The estimation of standard deviations in powder diffraction Rietveld refinements

It is shown that when the observed and calculated intensities in a powder diffraction pattern differ because of model errors which affect the calculated integrated intensities, in addition to the random counting errors, Rietveld refinement with weights determined solely by counting statistics yields estimated standard deviations for the crystal structure parameters which tend to be measures of the precision rather than the accuracy of these parameters. Under these conditions, e.s.d.'s calculated by Rietveld refinement may be significantly smaller than those obtained by integrated intensity refinement of the same data set. A method of adjusting Rietveld e.s.d.'s, to provide comparability with integrated intensity refinement, is proposed.