A parameter-free prediction of simulated crystal nucleation times in the Lennard-Jones system: from the steady-state nucleation to the transient time regime.

Large scale simulations of crystal nucleation from the liquid are performed using the Lennard-Jones potential to determine the time required for nucleation. By considering both transient and finite-size effects, we for the first time successfully predict the nucleation time without any parameter fitting in the Lennard-Jones system. All necessary parameters are derived from separate, equilibrium simulations. At small undercoolings, large system size effects are observed. The required system size is not only determined by the size of the critical nuclei, but also the characteristic spacing between them. Two distinct nucleation regions are predicted by theory and observed by the simulations, which are dominated by the transient time and the steady-state nucleation time, respectively.

Quantitative parameter-free prediction of simulated crystal-nucleation times.

We present direct comparisons between simulated crystal-nucleation times and theoretical predictions using a model of aluminum, and demonstrate that a quantitative prediction can be made. All relevant thermodynamic properties of the system are known, making the agreement of our simulation data with nucleation theories free of any adjustable parameters. The role of transient nucleation is included in the classical nucleation theory approach, and shown to be necessary to understand the observed nucleation times. The calculations provide an explanation on why nucleation is difficult to observe in simulations at moderate undercoolings. Even when the simulations are significantly larger than the critical nucleus, and when simulation times are sufficiently long, at moderate undercoolings the small concentration of critical nuclei makes the probability of the nucleation low in molecular dynamics simulations.