Interplay of Electron–Phonon Coupling and Lattice Dilation in Band Gap Tuning of Gd ₂ Ti _{1– <i>x</i>} Fe _<i>x</i> O ₅

The temperature dependence of the band gap Eg in semiconductors is governed by electron–phonon coupling (EPC) and lattice dilation (LD), as established in the foundational works of Fan, Brooks, and Bardeen–Shockley. Analogous to thermal effects, chemical substitution in a host lattice perturbs both EPC and LD, yet their individual contributions to Eg variation under substitution remain insufficiently understood. In this work, we investigate the role of EPC and LD in shaping the band gap of Fe-substituted Gd2TiO5 (Gd2Ti1–xFexO5; x = 0.03, 0.05, 0.07, 0.10), a multifunctional oxide with applications in photonic devices and nuclear waste immobilization. X-ray diffraction, Raman spectroscopy, and optical absorption measurements reveal a systematic increase in unit cell volume and reduction in the band gap with increasing Fe content. Raman line width broadening indicates enhanced structural disorder. To disentangle EPC and LD effects, we apply a thermodynamic chain rule decomposition of (dEgdT)P, adapted to compositional variation. Our analysis shows that EPC and LD effects play the major role in the band gap narrowing at low Fe concentrations, while at higher concentrations (>3%), only the EPC effect drives the band gap trend. The relative variation in Raman feature reveals a direct EPC–LD interplay, offering a spectroscopic signature of this balance. These results provide new insights into how chemical substitution mediates electronic and structural interactions in complex oxides, with implications for band gap engineering.