Family structure

From Online Dictionary of Crystallography

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 layer 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 for Crystallography, Volume C