论文标题
通过相田晶体模型的振幅扩展对晶体的粗粒化建模：概述
Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
论文作者
论文摘要
晶体系统的全面研究通常需要桥接原子和连续量表的方法。在这种情况下，粗粒的中尺度方法特别有趣，因为它们允许检查大型系统和时间尺度，同时保留一些微观细节。所谓的相位场晶体（PFC）模型在扩散时间尺度上方便地描述了连续的周期性场，该晶体在原子尺度上变化，并且与原子数密度有关。为了超越PFC模型的限制性原子长度尺度，Goldenfeld等人首先开发了复杂的幅度公式。 [物理。 Rev. E 72，020601（2005）]。尽管专注于大于晶格参数的长度尺度，但这种方法可以描述晶体缺陷，接口和晶格变形。它已被用来检查许多现象，包括液体/固体前沿，晶界能和紧张的膜。这项局部评论重点介绍了PFC模型及其发展的幅度扩展。提出了推导，连续限制，代表性应用程序和扩展的概述。也说明了一些实际方面，例如合适的数值方法和示例。最后，解决了模型，当前挑战和未来观点的功能和界限。
Comprehensive investigations of crystalline systems often require methods bridging atomistic and continuum scales. In this context, coarse-grained mesoscale approaches are of particular interest as they allow the examination of large systems and time scales while retaining some microscopic details. The so-called Phase-Field Crystal (PFC) model conveniently describes crystals at diffusive time scales through a continuous periodic field which varies on atomic scales and is related to the atomic number density. To go beyond the restrictive atomic length scales of the PFC model, a complex amplitude formulation was first developed by Goldenfeld et al. [Phys. Rev. E 72, 020601 (2005)]. While focusing on length scales larger than the lattice parameter, this approach can describe crystalline defects, interfaces, and lattice deformations. It has been used to examine many phenomena including liquid/solid fronts, grain boundary energies, and strained films. This topical review focuses on this amplitude expansion of the PFC model and its developments. An overview of the derivation, connection to the continuum limit, representative applications, and extensions is presented. A few practical aspects, such as suitable numerical methods and examples, are illustrated as well. Finally, the capabilities and bounds of the model, current challenges, and future perspectives are addressed.
