Kinetics of inherent processes counteracting crystallization in supercooled monatomic liquid

Abstract: 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 rate $g^{+}$ and the detachment rate $g^{-}$, which determine how particles change their belonging from one phase to another. In the present study, a {\it correspondence rule} between the rates $g^{+}$ and $g^{-}$ as functions of the size $N$ of growing crystalline nuclei is defined for the first time. In contrast to the well-known detailed balance condition, which relates $g^{+}(N)$ and $g^{-}(N)$ at $N=n_c$ (where $n_c$ is the critical nucleus size) and is satisfied only at the beginning of the nucleation regime, the found {\it correspondence rule} is fulfilled at all the main stages of crystallization kinetics (crystal nucleation, growth and coalescence). On the example of crystallizing supercooled Lennard-Jones liquid, the rate $g^{-}$ was calculated for the first time at different supercooling levels and for the wide range of nucleus sizes $N\in[n_c;\,40\,n_c]$. It was found that for the whole range of nucleus sizes, the detachment rate $g^{-}$ is only $\approx2$\% less than the attachment rate $g^{+}$. 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-D\"{o}ring-Zeldovich-Frenkel equation.