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 $tau_{rm w}$ before melting occurs. We find that the probability distribution of $tau_{rm w}$ is roughly exponential, and that the mean value $<tau_{rm w} >$ depends strongly on the excess of the initial steady temperature of the crystal above the superheating limit identified by other researchers. The mean $<tau_{rm w}>$ also depends strongly on system size in a way that we have quantified. For very small systems of $sim 100$ 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.
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