Dr. Vanessa Styles
Mathematical Models for Diffusion Induced Grain Boundary
Department of Mathematics
University of Sussex, Brighton, UK
We consider the numerical approximation of models
concerning the motion of grain boundaries in thin metallic films.
The grain boundary is forced to move by the diffusion, into the
thin film through the grain boundary, of atoms from an external metallic
We consider a phase field approach and a sharp interface approach. The basic phase field model consists of a double obstacle Allen Cahn equation with a forcing obtained from the solution of a degenerate diffusion equation. On the other hand the sharp interface model consists of forced mean curvature flow coupled to a diffusion equation holding on the interface itself.
A finite element approximation of the phase field model is presented and is shown to be convergent to a weak solution.
We also introduce a multi-order parameter phase field system and a sharp interface model to describe bi-directional diffusion induced grain boundary motion in the presence of triple junctions.
We present some numerical simulations that display double seam configurations typical of experimental observations.
Date: June 7, 2005; 14:50
Place: Wil C307 (TU-Dresden)