On the equivalence of the Rietveld method and the correlated integrated intensities method in powder diffraction

The Rietveld method is the most straightforward and statistically correct approach for the re®nement of crystal structure parameters from powder diffraction data. The equivalent two-stage approach, involving the re®nement of structural parameters based on integrated intensities extracted using the Pawley method, is extremely useful in circumstances such as the global optimization methods of structure determination, where a great many re®nements need to be performed very quickly. The equivalence is emphasized in a simple mathematical relationship between the goodness of ®ts obtained in Rietveld, Pawley and correlated integrated intensities re®nements. A rationale is given for determining the estimated standard deviations for structural variables from powder diffraction data.