In the current work, the Taguchi design of experiment and Grey relational analysis (GRA) was used to optimize various experimental parameters, such as mol% of Fe3+ doping, fuel, wt% of NH4Cl flux, calcination temperature for the preparation of Fe3+-doped zinc oxide (FZO) by solution combustion synthesis. The powder X-ray diffraction pattern of FZO exhibits that crystallite size is increasing with increase in calcination temperature and the band gap was found to decrease with increase in mol% of Fe3+. The surface morphology of FZO nanoparticles (NPs) studied using a scanning electron microscope was found to be distinctive structures such as cubic shape, irregular mesoporous particles, tiny clusters, large and spongy pores structure and so on. High-resolution transmission electron microscopy images, selected-area electron diffraction (SAED) pattern, and an energy-dispersive X-ray spectrum confirm the presence nanoscale FZO NPs, the polycrystalline nature and elemental composition. Various analyses, such as the signal-to-noise ratio ratio, analysis of variance (ANOVA) and GRA, were performed to validate the predicted optimal model. The ANOVA indicates that the crystallite size was significantly affected by calcination temperature with contribution factor 93.28%. Band gap energy was affected by both mol% of Fe3+ doping and calcination temperature with contribution 66.41% and 25.70%, respectively. Grey relational grading confirmed that the combination 5% doping, d-glucose fuel, 10% of flux and 600 °C calcination temperature can be used to get lower band gap energy (2.87 eV) and lower crystallite size (11.63 nm). Finally, Grey theory prediction helps us to choose a combination of 5% of doping, oxalic acid as a fuel, 5% of NH4Cl flux and 500 °C calcination temperature to obtain the required band gap of 2.61 eV and the crystallite size 10.12 nm. The FZO NPs were used for photocatalytic degradation of methyl orange (MO) dye. The photocatalytic degradation results showed that the MO dye removal rate efficiency is higher (82.30%) on the Grey theory prediction result as compared with other L9 orthogonal array.
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