Collaborative Research: Morphological Evolution in Materials

合作研究：材料的形态演化

• 批准号: 0511411
• 负责人: Xiaofan Li
• 金额: $ 12.19万
• 依托单位: Illinois Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0511411&HistoricalAwards=false
• 关键词: Collaborative; Research; Morphological; Evolution; Materials

The shapes of interfaces between phases at the microscopic level are of critical importance in predicting macroscopic material characteristics such as strength and electronic properties. Thus, understanding the evolution of microstructures in solids is a fundamental problem in materials science. Simulations in the presence of numerous evolving interfaces pose mathematical and computational challenges, especially in three dimensions. This interdisciplinary research and training program focuses on developing mathematical models and computational techniques to overcome the challenges of computationally studying surface defects in solids and coarsening in solid-solid and solid-liquid systems. The mathematical impacts of the study will include accurate and fast numerical methods for microstructural evolution in three dimensions and for evolution of defects on solid surfaces, using boundary integral methods and incorporating both diffusional and elastic effects. These techniques will be applied to (1) investigate coarsening in solid-solid and solid-liquid systems by performing two- and three-dimensional simulations, and (2) examine step flows (motion of atomic-height steps) on solid surfaces in three dimensions. These investigations will provide insights into materials issues encountered in high-temperature alloys and semiconductor thin film growth. Close collaborations with experimentalists will allow comparisons of the simulation and experimental results. The equations governing the proposed material systems are closely related to a host of mathematical descriptions for pattern formation in moving boundary problems. Therefore, the proposed modeling and computational techniques will have broad applications and will provide new tools for other research areas. Importantly, the proposed program will provide excellent training opportunities for graduate students interested in research at the interface of mathematics, computation, and engineering.

微观水平的相之间界面的形状对于预测宏观材料特征（例如强度和电子特性）至关重要。 因此，了解固体中微观结构的演变是材料科学中的一个基本问题。 在存在众多不断发展的界面的情况下，模拟构成了数学和计算挑战，尤其是在三个维度上。 该跨学科研究和培训计划着重于开发数学模型和计算技术，以克服计算研究固体中固体表面缺陷的挑战，并在固体固体和固体液体系统中凝结。 该研究的数学影响将包括三个维度的微观结构演化的准确而快速的数值方法，并使用边界积分方法以及融合了扩散和弹性效应。 这些技术将应用于（1）通过进行两维模拟和（2）在三个维度上在固体表面上检查阶段流（原子高步骤的运动），调查固体和固液系统中的变厚。 这些研究将提供对高温合金和半导体薄膜生长中遇到的材料问题的见解。 与实验者的密切合作将允许比较模拟和实验结果。 管理提出的材料系统的方程与移动边界问题中的模式形成的数学描述密切相关。 因此，拟议的建模和计算技术将具有广泛的应用程序，并将为其他研究领域提供新的工具。 重要的是，拟议的计划将为对数学，计算和工程界面的研究感兴趣的研究生提供极好的培训机会。