General symmetry properties of incommensurately modulated crystals described by projective representations of line groups

Abstract

After a detailed investigation of some fundamental general orthogonal symmetry properties of incommensurate condensed systems, the line groups are applied for describing the structure of such modulated crystals. It is demonstrated, that use of projective representations of these groups may give a more refined description of such structures and significantly extends applicability of the diffuse scattering formalism.