Small-angle scattering of particle assemblies

Small-angle scattering formulae for crystalline assemblies of arbitrary particles are derived from powder diffraction theory using the decoupling approximation. To do so, the pseudo-lattice factor is defined, and methods to overcome the limitations of the decoupling approximation are investigated. Further, approximated equations are suggested for the diffuse scattering from various defects of the first kind due to non-ideal particles, including size polydispersity, orientational disorder and positional fluctuation about their ideal positions. Calculated curves using the formalism developed herein are compared with numerical simulations computed without any approximation. For a finite-sized assembly, the scattering from the whole domain of the assembly must also be included, and this is derived using the correlation function approach.