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Analytical method for observed powder diffraction intensity data based on maximum likelihood estimation

Published online by Cambridge University Press:  16 April 2013

Takashi Ida  and
Fujio Izumi
Takashi Ida*
Affiliation:
Advanced Ceramics Research Center, Nagoya Institute of Technology, Nagoya, Japan
Fujio Izumi
Affiliation:
National Institute for Materials Science, Ibaraki, Japan
*
a)Author to whom correspondence should be addressed. Electronic mail: ida@ida.takashi@nitech.ac.jp
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Abstract

A new methodology based on maximum likelihood estimation for structure refinement using powder diffraction data is proposed. The method can not only optimize the parameters adjusted in Rietveld refinement but also parameters to specify errors in a model for statistical properties of the observed intensity. The results of structure refinements with relation to fluorapatite Ca5(PO4)3F, anglesite PbSO4, and barite BaSO4 are demonstrated. The structure parameters of fluorapatite and barite optimized by the new method are closer to single-crystal data than those optimized by the Rietveld method, while the structure parameters of anglesite, whose values optimized by the Rietveld method are already in good agreement with the single-crystal data, are almost unchanged by the application of the new method.

Keywords

powder diffraction datacrystal structureRietveld refinementmaximum likelihood estimationfluorapatiteanglesitebarite
Type
Technical Articles
Information
Powder Diffraction , Volume 28 , Issue 2 , June 2013 , pp. 124 - 126
Copyright
Copyright © International Centre for Diffraction Data 2013 

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References

Alexander, L., Klug, H. P., and Kummer, E. (1948). “Statistical factors affecting the intensity of X-rays diffracted by crystalline powders”, J. Appl. Phys. 19, 742–753.CrossRefGoogle Scholar
De Wolff, P. M. (1958). “Particle statistics in X-ray diffractometry. I. General theory”, Appl. Sci. Res. B 7, 102–112.CrossRefGoogle Scholar
Hill, R. J. (1992). “Rietveld refinement round robin. I. Analysis of standard X-ray and neutron data for PbSO4”, J. Appl. Crystallogr. 25, 589–610.CrossRefGoogle Scholar
Ida, T. and Izumi, F. (2011). “Application of a theory for particle statistics to structure refinement from powder diffraction data”, J. Appl. Crystallogr. 44, 921–927.CrossRefGoogle Scholar
Ida, T., Goto, T., and Hibino, H. (2009). “Evaluation of particle statistics in powder diffractometry by a spinner-scan method”, J. Appl. Crystallogr. 42, 597–606.CrossRefGoogle Scholar
Izumi, F. and Momma, K. (2007). “Three-dimensional visualization in powder diffraction”, Solid State Phenom. 130, 15–20.CrossRefGoogle Scholar
Miyake, M., Minato, I., Morikawa, H., and Iwai, S. (1978). “Crystal structures and sulphate force constants of barite, celestite, and angle site”, Am. Meneral. 63, 506–510.Google Scholar
Rodríguez-Carvajal, J. (1993). “Recent advances in magnetic structure determination by neutron powder diffraction”, Physica B 192, 55–69.CrossRefGoogle Scholar
Sudarsanan, K., Mackie, P. E., and Young, R. E. (1972). “Comparison of synthetic and mineral fluorapatite, Ca5(PO4)3F, in crystallographic detail”, Mater. Res. Bull. 7, 1331–1338.CrossRefGoogle Scholar
Toraya, H. (1998). “Weighting scheme for the minimization function in Rietveld refinement”, J. Appl. Crystallogr. 31, 333–343.CrossRefGoogle Scholar
Toraya, H. (2000). “Crystal structure refinement of α-Si3N4 using synchrotron radiation powder diffraction data: unbiased refinement strategy”, J. Appl. Crystallogr. 33, 95–102.CrossRefGoogle Scholar
Young, R. A., Sakthivel, A., Moss, T. S., and Paiva-Santos, C. O. (1995). “DBWS-9411 – an upgrade of the DBWS*.* programs for Rietveld refinement with PC and mainframe computers”, J. Appl. Crystallogr. 28, 366–367.CrossRefGoogle Scholar