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 the crystallizing Lennard-Jones liquid as an example, in the present work, we perform a 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 nc. We find that for the growing nuclei, whose sizes are larger than the critical size nc, 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 nc, 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 size n > 3nc particles.