Combined fitting of small- and wide-angle X-ray total scattering data from nanoparticles: benefits and issues

Simultaneous fitting of small- (SAS) and wide-angle (WAS) X-ray total scattering data for nanoparticles has been explored using both simulated and experimental signals. The nanoparticle types included core/shell metal and quantum-dot CdSe systems. Various combinations of reciprocal- and real-space representations of the scattering data have been considered. Incorporating SAS data into the fit consistently returned more accurate particle-size distribution parameters than those obtained by fitting the WAS data alone. A popular method for fitting the Fourier transform of the WAS data (i.e. a pair-distribution function), in which the omitted SAS part is represented using a parametric function, typically yielded significantly incorrect results. The Pareto optimization method combined with a genetic algorithm proved to be effective for simultaneous SAS/WAS analyses. An approach for identifying the most optimal solution from the Pareto set of solutions has been proposed.