Two-dimensionally modulated structure of the rare-earth polysulfide GdS(2-x) (x = 0.18 approximately equal to 13/72)

The crystal structure of GdS(2-x) is determined by single-crystal X-ray diffraction as a 144-fold superstructure of the ZrSSi structure type. The superstructure is described as a two-dimensional, commensurately modulated structure with the superspace group P4/n(alphabeta 1/2)(00)(ss) and with alpha = 1/4 and beta = 1/3. Structure refinements within the classical approach, employing the 144-fold supercell, fail because most of the superlattice reflections have zero intensities within the experimental resolution. Within the superspace approach the absent superlattice reflections are systematically classified as higher-order satellite reflections. Accordingly, the superspace approach has been used to refine the structure model comprising the basic structure positions and the amplitudes of the modulation functions of the three crystallographically independent atoms. The quality of fit to the diffraction data and the values of the refined parameters are independent of the assumption on the true symmetry (incommensurate or a 12 x 12 x 2, I-centred superlattice with different symmetries). Arguments of structural plausibility then suggest that the true structure is a superstructure with space group I4, corresponding to sections of superspace given by (t1, t2) equal to [(4n - 1)/48, (4m - 3)/48] or [(4n - 3)/48, (4m - 1)/48] (n and m are integers). Analysis of the structure, employing both superspace techniques (t plots) and the supercell structure model all show that the superstructure corresponds to an ordering of vacancies and an orientational ordering of S2(2-) dimers within the square layers of the S2 atoms.