Diffraction line profile from a disperse system: A simple alternative to Voigtian profiles

Abstract

A general expression is proposed for the peak profile produced by a system of simple-shape crystalline domains (sphere, cube, tetrahedron, octahedron) whose size is dispersed according to a gamma distribution. The analytical expression obtained is particularly suited to “on the fly” pattern simulation or profile fitting for nanocrystalline materials. An advantage of using the proposed profile expression is that it always corresponds to a physically meaningful, though a priori fixed, size distribution, whereas the traditionally employed Voigtian profiles can produce unphysical negative size distributions for certain combinations of profile parameters. The peak profile depends on the distribution mean and variance instead of the more common empirical parameters of peak width and shape.