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.

Zeolites 5A were obtained by ion exchange of a zeolite 4A, previously synthesized by the hydrothermal method from precursor kaolin, with the aim of removal As(V) from drinking water and Pb(II) from irrigation surface water. Zeolite 5A was characterized before and after adsorption by X-ray diffraction, scanning electron microscopy, energy dispersive spectroscopy, and X-ray photoelectron spectroscopy. To find the adsorption mechanisms of both As and Pb in real waters, experiments on adsorption kinetics, optimum pH, adsorbent dose, and adsorption isotherms were developed. Adsorption kinetics and adsorption isotherm models were evaluated, and the selection criterion for the appropriate model was made using the residual sum of squares (RSS) and Bayesian information criterion (BIC). As a result, removal adsorption of As(V) and Pb(II) was higher than 95% in 9 and 12 h, respectively. The estimated maximum adsorption capacities for As and Pb were 36.35 mg g⁻¹ and 46.67 mg g⁻¹, respectively. Zeolite 5A is a low-cost adsorbent, through which a concentration of less than 0.01 mg L⁻¹ of As and Pb was obtained in drinking and irrigation water, which is below the permissible limit established by the World Health Organization (WHO).

The adsorption characteristics of titanium dioxide nanoparticles (nano-TiO₂) for the removal of Pb(II) from irrigation water were investigated in this work. To accomplish this, several adsorption factors, such as contact time and pH, were tested to assess adsorption efficiencies and mechanisms. Before and after the adsorption experiments, commercial nano-TiO₂ was studied using X-ray diffraction (XRD), scanning and transmission electron microscopy (SEM and TEM), energy dispersive spectroscopy (EDS), and X-ray photoelectron spectroscopy (XPS). The outcomes showed that anatase nano-TiO₂ was remarkably efficient in cleaning Pb(II) from water, with a removal efficiency of more than 99% after only one hour of contact time at a pH of 6.5. Adsorption isotherms and kinetic adsorption data matched the Langmuir and Sips models quite well, showing that the adsorption process occurred at homogenous sites on the surface of nano-TiO₂ by forming a Pb(II) adsorbate monolayer. The XRD and TEM analysis of nano-TiO₂ following the adsorption procedure revealed a non-affected single phase (anatase) with crystallite sizes of 9.9 nm and particle sizes of 22.46 nm, respectively. According to the XPS data and analyzed adsorption data, Pb ions accumulated on the surface of nano-TiO₂ through a three-step mechanism involving ion exchange and hydrogen bonding mechanisms. Overall, the findings indicate that nano-TiO₂ has the potential to be used as an effective and long-lasting mesoporous adsorbent in the treatment and cleaning of Pb(II) from water bodies.