Monte Carlo Simulation of Vacancies in Rare‐Gas Crystals

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.

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