Mathematical Aspects of a Geometrical Theory of Crystalline Interfaces

Abstract

The mathematical aspects of the 0-lattice theory of crystalline interfaces are summarized. This theory gives the geometrical basis for describing grain and phase boundaries between arbitrary crystal structures. The 0-lattice theory is a generalised dislocation theory that produces the necessary dislocation structure for many types of boundaries including subgrain and coincidence boundaries. The essential feature of the theory is the possibility of separating the effects originating from the structures and relative orientation of the two crystals from those due to the location and orientation of the boundary. This is done by constructing a three-dimensional cell structure within the crystal lattices which are considered as interpenetrating. The boundary is then understood as a cut through this cell structure, where the cell structure itself represents the sum of all the possible boundaries for given crystal structures and relative orientation. Thus, this theory provides a way to gain a broad view of boundary problems. CRYSTALLINE INTERFACES; GRAIN BOUNDARIES; COINCIDENCE BOUNDARIES; DISLOCATIONS; 0-LATrICE THEORY