Overall Conclusions

As recommended, PC version of Rietica was used for refinements in the project. The program proved to be easy for use, but a couple of tricks supplied in CCP14 web site tutorial page were also very helpful for a quick start.

Refinement of the structure known from a 300K refinement with the group Pbnm gave a very good visual as well as numerical fit (R_wp=5.304) in the lower angle area. But, the same results applied to the whole range of data proved to be poor. Visual inspection of the fit in the higher angle area indicated that, before any other continuation, one would have to improve peakshape and halfwidth parameters, using the whole range of data.

Only after that became clear that the group Pbnm probably was not the right one (high final R-factor value: R_wp=14.061), and that a not included break in symmetry through a distortion of the unit cell (leading to the loss of the mirror plane) could be the reason for relatively poor fit with the high-symmetry group. Two lower-symmetry groups were then taken into refinement, and the best results were obtained with P2₁/n. This points out that the assumption that during the cooling from room temperature to 5K the sample underwent a phase transition was correct. Also, the assumption that the distortion of the unit cell was small proved to be correct (90 degrees to 89.76 degrees). This is also visible in comparison of final x and y coordinates of O3 and O4 atoms - they are almost the same - which "were" symmetricaly equivalent in the orthorhombic group.

The reasonable chemical data (bond lengths and angles) and the fact that instrumental parameters obtained in the output of the last refinement differ not much from those given as approximate values in the Instructions, are another proof of correctness of the refinement and starting assumptions.

A closer inspection of the fit obtained with this group and the difference profile reveals that an improvement of the background in 60 degrees to 90 degrees range still may be profitable. Namely, in this area all the differences tend to be positive, in comparison to the rest of the profile, where they are relatively equally dispersed above and under zero. On the other hand, another possible way to improve the fit and achieve better a R-factor value would be to refine thermal displacement factors (B) not as scalars, as they were considered in these refinements.

Comparison of the atom coordinates of the PbSO₄ structure at 5K and the corresponding for the same compound at room temperature reveal that x and y coordinates are almost the same, and that differences in the second decimal are visible only when z coordinates, which are hit by presence/absence of mirror plane, are considered. This is, of course, a consequence of change of the unit cell parameters due to the phase transition.

An expected fact, obtained after in refinement of the PbSO₄ structure at 5K, are several times lower thermal parameters values in comparison to those for the same compound measured at room temperature (for example, for atom O1, B^5K(O1)=0.5742 (by the way, the biggest of all in this structure at 5K temperature!), is in the best case only two fifths of B^300K₂₂(O1)=1.43, and much less then B^300K₁₁(O1)=2.11 and B^300K₃₃(O1)=2.95).