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Estimation of errors in the measurement of unit-cell parameters. I. Statistical uncertainties of peak positions of powder diffraction lines determined by individual profile fitting

Estimation of errors in the measurement of unit-cell parameters. I. Statistical uncertainties of... A formula for estimating the statistical uncertainty of peak positions, determined by individual profile fitting, has been derived. The magnitude of the statistical uncertainty is given by (sum of peak profile intensities)-1/2 x (full width at half-maximum) x F x G x Q x (goodness-of-fit index). The factor F depends on the shape of the diffraction profile; it becomes smaller by 40% when the profile shape changes from Lorentzian to Gaussian. The factor G represents the parameter correlation between the peak position and the parameter for profile asymmetry; it becomes unity when the profile shape is symmetric or the parameter for profile asymmetry is fixed during the least-squares fitting. The factor Q depends on the peak-to-background ratio. The formula was experimentally verified by using diffraction data sets for CeO2 and Si powders. The statistical uncertainty is essentially based on the counting statistics and profile width. Therefore, the peak position of a strong and sharp peak in the low-angle region can be determined more precisely than that of a weak and broadened peak in the high-angle region. The formula provides a guideline for optimizing experimental parameters for required precision. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Crystallography International Union of Crystallography

Estimation of errors in the measurement of unit-cell parameters. I. Statistical uncertainties of peak positions of powder diffraction lines determined by individual profile fitting

Journal of Applied Crystallography , Volume 34 (5): 558 – Sep 25, 2001

Estimation of errors in the measurement of unit-cell parameters. I. Statistical uncertainties of peak positions of powder diffraction lines determined by individual profile fitting

Journal of Applied Crystallography , Volume 34 (5): 558 – Sep 25, 2001

Abstract

A formula for estimating the statistical uncertainty of peak positions, determined by individual profile fitting, has been derived. The magnitude of the statistical uncertainty is given by (sum of peak profile intensities)-1/2 x (full width at half-maximum) x F x G x Q x (goodness-of-fit index). The factor F depends on the shape of the diffraction profile; it becomes smaller by 40% when the profile shape changes from Lorentzian to Gaussian. The factor G represents the parameter correlation between the peak position and the parameter for profile asymmetry; it becomes unity when the profile shape is symmetric or the parameter for profile asymmetry is fixed during the least-squares fitting. The factor Q depends on the peak-to-background ratio. The formula was experimentally verified by using diffraction data sets for CeO2 and Si powders. The statistical uncertainty is essentially based on the counting statistics and profile width. Therefore, the peak position of a strong and sharp peak in the low-angle region can be determined more precisely than that of a weak and broadened peak in the high-angle region. The formula provides a guideline for optimizing experimental parameters for required precision.

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References (15)

Publisher
International Union of Crystallography
Copyright
Copyright (c) 2001 International Union of Crystallography
Subject
statistical uncertainty, peak profile analysis, unit-cell parameters
ISSN
0021-8898
eISSN
1600-5767
DOI
10.1107/S0021889801008676
Publisher site
See Article on Publisher Site

Abstract

A formula for estimating the statistical uncertainty of peak positions, determined by individual profile fitting, has been derived. The magnitude of the statistical uncertainty is given by (sum of peak profile intensities)-1/2 x (full width at half-maximum) x F x G x Q x (goodness-of-fit index). The factor F depends on the shape of the diffraction profile; it becomes smaller by 40% when the profile shape changes from Lorentzian to Gaussian. The factor G represents the parameter correlation between the peak position and the parameter for profile asymmetry; it becomes unity when the profile shape is symmetric or the parameter for profile asymmetry is fixed during the least-squares fitting. The factor Q depends on the peak-to-background ratio. The formula was experimentally verified by using diffraction data sets for CeO2 and Si powders. The statistical uncertainty is essentially based on the counting statistics and profile width. Therefore, the peak position of a strong and sharp peak in the low-angle region can be determined more precisely than that of a weak and broadened peak in the high-angle region. The formula provides a guideline for optimizing experimental parameters for required precision.

Journal

Journal of Applied CrystallographyInternational Union of Crystallography

Published: Sep 25, 2001

Keywords: statistical uncertainty; peak profile analysis; unit-cell parameters.

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