Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 4 / 57 / b / Solution

Patterson maps give interatomic displacement vectors rather than absolute positions. The three strong half-cell vectors are consistent with a face-centered four-point Se substructure. One permissible coordinate set isEach nonzero vector occurs four times among the twelve ordered Se-Se pairs, explaining equal weights. These positions form a valid four-site orbit of the specified space group in a suitable origin convention.

A common translation of all four sites is invisible to a Patterson map; absolute coordinates are therefore not uniquely fixed by these three peaks. Subsequent phases are stated in the origin convention above. The remaining atoms need not have face-centered translational symmetry merely because the dominant Se substructure does.