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 er...

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Bibliographic Details
Published in:Journal of applied crystallography 2011-10, Vol.44 (5), p.921-927
Main Authors: Ida, T., Izumi, F.
Format: Article
Language:English
Subjects:
Atoms & subatomic particles
Crystallography
Data analysis
Diffraction
Errors
Fluorapatite
Mathematical models
maximum-likelihood methods
particle statistics
powder diffraction
Powder metallurgy
Rietveld method
Single crystals
Statistical analysis
Statistics
structure refinement
Theory
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Summary: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.
ISSN:1600-5767
0021-8898
1600-5767
DOI:10.1107/S0021889811031013