Small-angle X-ray scattering intensity of multiscale models of spheres

Abstract

The different approaches found in the literature to compute small-angle X-ray scattering intensities of stochastic Boolean models from their analytical formulations or their numerical realizations are reviewed. The advantages and drawbacks of the methods for the interpretation of small-angle X-ray scattering curves are investigated. Examples of multiscale models built from union and intersection of Boolean models of spheres and from Gamma or lognormal radius distributions are given. The scattering intensity computed from projections of realizations of such models is compared with the intensity computed from their analytical covariance. It appears that computation from projection induces a strong finite-size effect with a relative constant variance equal to 0.5. Comparison of scattering intensities of an intersection of Boolean model and the corresponding Cox model shows only subtle differences.