Multi-scale modeling of solidification phenomena using the phase-field crystal methodology:

提出的研究将探索和发展一类新的连续介质模型——被称为“相场晶体模型”——用于多组分合金凝固现象的定量建模。这些模型的独特优势是，它们在空间上是原子解析的，但在比当前分子动力学长许多数量级的时间尺度上运行。一方面，它们通过与经典密度泛函理论的联系，与物质的原子尺度性质有着密切的联系。另一方面，它们的动力学在时间上是细粒度的，这使得在控制相变动力学的相同[扩散]时间尺度上模拟弹塑性，晶界相互作用和拓扑缺陷的许多方面成为可能。这项工作将从推导一套多组分合金的相场晶体模型开始，这些模型与从分子动力学和分析方法计算的直接相关函数相关联。这些模型将被用于研究热力学、晶体缺陷和弹性在材料科学中涉及纳米微观结构演变的几个重要应用中的相互作用，这些应用通常是传统相场理论和分子动力学所无法达到的。此外，所提出的研究将扩展和进一步发展数学和数值方法，以使新的合金相场晶体模型具有更高的长度尺度。这将具有指导形成用于更高尺度的改进（即定量）传统相场模型的优势。该研究将为两名研究生提供高水平的材料科学与工程方面的科学和应用培训。

The proposed research will explore and develop a new class of continuum models --coined "phase-field-crystal models"-- for quantitative modeling of solidification phenomena in multi-component alloys. The unique advantage of these models is that they are atomically resolved in space but operate on time scales many orders of magnitudes longer than current molecular dynamics. They contain, on the one hand, an intimate connection to atomic-scale properties of matter, through their connection with classical density functional theory. On the other hand, their dynamics is course-grained in time, which makes it possible to simulate many aspects of elasto-plasticity, grain boundary interactions and topological defects on the same [diffusive] time scales that govern phase transformation kinetics. This work will begin by deriving a suite of phase-field-crystal models for multi-component alloys that are linked to direct correlations functions computed from molecular dynamics and analytical methods. These models will be used, in their own right to study the interplay of thermodynamics, crystal defects and elasticity on several important applications involving nano-microstructure evolution in materials science, which have been typically inaccessible to traditional phase field theory and molecular dynamics. In addition, the proposed research will extend and further develop mathematical and numerical methods to course-grain the new alloy phase-field-crystal models to higher length scales. This will have the advantage of guiding the formation of improved (i.e. quantitative) traditional phase field models for use on higher scales. The research will provide a high level of scientific and applied training in materials science and engineering for two graduate students.