Deformation of internal boundaries

A geometrical analysis of the deformation of internal boundaries is presented using the slip systems as reference co-ordinate axes to describe the orientation of the two phases adjacent to the boundary. The present analysis can be applied to any type of boundary such as a grain boundary, a twin boundary or a two-phase interface. The nature of the disturbance left by a dislocation cutting through the boundary is characterized by a boundary dislocation, the Burgers vector of which can be determined from the orientation relationship between the adjacent slip systems. Whenever the crystal dislocation, cutting through the boundary, has a Burgers vector component normal to the boundary, the disturbance also possesses a ledge character, the motion of which may cause both grain boundary sliding as well as migration. The formulae derived are applied to simple cases to determine the nature of the boundary dislocations.