Research on the Optical and EPR Spectral Data and the Local Structure for the Tetragonal $Nb^{4+}$ Center in Glasses

Two optical bands and four EPR (or spin-Hamiltonian) parameters (g factors $g_{∥}$, $g_{⊥}$ and hyperfine structure constants $A_{∥}$, $A_{⊥}$) of the tetragonally-compressed $Nb^{4+}$ octahedral center in glasses are calculated from two methods, the complete diagonalization (of energy matrix) method and the perturbation theory method. Both methods are founded on the two-spin-orbit-parameter model where both the contribution to the spectral data from the spin-orbit parameter of central $d^{n}$ ion and that of ligand ion via covalence effect are considered. The calculated results from both the complete diagonalization (of energy matrix) method and perturbation theory method show reasonable agreement with the experimental values. The signs and possible misprint for the observed hyperfine structure constants $A_{∥}$ and $A_{⊥}$ are suggested, and the local structure of the tetragonal $Nb^{4+}$ center in glasses due to the Jahn-Teller effect is gained from the calculations. The results are discussed.