This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The investigator and colleagues study the prediction and morphological control of two-phase microstructures in solid/liquid and solid/solid diffusional phase transitions. Much of the research in this area is concerned with detailed and extensive studies of complex patterns such as dendritic growing shapes. In many applications (e.g. castings), it is desirable to control the formation of dendrites and grow compact shapes, which, however, has been much less studied. This project helps to fill the gap and aims to develop guidelines by which microstructures with desired shapes may be grown. The research team plans to (1) develop a suitable nonlinear theory of compact precipitate growth including existence, uniqueness, and stability of self-similar shapes; (2) develop and employ state-of-the-art adaptive 3D numerical methods to test the validity and limitations of theory; (3) compare theoretical and numerical results with existing experiments to test the validity of the mathematical assumptions and to verify the accuracy of predictions derived from the theory and simulations.
Diffusional phase transformations deal with transformations of melts into precipitates (and vice-versa) as well as the separation of solids (e.g. metal alloys) into distinct phases. These phenomena have importance for a variety of processes including casting, welding and soldering, crystal growth, and related problems concerning protein and macromolecular crystallization. For example, crystal growth processes for technological applications began in the late 19th century, and form the cornerstone of virtually all modern semiconductor electronics and photonics today. The research activities will provide new mathematical theory and numerical simulations that can be used to develop guidelines for controlling the morphology of certain solidified materials. The new mathematical theory and adaptive numerical methods developed in the project have applications to a broader set of related problems including multiphase flows, biostructures and growth of solid tumors. In addition, this project will provide valuable interdisciplinary training opportunities for young researchers.
