Using the phase field crystal model (PFC model), an analysis of slow and fast dynamics of solid-liquid interfaces in solidification and melting processes is presented. Dynamical regimes for cubic lattices invading metastable liquids (solidification) and liquids propagating into metastable crystals (melting) are described in terms of the evolving amplitudes of the density field. Dynamical equations are obtained for body-centered cubic (bcc) and face-centered cubic (fcc) crystal lattices in one- and two-mode approximations. A universal form of the amplitude equations is obtained for the three-dimensional dynamics for different crystal lattices and crystallographic directions. Dynamics of the amplitude's propagation for different lattices and PFC mode's approximations is qualitatively compared. The traveling-wave velocity is quantitatively compared with data of molecular dynamics simulation previously obtained by Mendelev et al. [Modell. Simul. Mater. Sci. Eng. 18, 074002 (2010)] for solidification and melting of the aluminum fcc lattice.

中文翻译：

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立方晶格凝固和熔化的行波

使用相场晶体模型（PFC模型），分析了凝固和熔融过程中固液界面的慢速和快速动力学。根据密度场的变化幅度描述了侵入亚稳态液体（凝固）和传播到亚稳态晶体（熔融）的立方晶格的动力学机制。以一模和二模近似法获得了以体心立方（bcc）和以面心立方（fcc）晶格的动力学方程。对于不同晶格和晶体学方向的三维动力学，获得了振幅方程的通用形式。定性地比较了不同晶格和PFC模式近似值的幅度传播动力学。等。[ Modell。同谋 母校 科学 。 18，074002（2010）]用于凝固和铝FCC晶格的融化。