过冷单原子液体内禀反晶化过程的动力学
Kinetics of inherent processes counteracting crystallization in supercooled monatomic liquid
摘要：
过冷液体的结晶主要由两个竞争过程决定，这两个竞争过程与颗粒（原子）从液相到结晶相的转变以及颗粒从结晶相到液相的返回有关。这些过程的定量特征是所谓的附着率$g^{+}$和脱离率$g^{-}$，它们决定了颗粒如何从一个相改变到另一个相。在本研究中，{ \it对应规则}之间的速度$g^{+}$和$g^{-}$作为生长晶核的大小$N$的函数被定义为第一次。与公知的详细平衡条件相反，所发现的{ \it对应规则}在结晶动力学的所有主要阶段（晶体成核、生长和聚结）都得到满足，所述平衡条件在$N=n_c$（其中$n_c$是临界核尺寸）下关联$g^{+}(N)$和$g^{-}(N)$，并且仅在成核状态的开始时得到满足。以过冷Lennard-Jones液体结晶为例，首次计算了不同过冷度和宽晶核尺寸范围内的$N\in[n_c;\,40\,n_c]$速率。结果发现，对于整个核尺寸范围，脱离率$g^{-}$仅比附着率$g^{+}$小$\approx2$ %。这直接证明了在结晶的所有阶段，反结晶过程的作用仍然很重要。在此基础上，提出了一个核尺寸随时间变化的分布函数的动力学方程，该方程是著名的动力学Becker-Döring-Zeldovich-Frenkel方程的替代。
英文摘要：
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-Döring-Zeldovich-Frenkel equation.
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