# The kinetics of homogeneous melting beyond the limit of superheating

Source: [The kinetics of homogeneous melting beyond the limit of superheating](<https://www.sota2.com/research/paper/68fa2fc21e209131ce86f40a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T17:47:26.067Z

Authors: D. Alf\\\`e, C. Cazorla, M. J. Gillan

Published: 2011-04-12T09:16:12.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1104.2147>)

[PDF](<https://arxiv.org/pdf/1104.2147.pdf>)