Generation of almost rectangular, square, and hexagonal two-dimensional supercells

Abstract

This study outlines procedures to make 2D supercells, of arbitrary crystals and orientations, with a given size and are almost commensurate with rectanglar, square, or hexagonal lattices. Quantitative measures on the commensurateness, or alikeness, are proposed. The outlined algorithms would be useful in defect calculations, including desorption and absorption, and generation of approximate 2D coincidence site lattices for epitaxial interface models with small lattice mismatch.

Keywords

• 2D supercell
• almost rectangular
• almost square
• almost hexagonal
• basis vectors
• algorithm