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 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.

The process of homogeneous crystal nucleation has been considered in a model liquid, where the interparticle interaction is described by a short-range spherical oscillatory potential. Mechanisms of initiating structural ordering in the liquid at various supercooling levels, including those corresponding to an amorphous state, have been determined. The sizes and shapes of formed crystal grains have been estimated statistically. The results indicate that the mechanisms of nucleation occurs throughout the entire considered temperature range. The crystallization of the system at low supercooling levels occurs through a mononuclear scenario. A high concentration of crystal nuclei formed at high supercooling levels (i.e., at temperatures comparable to and below the glass transition temperature T g ) creates the semblance of the presence of branched structures, which is sometimes erroneously interpreted as a signature of phase separation. The temperature dependence of the maximum concentration of crystal grains demonstrates two regimes the transition between which occurs at a temperature comparable to the glass transition temperature T g .In terms of thermodynamics, a supercooled liquid is in a state of unstable equilibrium, which results in the appearance of domains of a crystal phase in it [1][2][3][4][5][6]. At the same time, the character of the process of structural ordering should significantly depend on the conditions under which the supercooled state was formed, in particular, on the cooling rate of the liquid and on its final supercooling level ∆T /T m = 1 − T /T m , where T m is the melting temperature of the system [2,7,8]. At low and moderate supercooling levels covering the temperature range T g < T < T m , crystallization is usually initiated through the scenario of crystal nucleation, which is described within classical nucleation theory [1,2,8]. At temperatures below the glass transition temperature T g , which correspond to high supercooling * Electronic address: bulatgnmail@gmail.com arXiv:1812.06279v1 [cond-mat.mtrl-sci] 15 Dec 2018 of the system T g 0.78 /k B . This surprising nontrivial result requires a more detailed analysis and test in application systems with another characteristic interparticle interaction (polymers, colloidal systems, etc).We are grateful to Prof. S.V. Demishev and V.V. Glushkov (Prokhorov Genereal Physics Institute, Russian Academy of Sciences, Moscow) for stimulating discussions and recommendations.

Control of the crystallization process at the microscopic level makes it possible to generate the nanocrystalline samples with the desired structural and morphological properties, that is of great importance for modern industry. In the present work, we study the influence of supercooling on the structure and morphology of the crystalline nuclei arising and growing within a liquid metallic film. The cluster analysis allows us to compute the diffraction patterns and to evaluate the morphological characteristics (the linear sizes of the homogeneous part and the thickness of the surface layer) of the crystalline nuclei emergent in the system at different levels of supercooling. We find that the liquid metallic film at the temperatures corresponded to low supercooling levels crystallizes into a monocrystal, whereas a polycrystalline structure forms at deep supercooling levels. We find that the temperature dependence of critical size of the crystalline nuclei contains two distinguishable regimes with the crossover temperature T/T g ≈ 1.15 (T g is the glass transition temperature), which appears due to the specific geometry of the system.

Crystallization kinetics has features that are universal and independent of the type of crystallized system. The possibility of using scaling relations to describe the temperature dependences of the surface self-diffusion coefficient , which is one of the key characteristics of crystallization kinetics, has been demonstrated in application to various crystallized molecular glasses. It has been shown that the surface self-diffusion coefficient as a function of the dimensionless temperature is reproduced by a power law and is universally scaled for all considered systems. The analysis of experimental data has revealed a correlation between the crystallization kinetic characteristics, index of fragility, and criterion of the glass-forming ability of a liquid. It has been shown that this correlation can be obtained within the generalized Einstein-Stokes relation.

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