Relationship between the atomic pair distribution function and small-angle scattering: implications for modeling of nanoparticles

The relationship between the equations used in the atomic pair distribution function (PDF) method and those commonly used in small-angle-scattering (SAS) analyses is explicitly shown. The origin of the sloping baseline, -4pirrho0, in PDFs of bulk materials is identified as originating from the SAS intensity that is neglected in PDF measurements. The nonlinear baseline in nanoparticles has the same origin, and contains information about the shape and size of the nanoparticles.