Study of solid-liquid phase transition using the modified weighted density approximation of inhomogeneous hard sphere systems

In this article we first introduce the weighted density approximation (WDA) to study the classical inhomogeneous system such as inhomogeneous fluids. Then we introduce the modified weighted density approximation (MWDA) to calculate the structure and thermodynamical properties of the FCC hard sphere crystal. The MWDA is a self consistent method where the free energy is expressed as an unperturbed expression. Usually the required input is the Percus-Yevick (PY) direct correlation function of hard sphere. In addition to this, we use the hard sphere DCF introduced by Roth et al. [J. Phys. Condense Matter, 14, 12063 (2002).], here we call it RELK, we also introduce a new expression for the DCF which is a combination of the PY and RELK. This new expression gives the best result for the DCF of hard sphere, as it compared with the Monte Carlo simulation. In our calculation we use all these DCFs to calculate the free energy and freezing parameters of FCC hard sphere crystals. Although we obtained the better results using the PY-RELK DCF but it seems we should improve the MWDA to get better result.