It was recalled that this model had been enormously successful in explaining grain boundary structures in cubic materials with metallic, ionic and covalent bonding. However, the application of these very simple geometrical ideas was more complicated in non-cubic materials and phase boundaries, where the special conditions which were necessary for lattice coincidence did not usually exist. Nevertheless, it was sometimes possible to form a coincidence site lattice which was appropriate to these cases if a small strain was applied to the crystal lattice. In such cases, it was required to consider a so-called constrained coincidence site lattice. The present work was concerned with the development of methods for finding appropriate constrained coincidence site lattices. The necessary modifications which had to be made to the O-lattice theory in order to obtain constrained coincidence site lattice boundaries were described, and examples were given of their application to hexagonal, tetragonal and orthorhombic materials. It was demonstrated that many of the accepted truths concerning coincidence site lattice boundaries failed catastrophically in the case of constrained coincidence. For example, the boundary energy was no longer a minimum at the exact coincidence orientation, -values could be odd or even and varied systematically with misorientation angle, and the -values at a triple junction did not have to obey the quotient rule.

A.H.King, A.Singh: Journal of the Physics and Chemistry of Solids, 1994, 55[10], 1023-33