Refinement of dataset B

Introduction:-

The refinement of dataset B focusses on the relaxation of the crystal structure from 300K to 5K. This results in the crystal lattice becomes slightly destorted from orthorhombic to monoclinic, resulting in the loss of mirror symmetry in the z-axis. This has the effect of reducing the corresponding symmetry in the other directions to either P 1 2₁/n 1 and P 2₁/b 1 1. Hence two refinements were performed to establish which of the symmetry groups was relevent to the experimental data collected.

There were a few changes made to the starting parameters used to refine dataset A.

• O(3) was split into two to reflect the loss of the mirror symmetry, therefore O(4) was added with the same parameter values as O(3) apart from a different z value 2*3/4(mirror plane in datasetA)-0.9(z).
• P 1 2₁/n 1 refined b angle, which was off-set to 90.5^o to accommodate the difference in lattice parameters due to the structure relaxation
• P 1 2₁/n 1 refined a angle due to the effect of the loss of mirror symmetry and creation of 21 screw axis perpendicular to the b-glide plane (The refinement above is the opposite)

The corresponding table 4.1 provides a comparison of the two refinement and by following the relevant links will show the refinements side-by-side for comparison.

Table 4.1 Results, original parameters and refinements of datasetB using lower-symmetry groups

ur - unrefined parameter

Originally, the refinement of P2₁/n was successful and the refinement of P2₁/b became unstable at the third refinement (the lattice parameters). This was rectified by the default nature of the input section of the program registered the entry of P2₁/b as the symmetry group asP 1 2₁/b 1. In fact, the symmetry required in full is P 2₁/b 1 1 and once the input file of the progam was changed to reflect this and the data became more refineable.

The P2₁/b symmetry group refinement is not the best refinement of the data, even though it refined down to Rp=9.7%, the refinement did not converge very well. There one major significant difference that appears to be a small factor but it accounts for a large effect between the refined parameters of each symmetry group. The refined angle may look as if they are very similar, but these results are probably the most significant difference between the two resultant refinements. The a angle refined by P2₁/b is much closer to 90 degrees than the P2₁/n, which means that as the refined angle tends towards ninety, the symmetry tends towards orthorhombic and therefore the refinement becomes more poorer or more unstable.

The P2₁/n symmetry refined to a final converged Rp value of 3.9%. It is this refinement that is the more accurate and valid, showing that the structure of the lead sulphate atom at 5K has reduced in symmetry

The final graphs can be viewed on page 5.