Application of a theory for particle statistics to structure refinement from powder diffraction data

A new methodology is proposed for structure refinement using powder diffraction data, from which models for particle statistics and any other statistical errors can be formally optimized. This method is nothing but a straightforward implementation of the maximum-likelihood method, extended to the error estimation. Structure parameters refined by the method for fluorapatite [Ca₅(PO₄)₃F], anglesite (PbSO₄) and barite (BaSO₄) become significantly closer to those obtained by single-crystal structure analyses in comparison with the results of the conventional Rietveld method.