Exact model calculations of the total radial distribution functions for the X-ray diffraction case and systems of complicated chemical composition

An algorithm to simulate the radial distribution functions (RDFs) for systems of complex chemical composition is presented which takes into account the exact formulae of the RDF theory in the case of X-ray diffraction. The representation of the partial RDFs of the structural models by histograms allows the method to be used for a wide set of models, for example structures generated with stochastic simulations like the Monte Carlo method. The sensitivity of the results in relation to histogram step size and histogram noise is investigated. A step size of about half the full width at half-maximum (FWHM) of the partial RDF peaks is sufficiently small to make the algorithm reasonably insensitive to the particular step size and to histogram noise. A solution is proposed to calculate the RDF for powders of nanocrystalline particles with complex structures, for which not all interatomic distances can be defined accurately.