Theoretical studies on the g-factors and the local structure of W5+ ions in tungsten phosphate glasses

 In this work, we adopt the three-order perturbation formulae for g-factors (g//, g^) of d1 ions in the octahedral environment to calculate the g-factors of W5+ ions in tungsten phosphate glasses containing lithium (P2O5-Li2WO4-Li2O). In the light of the high valence state of the studied W5+ centers and hence the strong covalency of the studied octahedral [WO6]7- cluster, we consider the contributions to g-factors from the ligand orbital and spin-orbit (SO) coupling interactions based on the cluster approach. The required tetragonal crystal-field parameters are calculated from the local structure of W5+ ions based on the superposition model. According to the theoretical calculations, we find that the octahedral [WO6]7- clusters possess the tetragonally compressed distortion with a shorter W-O bond length (≈1.54 Å) and a longer one (≈2.26 Å) along C4 axis and four normal W-O bond length (≈1.94 Å) in the perpendicular plane, which infers that the W5+ ions are in the form of tungstyl ions (i.e., WO3-). Based on the local structural data, the theoretical values of g// and g^ agree well with the experimental values.