Studies of the crystallography of arbitrary grain boundaries by O-lattice construction: Application to bulk YBa₂Cu₃O_7-δ

Abstract

We report our procedure for analysing the crystallography of arbitrary grain boundaries (arbitrary relative orientation with an arbitrary path of the interface between adjacent crystals). The approach is based on constructions of the O-lattice and b-net to derive the possible Burgers vector of arrays of grain-boundary dislocations for any given geometry of the grain boundary (boundary misorientation and boundary plane normal) using Bollmann's O-lattice theory. The configurations of the boundary dislocations associated with these Burgers vectors are then refined by taking the dislocation reaction into account, and comparing them with the experimentally determined Burgers vectors, line directions and line spacings of the dislocations using a modified Frank dislocation model. We applied our procedure to analyse the grain boundary in orthorhombic YBa₂Cu₃O_7-δ superconducting oxides. Our results suggest that the methodology is valuable in determining the structure of arbitrary grain boundaries and is valid even in low-symmetry crystals.