WEIGHTING SCHEME FOR THE MINIMIZATION FUNCTION IN RIETVELD REFINEMENT

A new weighting scheme for the minimization function used in the Rietv eld method for structure refinement using powder diffraction data is p roposed. 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 o n weak intensities than weighting schemes currently used in the form w = 1/Y-o in Rietveld refinement. The weight function was tested by usi ng X-ray diffraction data-sets of Ca-5(PO4)(3)F, alpha-SiO2, Mg2SiO4 a nd monoclinic ZrO2 powders measured with laboratory sources and synchr otron radiation. By using the new weighting scheme, the accuracy of po sitional parameters of the test sample was significantly improved rela tive-to the weight function 1/Y-o, which weights the medium and strong intensities more heavily, is in accordance with statistical theory an d gives a better overall fit between the observed and calculated powde r patterns. Plots of [w(Y-o - Y-c)(2)] (Y-c = calculated profile inten sity) against the groups of Y-o give a uniform distribution for the pr esent weighting scheme. Weighted difference plots w(1/2)(Y-o - Y-c) ca n be used for examining the correctness of the model instead of conven tional (Y-o - Y-c) plots. The use of high-resolution powder diffractio n data and the proper weighting of profile intensity in the least-squa res refinement are important for obtaining accurate structural paramet ers in Rietveld refinement.