Improvements and considerations for size distribution retrieval from small-angle scattering data by Monte Carlo methods

Abstract

A method is presented and applied, capable of retrieving form-free particle size distributions complete with uncertainties from small-angle scattering patterns. Special attention is paid to particle observability in the scattering patterns, accurate estimation of data uncertainty and the effect of uncertainty on the resulting size distribution statistics.

Abstract

Monte Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve form-free particle size distributions from small-angle scattering patterns of non-interacting low-concentration scatterers such as particles in solution or precipitates in metals. Improvements are presented to existing MC methods, such as a non-ambiguous convergence criterion, nonlinear scaling of contributions to match their observability in a scattering measurement, and a method for estimating the minimum visibility threshold and uncertainties on the resulting size distributions.