Atoms, Defects and the Kinetics of Phase Transformations

California Institute Of Technology, Pasadena CA

Investigators

Abstract

A fundamental understanding of the kinetics of phase boundaries, and more broadly hysteresis, remains an open challenge in the study of active materials. The lack of kinetic information is a consistent difficulty in various problems including dislocation mechanics and growth of thin films. The research in the current award, though focussed on active materials, will impact these areas. There is now an accepted framework to model this based on the notion of kinetic relations, but it is phenomenological in that it does not address why some phase boundaries are more mobile than others and how one can change the mobility. This project examines through computation and rigorous mathematics whether one can derive a kinetic relation starting from a more fundamental or smaller scale description of materials in the context of displacive phase transformations. Two scales are of particular interest, atoms and defects. First, the project seeks to understand the atomic-continuum linkage by starting from an atomistic (discrete) model capable of phase transformations and passing to the continuum in such a manner that captures the essential dynamics of the phase transformation process. Second, the project seeks to understand the role of defects such as vacancies, impurities and second phase precipitates in determining the overall propagation of a phase boundary. This leads to the mathematical problem of homogenization of a non-local free boundary problem. Active materials like shape-memory materials and ferroelectric materials possess unusual but useful properties that make them vital for a variety of applications like dental braces, cardiac stents, space antennas, ultrasonic devices, pressure sensors and microactuators. The unusual properties arise from very characteristic and intricate patterns that these materials can form at a microscopic scale. Over the last decade, much advance has been made in understanding the nature of the microstructure, its relation to basic crystallography and its consequences for material properties. In particular, a sophisticated mathematical theory for static microstructures has emerged, and this theory has had important practical impact by predicting and explaining new phenomena and applications. However, much remains unknown regarding how the microstructure changes as we apply stress to these materials. This is important since it determines an important property of these materials known as hysteresis or shape memory. Work supported by this award will build a mathematical theory of the evolution of microstructure. It will also train graduate and undergraduate students in research in the emerging and important area of multiscale modeling.