Patterson Functions and Diffuse Scattering
Although diffraction can be understood as wave interference involving wave scattering from individual atoms, in kinematical theory the diffraction intensity can also be understood as contributions from pairs of atoms, weighted by phase factors. The Patterson function is defined, and used to describe disorder from atom displacements and chemical disorder. The diffuse scattering from these types of disorder is explained. Local correlations in atomic displacements and short-range order are used to explain modulations in the diffuse scattering. This chapter explains how to obtain the pair distribution function by Fourier transformation of the diffraction pattern. Diffraction methods are extended for measuring structural features of amorphous materials and measuring structures of larger objects by small-angle scattering. The basic methods for analyzing small-angle scattering experiments are presented.