A layered material with approximate composition PbNbS₃ was found to have a very similar X-ray-diffraction pattern to that of Sn_1.17NbS_3.17. Single-crystal studies revealed that the PbS portion could be described with cell parameters of a = 5.834 Å, b = 5.801 Å, c = 11.90 Å and the NbS₂ part with cell parameters of a = 3.313 Å, b = 5.801 Å, c = 2 × 11.90 Å.

(a) Give a brief description of the likely structure of "PbNbS3". (b) State how large the a axis would need to be to describe this structure using a conventional crystallographic unit cell. (c) From the cell parameters given, calculate the true compos- ition of "PbNbS3". (d) Suggest why the caxi of the NbS part of the structure is double that of the PbS part. (e) Suggest a likely structure for a material of composition Pb1.14Nb2S5.14.