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An Analytical Approximation for a Size-Broadened Profile Given by the Lognormal and Gamma Distributions
Published
Author(s)
N Popa, Davor Balzar
Abstract
We consider the size-broadened profile given by the lognormal and gamma size distributions of spherical crystallites. We show that the Voigt function and its approximations, as common models for a size-broadened profile, fail both for very narrow and broad size distributions. An analytical approximation for the size-broadened profiles is derived that can be analytically convolved withthe strain-broadened and instrumental-broadened profiles. The method is tested on the two CeO2 powders; one shows super-Lorentzian profiles that we successfully model under the assumption of a broad lognormal size distribution. We argue that the size-broadened line profile is not very sensitive to the variations in size distribution and that an apparent domain size or even column-length distribution function can correspond to significantly different size distributions.
Citation
Journal of Applied Crystallography
Volume
35
Issue
Part 3
Pub Type
Journals
Keywords
crystallite size distribution, diffraction line broadenings, gamma distribution, lognormal distribution
Citation
Popa, N.
and Balzar, D.
(2002),
An Analytical Approximation for a Size-Broadened Profile Given by the Lognormal and Gamma Distributions, Journal of Applied Crystallography
(Accessed June 5, 2023)