An Analytical Approximation for a Size-Broadened Profile Given by the Lognormal and Gamma Distributions
N Popa, Davor Balzar
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.
Journal of Applied Crystallography
crystallite size distribution, diffraction line broadenings, gamma distribution, lognormal distribution
and Balzar, D.
An Analytical Approximation for a Size-Broadened Profile Given by the Lognormal and Gamma Distributions, Journal of Applied Crystallography
(Accessed June 5, 2023)