Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T14:02:53.737Z Has data issue: false hasContentIssue false
  • English
  • Français

Convolution and deconvolutional treatment on sample transparency aberration in Bragg–Brentano geometry

Published online by Cambridge University Press:  02 May 2022

Takashi Ida Open the ORCID record for Takashi Ida [Opens in a new window]
Takashi Ida*
Affiliation:
Advanced Ceramics Research Center, Nagoya Institute of Technology, Tajimi, Japan
*
a)Author to whom correspondence should be addressed. Electronic mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Exact and approximate mathematical models for the effects of sample transparency on the powder diffraction intensity data are examined. Application of the formula based on the first-order approximation about the deviation angle is justified for realistic measurement and computing systems. The effects of sample transparency are expressed by double convolution formulas applying two different scale transforms, including three parameters, goniometer radius R, penetration depth μ−1, and thickness of the sample t. The deconvolutional treatment automatically recovers the lost intensity and corrects the peak shift and asymmetric deformation of peak profile caused by the sample transparency.

Keywords

sample transparencyBragg–Brentano geometryconvolutiondeconvolutional treatment
Type
Technical Article
Information
Powder Diffraction , Volume 37 , Issue 1 , March 2022 , pp. 13 - 21
Check for updates
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of International Centre for Diffraction Data

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. and Stegun, I. (1964). Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Dover Publications, New York).Google Scholar
Deutsch, M., Förster, E., Hölzer, G., Härtwig, 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. doi:10.6028/jres.109.006CrossRefGoogle Scholar
Ida, T. (1998). “An efficient method for calculating asymmetric diffraction peak profiles,” Rev. Sci. Instrum. 69, 2268–2272. doi:10.1063/1.1149220CrossRefGoogle Scholar
Ida, T. (2020). “Equatorial aberration of powder diffraction data collected with an Si strip X-ray detector by a continuous-scan integration method,” J. Appl. Crystallogr. 53, 679–685. doi:10.1107/S1600576720005130CrossRefGoogle Scholar
Ida, T. (2021). “Continuous series of symmetric peak profile functions determined by standard deviation and kurtosis,” Powder Diffr. 36, 222–232. doi:10.1017/S0885715621000567CrossRefGoogle Scholar
Ida, T. and Kimura, K. (1999). “Effect of sample transparency in powder diffractometry with Bragg-Brentano geometry as a convolution,” J. Appl. Crystallogr. 32, 982–991. doi:10.1107/S0021889899008894CrossRefGoogle Scholar
Ida, T. and Toraya, H. (2002). “Deconvolution of the instrumental functions in powder X-ray diffractometry,” J. Appl. Crystallogr. 36, 181–187. doi:10.1107/S0021889801018945CrossRefGoogle Scholar
Ida, T., Shimazaki, S., Hibino, H., and Toraya, H. (2003). “Diffraction peak profiles from spherical crystallites with lognormal size distribution,” J. Appl. Crystallogr. 36, 1107–1115. doi:10.1107/S0021889803011580CrossRefGoogle Scholar
Ida, T., Ono, S., Hattan, D., Yoshida, T., Takatsu, Y., and Nomura, K. (2018). “Improvement of deconvolution-convolution treatment of axial-divergence aberration in Bragg-Brentano geometry,” Powder Diffr. 33, 121–133. doi:10.1017/S0885715618000349CrossRefGoogle Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007). Numerical Recipes (Cambridge University Press, London), 3rd ed.Google Scholar
Rosin, P. and Rammler, E. (1933). “The laws governing the fineness of powdered coal,” J. Inst. Fuel. 7, 29–36.Google Scholar
Supplementary material: File

Ida supplementary material

Ida supplementary material

Download Ida supplementary material(File)
File 839.5 KB