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.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
Standard Grant (Standard)
Application #
Program Officer
Victor Roytburd
Project Start
Project End
Budget Start
Budget End
Support Year
Fiscal Year
Total Cost
Indirect Cost
University of Utah
Salt Lake City
United States
Zip Code