Abstract
Various crystallite size estimation methods were used to analyze X-ray diffractograms of spherical cerium dioxide and titanium dioxide anatase nanoparticles aiming to evaluate their reliability and limitations. The microstructural parameters were estimated from several integral breadth methods such as Scherrer, Monshi, Williamson–Hall, and their variants: (i) uniform deformation model, (ii) uniform strain deformation model, and (iii) uniform deformation energy density model. We also employed the size–strain plot and Halder–Wagner method. For this purpose, an instrumental resolution function of an Al2O3 standard was used to subtract the instrumental broadening 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. The Rietveld whole powder pattern decomposition method was introduced for comparison purposes, being the best candidate to fit the X-ray diffraction data of metal-oxide nanoparticles. Refined microstructural parameters were obtained using the anisotropic spherical harmonic size approach and correlated with the above estimation methods and transmission electron microscopy images. In addition, μ-Raman spectra were recorded for each material, estimating the mean crystallite size for comparison by means of a phonon confinement model.
Highlights
Nanoparticles (NPs) can be obtained through various physical, chemical, or biological synthesis methods [1]
For the Al2 O3 refinement, the TCH profile was employed to obtain the instrumental parameters of the equipment, which was added to the instrumental resolution file (IRF) and later used to determine the average crystallite sizes of the CeO2 and TiO2 NPs
It is important to highlight that the Scherrer equation could only be used in the cases: (i) for average sizes up to 100–200 nm; (ii) sample and signal/noise ratio, because the broadening of the XRD peak decreased as the crystallite size increased and it was difficult to separate the broadening from the peak [21]; and (iii) since a line profile standard could not have residual broadening due to the domain size or strain, or other sources, a well-crystallized powder had to be employed
Summary
Nanoparticles (NPs) can be obtained through various physical, chemical, or biological synthesis methods [1]. The Rietveld method (RM) is a tool for analyzing crystalline structures [13], which is based on the theoretical refinement of the structural or cell parameters, atomic displacements, anisotropy, cell stresses, shape, and anisotropy effects, among others, leading to a convergence between the values of the experimental diffractogram curves and the theoretical model [14]. This refinement is suitable when making a multiphasic analysis (percentual phase concentration). Crystallite sizes were estimated from μ-Raman measurements by means of a phonon confinement model
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