A density functional model was presented for the thermodynamic properties of a Lennard-Jones system in the crystalline state having a small fraction of vacancies present in the lattice. The test density function was modified from its usual form in order to take account of the presence of vacancies in the lattice structure. The repulsive part of the Lennard-Jones potential was treated in terms of an equivalent hard sphere system while the contribution from the long attractive part was treated perturbatively. The properties of the equivalent hard sphere in the inhomogeneous state was obtained by using the weighted density functional approach. The thermodynamic behaviour was studied by locating the state of minimum free energy. The dependence of the vacancy concentration upon temperature at the coexistence point of crystal and liquid was obtained.

Perturbation Theory for Classical Solids with Vacancy Defects. S.P.Singh, S.P.Das: Physical Review B, 2007, 75[14], 144113 (9pp)