A knowledge of grain boundaries (GBs) and interfaces is essential in establishing the relationship between the structural details of the boundaries and the strength of superconducting coupling and critical current densities at the boundaries in textured Bi cuprates. As a step towards such understanding, we studied GB crystallography and lattice mismatch using the constrained Coincidence-Site-Lattice (cCSL) theory. We note that to characterize arbitrary GBs in a complex system such as Bi2212, it would be desirable to find some simple analytical solutions for the cCSL approach.
We report our new concept of a “two-mirrors” model (2M-model), which allow us, in principle, to find sufficient conditions to generate corresponding analytical solutions for CSL (or cCSL), when it is applied to crystals with cubic, hexagonal, or orthorhombic symmetry. The 2M-model is based on the fact that any boundary can be described by rotating one crystal relative to the other along a common axis.