Volume and pressure-dependent thermodynamic properties of sodium

•Volume and pressure effects on Grüneisen parameter and melting curve of sodium were studied.•Numerical calculations were performed for sodium up to pressure 65 GPa.•This research proposes the new good model for determining Grüneisen parameter and melting temperature at high pressure.

In this work, the volume and pressure effects on thermodynamic quantities including Grüneisen parameter and melting temperature of sodium have been studied of to 65 GPa. The volume dependence of Grüneisen parameter of sodium has been firstly analyzed. Based on this result and the Lindemann criterion of melting we derived the analytical expression of volume-dependent melting temperature. Combining with Vinet equation-of-state, the melting curve of sodium at high pressure has been proposed. Numerical calculations were performed for solid sodium up to pressure 65 GPa. Theoretical calculations are compared with available experimental data showing the good and reasonable agreements in the pressure range 0–30 GPa. This research proposes the good volume- and pressure-dependent Grüneisen parameter as well as the potential of Lindemann criterion approach on predicting high-pressure melting of materials.