Title: Improved modeling of nanocrystals from atomic pair distribution function data
Description: Accurate determination of the structure of nanomaterials is a key step towards understanding and controlling their properties. This is especially challenging for small nanoparticles, where traditional electron microscopy provides partial information about the morphology and internal atomic structure for a limited number of particles, and x-ray powder diffraction data is often broad and diffuse and not amenable to quantitative crystallographic analysis. In these cases a better approach is to use atomic pair distribution function (PDF) analysis of synchrotron x-ray total scattering data, in tandem with high-resolution imaging techniques. Even with these tools available, extracting detailed models of nanoparticle cores is notoriously difficult and time consuming. For many years, poor fits were considered to be a de facto limitation of nanoparticle studies using PDF methods, and semi-quantitative analyses were commonly employed. In this work, we aim to challenge this assumption. We started with a survey of 12 canonical metallic nanomaterials, both elemental and alloyed, prepared using different synthesis methods, with significantly different shapes and sizes as disparate as 2 nm wires and 40 nm particles, using PDF data collected at multiple synchrotron sources and beamlines.

Widely applied shape-tuned attenuated crystal (AC) fcc models proved inadequate, yielding structured, coherent, and correlated fit residuals. However, equally simple discrete cluster models could account for the largest amplitude features in these difference signals. A hypothesis testing based approach to nanoparticle structure modeling systematically ruled out effects from crystallite size, composition, shape, and surface faceting as primary factors contributing to the AC misfit, and it was found that these previously ignored signals could be explained as originating from well defined domain structures in the nanoparticle cores. This analysis gave insight into how sensitive PDF analyses could be towards identifying the presence of interfaces inside ultrasmall nanoparticle cores using atomistic modeling, but still hinged on manual trial-and-error testing of clusters from different structural motifs. To address this challenge, we developed a structure screening methodology, called cluster-mining, wherein libraries of clusters from multiple structural motifs were built algorithmically and individually refined against experimental PDFs.

This differs from traditional approaches for crystallographic analysis of nanoparticles where a single model containing many refinable parameters is used to fit peak profiles from a measured diffraction pattern. Instead, cluster-mining uses many structure models and highly constrained refinements to screen libraries of discrete clusters against experimental PDF data, with the aim of finding the most representative cluster structures for the ensemble average nanoparticle from any given synthesis. Finally, we wanted to identify other nanomaterial systems where this approach might prove useful, and demonstrated that the PDF was also capable of detecting seemingly subtle morphological variations in highly faceted titania photocatalyts. This opens a new avenue towards characterizing shape-controlled metal oxide nanomaterials with well-defined surface facets. To extend this work in the future, our goal is to develop new tools for building discrete nanoparticles algorithmically, integrate statistical approaches to make model selection more efficient, and ultimately, move towards an atomic scale understanding of nanoparticle structure that is comparable to bulk materials.