Kinematic Scattering by Nanocrystals

Various formulations are compared which describe diffraction from ultra-thin single-crystal films in the symmetric scattering configuration, showing that, for this thickness range, several implicit assumptions in these formulations are no longer satisfied. Consequently, the position, integrated intensity and integral breadth of a diffraction peak cannot be related to the lattice spacing of the material or the number of unit cells along the diffraction vector using traditional analysis methods. Some simple equations are proposed to obtain the correct values of these parameters for this specific sample/diffraction geometry combination. More generally, the development of rigorous formalisms for analyzing diffraction from nanocrystals is proposed.