On the self-consistent statistical theory of vacancies

We report here a new method of describing the effect of the presence of vacancies on the structure, dynamics and thermodynamics of a crystal. The unsymmetrized self-consistent approximation is used to determine the potential energy in which the defective structure and the anharmonicity appear from the beginning. In order to stress the power of this method, we calculate the free energy of formation of a vacancy and the concentration of vacancy in a two-dimensional triangular Lennard-Jones crystal. A comparison with Monte Carlo simulation is given and a possible application to experimentally accessible systems is discussed.