Perturbation theory for classical solids with vacancy defects

Abstract

We present a density functional model 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 is modified from its usual form to take into account the presence of vacancies in the lattice structure. The repulsive part of the Lennard-Jones potential is treated in terms of an equivalent hard sphere (EHS) system while the contribution from the long attractive part is treated perturbatively. The properties of the EHS in the inhomogeneous state is obtained with the weighted density functional approach. The thermodynamic behavior is studied by locating the state of minimum free energy. The dependence of the vacancy concentration on temperature at the coexistence of crystal and liquid is obtained.