Diffraction enhancement of symmetry and modular structures

Diffraction enhancement of symmetry (DES) is the phenomenon according to which the symmetry of the diffraction pattern of a crystal can be higher than the point symmetry of the structure that has produced it. The most well known example is that of Friedel's law, which is however violated in the presence of resonant scattering. This phenomenon is addressed in monoarchetypal modular structures and it is shown that a sufficient condition for DES is that both the module and the family of stacking vectors are invariant under an isometry that is not a symmetry operation for the structure. In general, DES is still observed in the presence of significant resonant scattering. The example of SiC polytypes, where the phenomenon has been confirmed experimentally, is studied in detail but the conclusions depend only on the symmetry of the layer and on the stacking vectors: the same applies therefore to all compounds sharing these features, like ZnS.