Calculation of Interfacial Dislocation Structures: Revisit to the O-lattice Theory

This article clarifies a geometric method for calculating interfacial dislocation structures, to provide virtually unique initial dislocation structures for further relaxation. Ambiguities in specifying the misfit deformation and Burgers vectors are effectively eliminated. The physical basis for the method is a hypothesized periodicity correspondence between the structure within a good matching site (GMS) cluster (GMSC) and the conserved structure between dislocations. It is proposed to attribute each interfacial dislocation with a couple of correlated Burgers vectors. A set of Burgers vectors from each real lattice is identified according to the translation symmetry in a GMSC. A GMSC principle is suggested to guide the formulation of the deformation matrix A. The O-lattice theory is applied to quantify the distribution of GMSCs at the O-elements and poor matching regions at the O-cell walls. Configuration of dislocations in a general semicoherent interface is determined according to the effective O-cell wall traces in the interface. The relationship between GMS/GMSC and coincidence-site-lattice/O-lattice is elucidated for describing secondary dislocations. Several controversial issues on dislocation descriptions are discussed, including the decomposition of a net Burgers vector content, the influence of reference lattice, and the relationship between secondary dislocations and atomic steps.