Group-theoretic method for determining the number of superlattices in alloys of a given composition

The influence of the crystallographic symmetry of the lattice of an alloy on the various configurations of occupation of the sublattices by different species of atoms is investigated with regard for the concentrations of the latter. Two occupation configurations are considered to be equivalent if one can be reduced to the other by a transformation from the Fedorov lattice group. The equivalence classes of occupation configurations correspond to superlattices in the alloy. The machinery of the theory of group representations and the theory of invariants is used to determine the number of superlattices and their geometry.