surrounding liquid, because variations in ρ due to the atomic structure only become visible at higher angles. This means that the total integrated intensity of the SAS pattern (in 3D) is an invariant quantity proportional to the square Δρ2. In 1-dimensional projection, as usually recorded for an isotropic pattern this invariant quantity becomes , where the integral runs from q=0 to wherever the SAS pattern is assumed to end and the diffraction pattern starts. It is also assumed that the density does not vary in the liquid or inside the particles, i.e. there is binary contrast. SAXS is described in terms of the electronic density where SANS is described in terms of a neutron scattering length density. Porod's law At wave numbers that are relatively large on the scale of SAS, but still small when compared to wide-angle Bragg diffraction, local interface intercorrelations are probed, whereas correlations between opposite interface segments are averaged out. For smooth interfaces, one obtains Porod's law: This allows the surface area S of the particles to be determined with SAS. This needs to be modified if the interface is rough on the scale q−1. If the roughness can be described by a fractal dimension d between 2-3 then Porod's law becomes: Scattering from particles Small-angle scattering from particles can be used to determine the particle shape or their size distribution. A small-angle scattering pattern can be fitted with intensities calculated from different model shapes when the size distribution is known. If the shape is known, a size distribution may be fitted to the intensity. Typically one assumes the particles to be spherical in the latter case. If the particles are in solution and known to have uniform size dispersity, then a typical strategy is to measure different concentrations of particles in the solution. From the SAXS patterns obtained one can extrapolate to the intensity pattern one would get for a single particle. This is a necessary procedure that eliminates the concentration effect, which is a small shoulder that appears in the intensity patterns due to the proximity of neighbouring particles. The average distance between particles is then roughly the distance 2π/q*, where q* is the position of the shoulder on the scattering vector range q. The shoulder thus comes from the structure of the solution and this contribution is called the structure factor. One can write for the small-angle X-ray scattering intensity: where is the