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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Numerical Analysis Seminars: " Diffusion-induced grain boundary motion: a physical process modelled by three coupled free-boundary problems"

Presented by Oliver Penrose (Heriot-Watt),

10 May 2002 00:00 in CM105

" DIGM occurs when a thin polycrystalline specimen made of one metal (the solvent) is put in the vapour of another metal (the solute). The solute diffuses into the specimen along grain boundaries and sets up elastic stresses which cause the grain boundary to move. The shape of the moving grain boundary is determined by a differential equation which balances this elastic force against the forces due to the curvature of the boundary and the resistance to its motion. Meanwhile, the shapes of the surfaces of the two grains also satisfy differential equations, because solvent atoms diffuse along the surface and their chemical potential depends on its curvature. The DE's for the grain boundary and the two grain surfaces are coupled by conditions at the triple junction where they meet. I will show some cases where the resulting mathematical problem can be solved to determine such things as the speed of a steadily moving grain boundary."

Contact David.Bourne@durham.ac.uk for more information