Incommensurate phases

Incommensurately modulated crystalline phases are part of a more general family called aperiodic crystals. Their symmetry is treated within the theoretical framework of superspace groups that is a generalization of the 3D space groups that are used for conventional crystalline structures. Aperiodic structures are conveniently embedded in superspace with dimensions varying from (3+1) to (3+3)D. They do occur in all types of material, organic and inorganic, metal and alloys, minerals and macromolecules under various pressure and temperature. Some examples of incommensurate structures are presented along with their chemical and physical properties.