Studies on the local structures of the substitutional and interstitial Ni3+ centers in rutile

The local structures of the two rhombic Ni3+ centers (on the substitutional and interstitial sites) in rutile (TiO2) are theoretically studied from the perturbation formulas of the g factors for a 3d7 ion of low spin (S=1/2) in rhombically distorted octahedra. In these formulas, the contributions to the g factors from the low symmetrical parts of the crystal-fields as well as the spin-orbit coupling interaction and orbitals of the ligands are taken into account. From the investigations, the ligand octahedron in the substitutional Ni3+ center may suffer a slightly larger axial elongation (characterized by the axial distortion angle Δαs∼-1.09o) than that (ΔαsH∼-0.73o) in the host and the much smaller perpendicular distortion (characterized by the rhombic distortion angle Δθs∼-0.75o) than that (ΔθsH∼-9.0o) in the host due to the Jahn-Teller effect. For the interstitial Ni3+ center, the ligand octahedron is found to undergo a smaller compression (characterized by the axial distortion angle Δαi∼1.48o) than that (ΔαiH∼8.17o) in the host and a slighter rhombic distortion (Δθi∼0.1o) than that (ΔθiH∼7.0o) in the host due to the Jahn-Teller effect. The calculated g factors based on the above structural parameters show better agreement than those based on the host structural parameters and those in absence of the spin-orbit coupling and the orbitals of the ligands with the experimentally observed values