The kinetics of homogeneous melting beyond the limit of superheating

TL;DR

This study uses molecular dynamics simulations to analyze the time-scales and probability distributions of homogeneous melting in superheated Fe crystals, revealing size and temperature dependencies and evaluating the Z method's accuracy.

Contribution

It provides detailed statistical analysis of melting times beyond superheating limits and assesses the reliability of the Z method for melting point determination.

Findings

Probability distribution of melting time is roughly exponential.

Mean melting time depends strongly on excess temperature and system size.

Small systems exhibit persistent solid-liquid alternation.

Abstract

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.