  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.
