Systematic derivation of maximally orthogonalized supercells

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