Determination of a melting curve using the one-phase approach

• Kechin's one-phase approach to predicting a melting curve proven effective.
• Convergence of the Padé approximation confirmed.
• Solution found valid for a pressure range of four orders of magnitude.
• Simon's equation identified as the melting curve of the modified Lennard-Jones solid.
• This identification justified from the thermodynamic conditions for the solid phase.

The melting curve of the modified Lennard-Jones solid is derived using a one-phase approach. The Padé approximation employed for solving the melting-curve equation converges at the middle stage, giving rise to the well-known Simon curve that satisfactorily captures the actual melting curve found from a molecular dynamics simulation over a pressure range of four orders of magnitude. This situation is justified because the solid under consideration was shown to satisfy the thermodynamic condition under which Simon's curve becomes exact.