Peter Voorhees: Interfacial Evolution in Materials

Central to predicting a broad array of materials properties is the need to know the morphology and spatial distribution of interfaces in a material. These interfaces could be between grains, crystallographic variants of a given phase, or between two phases. A promising approach to predicting the morphology of interfaces for a given processing pathway is the phase field method. In this approach interfaces are modeled as continuous transition regions and thus the boundary conditions that are normally placed at the interfaces in the traditional approach are embedded in the defining partial differential equation. Thus, phase field equations hold throughout the entire domain, thus obviating the need to explicitly track the location of the boundary. A further advantage of phase field methods is the ability to include a very wide range of driving forces for interface motion, from magnetic to electrical and chemical and that they allow for topological transitions. Finally, the flexibility of the method enables experimentally measured complex three-dimensional structures to be used as initial conditions in a phase field code. If the morphology of the interfaces is measured using a non-destructive technique, such as X-ray tomography, then it is possible to compare the detailed morphology predicted by simulation and that measured experimentally at a later time. The phase field equations will be developed, and the connection with experiment will be emphasized. Finally, a discussion of the phase field crystal method, a phase field method that models the atomic evolution of materials on diffusive time scales, will be given.