Collaborative Research: Towards a Predictive Theory of Microstructure Evolution in Polycrystalline Materials

大多数技术上有用的材料--从米到纳米，从飞机到微处理器--都是多晶体材料。晶体是原子有序排列的材料。多晶微结构是由由晶界/界面隔开的无数小的单晶胞/晶组成。晶界在很大范围内决定材料的性质方面起着至关重要的作用。这些性能包括机械强度和延展性、电阻率、磁性硬度等；它们强烈影响工程系统中材料的性能。多晶体工程中的一个重大挑战是开发出规范的制造工艺技术，能够产生一系列能够产生所需材料性能的颗粒排列。设计颗粒结构的一种方法是开始结构的颗粒生长或粗化。这个项目的目的是通过实验、模拟和数学模型的紧密结合来开发一种预测晶体生长的理论。该项目将涉及跨学科研究，并将通过开发新的、预测性和规范性的实验、分析和计算工具来加强工程材料和系统的基础设施，这些工具将有助于设计具有可预测特性的材料微结构。拟议计划中出现的新知识和新工具将对工程系统中使用的多晶材料的性能和可靠性产生影响。该项目还将通过对拟议研究中的研究生和本科生进行培训和教育，直接影响劳动力发展。此外，研究人员还将参与外展活动，包括培训STEM中未被充分代表的群体。颗粒生长可以被视为大型亚稳态网络的演化，并且可以通过一组关于单个颗粒生长的确定性局部演化规律来数学建模，并结合描述它们之间相互作用的随机模型。因此，为了发展一种预测理论，将使用实验、模拟和数学模型来研究晶粒生长过程中微观组织演变的广泛的统计测量方法。这项工作的主要目标将是确定/导出可能的随机过程，这些过程推动各种统计指标的演变，了解它们之间可能的联系，并建立与材料属性的联系。作为该项目的一部分，数学分析、偏微分方程、统计学、科学计算、数值分析和高性能计算的工具将与实验数据和实验紧密结合。通过集成的协同方法将实验、数值模拟和数学模型融合在一起是拟议计划的标志，这对于改进现有的颗粒生长模型和指导新实验的设计是必不可少的。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Most technologically useful materials - spanning the length scale from meters to nanometers, from aircraft to microprocessors - are polycrystalline. Crystals are materials with ordered arrangements of atoms. Polycrystalline microstructures are composed of a myriad of small monocrystalline cells/grains separated by grain boundaries/interfaces. Grain boundaries play a crucial role in determining the properties of materials across a wide range of scales. These properties include mechanical strength and ductility, electrical resistivity, magnetic hardness, etc.; they strongly impact the performance of materials in engineered systems. A grand challenge problem in the engineering of polycrystals is to develop prescriptive manufacturing process technologies capable of producing an arrangement of grains that yields a desired set of materials properties. One method by which the grain structure is engineered is grain growth or coarsening of a starting structure. This project is aimed at developing a predictive theory of grain growth through close integration of experiments, simulations, and mathematical models. The project will involve interdisciplinary research and will enhance the infrastructure of engineered materials and systems through the development of new, predictive and prescriptive experimental, analytical and computational tools that will help in the design of material microstructures with predictable properties. The new knowledge and tools that will emerge from the proposed program will have an impact on the performance and reliability of polycrystalline materials used in engineered systems. This project will also directly impact workforce development through training and education of graduate and undergraduate students in the proposed research. In addition, the investigators will engage in outreach activities that include training of underrepresented groups in STEM.Grain growth can be viewed as the evolution of a large metastable network, and can be mathematically modeled by a set of deterministic local evolution laws for the growth of an individual grain combined with stochastic models to describe the interaction between them. Hence, to develop a predictive theory, a broad range of statistical measures for microstructure evolution during grain growth will be investigated using experiments, simulation, and mathematical modeling. The main goal of this effort will be to identify/derive possible stochastic processes that drive the evolution of various statistical measures, understand possible links between them, and establish connections to materials properties. As a part of the project, tools from mathematical analysis, partial differential equations, statistics, scientific computing, numerical analysis and high-performance computing will be closely integrated with experimental data and experiments. The convergence of experiments, numerical simulation and mathematical modeling through an integrated synergistic approach is the hallmark of the proposed program, and it is essential in order to improve upon existing models of grain growth and guide the design of new experiments.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.