A re-interpretation of the ‘coincidence model’ for grain boundaries

Abstract

A new interpretation of the coincidence model of a grain boundary is proposed. A relative translation (without rotation) of two crystals which have a coincidence orientation relationship can lower the energy and therefore increase the stability of the boundary between them. Hence a coincidence boundary will not contain coincidence sites or shared atom sites, as was assumed by the lattice coincidence and boundary coincidence models in order to explain the different properties of coincidence and non-coincidence boundaries. It is proposed that the physical criterion for the special properties of a coincidence boundary is not coincidence per se; it is the condition for small, periodically repeating units of the structure. In boundaries that correspond exactly to a coincidence orientation all structural units are equal. Departure from the exact coincidence orientation relationship results in appropriate ‘mixing’ of units that correspond to the neighbouring coincidence orientation. The structure of non-symmetrical boundaries is discussed.