THE APPLICATION OF THE SUPERSPACE GROUP ON THE VERNIER STRUCTURES

The nonstoichiometric compound Ba1+xFe2S4(0.062≤x≤0.143) and the rare earth-transition rnetal tetraborides R1+εFe4B4(ε≈ 0.1, R = Ce, Pr, Nd, Sm, Gd, Tb), both composed of two interpenetrating substructures, are examples of the vernier structures. In present paper, the symmetry of the crystal structure in these two systems is characterized by the superspace group approach developed by de Wolff et al. The superspace group for Ba1+xFe2S4 compound is P1IssI4/mmm and the one for all R1+εFe4B4 compounds is P1Iss(P42/ncm). The diffraction selection rules in the commensurate models for the vernier structures, those often occur and are not related to the systematic absences of the three-dimensional space groups, are explained according to the results of the systematic absences discussed in the superspace. Such diffraction selection rules are very useful to predict where the measurable intensities can be found in the case of crystal structure analysis for the vernier structures.