Theoretical studies of the local structure and the epr parameters for tetragonal Cu$^{2+}$ center in mixed alkali cadmium phosphate glasses

Abstract

The local structure of the Cu$^{2+}$ center in mixed alkali cadmium phosphate (10Li$_2$O-10Na$_2$O-20CdO-59.5P$_2$O$_5$) glass is theoretically investigated from the optical spectral data and high-order perturbation formulas of the electron paramagnetic resonance (EPR) parameters ($g$-factors $g_{\|}, g_{\bot}$ and the hyperfine structure constants $A_{\|}, A_{\bot}$) for a 3d$^9$ ion in a tetragonally elongated octahedron. In these formulas, the ligand orbital and spin-orbit coupling contributions are taken into account based on the cluster approach in view of moderate covalency. The required crystal-field parameters are determined by the superposition model. According to the calculations, the impurity-ligand distances parallel and perpendicular to the C$_4$ axis of [CuO$_6$]$^{10-}$ cluster are found to be, respectively, $R_{\|} \approx 2.051$ \AA\, and $R_{\bot}\approx 2.029$ \AA\, due to Jahn-Teller effect. Based on the above local structure data, the optical spectra are satisfactorily interpreted. The signs of $ A_{\|} $ and $ A_{\bot} $ for the Cu$^{2+}$ center are suggested in the discussion.