A study was made of the coupled motion of a grain boundary in a bicrystal which was attached at a groove root to an exterior surface which evolves according to surface diffusion in a quarter-loop geometry, and prove the existence of a unique traveling wave solution for various partially linearized formulations. The results complemented and completed Mullins’ 1958 analysis, in which the groove root and the velocity were determined as a function of the groove depth. It was demonstrated that the net effect of the coupling to the exterior surface was to reduce the overall velocity, relative to a freely moving grain boundary, by a factor which was small (about 3.5%) for typical parameter values. For extreme values of the parameters, the coupling could cause an increase in the overall grain boundary velocity. No jerky or stop-and-go motion was predicted by the present solution.

A Traveling Wave Solution for Coupled Surface and Grain Boundary Motion. J.Kanel, A.Novick-Cohen, A.Vilenkin: Acta Materialia, 2003, 51[7], 1981-9