Strain and Grain Size of CeO₂ and TiO₂ Nanoparticles: Comparing Structural and Morphological Methods

Abstract

Various crystallite size estimation methods were used to analyze X-ray diffractograms of spherical cerium dioxide and donut-like titanium dioxide anatase nanoparticles aiming to evaluate their reliability and limitations. The microstructural parameters were estimated from Scherrer, Monshi, Williamson-Hall, and their variants: i) uniform deformation model, ii) uniform strain deformation model, and iii) uniform deformation energy density model, and also size-strain plot, and Halder-Wagner method. For that, and improved systematic Matlab code was developed to estimate the crystallite sizes and strain, and the linear regression analysis was used to compare all the models based on the coefficient of determination, where the Halder Wagner method gave the highest value (close to 1). Therefore, being the best candidate to fit the X-ray Diffraction data of metal-oxide nanoparticles. Advanced Rietveld was introduced for comparison purposes. Refined microstructural parameters were obtained from a nanostructured 40.5 nm Lanthanum hexaboride nanoparticles and correlated with the above estimation methods and transmission electron microscopy images. In addition, electron density modelling was also studied for final refined nanostructures, and μ-Raman spectra were recorded for each material estimating the mean crystallite size and comparing by means of a phonon confinement model.