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Poisson errors and adaptive rebinning in X-ray powder diffraction data

Published online by Cambridge University Press:  10 October 2018

Marcus H. Mendenhall Open the ORCID record for Marcus H. Mendenhall [Opens in a new window]
Marcus H. Mendenhall*
Affiliation:
National Institute of Standards and Technology (NIST), 100 Bureau Drive, Gaithersburg, MD 20899, USA
*
a)Author to whom correspondence should be addressed. Electronic mail: [email protected]
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Abstract

This work provides a short summary of techniques for formally-correct handling of statistical uncertainties in Poisson-statistics dominated data, with emphasis on X-ray powder diffraction patterns. Correct assignment of uncertainties for low counts is documented. Further, we describe a technique for adaptively rebinning such data sets to provide more uniform statistics across a pattern with a wide range of count rates, from a few (or no) counts in a background bin to on-peak regions with many counts. This permits better plotting of data and analysis of a smaller number of points in a fitting package, without significant degradation of the information content of the data set. Examples of the effect of this on a diffraction data set are given.

Keywords

powder diffractionpoisson statisticsadaptive rebinning
Type
Technical Article
Information
Powder Diffraction , Volume 33 , Issue 4 , December 2018 , pp. 266 - 269
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Creative Commons
This is a work of the U.S. Government and is not subject to copyright protection in the United States
Copyright
Copyright © International Centre for Diffraction Data 2018

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References

Bruker AXS (2014). Topas v5, a component of DIFFRAC.SUITE, 2014. https://www.bruker.com/products/x-ray-diffraction-and-elemental-analysis/x-ray-diffraction/xrd-software.html.Google Scholar
Cheary, R. W. and Coelho, A. (1992). A fundamental parameters approach to X-ray line-profile fitting. J. Appl. Cryst. 25, 109–121.Google Scholar
Cheary, R. W., Coelho, A. A., and Cline, J. P. (2004). Fundamental parameters line profile fitting in laboratory diffractometers. J. Res. NIST 109, 1–25.Google Scholar
Kirkpatrick, J. M. and Young, B. M. (2009). Poisson statistical methods for the analysis of low-count gamma spectra. IEEE Trans. Nucl. Sci. 56, 1278–1282.Google Scholar
Mendenhall, M. H., Mullen, K., and Cline, J. P. (2015). An implementation of the fundamental parameters approach for analysis of X-ray powder diffraction line profiles. J. Res. NIST 120, 223–251.Google Scholar
Mendenhall, M. H., Henins, A., Windover, D., and Cline, J. P. (2016). Characterization of a self-calibrating, high-precision, stacked-stage, vertical dual-axis goniometer. Metrologia 53, 933–944.Google Scholar
Mendenhall, M. H., Henins, A., Hudson, L. T., Szabo, C. I., Windover, D., and Cline, J. P. (2017). High-precision measurement of the X-ray Cu Kα spectrum. J. Phys. B At. Mol. Opt. Phys., 50, 115004.Google Scholar
NIST (2010). Standard Reference Material 660b. https://www-s.nist.gov/srmors/view_detail.cfm?srm=660b.Google Scholar
Pawley, G. S. (1980). EDINP, the Edinburgh powder profile refinement program. J. Appl. Cryst. 13, 630–633.Google Scholar
Wikipedia (2018). Poisson Distribution. https://en.wikipedia.org/wiki/Poisson_distribution.Google Scholar