An Analytical Approximation for a Size-Broadened Profile Given by the Lognormal and Gamma Distributions

Published

June 1, 2002

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 May 11, 2025)