Finding alike supercells of two crystals

Abstract

An algorithm is proposed that finds supercells of two arbitrary crystals that are ‘alike’, or in other words, have almost the same lattice parameters. The given input is the primitive cells of two crystals, crystal 1 and 2, and their supercell sizes, N and N’, respectively, and the output is transformation matrices to (almost) maximally orthogonalized alike supercells. The algorithm was applied to comparison of prototypical sc, bcc, fcc, and hcp crystals, as well as perovskite crystals. The proposed algorithm can be used to identify orientational relationships between crystals and, in addition, provide relationships on all basis vectors. Further applications of the algorithm include the conversion of basis vectors between closely related crystals with very different choices of basis vectors and grain boundary model generation using an approximate coincidence site lattice.

Keywords

• alike supercells
• maximally orthogonalized supercell
• orientational relationship
• grain boundary
• coincidence site lattice