - 170 \text{GPa}$ for temperatures up to $\sim 2000 \text{K}$. The experimental signatures of the transition are (i) a negative pressure-temperature slope, (ii) a plateau in the heating curve, assumed to be related to the latent heat of transformation, and (iii) an abrupt increase in the reflectance of the sample. We present a finite element simulation that accurately takes into account the position and time dependence of the heat deposited by the laser pulse. We calculate the heating curves and the sample reflectance and transmittance. This simulation confirms that the observed plateaus are related to the phase transition, however we find that large values of latent heat are needed and may indicate that dynamics at the transition are more complex than considered in current models. Finally, experiments are proposed that can distinguish between a change in optical properties due to a transition to a metallic state or due to closure of the bandgap in molecular hydrogen.