Lindemann Criterion and the Anomalous Melting Curve of Sodium

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.