A new approach to calculating powder diffraction patterns based on the Debye scattering equation

A new method is defined for the calculation of X-ray and neutron powder diffraction patterns from the Debye scattering equation (DSE). Pairwise atomic interactions are split into two contributions, the first from lattice-pair vectors and the second from cell-pair vectors. Since the frequencies of lattice-pair vectors can be directly related to crystallite size, application of the DSE is thereby extended to crystallites of lengths up to ~200 nm. The input data correspond to unit-cell parameters, atomic coordinates and displacement factors. The calculated diffraction patterns are characterized by full backgrounds as well as complete reflection profiles. Four illustrative systems are considered: sodium chloride (NaCl), α-quartz, monoclinic lead zirconate titanate (PZT) and kaolinite. The effects of varying crystallite size on diffraction patterns are calculated for NaCl, quartz and kaolinite, and a method of modelling static structural disorder is defined for kaolinite. The idea of partial diffraction patterns is introduced and a treatment of atomic displacement parameters is included. Although the method uses pair distribution functions as an intermediate stage, it is anticipated that further progress in reducing computational times will be made by proceeding directly from crystal structure to diffraction pattern.