Numerical simulation of grain-boundary grooving by surface diffusion

A numerical investigation of grain-boundary grooving by surface diffusion has been carried out. The surface diffusion is driven by surface curvature gradients, and a fixed dihedral angle is assumed at the groove tip. The corresponding mathematical system is an initial boundary value problem in a one-dimensional nonlinear partial differential equation. The numerical results show excellent agreement with Mullins' analytical ″small slope″ (i.e. dihedral angle close to 180° ) solution of the linearized mathematical system. Our simulation extends Mullins' solution, since it is applicable to larger groove widths and a complete range of dihedral angles. As an example, we apply our technique to two adjacent grooves. The evolution of the surface profile shows clearly that the two grooves grow initially independently, while they interact at a later stage, resulting in changes in their growth kinetics.