Introduction
This project aims to compare and contrast the refinement effect of tempertature on structure of lead sulphate by the use of the Rietveld refinement technique.
The first section will describe the results of the refinement of a small data set (A). This was used to help develop a refinement strategy and to gain an understanding of how the refinement process works. At the end of this section, the full data set (B) will be refined using the already refined parameters from A.
The second section will investigate the refinement of data set B using a lower symmetry space group. These refinements will be contrasted and the overall set of results discussed with reference to a case study already made using the data from a higher temperature run.
Data File A Refinement
This refinement utilised the Rietica version167a software downloaded from the CCP14 mirror site. The data file used was the column format based upon 2q, intensity and s - data file A from the project outline. The experiemental data was collected at 5K on the high-resolution powder Neutron diffractometer, D2B at the ILL in Grenoble. Table 1.1 provides a summation of the parameters refined, teh results obtained and the strategy used.
Table 1.1 : Relevant parameters and results for datasetA
| Parameter | Set Value | Refined value | Order of refining | No cycles | Rp (%) | Rwp (%) |
| Minimum Bond Length | 0.00 Å | - | - | |||
| Maximum Bond Length | 3.00 Å | - | - | |||
| Space Group | P B N M | - | - | |||
| Phase Scale (c) | 1.0 (Arbritary start value) | 2.856 (2) | 2 | 4 | 43.412 | 51.32 |
| Overall thermal Biso | 0.00 | -0.882 | 9 | 6 | 4.048 | 5.222 |
| Z (number of molecular units) | 4 | |||||
| Cell Parameters | ||||||
| a | 7.0 Å | 6.9287 (3) Å | 3 | 8 | 24.823 | 31.147 |
| b | 8.5 Å | 8.4184 (3) Å | 3 | 8 | 24.823 | 31.147 |
| c | 5.4 Å | 5.3700 (3) Å | 3 | 8 | 24.823 | 31.147 |
| Atom List co-ordinates | x, y, z, B, n | |||||
| Pb | 0.15, 0.20, 1/4, 1.0, 0.5 | 0.1692 (2), 0.1890 (2), ur, ur, ur | 5 | 6 | 13.327 | 17.699 |
| S | 0.20, 0.50, 0.75, 1.0, 0.5 | 0.1942 (2), 0.4429 (2), ur, 0.983, ur | 8 | 6 | 5.279 | 7.171 |
| O(1) | 0.10, 0.60, 0.75, 1.0, 0.5 | 0.09117 (3), 0.59420 (3), ur, ur, ur | 6 | 7 | 13.199 | 17.372 |
| O(2) | 0.00, 0.30, 0.75, 1.0, 0.5 | 0.04453 (3), 0.30944 (3), ur, ur, ur | 7 | 6 | 8.408 | 11.574 |
| O(3) | 0.30, 0.40, 0.90, 1.0, 1.0 | 0.30869 (3), 0.41843 (3), 0.97511 (3), ur, ur | 4 | 6 | 14.431 | 20.015 |
| 2q minimum | 8.0 | |||||
| 2q maximum | 62.475 | |||||
| 2q step | 0.025 | |||||
| Zero error | 0 | 0.091 (2) | 3 | 8 | 24.823 | 31.147 |
| Wavelength of incident beam - g1 | 1.594 | |||||
| Wavelength of incident beam - g2 | 1.594 | |||||
| Polynomial First order background | ||||||
| B0 | 0 | -381.89 | 1 | 3 | 45.612 | 57.93 |
| B1 | 0 | 82.28 | 1 | 3 | 45.612 | 57.93 |
| B2 | 0 | -3.17 | 1 | 3 | 45.612 | 57.93 |
| B3 | 0 | 0.054 | 1 | 3 | 45.612 | 57.93 |
| B4 | 0 | -0.00033 | 1 | 3 | 45.612 | 57.93 |
| B-1 | 0 | 5191.3 | 1 | 3 | 45.612 | 57.93 |
| U | 0.05°2 | 0.702 °2 | 9 | 6 | 4.048 | 5.222 |
| V | -0.15°2 | -0.555°2 (1) | 9 | 6 | 4.048 | 5.222 |
| W | 0.20°2 | 0.283°2 (1) | 9 | 6 | 4.048 | 5.222 |
*ur = unrefined parameter
Click on parameter for relevant information on that refinement. the strategy used is explained by following the links according to the order of refinement.
Peak Shape set to : Pseudo-Voigt (Howard Asymmetric)
Histograms set to : Neutron CW data
All other functions on the software remained as default
The final plot managed to obtain an r value of approximately 3.833% by additional refinement of some of the individual isotropic temperature factors. The full set of atomic co-ordinates can be found in the discussion section on page 6, where the structure of the lead sulphate is compared at 5K and 300K.
