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.

GRAPHICAL ABSTRACT

IMPACT STATEMENT

Quantitative measures on how commensurate a 2D unit cell is with a rectangular, square, or hexagonal lattice are proposed together with procedures to make an almost rectangular, square, or hexagonal supercell of an arbitrary crystal.

KEYWORDS:

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

Acknowledgements

The VESTA code [38] was used to draw Figures 2 and 4–7.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was funded by Kakenhi Grant-in-Aid for Transformative Research Areas(B)[No. 21H05101] from the Japan Society for the Promotion of Science (JSPS).