A phase-field crystal model (PFC model) which takes into account exponential relaxation of the atomic flux and its fluctuations is developed. The model corresponds to a system undergoing phase transformation described with a partial differential equation of hyperbolic type. Such a model covers slow and rapid regimes of interface propagation at small and large driving forces during melting and solidification. The analysis is done for the evolution of atomic crystal lattices appearing from a metastable homogeneous liquid for the chemically pure system supercooled below its critical temperature. Numerical simulation of the system “Liquid - Body Centered Cubic (BCC) crystal lattice” allows us to formulate the hypothesis about the formation of metastable periodic solutions (atomic configurations which are not in the thermodynamic equilibrium) during the relaxation of atomic configurations to the stable equilibrium. These metastable states may be destroyed (or even avoided) due to the action of colored noise. Namely, considering spatiotemporal correlations of the atomic flux fluctuations, we have found that the temporal correlations promote selecting long-range atomic lattices, whereas the spatial correlations corresponding to the periodic structure scales decelerate such processes.

中文翻译：

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相场晶体模型中结构形成的相关噪声影响

开发了一种考虑原子通量及其波动的指数弛豫的相场晶体模型（PFC 模型）。该模型对应于用双曲线型偏微分方程描述的相变系统。这样的模型涵盖了熔化和凝固过程中在大小驱动力下界面传播的缓慢和快速状态。该分析是针对化学纯系统在其临界温度以下过冷时从亚稳态均质液体中出现的原子晶格的演变而完成的。系统“液-体中心立方 (BCC) 晶格”的数值模拟使我们能够制定关于在原子配置松弛到稳定期间形成亚稳态周期解（不在热力学平衡中的原子配置）的假设平衡。由于有色噪声的作用，这些亚稳态可能会被破坏（甚至避免）。也就是说，考虑到原子通量波动的时空相关性，我们发现时间相关性促进了选择长程原子晶格，而与周期结构尺度相对应的空间相关性则减缓了这种过程。