Continuous distribution of dislocations in intercrystalline boundaries

The structure of a dislocation network in a crystal boundary depends, among other parameters, on the two crystal structures and their relation, i.e. the linear transformation leading from one crystal lattice to the other. For the same transformation, the structure of the network is related to the crystal structure. The link between the transformation and the many possible dislocation networks is described by a theorem which states that the displacement field of the linear transformation in the boundary can be described in an infinite number of ways by continuous dislocation distributions. The discrete dislocations are then obtained by grouping the continuous dislocations. The O-lattice theory is discussed in relation to these new aspects, particularly with respect to the features which tend to be conserved in the boundary. A special discussion is given of the case where a common crystallographic axis, without the relaxation pattern being periodic, represents the preferred state.