Pair distribution function analysis of discrete nanomaterials in PDFgui

Pair distribution functions (PDFs) are a leading tool for atomic structure analysis of nanomaterials. However, the most widely used programs for refining atomic structure against PDF data are based on extended crystallographic models, which cannot be applied to discrete, whole nanoparticles. This work describes a straightforward approach to simulate and refine atomistic models of discrete clusters and nanoparticles employing widely used PDF modelling programs such as PDFgui [Farrow et al. (2007). J. Phys. Condens. Matter , 19 , 335219] that utilize extended crystallographic models. In this approach, the whole particle to be modelled is contained within an expanded, and otherwise empty, unit cell that is sufficiently large to avoid correlations between atoms in neighbouring unit cells over the r range analysed. The PDF of the particle is simulated as a composite using two conventional `phases': one that calculates the atom–atom correlations and one that approximates the local number density. This approach is first validated for large nanoparticles that are well modelled by a conventional shape factor model, and then applied to simulate the PDF of discrete particles and low-dimensional materials (graphene and MXene) and to model the experimental PDF data for single-layer FeS nanosheets. A comparison of this approach with the DiffPy-CMI program [Juhás et al. (2015). Acta Cryst. A 71 , 562–568], which calculates the PDF of discrete species, shows that the composite modelling approach is equally or more accurate. Example input files for implementing this approach within PDFgui and TOPAS [Coelho (2018). J. Appl. Cryst. 51 , 210–218], and recommendations for selecting model parameters for reliable application of this refinement strategy, are provided.