Implications of size dispersion on X-ray scattering of crystalline nanoparticles: CeO₂ as a case study

Abstract

Controlling the shape and size dispersivity and crystallinity of nanoparticles (NPs) has been a challenge in identifying these parameters' role in the physical and chemical properties of NPs. The need for reliable quantitative tools for analyzing the dispersivity and crystallinity of NPs is a considerable problem in optimizing scalable synthesis routes capable of controlling NP properties. The most common tools are electron microscopy (EM) and X-ray scattering techniques. However, each technique has different susceptibility to these parameters, implying that more than one technique is necessary to characterize NP systems with maximum reliability. Wide-angle X-ray scattering (WAXS) is mandatory to access information on crystallinity. In contrast, EM or small-angle X-ray scattering (SAXS) is required to access information on whole NP sizes. EM provides average values on relatively small ensembles in contrast to the bulk values accessed by X-ray techniques. Besides the fact that the SAXS and WAXS techniques have different susceptibilities to size distributions, SAXS is easily affected by NP–NP interaction distances. Because of all the variables involved, there have yet to be proposed methodologies for cross-analyzing data from two techniques that can provide reliable quantitative results of dispersivity and crystallinity. In this work, a SAXS/WAXS-based methodology is proposed for simultaneously quantifying size distribution and degree of crystallinity of NPs. The most reliable easy-to-access size result for each technique is demonstrated by computer simulation. Strategies on how to compare these results and how to identify NP–NP interaction effects underneath the SAXS intensity curve are presented. Experimental results are shown for cubic-like CeO2 NPs. WAXS size results from two analytical procedures are compared, line-profile fitting of individual diffraction peaks in opposition to whole pattern fitting. The impact of shape dispersivity is also evaluated. Extension of the proposed methodology for cross-analyzing EM and WAXS data is possible.