Experimental statistic design applied for obtaining Zn:xCe by microwave-assisted hydrothermal method with photocatalytic property

In this study, the nanostructures of pure ZnO and ZnO:xCe³⁺ were prepared using statistic design—factorial design 3^(3-1)—3-level and mixed-level factorials and fractional with replicates in the central point, totaling 11 experiments. The experiments were performed using the microwave-assisted hydrothermal (MAH) method with Ce³⁺ concentration of 2 and 4 mol% at 60, 110, and 160 ℃ for 10, 20, and 30 min. X-ray diffraction (XRD), scanning electron microscopy (SEM), and optical diffuse reflectance were used to characterize the products. The fractional factorial design indicated the optimal design area, and the studies were continued by ridge analysis. The analysis of variance (ANOVA), the Pareto, and the model adjusted to the conditions proposed in this study due to the determination coefficient of 99.9%, variance (R²), and response surface generated were satisfactory, thus having an optimization in the process of obtaining ZnO doped with Ce.