Homometric structures in MX₂-type compounds

Representation of close-packed structures by Zhdanov symbols is compact and quite informative, but sometimes quite misleading also. Similar-looking symbols may or may not represent the same structure. Some structures look different but can always be brought to coincide by some symmetry operation like translation, rotation or inversion. Therefore, these are various manifestations of the same structure and will give rise to the same intensities on calculation. But there are certain pairs of structures which although giving rise to the same X-ray diffraction intensities on calculation cannot be brought to coincide by any of these symmetric operations. In the MX₂ type of compound it has been shown theoretically that two homometric structures are those in which X atoms are at the same position but M atoms shift their position in such a way that they occupy the voids of the first structure. Under what conditions the intensities of two structures remain the same (homometric structures) is examined in this paper.