Modulated structures of some group V transition metal compounds

Crystals usually are considered as being built by a three-dimensional periodic array of relatively simple basic units. With the aid of e.g. X-ray diffraction the periodicity of this array and the arrangement of the atoms within the basic unit -the unit cell- can be determined. This is indeed the case for most com¬pounds studied so far;however, also crystals exist with two (or more) periodicities in the same direction of space. Frequently, the shorter of these periodicities is that of a simple "basic" structure, the average structure; the real (modulated) structure is derived from the average one by one (or more) modulation(s) with a longer periodicity. A modulated structure is called commensurate if the two periodicities have rational ratios and incommensurate if this is not the case. In the former case the modulated structure can be regarded as a superstructure and the crystal can be constructed by a three-dimensional array of "supercells". In the lattter case this is not possible, however. For the description of an incommensurate structure the classical space groups are insufficient. Recently, largely due to the work of De Wolff, Janney, and Janssen, the classical theory has been extended to the case of additional periodicities ("superspace groups"). Applications of this new theory in the study of the structures of some sulfides and tellurides of transition metals of group V are reported in this thesis.