过热极限以上的均匀熔化动力学
The kinetics of homogeneous melting beyond the limit of superheating
摘要：
利用分子动力学模拟研究了过热晶体均匀熔化的时间尺度。所使用的相互作用模型是一个嵌入原子模型的Fe在以前的工作中，和熔融过程中模拟的微正则$(N, V, E)$系综。我们研究了含有96 - 7776个原子的周期重复系统，初始系统总是没有自由表面或其他缺陷的完美晶体。对于每个选定的总能量$E$和原子数$N$，我们进行数百次统计独立的模拟，每次模拟持续500 ps和10 ns之间，以收集熔化发生前等待时间$τ_{\rm w}$的统计数据。我们发现，概率分布的$τ_{\rm w}$是大致指数，和平均值$<τ_{\rm w} >$强烈依赖于过剩的初始稳定温度的晶体以上的过热限制由其他研究人员确定。平均$<τ_{\rm w}>$还以我们已经量化的方式强烈依赖于系统大小。对于非常小的系统的$\sim 100$原子，我们观察到一个持久的固体和液体状态之间的交替，我们解释了为什么会发生这种情况。我们的研究结果使我们能够得出结论，最近提出的Z方法的可靠性，用于确定模拟材料的熔化性能，并建议方法的错误的校正方法。
英文摘要：
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 $τ_{\rm w}$ before melting occurs. We find that the probability distribution of $τ_{\rm w}$ is roughly exponential, and that the mean value $<τ_{\rm w} >$ depends strongly on the excess of the initial steady temperature of the crystal above the superheating limit identified by other researchers. The mean $<τ_{\rm w}>$ 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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