A Comparable Study on the EPR g Factors and the Local Structures of the Substitutional and Interstitial Mo5+ Centers in Rutile

Abstract

The electron paramagnetic resonance (EPR) g factors and the local structures of Mo⁵⁺ centers on the substitutional and interstitial sites in rutile are theoretically studied from the perturbation formulas of these parameters for a 3d¹ ion in rhombically compressed and elongated octahedra, respectively. In the calculation formulas, the crystal field parameters are determined from the superposition model, and the contributions from the spin–orbit coupling (SOC) of the ligands are taken into account. Based on the calculations, the ligand octahedron in the substitutional Mo⁵⁺ center may suffer a larger axial compression with the parallel and perpendicular impurity—ligand length bonds R′_||s ≈ 1.932 and R′_⊥s ≈ 1.975 Å) than the bond lengths R_||s ≈ 1.99 and R_⊥s ≈ 1.94 Å in the host and the much smaller perpendicular distortion (i.e., θ_s′ ≈ 87.32º) than that θ_s ≈ 81.21º) in the host related to the ideal angle θ₀ ≈ 90º in a regular octahedron due to the Jahn–Teller (JT) effect. For the interstitial Mo⁵⁺ center, the ligand octahedron exhibits the axial elongation (i.e., R′_||i ≈ 2.155 and R′_⊥i ≈ 1.987 Å) rather than a compressed octahedra with R_||i ≈ 1.67 and R_⊥i ≈ 2.23 Å in the host and a smaller rhombic distortion (θ_i′ ≈ 95.2º) than that θ_i ≈ 97º in the host related to θ₀ due to the JT effect. The reasonableness of these results are discussed.