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Weighting Scheme for the Minimization Function in Rietveld Refinement
Author(s) -
Toraya H.
Publication year - 1998
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889897011096
Subject(s) - weighting , rietveld refinement , diffraction , monoclinic crystal system , powder diffraction , intensity (physics) , function (biology) , synchrotron radiation , mathematics , minification , crystallography , chemistry , algorithm , physics , crystal structure , optics , mathematical optimization , evolutionary biology , acoustics , biology
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 Ca 5 (PO 4 ) 3 F, α ‐SiO 2 , Mg 2 SiO 4 and monoclinic ZrO 2 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.