A new procedure for analyzing the nucleation kinetics of freezing in computer simulation

Abstract

A new method for deriving the size of the critical nucleus and the Zeldovich factor directly from kinetic data is presented. Moreover, in principle, the form of G(n), the free energy of formation of nuclei consisting of n molecules, can be inferred. The method involves measuring times of first appearance of nuclei of size n in the transient regime and applying the Becker-Doring theory. Times of first appearance exhibit the same characteristics as the conventional times associated with N(n,t), the number of nuclei of at least size n per unit volume that have materialized at time t. That is, they are well represented by three nucleation parameters, the reduced moment, the time lag, and the steady state nucleation rate. But unlike the conventional steady state rate which is independent of n, the steady state times of first appearance vary with n. In order to characterize the three nucleation parameters with precision, however, thousands of independent stochastic events with known n are required. Such sets of data are readily generated in molecular dynamic simulations but, so far, not in laboratory experiments. Results are illustrated by an analysis of simulations of the spontaneous freezing of large clusters of SeF6.

Analysis of nucleation using mean first-passage time data from molecular dynamics simulation

“…As a result, simplifying assumptions are often invoked, such as a large separation between the time scales of nucleation and growth. The methods proposed by Bartell and Wu 13 and Wedekind et al 14 invoke this assumption in order to estimate the nucleation rate, critical nucleus size, and Zeldovich factor, which is related to the curvature of the free energy surface around the critical nucleus size, from MD simulations. The method described by Wedekind et al 14 is based on the mean first-passage time (MFPT) of the largest cluster, obtained from a large set of independent nucleation runs, and is applicable when the characteristic time scale for nucleation is much larger than the time scale for growth in the system under study.…”

Cavitation in a metallic liquid: Homogeneous nucleation and growth of nanovoids

“…The steady-state nucleation or barrier-crossing rate J, the critical nucleus size n * , and the Zeldovich factor Z, can be evaluated with the MFPT method. 11,36,37 Here, we follow the general MFPT methodology 37 which has been presented and applied to different physical processes by Wedekind and co-workers, 11,38,39 Bartell and Wu, 40 and Zheng et al 10 For most activated processes such as nucleation of cavities/voids (daughter phase) from a liquid (parent phase), the dynamics can be described by the Fockker-Planck equation 11,41 ∂P…”

On the reaction coordinate for seeded crystallisation

“…It may appear that, under the strong undercooling conditions studied here, direct methods such as the MFPT approach [24][25][26][27][28] provide a more convenient way for the calculation of nucleation rates. However, as found recently 23 , the MFPT analysis is affected by the nonMarkovianity of the time evolution of the largest cluster size used as reaction coordinate resulting in large inaccuracies in the rate estimate.…”

“…Although recognized to have its faults, this reaction coordinate still performs best in comparison with other suggested collective variables 18,19 . The deficiency of the size of the largest crystalline cluster becomes particularly apparent 23 in the calculation of crystal nucleation rates within the framework of mean first-passage time (MFPT) analysis [24][25][26][27][28] . In this approach, which is practical only for large undercooling, one carries out straightforward molecular dynamics simulations starting in the metastable liquid.…”