Consequences of the monoclinic superspace group description of triclinicNbS3

Type-I ${\mathrm{NbS}}_3$ crystallizes in the triclinic space group P1¯. Alternatively, the structure of ${\mathrm{NbS}}_3$ can be described as a commensurate modulation of the monoclinic ${\mathrm{ZrSe}}_3$-structure type. The symmetry is then given by the monoclinic superspace group $P_{11¯}^{P{2}_1/m}$ (0 β 0), with β=0.5. In this paper the relation between the superspace group and the possible three-dimensional space groups of the superstructure is considered in detail. It is shown that the structure of ${\mathrm{NbS}}_3$, as determined by Rijnsdorp and Jellinek [J. Solid State Chem. 25, 325 (1978)] in P1¯, is in accordance with the additional restrictions imposed by the superspace group. The consequences of the superspace group symmetry for the diffraction pattern are derived. It is shown that the pattern of main reflections exhibits the full symmetry, including systematic absences, of the average structure space group P$2_1$/m, while the satellites reduce the three-dimensional (3D) symmetry to P1¯. Finally, consideration of a property like strain and conductivity shows that such a second rank tensor obeys the monoclinic symmetry restrictions, despite the fact that the true 3D symmetry is only triclinic.