Family structure

By superposing two or more identical copies of the same polytype translated by a superposition vector (i.e. a vector corresponding to a submultiple of a translation period) a fictitious structure is obtained, which is termed a superposition structure. Among the infinitely possible superposition structures, that structure having all the possible positions of each OD layers is termed a family structure: it exists only if the shifts between adjacent layers are rational, i.e. if they correspond to a submultiple of lattice translations.

The family structure is common to all polytypes of the same family. From a group-theoretical viewpoint, building the family structure corresponds to transforming (“completing”) all the local symmetry operations of a space groupoid into the global symmetry operations of a space-group.

See also

Chapter 9.2 of International Tables of Crystallography, Volume C