Kinetics of inherent processes counteracting crystallization in supercooled monatomic liquid

Crystallization of supercooled liquids is mainly determined by two competing processes associated with the transition of particles (atoms) from liquid phase to crystalline one and, vice versa, with the return of particles from crystalline phase to liquid one. The quantitative characteristics of these processes are the so-called attachment rateg+and the detachment rateg-, which determine how particles change their belonging from one phase to another. In the present study, acorrespondence rulebetween the ratesg+andg-as functions of the sizeNof growing crystalline nuclei is defined for the first time. In contrast to the well-known detailed balance condition, which relatesg+(N)andg-(N)atN=nc(wherenis the critical nucleus size) and is satisfied only at the beginning of the nucleation regime, the foundcorrespondence ruleis fulfilled at all the main stages of crystallization kinetics (crystal nucleation, growth and coalescence). On the example of crystallizing supercooled Lennard-Jones liquid, the rateg-was calculated for the first time at different supercooling levels and for the wide range of nucleus sizesN∈[nc;40nc]. It was found that for the whole range of nucleus sizes, the detachment rateg-is only≈2% less than the attachment rateg+. This is direct evidence that the role of the processes that counteract crystallization remains significant at all the stages of crystallization. Based on the obtained results, a kinetic equation was formulated for the time-dependent distribution function of the nucleus sizes, that is an alternative to the well-known kinetic Becker-Döring-Zeldovich-Frenkel equation.