通过相场晶体模型振幅展开进行晶体粗粒化建模：综述
Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
AI总结：
本文综述PFC模型的复振幅展开，介绍其推导、连续介质联系、数值方法、应用扩展及局限前景。
摘要：
对晶体系统的全面研究通常需要连接原子尺度与连续介质尺度的方法。在此背景下，粗粒化介观尺度方法尤其受到关注，因为它们允许考察大系统和长时间尺度，同时保留部分微观细节。所谓的相场晶体（Phase-Field Crystal，PFC）模型通过一个在原子尺度上变化并与原子数密度相关的连续周期场，方便地在扩散时间尺度上描述晶体。为了超越PFC模型受限制的原子长度尺度，Goldenfeld等人首先发展了复振幅表述[Phys. Rev. E 72, 020601 (2005)]。该方法聚焦于大于晶格参数的长度尺度，同时能够描述晶体缺陷、界面和晶格变形。它已被用于考察许多现象，包括液/固前沿、晶界能和应变薄膜。本专题综述聚焦于PFC模型的这种振幅展开及其发展。文中概述了其推导、与连续介质极限的联系、代表性应用和扩展，还说明了若干实际方面，例如合适的数值方法和示例。最后，讨论了该模型的能力与界限、当前挑战以及未来前景。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
