Atomic structure analysis at the nanoscale using the pair distribution function: simulation studies of simple elemental nanoparticles

The pair distribution function (PDF), as determined from total X-ray or neutron scattering, is a valuable probe of atomic arrangements in nanoparticles. Structural information in the experimental PDF is modified by the effects of particle shape, particle size, extended defects and internal substructure. This study uses synthetic PDF data, generated for simple elemental nanoparticles having different degrees of displacive atomic disorder in the particle surface compared with the interior, to explore the feasibility of reliably extracting key features (i.e. a lattice constant, particle diameter, atomic displacement parameters for the interior and the surface, and thickness of the surface layer) from experimental data in the absence of systematic errors using a statistical modeling approach. This approach determines a model PDF via simulation of an ensemble of nanoparticles. Several methods for model optimization were tested and a differential evolution algorithm was selected as the most reliable and accurate. Fitting synthetic PDF data using this algorithm was demonstrated to estimate all features well with small standard uncertainties. Identification of larger displacive atomic disorder in the particle surface compared with the interior was shown to be possible via model selection. Software for nanoparticle simulation and model optimization is provided in open-source form, to allow reproduction and extension of the results presented here.