Percus–Yevick Equation Applied to the Melting Problem with Application to Argon

For the melting transition, the solid is represented by an anharmonic model and the liquid is described by the Percus–Yevick approximation. The behavior of the liquid at high densities is studied on the isotherms $\text{kT\hspace{0.17em}/\hspace{0.17em}ε\hspace{0.17em}=\hspace{0.17em}1.3, 1.8,}\mathrm{and}\text{2.0}$ , where $k$ is the Boltzmann's constant, $T$ is the temperature, and $\epsilon$ is the well depth of the Lennard‐Jones 12–6 pair potential. No solutions of the Percus–Yevick equation were found for ${\mathrm{\rho \sigma }}^3$ above 1.3, where ${\rho }_1$ is the particle density and $\sigma$ is the radial parameter of the Lennard‐Jones potential. The liquid structure is found to be very different from the solid structure near the melting line. The liquid pressures are about 50% low for experimental melting densities of argon. This discrepancy gives rise to melting pressures up to twice the experimental values.