Theoretical Studies of the Local Structure and EPR Parameters of Tetragonally Distorted Tetrahedral Cu²⁺ Sites in Phosphate Glasses

Abstract—In this work, we theoretically investigate the local structure and electronic paramagnetic resonance (EPR) parameters (g-factors g_i and A-constants A_i, i = //, ⊥) of tetragonal Cu²⁺ centers in phosphate glasses (xCuO⋅(1 – x)[2P₂O₅⋅Na₂O] (0.5< x < 5 mol %)) with the aid of the three-order perturbation formulae of these parameters for 3d⁹ ions in tetragonally distorted tetrahedra based on the cluster approach. In our calculations, both contributions to EPR parameters from the spin-orbit (SO) coupling interactions of the central Cu²⁺ ions and the ligand orbital and SO coupling interactions are included. The crystal-field parameters related to the splitting of d-orbitals are calculated from the superposition model and the local structures of the studied Cu²⁺ centers in the glasses. Based on the calculations, the local bond angle is found to be about 3.78° larger than that of the ideal tetrahedral site, resulting in a slightly compressed ligand tetrahedron. The relative contributions to the g-factors from the ligand orbital and SO coupling interactions are more important than those from the third-order perturbation terms. The theoretical results show good agreement with the experimental values. The signs and the less anisotropy (ΔA = |A_//| – |A_⊥| ) of A-constants for the tetrahedral Cu²⁺ centers are discussed.