Grain boundaries in materials with a hexagonal, rhombohedral or tetragonal lattice: the connection between different treatments of approximate coincidence

The relative orientation of the lattices of two neighbouring grains of the same phase can be described by a rotation R. It can be decomposed as a product R = R_⊥R_|| of two rotations with axes perpendicular and parallel to a given direction. This direction is chosen parallel to the principal symmetry axis in the case of hexagonal, rhombohedral or tetragonal lattices. The parameter introduced by Bonnet & Durand [Philos. Mag. (1975). 32, 997-1006] to describe the deformation connected with approximate coincidence in such lattices satisfies =Δ sin Φ, where Δ is the relative deviation between the experimental and the coincidence value of the axial ratio c/a and Φ is the angle of R_⊥. Addition of the value of sin Φ to tables of coincidence rotations makes it possible to compute in a simple manner for any experimental value of c/a.