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Improvement of deconvolution–convolution treatment of axial-divergence aberration in Bragg–Brentano geometry

Published online by Cambridge University Press:  29 June 2018

Takashi Ida ,
Shoki Ono ,
Daiki Hattan ,
Takehiro Yoshida ,
Yoshinobu Takatsu  and
Katsuhiro Nomura
Takashi Ida*
Affiliation:
Advanced Ceramics Research Center, Nagoya Institute of Technology, Asahigaoka, Tajimi, Gifu 507-0071, Japan
Shoki Ono
Affiliation:
Advanced Ceramics Research Center, Nagoya Institute of Technology, Asahigaoka, Tajimi, Gifu 507-0071, Japan
Daiki Hattan
Affiliation:
Advanced Ceramics Research Center, Nagoya Institute of Technology, Asahigaoka, Tajimi, Gifu 507-0071, Japan
Takehiro Yoshida
Affiliation:
Advanced Ceramics Research Center, Nagoya Institute of Technology, Asahigaoka, Tajimi, Gifu 507-0071, Japan
Yoshinobu Takatsu
Affiliation:
Advanced Ceramics Research Center, Nagoya Institute of Technology, Asahigaoka, Tajimi, Gifu 507-0071, Japan
Katsuhiro Nomura
Affiliation:
Inorganic Functional Materials Research Institute, National Institute of Advanced Industrial Science and Technology, Anagahora, Shimoshidami, Moriyama, Nagoya, Aichi 463-8560, Japan
*
a)Author to whom correspondence should be addressed. Electronic mail: ida.takashi@nitech.ac.jp
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Abstract

An improved method to correct observed shift and asymmetric deformation of diffraction peak profile caused by the axial-divergence aberration in Bragg–Brentano geometry is proposed. The method is based on deconvolution–convolution treatment applying scale transform of abscissa, Fourier transform, and cumulant analysis of an analytical model for the axial-divergence aberration. The method has been applied to the powder diffraction data of a standard LaB6 powder (NIST SRM660a) sample, collected with a one-dimensional Si strip detector. The locations, widths and shape of the peaks in the deconvolved–convolved powder diffraction data have been analyzed. The finally obtained whole powder diffraction pattern ranging from 10° to 145° in diffraction angle has been simulated by the Pawley method applying a symmetric Pearson VII peak profile model to each peak with ten background, two peak-shift, three line-width, and two peak-shape parameters, and the Rp value of the best fit has been estimated at 4.4%.

Keywords

axial-divergence aberrationBragg–Brentano geometrydeconvolutionconvolution
Type
Technical Article
Information
Powder Diffraction , Volume 33 , Issue 2 , June 2018 , pp. 121 - 133
Copyright
Copyright © International Centre for Diffraction Data 2018 

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References

Antoniadis, A., Berruyer, J., and Filhol, A. (1990). “Maximum-likelihood methods in powder diffraction refinements,” Acta Crystallogr. Sect. A: Found. Crystallogr. 46, 692–711.Google Scholar
Cheary, R. W. and Coelho, A. (1992). “A fundamental parameters approach to x-ray line-profile fitting,” J. Appl. Crystallogr. 25, 109–121.Google Scholar
Deutsch, M., Förster, E., Hölzer, G., Hartwig, J., Hämäläinen, K., Kao, C.-C., Huotari, S., and Diamant, R. (2004). “X-ray spectrometry of copper: new results on an old subject,” J. Res. Natl. Inst. Stand. Technol. 109, 75–98.Google Scholar
Ida, T. (1998). “Formula for the asymmetric diffraction peak profiles based on double Soller slit geometry,” Rev. Sci. Instrum. 69, 2268–2272.Google Scholar
Ida, T. (2008). “New measures of sharpness for symmetric powder diffraction peak profile,” J. Appl. Crystallogr. 41, 393–401.Google Scholar
Ida, T. (2016). “Experimental estimation of uncertainties in powder diffraction intensities with a two-dimensional X-ray detector,” Powder Diffr. 31, 216–222.CrossRefGoogle Scholar
Ida, T. and Hibino, H. (2006). “Symmetrization of diffraction peak profiles measured with a high-resolution synchrotron X-ray powder diffractometer,” J. Appl. Crystallogr. 39, 90–100.Google 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.Google Scholar
Ida, T. and Izumi, F. (2013). “Analytical method for observed powder diffraction intensity data based on maximum likelihood estimation,” Powder Diffr. 28, 124–126.Google Scholar
Ida, T. and Kimura, K. (1999a). “Flat-specimen effect as a convolution in powder diffractometry with Bragg–Brentano geometry,” J. Appl. Crystallogr. 32, 634–640.CrossRefGoogle Scholar
Ida, T. and Kimura, K. (1999b). “Effect of sample transparency in powder diffractometry with Bragg–Brentano geometry as a convolution,” J. Appl. Crystallogr. 32, 982–991.Google Scholar
Ida, T. and Toraya, H. (2002). “Deconvolution of the instrumental functions in powder X-ray diffractometry,” J. Appl. Crystallogr. 35, 58–68.Google 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.Google Scholar
Ida, T., Ono, S., Hattan, D., Yoshida, T., Takatsu, Y., and Nomura, K. (2018). “Deconvolution-convolution treatment on powder diffraction data collected with Cu Kα X-ray and Ni Kβ filter,” Powder Diffr. 33, 80–87.Google Scholar
McCusker, L. B., Von Dreele, R. B., Cox, D. E., Loër, D., and Scardi, P. (1999). “Rietveld refinement guidelines,” J. Appl. Crystallogr. 32, 36–50.CrossRefGoogle Scholar
Pawley, G. S. (1981). “Unit-cell refinement from powder diffraction scans,” J. Appl. Crystallogr. 14, 357–361.Google Scholar
Thompson, P., Cox, D. E., and Hastings, J. B. (1987). “Rietveld refinement of debye-scherrer synchrotron X-ray data from Al2O3,” J. Appl. Crystallogr. 20, 79–83.Google Scholar