Linking Defect-Controlled Grain Growth and Band-Edge Optical Response in Chymosin-Assisted Pechini-Derived CeO_2−δ Nanoparticles

We investigate how grain growth, strain relaxation, and vacancy chemistry shape the near-edge optical response of nanocrystalline CeO${}_{2-\delta }$ prepared by a chymosin-assisted Pechini route from nitrate–citrate precursors. Rietveld line-profile analysis shows that phase-pure CeO${}_{2-\delta }$ forms after calcination between 400 and 1000 ${}^{\circ }$C. Over this range, the average crystallite size increases from ≈3.4 to ≈57 nm, while the microstrain decreases from 0.79% to 0.05%, with size–strain scaling consistent with interface-controlled grain growth that follows a normal growth law with exponent $m=2$ and activation energy $Q\approx 155$ kJ mol${}^{-1}$. Raman spectroscopy tracks the sharpening of the $F_{2g}$ mode and the fading of defect-related bands, X-ray photoelectron spectroscopy reveals a nonmonotonic evolution of the surface Ce${}^{3+}$ fraction and separates lattice from adsorbed oxygen species, and electron paramagnetic resonance detects vacancy-bound Ce${}^{3+}$ polarons that weaken at high temperature. Diffuse-reflectance UV–Vis spectra show a modest blue shift of the apparent band gap from $E_g\approx 2.78$ to 2.95 eV as crystallites coarsen, while the Urbach energy $E_u$ follows the Ce${}^{3+}$ content and sub-gap tailing. The structural, spectroscopic, and optical results together map out a quantitative connection between grain growth, vacancy populations, and near-edge optical properties in CeO${}_{2-\delta }$ nanoparticles.