First-Principles Investigation of Structural, Electronic, and Optical Transitions in FexZr1−xO2 Solid Solutions

First-principles density-functional theory (PBE, Quantum ESPRESSO) was employed to quantify how Fe substitution modulates the structural, elastic, electronic, and optical behaviour of cubic fluorite FexZr1−xO2 (x = 0.00–1.00). The fluorite FeO2 end member was treated as a hypothetical ambient-pressure limit to trace trends across the solid solution (experimental FeO2 being stabilized in the high-pressure pyrite phase). Mechanical stability was verified via the cubic Born criteria, and composition-dependent stiffness and anisotropy were assessed through Voigt–Reuss–Hill moduli, Pugh ratio, and elastic indices. A strong band-gap narrowing was found—from 3.41 eV (x = 0) to ≈0.02 eV (x = 0.50)—which was accompanied by a visible–NIR red-shift, large absorption (α ≈ 105 cm−1 at higher x), and enhanced refractive index and permittivity; metallic-like response was indicated at high Fe content. Spin-polarized calculations converged to zero total and absolute magnetization, indicating a non-magnetic ground state at 0 K within PBE. The effect of oxygen vacancies (V0)—expected under Fe3+ charge compensation—was explicitly considered: V0 is anticipated to influence lattice metrics, elastic moduli (B, G, G/B), and sub-gap optical activity, potentially modifying stability and optical figures of merit. Stoichiometric (formal Fe4+) predictions were distinguished from V0-rich scenarios. Absolute band gaps may be underestimated at the PBE level.