Boundary plane-oriented grain boundary model generation

This study proposes algorithms for building tilt grain boundary (GB) models with a boundary plane-oriented approach that does not rely on existence of a coincidence site lattice (CSL). As conventional GB model generation uses the CSL of superimposed grains as the starting point, our totally different approach allows systematic treatment of diverse grain boundary systems that was previously not possible. Candidates of a pair of GB planes for a selected rotation axis, constituting a symmetrical or asymmetrical tilt GB, are thoroughly obtained by computational search that is applicable to any crystal structure. A GB interface for feasible computational analysis would have two-dimensional (2D) periodicity shared by the 2D lattices of the two GB planes, hence surface-slab supercells (slab-and-vacuum models) with common in-plane basis vectors of the shared 2D lattice are obtained. Finally, a procedure to obtain a GB-model supercell with alternately stacking such slabs is given. Symmetry operations of each slab may be considered such that the iterated interfaces are symmetrically equivalent, which is beneficial in ab initio calculations. The proposed algorithms allow streamlined generation of GB models, both symmetric and asymmetric, with or without an exact 3D-CSL relation.