Stability of grain-boundary motion in the presence of impurities

The impurity-drag effect in grain-boundary motion has been examined by Cahn who considered the one-dimensional uniform motion of a single planar grain boundary through a dilute atmosphere of impurity atoms. Later Roy and Bauer proposed a two-dimensional model which, allowing deformations of the grain boundary and lateral diffusion of the impurity atoms, gives rise to a morphological instability of the grain boundary. In the present note we point out a serious deficiency of this approach and, after correction, find a significantly different stability behavior.