GENERALIZING THE COINCIDENCE SITE LATTICE MODEL TO NONCUBIC MATERIALS

The CSL model has had enormous success in explaining grain boundary structures in cubic materials with metallic, ionic and co-valent bonding. This inspires great confidence in very simple geometrical ideas, but the application of these ideas is more complicated in non-cubic materials and phase boundaries, where the special conditions necessary for lattice coincidence do not generally exist. It is, however, sometimes possible to form a CSL appropriate to these cases if a small strain is applied to the crystal lattice. In such cases we are concerned with a Constrained Coincidence Site Lattice, or CCSL rather than a CSL. In this paper we discuss the development of methods of finding appropriate CCSLs, and their abundance. We provide the necessary modifications to the O-lattice theory for CCSL boundaries and give examples of its application to hexagonal, tetragonal and orthorhombic materials. Finally, we will demonstrate that many of the ''ancient truths'' about the CSL boundaries fail catastrophically in the realm of constrained coincidence: for example, the boundary energy is no longer a minimum at the exact coincidence orientation; C-values may be odd or even, and do vary systematically with misorientation angle; and the Sigma-values at a triple junction need not obey the ''quotient rule''.