The use of Monte-Carlo simulations to calculate small-angle scattering patterns

Determining the morphology that corresponds to an experimentally observed scattering pattern is a non-trivial problem in small-angle scattering. The purpose of this paper is to describe methods to calculate small-angle scattering patterns from a given morphology via Monte-Carlo methods. In these methods, scattering intensities are calculated from pairs of randomly selected points. This paper reviews the different formulas and procedures that have been used. Multiple studies have shown that the Monte-Carlo method gives accurate results for various morphologies having no interparticle interference. In certain cases, these calculations have been used to fit experimental patterns according to a minimization criterion. For morphologies with interparticle interference, these methods have not been very successful for reasons that are not entirely clear.