Small-angle scattering for beginners

Many experimental methods are available for the characterization of nanostructures, but most of them are limited by stringent experimental conditions. When it comes to analysing nanostructures in the bulk or in their natural environment - even as ordinary as water at room temperature - small-angle scattering (SAS) of X-rays or neutrons is often the only option. The rapid worldwide development of synchrotron and neutron facilities over recent decades has opened unprecedented possibilities for using SAS in situ and in a time-resolved way. But, in spite of its huge potential in the field of nanomaterials in general, SAS is covered far less than other characterization methods in non-specialized curricula. Presented here is a rigorous discussion of small-angle scattering, at a technical level comparable to the classical undergraduate coverage of X-ray diffraction by crystals and which contains diffraction as a particular case.