Multiphase approximation for small-angle scattering

Abstract

The two-phase approximation in small-angle scattering is well known and is still the dominant approach to data analysis. The intensity scattered at small angles is proportional to the second power of the difference between the scattering densities of the two phases. Nevertheless, scattering contrast variation techniques are widely used, and they are obviously suitable for multiphase systems or systems with gradually varying scattering density, since if no parasitic scattering contributions are present the scattering contrast variation would only change a proportionality coefficient. It is shown here that the scattered intensity at small angles of a multiphase system can be represented as a sum of the scattering of two-phase systems and terms describing interference between all pairs of phases. Extracting two-phase scattering patterns from multiphase samples by contrast variation is possible. These two-phase patterns can be treated with the usual small-angle scattering formalism. The case of gradually varying scattering density is also discussed.