Weighting scheme for the minimization function in Rietveld refinement

A new weighting scheme for the minimization function used in the Rietveld method for structure refinement using powder diffraction data is proposed. It has the form w = 1/Y-o(e) with e similar or equal to 2 (Y-o = observed profile intensity) and gives relatively heavier weights on weak intensities than weighting schemes currently used in the form w = 1/Y-o in Rietveld refinement. The weight function was tested by using X-ray diffraction data-sets of Ca-5(PO4)(3)F, alpha-SiO2, Mg2SiO4 and monoclinic ZrO2 powders measured with laboratory sources and synchrotron radiation. By using the new weighting scheme, the accuracy of positional parameters of the test sample was significantly improved relative-to the weight function 1/Y-o, which weights the medium and strong intensities more heavily, is in accordance with statistical theory and gives a better overall fit between the observed and calculated powder patterns. Plots of [w(Y-o - Y-c)(2)] (Y-c = calculated profile intensity) against the groups of Y-o give a uniform distribution for the present weighting scheme. Weighted difference plots w(1/2)(Y-o - Y-c) can be used for examining the correctness of the model instead of conventional (Y-o - Y-c) plots. The use of high-resolution powder diffraction data and the proper weighting of profile intensity in the least-squares refinement are important for obtaining accurate structural parameters in Rietveld refinement.