Analysis of small-angle scattering data dominated by multiple scattering for systems containing eccentrically shaped particles or pores

A previously developed formalism to interpret the beam broadening due to multiple small-angle scattering of a collimated beam of radiation in condensed matter is extended to treat the case of nonspherical scattering particles or pores. The new formalism concerns the situation where coherent single-particle scattering is incoherently, or stochastically, compounded by a random system of spheroidal particles, of any given mean aspect ratio, in a uniform matrix. By appropriate transformation of axes to reflect a spheroidal particle symmetry, Bethe's analysis of scattering when the sample thickness greatly exceeds the scattering mean free path is combined with the dynamical analysis of single-particle scattering to model the beam broadening arising from a system containing nonspherical scattering objects. For the range of experimental parameters used in practical small-angle scattering studies of technological materials such as porous ceramics, it is shown that, while the previous formulation suffices for spheres, globules and even short capillary pores, the variation in beam broadening as a function of incident wavelength exhibits distinguishable signatures for systems in which a collapsed planar or extreme capillary scattering morphology predominates.