Proper usage of Scherrer's and Guinier's formulas in X-ray analysis of size distribution in systems of monocrystalline CeO2 nanoparticles

Abstract

In nowadays, X-ray diffraction and scattering phenomena are widely used as analytical tools in the optimization and control of nanomaterial synthesizing processes. In systems of monocrystalline nanoparticles with size distribution, the physical meaning of size values as determined by using Xray methods is still controvertial. To answer such fundamental issue, series of virtual nanoparticles with sizes ranging from 1 nm to 90 nm were generated and their exact scattering power computed via pair distance distribution function. Composed X-ray diffraction and scattering patterns from systems of virtual nanoparticles demonstrated that diffraction and scattering phenomena see the size distributions with different weightings. Therefore, combining both phenomena leads to the determination of size distribution in the systems. In practice, X-ray diffraction and small-angle scattering experiments were applied to solve the size distributions in a series of samples of cubic ceria nanoparticles, revealing a systematic size dispersion as a function of synthesis parameters.