Group representation of bicrystal invariant translations with an application to the topology of secondary grain boundary dislocations

Abstract

All DSC-Lattice translations of one lattice with respect to the second lattice of a bicrystal are described as a group. It is shown that the matrix representation of this group can be used to solve topological problems connected with secondary grain boundary dislocations (SGBDs) such as finding the step in the boundary associated with the SGBD. We have formulated this problem by establishing the step vector S associated with the Burgers vector b of the SGBD in a cubic bicrystal. The problem is then solved in 2D, and the way to generalize to 3D is indicated.