Density functional theory of vacancies

Abstract

The density functional (DF) theory of freezing is extended to predict the equilibrium concentration of vacancies in the crystal. The vacancy density in the crystal at phase coexistence is predicted to be approximately 5×10−5 for the Lennard-Jones model system near the triple point, which is comparable to concentrations measured in real systems such as argon and krypton. The dependence of the vacancy density on the temperature and pressure of the system is investigated using the new DF formalism. The concentration of vacancies in the hard sphere crystal at coexistence is also calculated, and it is found to be very small. The perfect crystal approximation, used earlier by us and others, is found to be very accurate for both the hard sphere and Lennard-Jones systems.