On the diffraction enhancement of symmetry

Diffraction symmetry is in general specified by the point group of a crystal. However, there are some exceptional cases in which the diffraction symmetry becomes, other than as a result of Friedel's law, higher than the point-group symmetry (diffraction enchancement of symmetry). Using a general expression for the square of the structure amplitude, the necessary conditions for the diffraction enhancement have been systematically investigated for the following four kinds of structures: (1) crystals composed of essentially the same substructures, (2) different substructures which have the same symmetry, (3) substructures with the same point group and different space groups, and (4) substructures with isomorphic point groups. It has been shown that symmetry enhancement like 4/m, 4/mmm, m1 (1m), 6/m or 6/mmm does occur in addition to 2/m or mmm as suggested by Sadanaga & Takeda [Acta Cryst. (1968) B24, 144] and by Marumo & Saito [Acta Cryst. (1972) B28, 867].