Fig. 1

Illustration on a hypothetical disordered 2D crystal of the main concepts and tasks of the supercell algorithm workflow. a Input structure consisting of crystallographic positions and occupation values for each atom type, as typically defined in a cif file. b Crystallographic sites are sorted into groups 1, 2, and 3. c All atom types and corresponding occupancies are then assigned to a group. d \(2\times 2\) supercell made from cell (b). e Atoms (in gray, red, green and blue) and vacancies (treated as special atoms, in white) used for permutations within the groups. f Two examples out of many possible resulting periodic structures with full occupancy (or vacancy) of all sites. Stages I–IV are described in detail in text. Numbers of permutations \(P_i\) were calculated with formula (1)