Effect of annealing temperature on the luminescence of Ce_1−xPO₄: Tb_x³⁺ nanocrystals: A novel theoretical model and experimental verification

Terbium-doped cerium phosphate nanocrystals are successfully synthesized through microwave-assisted sol–gel method and are annealed at different temperatures for detailed investigation on structural and optical properties. The structural characterization carried out using X-ray diffraction analysis confirmed that all the samples are crystallized in monoclinic structure having chemical formula CePO₄ and revealed the thermal stability of the synthesized samples. A novel theoretical model is proposed to investigate the influence of annealing temperature on Tb³⁺ by analyzing I₄/I₃—annealing temperature plot in which two regions are distinguished as above and below the crystallization temperature. A generalized equation derived in terms of rate constants for I₄/I₃ helps to frame four distinct cases describing the role of different radiative and nonradiative relaxations in the Tb³⁺ luminescence from ⁵D₃ and ⁵D₄ levels. The subsequent evaluation of each case described the role of defects, cross-relaxation and multiphonon relaxation in the variation of I₄/I₃ with annealing temperature and verified by the experimentally observed data with the help of TEM, FESEM, TGA and decay analysis.