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International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 8.6, p. 712
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Sakata & Cooper (1979![[link]](/graphics/greenarr.gif)
) criticized the Rietveld method on the grounds that different residuals ![[ y_{i}\left ({\rm obs.}\right) -y_{i}\left ({\rm calc.}\right) ]](/teximages/cbch8o6/cbch8o6fd12.svg)
related to the same Bragg peak are correlated with one another, and they asserted that this correlation leads to an uncertainty in the standard uncertainties of the structural parameters. Prince (1981) has challenged this conclusion and stated that the s.u.'s given by the Rietveld procedure are correct if the crystallographic model adequately fits the data. However, even if the s.u.'s are correct, they are measures of precision rather than accuracy, and attempts to assess accuracy are hampered by lack of information concerning correlations between systematic errors (Prince, 1985, 1993).
References
Prince, E. (1981). Comparison of profile and and integrated-intensity methods in powder refinement. J. Appl. Cryst. 14, 157–159.Google Scholar
Prince, E. (1985). Precision and accuracy in structure refinement by the Rietveld method. Structure and statistics in crystallography, edited by A. J. C. Wilson. New York: Adenine Press.Google Scholar
Prince, E. (1993). Mathematical aspects of Rietveld refinement. The Rietveld method. IUCr Monographs on Crystallography, No. 5, edited by R. A. Young, pp. 43–54. Oxford University Press.Google Scholar
Sakata, M. & Cooper, M. J. (1979). An analysis of the Rietveld profile refinement method. J. Appl. Cryst. 12, 554–563.Google Scholar
