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 refinement of crystal structure parameters from powder diffraction data. The equivalent two-stage approach, involving the refinement 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 refinements need to be performed very quickly. The equivalence is emphasized in a simple mathematical relationship between the goodness of fits obtained in Rietveld, Pawley and correlated integrated intensities refinements. A rationale is given for determining the estimated standard deviations for structural variables from powder diffraction data.