Statistical distribution of thermal vacancies close to the melting point

A detailed description of the statistical distribution of thermal vacancies in an homogeneous crystal near its melting point is presented, using the embedded atom model for copper as an example. As the temperature increase, the average number of thermal vacancies generated by atoms migrating to neighboring sites increases according to Arrhenius' law. We present for the first time a model for the statistical distribution of thermal vacancies, which according to our atomistic computer simulations follow a Gamma distribution. All the simulations are carried out by classical molecular dynamics and the recognition of vacancies is achieved via a recently developed algorithm. Our results could be useful in the further development of a theory explaining the mechanism of homogeneous melting, which seems to be mediated by the accumulation of thermal vacancies near the melting point.