The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si.

This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

单组分材料和固溶体合金结晶过程的分子动力学 (MD) 模拟结果揭示了晶液界面速度的复杂温度依赖性，其特征是在低于 10-30% 过冷度时增加到最大值平衡熔化温度随后在更深的过冷水平下逐渐降低速度。在定性水平上，结晶前沿速度的这种非单调行为与 Wilson-Frenkel 模型描述的扩散控制结晶过程一致，其中界面速度在熔化温度附近几乎线性增加定义为相变的热力学驱动力的增长，而随着过冷度的进一步增加原子迁移率的降低驱动速度通过最大值并在较低温度下逐渐减小。然而，在定量水平上，扩散模型无法用某些模型材料的单一参数集描述整个温度范围内的 MD 模拟结果。现有理论模型在充分描述 MD 结果方面的有限能力在目前对两种材料（铬和硅）的研究中得到了说明。还证明了 MD 结果可以很好地通过从 hodograph 方程得到的解来描述，该方程先前是从锐界面极限中的动力学相场模型（动力学 PFM）中发现的。Hodograph 方程在整个温度范围内描述 MD 模拟预测的能力与将慢（相场）和快速（梯度流）变量引入到原始动力学 PFM 中有关，从中可以得到 hodograph 方程。慢相场变量负责描述小过冷度下的数据，而快速梯度流变量解释了高过冷度下的局部非平衡效应。这两种类型变量的引入使得正弦图方程的解足够灵活，可以可靠地描述在 Cr 和 Si 的 MD 模拟中预测的动力学曲线的所有非线性。

本文是主题问题“复杂系统中的传输现象（第 1 部分）”的一部分。