Systematic derivation of maximally orthogonalized supercells

Abstract

Generation of supercells with a desirable size and reasonable geometry, such as basis vectors with a similar length and are close to orthogonality, is useful for defect calculations and dilute alloy calculations. Identification of relations between basis vectors of similar crystals described using very different lattice parameters is beneficial in crystal structure analysis. A computational algorithm, applicable to any crystal, is described, which finds supercells with a certain size N and maximally and almost maximally orthogonalized basis vectors. The number of maximally orthogonalized supercells, as well as the computational cost, scales as roughly O(N2). The algorithm is demonstrated to obtain supercells of bcc, fcc, and sc lattices that have basis vectors with the same lengths and are exactly or close to orthogonality and also supercells of an ideal hcp lattice that have an identical basis vector length or orthogonality. The algorithm is also applied to convert different basis vector choices in energy application-related materials Ag3Sc2(PO4)3, LiCoO2, and Li2MnO3.

Keywords

• supercell
• maximally orthogonalized
• basis vectors
• algorithm