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^e_o with e ≃ 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 Ca₅(PO₄)₃F, α-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.