The kinetics of homogeneous melting beyond the limit of superheating

Molecular dynamics simulation is used to study the time-scales involved in the homogeneous melting of a superheated crystal. The interaction model used is an embedded-atom model for Fe developed in previous work, and the melting process is simulated in the microcanonical (N, V, E) ensemble. We study periodically repeated systems containing from 96 to 7776 atoms, and the initial system is always the perfect crystal without free surfaces or other defects. For each chosen total energy E and number of atoms N, we perform several hundred statistically independent simulations, with each simulation lasting for between 500 ps and 10 ns, in order to gather statistics for the waiting time τ(w) before melting occurs. We find that the probability distribution of τ(w) is roughly exponential, and that the mean value <τ(w)> depends strongly on the excess of the initial steady temperature of the crystal above the superheating limit identified by other researchers. The mean <τ(w)> also depends strongly on system size in a way that we have quantified. For very small systems of ~100 atoms, we observe a persistent alternation between the solid and liquid states, and we explain why this happens. Our results allow us to draw conclusions about the reliability of the recently proposed Z method for determining the melting properties of simulated materials and to suggest ways of correcting for the errors of the method.