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 1000 K at 31 GPa. This maximum does not occur due to a solid–solid 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.