Simultaneous Analysis of Wide Angle X-Ray Scattering Data (WAXS) and Extended X-Ray Absorption Fine Structure Spectroscopy (EXAFS) of Very Small Nanoparticles

Although experiments investigating the atomistic structure of disordered materials are today facile through modern instruments for X-ray scattering and spectroscopy, it is still a challenge to extract the relevant information especially in case of very small nanoparticles with a diameter smaller than 10 nm. In our contribution we will present recent advances in data analysis of this inverse problem using Reverse Monte Carlo (RMC) analysis [1].<br/><br/>RMC simulations enable the analysis of WAXS data as well as EXAFS spectra via partial pair distribution functions (pPDF) obtained from a physical, structural model. In case of nanoparticles and scattering data this approach suffers from the termination of the pPDFs due to the finite size of the particles. This produces artifacts in the computed scattering intensity due to the long-range probing distance of scattering which are eliminated by using the Debye scattering equation (DSE) for computing the scattering intensity from a particle model. Computational efficiency is provided by binning the distance distribution of atom pairs in the DSE.<br/><br/>Data fusion, i. e. simultaneous refinement of WAXS data and EXAFS spectra of small nanoparticles, is thus enabled using a mutual structural model. Therefore, this method allows the self-consistent extraction of complementary information on the local structure contained in EXAFS and on the long-range order in WAXS data. We describe this novel method for the nanocrystalline complex oxide LaFeO₃ [1]. The results are highly relevant for example for heterogeneous catalysis [2].<br/><br/>The method described can be further developed to additionally include small angle scattering data and provides an interface either via the (atomistic) structural model or the pPDFs to other physics simulation and materials modeling methods such as molecular dynamic (MD) simulations or density functional theory (DFT) modeling.<br/><br/>[1] M. Winterer and J. Geiß, <i>Combining reverse Monte Carlo analysis of X-ray scattering and extended X-ray absorption fine structure spectra of very small nanoparticles</i>, J. Appl. Cryst. <b>56</b> (2023) 103-109; doi.org/10.1107/S1600576722010858<br/>[2] J. Geiss, J. Bueker, J. Schulte, B. Peng, M. Muhler, M. Winterer, <i>LaCo_1-xFe_xO₃ Nanoparticles in Cyclohexene Oxidation</i>, J. Phys. Chem. C <b>127</b> (2023) 5029–5038; doi.org/10.1021/acs.jpcc.2c08644