Application of the Debye function to systems of crystallites

The Debye function was used to simulate the X-ray powder diffraction patterns from loose-packed systems of nanocrystals. The resulting patterns contain local atomic lattice information in the wide-angle region as well as long range, inter-particle structure features in the small-angle region. Both monodisperse and polydisperse systems of particles were considered in this study. The minimum number of particles necessary in the system to generate an accurate pattern is shown to increase with the system polydispersity. Diffraction patterns from a powder of uniformly oriented particles were simulated to show that the observation of coherency in bulk nanocrystalline materials is unlikely. Furthermore, the accuracy of the Williamson–Hall plot was studied by analyzing the simulated patterns. Whereas this study was focused on systems of loose particles, the results also might suggest some guidelines and considerations when diffraction patterns are simulated from atomistic models of nanocrystalline bulk materials.