Nanoparticle size distribution from inversion of wide angle X-ray total scattering data

An increasingly important issue in nanoscience and nanotechnology is the accurate determination of nanoparticle sizing. Wide angle X-ray total scattering (WAXTS) data are frequently used to retrieve the Particle Size Distributions (PSDs) of nanocrystals of highly technological relevance; however, the PSD shape typically relies on an a-priori assumption. Here, we propose a modified version of the classical iterative Lucy-Richardson (LR) algorithm, which is simple, fast and highly reliable against noise, and demonstrate that the inversion of WAXTS data can be profitably used for recovering accurate PSD regardless of its shape. Computer simulations based on the use of the Debye Scattering Equation (DSE) modelling WAXTS data show that the algorithm is capable of recovering accurate PSDs even when the sample is made of a mixture of different polymorphs and/or exhibits microstrain effects. When applied to the inversion of WAXTS data taken on real samples, the method requires accurate modelling of the nanoparticle crystal structure, which includes structural defects, microstrain and surface induced distortions. Provided that this information is correctly fed to the program, the inversion algorithm reconstructs the WAXTS data with high accuracy and recovers highly robust (against noise) PSDs. Two examples reporting the characterization of Magnetite-Maghemite and commercial P25-Titania nanopowders, are discussed. We demonstrate that pre-assumption of wrong PSD shape leads to inaccurate number-based average sizes in highly polydisperse samples.