Lindemann Criterion and the Anomalous Melting Curve of Sodium

TL;DR

This paper investigates sodium's high-pressure melting curve using ab-initio calculations, linking the steep decline after 1000K at 31 GPa to changes in Debye temperature and elastic constants, supporting the Lindemann criterion.

Contribution

It provides a detailed ab-initio analysis of Debye temperature and elastic constants up to 102 GPa, explaining the anomalous melting behavior of sodium.

Findings

Debye temperature decreases with pressure beyond 31 GPa

Elastic constants show significant variation at high pressure

Melting curve behavior aligns with Lindemann criterion predictions

Abstract

Recent reports of the melting curve of sodium at high pressure have shown that it has a very steep descent after a maximum of around 1000K at 31 GPa. This is not due to a phase transition. According to the Lindemann criterion, this behaviour should be apparent in the evolution of the Debye temperature with pressure. In this work, we have performed an "ab-initio" analysis of the behaviour of both the Debye temperature and the elastic constants up to 102 GPa, and find a clear trend at high pressure that should cause a noticeable effect on the melting curve.