Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-19T06:25:37.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental estimation of uncertainties in powder diffraction intensities with a two-dimensional X-ray detector

Published online by Cambridge University Press:  04 July 2016

Takashi Ida
Takashi Ida*
Affiliation:
Advanced Ceramics Research Center, Nagoya Institute of Technology, Asahigaoka, Tajimi, Gifu 507-0071, Japan Aichi Synchrotron Radiation Center, Minamiyamaguchi-cho, Seto, Aichi 489-0965, Japan
*
a)Author to whom correspondence should be addressed. Electronic mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A method to obtain both one-dimensional powder diffraction intensities I(2θ) and statistical uncertainties σ(2θ) from the data collected with a flat two-dimensional X-ray detector is proposed. The method has been applied to analysis of the diffraction data of fine quartz powder recorded with synchrotron X-ray. The profile and magnitude of the estimated uncertainties σ(2θ) have shown that the effects of propagation of the errors in 2θ are dominant as the uncertainties about the observed intensity values I(2θ). The powder diffraction intensity data I(2θ), including nine reflection peaks have been analyzed by the Rietveld method incorporating the experimentally estimated uncertainties σ(2θ). The observed I(2θ) data have been reproduced with a symmetric peak profile function (R wp = 0.84 %), and no significant peak shifts from calculated locations have been detected as compared with the experimental errors. The optimized values of the lattice constants of the quartz sample have nominally been estimated at a = 4.9131(4) Å and c = 5.4043(2) Å, where the uncertainties in parentheses are evaluated by the Rietveld optimization based on the estimated uncertainties σ(2θ) for intensities I(2θ). It is likely that reliability of error estimation about unit-cell dimensions has been improved by this analytical method.

Keywords

uncertaintyerror2D X-ray detectorsynchrotron X-raymaximum-likelihood method
Type
Technical Articles
Information
Powder Diffraction , Volume 31 , Issue 3 , September 2016 , pp. 216 - 222
Check for updates
Copyright
Copyright © International Centre for Diffraction Data 2016 

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

Alexander, L., Klug, H. P., and Kummer, E. (1948). “Statistical factors affecting intensity of X-rays diffracted by crystalline powders,” J. Appl. Phys. 19, 742–753.Google Scholar
Brice, J. C. (1980). “The lattice constants of a-quartz,” J. Mat. Sci. 15, 161–167.CrossRefGoogle Scholar
Caglioti, G., Paoletti, A., and Ricci, F. P. (1958). “Coice of collimators for a crystal spectrometer for neutron diffraction,” Nucl. Instrum. 3, 223–228.Google Scholar
Debye, P. and Scherrer, P. (1916). “Interferenz an regellos orientierten teilchen im röntgenlicht I,” Phys. Z. 17, 277–283.Google Scholar
De Wolff, P. M. (1958). “Particle statistics in X-ray diffractometry,” Appl. Sci. Res. B 7, 102–112.CrossRefGoogle Scholar
De Wolff, P. M., Taylor, J. M., and Parrish, W. (1959). “Experimental study of effect of crystallite size statistics on X-ray diffractometer intensities,” J. Appl. Phys. 30, 63–69.Google Scholar
Hull, A. W. (1917). “A new method of x-ray crystal analysis,” Phys. Rev. 10, 661–697.Google Scholar
Ida, T. (2011). “Particle statistics of a capillary specimen in synchrotron powder diffractometry,” J. Appl. Crystallogr. 44, 911–920.Google Scholar
Ida, T. (2013). “Powder x-ray structure refinement applying a theory for particle statistics,” Solid State Phenom. 203/204, 3–8.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.CrossRefGoogle 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., 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
Ingham, B. (2014). “Statistical measures of spottiness in diffraction rings,” J. Appl. Crystallogr. 47, 166–172.CrossRefGoogle Scholar
Izumi, F. and Momma, K. (2007). “Three dimensional visualization in powder diffraction,” Solid State Phenom. 130, 15–20.Google Scholar
Kahn, R., Fourme, R., Gadet, A., Janin, J., Dumas, C., and Andre, D. (1982). “Macromolecular crystallography with synchrotron radiation: photographic data collection and polarization correction,” J. Appl. Crystallogr., 15, 330–337.Google Scholar
Sulyanov, S. N., Popov, A. N., and Kheiker, D. M. (1994). “Using a two-dimensional detector for x-ray powder diffractometry,” J. Appl. Crystallogr., 27, 934–942.CrossRefGoogle Scholar
Yang, X., Juháa, P., and Billinge, S. J. L. (2014). “On the estimation of statistical uncertainties on powder diffraction and small-angle scattering data from two-dimensional X-ray detectors,” J. Appl. Crystalogr. 47, 1273–1283.Google Scholar