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

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.