Direct evaluation of attachment and detachment rate factors of atoms in crystallizing supercooled liquids

TL;DR

This study quantitatively evaluates the attachment and detachment rate factors of atoms in crystallizing supercooled liquids using molecular dynamics, revealing size-dependent behaviors and establishing a power law for nuclei larger than the critical size.

Contribution

It introduces a model-free numerical approach to directly estimate kinetic rate factors and critical nucleus size in crystallization processes.

Findings

Rate factors follow a power law for nuclei larger than critical size.

Subnucleation regime shows microscopic property dependence, not universal laws.

Growth rate stabilizes for nuclei larger than three times the critical size.

Abstract

Kinetic rate factors of crystallization have a direct effect on formation and growth of an ordered solid phase in supercooled liquids and glasses. Using crystallizing Lennard-Jones liquid as an example, in the present work we perform a \textit{direct} quantitative estimation of values of the key crystallization kinetic rate factors -- the rate $g^{+}$ of particle attachments to a crystalline nucleus and the rate $g^{-}$ of particle detachments from a nucleus. We propose a numerical approach, according to which a statistical treatment of the results of molecular dynamics simulations was performed without using any model functions and/or fitting parameters. This approach allows one to accurately estimate the critical nucleus size $n_{c}$. We find that for the growing nuclei, whose sizes are larger than the critical size $n_{c}$, the dependence of these kinetic rate factors on the nucleus size $n$ follows a power law. In the case of the subnucleation regime, when the nuclei are smaller than $n_{c}$, the $n$-dependence of the quantity $g^{+}$ is strongly determined by the inherent microscopic properties of a system and this dependence cannot be described in the framework of any universal law (for example, a power law). It has been established that the dependence of the growth rate of a crystalline nucleus on its size goes into the stationary regime at the sizes $n>3n_{c}$ particles.