1.13 An accuracy assessment of the refinement of crystallographic  (Page 3/3)

Comparison of the methods

Method 1

Since Method 1 does not refine the %Cr and relies on an input for the Al and Cr percent composition of the "bulk" material, i.e., the %Cr in the total mass of the material ( [link] , Column 1), as opposed to the analysis of the single crystal on which X-ray diffraction was performed, ( [link] , Column 2), the closer these values were to the "actual" value determined by WDS for the crystal on which X-ray diffraction was performed ( [link] , Column 1 versus 2) then the closer the overall refinement of the structure to those of Methods 2 - 4.

While this assumption is obviously invalid for many of the samples, it is one often used when bulk data (for example, from NMR) is available. However, as there is no reason to assume that one crystal is completely representative of the bulk sample, it is unwise to rely only on such data.

Method 2

This method always produced final, refined, occupancy values that were close to those obtained from WDS ( [link] ). This approach assumes that the motion of the central metal atoms is identical. While this is obviously not strictly true as they are of different size, the results obtained herein imply that this is a reasonable approximation where simple connectivity data is required. For samples where the amount of one of the elements (i.e., Cr) is very low so low a good refinement can not often be obtained. In theses cases, when refining the occupancy values, that for Al would exceed 1 while that of Cr would be less than 1!

Method 3

In some cases, despite the interrelationship between the occupancy and the displacement parameters, convergence was obtained successfully. In these cases the refined occupancies were both slightly closer to those observed from WDS than the occupancy values obtained using Method 2. However, for some samples with higher Cr content the refinement was unstable and would not converge. Whether this observation was due to the increased percentage of Cr or simply lower data quality is not certain.

While this method does allow refinement of any differences in atomic motion between the two metals, it requires extremely high quality data for this difference to be determined reliably.

Method 4

This approach adds little to the final results.

Correlation between analyzed composition and refined composition

[link] shows the relationship between the chromium concentration (%Cr) determined from WDS and the refinement of X-ray diffraction data using Methods 2 or 3 (labeled in [link] ). Clearly there exists a good correlation, with only a slight divergence at high Cr concentration. This is undoubtedly a consequence of trying to refine a low fraction of a light atom (Al) in the presence of a large fraction of a heavier atom (Cr). X-ray diffraction is, therefore, an accurate method of determining the M:M' ratios in crystalline solid solution.

Bibliography

• S. G. Bott, B. D. Fahlman, M. L. Pierson, and A. R. Barron, J. Chem. Soc., Dalton Trans. , 2001, 2148.
• K. R. Dunbar and S. C. Haefner, Inorg. Chem., 1992, 31 , 3676.
• J. Glusker, M. Lewis, and M., Rossi, Crystal Structure Analysis for Chemists and Biologists VCH: New York (1994).
• K. Yoon and G. Parkin, Inorg. Chem. , 1992, 114 , 31.