The statistical moment method is used to investigate the melting of the crystal under pressure. First, we propose fundamental equations to determine characteristic physical quantities at the melting point such as the melting temperature \(T_{m}\) , the volume change \(\Delta v_{m}\) , the enthalpy change \(\Delta H_{m}\) , the entropy change \(\Delta S_{m}\) , the thermal conductivities \(\kappa_{S}\) , \(\kappa_{L}\) of the solid phase and the liquid phase, the thermal diffusivities \(\lambda_{S}\) , \(\lambda_{L}\) of the solid phase and the liquid phase. Subsequently, based on this received information, we continue to consider the laser-induced melting process and the laser welding process theoretically. We mathematically executed this melting theory for two transition metals including aluminum and copper up to pressure 20 GPa. Our numerical results correspond well with previous experiments, simulations, and other theoretical calculations.
