Small-angle scattering from particles having an irregular inner structure

A model is presented for the scattering pattern of a dilute dispersion of particles having an irregular inner structure, made of two phases randomly distributed. For isotropic particles in a dispersant medium, the correlation function of the inner structure has, in the limit of small distances, the same exponential form as that for a two-phase system, provided that the characteristic length scale of the inner structure is small compared to the particle dimension. The scattering pattern of spherical particles is presented in a form suitable for analysis using the contrast-variation method. The cross-term, related to the orientation average of the scattering amplitude, is absent for a random inner structure. The heterogeneous part of the scattering curve is the same as for a randomly distributed two-phase structure. The sphere method is used to simulate the scattering behaviour of particles having an irregular inner structure and to demonstrate the validity of the proposed model.