Mathematical Sciences: Presidential Young Investigator Award

本项目的研究内容是对大型高质量晶体生产过程中由热应力、机械应力和熔体重量引起的与生长有关的缺陷进行建模和分析。其目的是描述决定晶体结构和组成的热、溶质和熔体传输的科学现象，并阐明这些传输机制的耦合动力学。这项研究的结果将有助于材料加工技术的设计，通过确定最佳的温度分布和冻结速度来控制凝固界面，并将晶体中的热应力降至最低。将实施渐近/数值耦合方法，以利用与这些问题相关的长度和时间尺度上的差异。方法是将控制方程简化为一个系统，该系统更易于分析，但保留了过程的大部分物理特性。更简单的系统可以是描述自由凝固界面形状的单个演化方程，或者是一组耦合的场以及对任何可变形界面的一致描述。要达到生长晶体的特定标准，将需要一个系统参数解流形的位置，从而产生最佳的生长条件。这些分析技术将被开发用于定向凝固、浮区、晶片和纤维生长系统。

The research in this project is concerned with the modeling and analysis of growth-related defects induced by thermal and mechanical stresses and melt weight in the production of large high quality crystals. The goals are to describe the scientific phenomena of heat, solute, and melt transport determining the crystal structure and composition, and to elucidate the coupled dynamics of these transport mechanisms. The results of this study will aid the design of material processing technique by defining optimal temperature profiles and freezing rates to gain control over the solidifying interface and to minimize thermal stresses in the crystal. Coupled asymptotic/numerical methods will be implemented to take advantage of the disparity in length and time scales associated with these problems. The approach is to reduce the governing equations to a system which is simpler for analysis, but which retains much of the physics of the process. The simpler system may be a single evolution equation describing the shape of free solidifying interface, or a coupled set of fields together with a consistent description of any deformable interfaces. The achievement of specified criteria for the grown crystal will require the location of a system parameter solution manifold yielding the optimal growth conditions. These techniques of analysis will be developed for directional solidification, float-zone, crystal sheet, and fiber growth systems.