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 the 1958 analysis by Mullins, where the groove root and the velocity as a function of groove depth were determined. 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 may 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