## Abstract

Homogeneous melting of superheated crystals at constant energy is a dynamical process, believed to be triggered by the accumulation of thermal vacancies and their self-diffusion. From microcanonical simulations we know that if an ideal crystal is prepared at a given kinetic energy, it takes a random time t_{w} until the melting mechanism is actually triggered. In this work we have studied in detail the statistics of t_{w} for melting at different energies by performing a large number of Z-method simulations and applying state-of-the-art methods of Bayesian statistical inference. By focusing on a small system size and short-time tail of the distribution function, we show that t_{w} is actually gamma-distributed rather than exponential (as asserted in a previous work), with decreasing probability near t_{w}∼0. We also explicitly incorporate in our model the unavoidable truncation of the distribution function due to the limited total time span of a Z-method simulation. The probabilistic model presented in this work can provide some insight into the dynamical nature of the homogeneous melting process, as well as giving a well-defined practical procedure to incorporate melting times from simulation into the Z-method in order to correct the effect of short simulation times.

Original language | English |
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Pages (from-to) | 546-557 |

Number of pages | 12 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 515 |

DOIs | |

Publication status | Published - 1 Feb 2019 |

## Keywords

- Bayesian
- Gamma distribution
- Melting
- Microcanonical
- Waiting times

## ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics