Monte Carlo Simulation of Vacancies in Rare-Gas Crystals

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Abstract
The thermodynamics of vacancy formation in rare-gas crystals is studied by using Monte Carlo simulation of a many-body system. In the calculations, we assume a pairwise-additive Lennard-Jones potential and measure the change in Helmholtz free energy associated with reversibly adding a particle to a crystal containing a single vacancy. The addition is carried out by varying a coupling parameter joining one particle to the others in the crystal. Results for both 32- and 108-particle systems show that in a macroscopic (rare-gas) crystal near the triple point (1) the fraction of lattice sites vacant is about 1/3000, and (2) relaxation of particles neighboring a vacant site is less than 1% of an equilibrium interparticle spacing. These calculations are in excellent agreement with the earlier work of Glyde.