Distribution of melting times and critical droplet in kinetic Monte Carlo and molecular dynamics

A kinetic Monte Carlo model on a lattice, based on a reaction-like mechanism, is used to investigate the microscopic properties of the homogeneous melting of a metastable crystal. The kinetic Monte Carlo model relies on nearest-neighbors interactions and a few relevant dynamical parameters. To examine the reliability of the model, careful comparison with molecular dynamics simulations of a hard sphere crystal is drawn. A criterion on the critical nature of a microscopic configuration is deduced from the bimodal character of the probability density function of melting time. For kinetic Monte Carlo simulations with dynamical parameter values which fit the molecular dynamics results, the number of liquid sites of the critical droplet is found to be smaller than 300 and the ability of the critical droplet to invade the entire system is shown to be independent of the droplet shape as long as this droplet remains compact. In kinetic Monte Carlo simulations, the size of the critical droplet is independent of the system size. Molecular dynamics evidences a more complex dependence of melting time on system size, which reveals non-trivial finite size effects.