Generalization of the Fedorova-Schmidt method for determining particle size distributions

TL;DR

This paper extends the Fedorova-Schmidt method to determine particle size distributions from small-angle scattering data, accommodating polynomial correlation functions for various particle shapes.

Contribution

It generalizes the original method to include polynomial correlation functions of any degree, enabling analysis of diverse particle geometries.

Findings

Derived an integral transform for polynomial correlation functions.

Applied the method to tetrahedral, octahedral, and cubical particles.

Enhanced the applicability of particle size distribution analysis.

Abstract

One reports the integral transform that determines the particle size distribution of a given sample from the small-angle scattering intensity under the assumption that the particle correlation function is a polynomial of degree M. The Fedorova-Schmidt solution [J. Appl. Cryst. 11, 405, (1978)] corresponds to the case M = 3. The procedure for obtaining a polynomial approximation to a particle correlation function is discussed and applied to the cases of polidisperse particles of tetrahedral or octahedral or cubical shape.