Study of MWDA functional theory: freezing of simple liquids

In this paper fusion liquid-solid phase by numerical method using weighted density functional theory (MWDA), hard-sphere potential model (HS) and function (PY) by calculating total free energy of liquid metals such as sodium, magnesium and aluminum has been studid. Then we calculated the amount of density of the solid and liquid coexist using free energy graph according to density of hard-sphere fluid and solids fcc, bcc and hcp wich these results good agreement with Mont Carllo simulation results and other Previous works. Finally we study stability lattices fcc, bcc and hcp, according to their energy. Finally we study stability lattices fcc, bcc and hcp, according to their energy.