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 tw until the melting mechanism is actually triggered. In this work we have studied in detail the statistics of tw 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 tw is actually gamma-distributed rather than exponential (as asserted in a previous work), with decreasing probability near tw∼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