Investigations of the optical spectral bands, g factors and local structure for the tetragonal Cr⁵⁺ tetrahedral clusters in Cr-doped silica glasses

Graphical abstract: By considering the dynamic effect owing to the vibrational motion of ligands, the anisotropic g factors (g_// < g_⊥), the isotropic g factors (g_// = g_⊥) and the anisotropic g factors (g_// > g_⊥) for the different tetragonal (CrO₄)³⁻ clusters in glasses are reasonably explained in a unified way. - Highlights: • g Factors and also optical band positions of Cr⁵⁺ in silica glasses are calculated. • The calculation is based on the two (CF and CT)-mechanism model. • The dynamic effect due to the vibrational motion of ligands is considered. • Local structure of (CrO₄)³⁻ cluster in Cr-doped silica glasses is obtained. • Three types of g factors for different (CrO₄)³⁻ are explained in a unified way. - Abstract: In this paper, the weaknesses and mistakes in the assignments of some optical absorption bands and the theoretical calculations of g factors (g_// < g_⊥) in the previous papers for the tetragonally-elongated (CrO₄)³⁻ clusters in Cr-doped silica glasses prepared with sol–gel method are pointed out and corrected. On the basis of these, the g factors g_// and g_⊥ for this Cr⁵⁺ cluster are calculated from the high-order perturbation formulas based on the two-mechanism model (where the contributions to g factors due to both the crystal field (CF) mechanism in the widely-used CF theory and the charge-transfer (CT) mechanism are included) for the tetragonally-elongated d¹ tetrahedral clusters with the ground state |d_x²_−y²〉. From the calculated values and by considering the small admixture between the ground state |d_x²_−y²〉 and the first excited state |d_z²〉 owing to the vibrational motion of ligands (note: this dynamic effect leads the elongated (CrO₄)³⁻ cluster to become the twinkling compressed one), the calculated g_// and g_⊥ are in reasonable agreement with the experimental values. In the calculations, the needed CF energy levels (corresponding to the optical spectral bands) are obtained from CF theory in which the CF parameters are estimated from the superposition model. Thus, the optical band positions of (CrO₄)³⁻ cluster in silica glassed are explained and the local structure of static (CrO₄)³⁻ cluster is obtained. By considering the dynamic effect, the isotropic g factors (g_// = g_⊥) at room temperature for another (CrO₄)³⁻ cluster in silica glasses and the anisotropic g factors (g_// > g_⊥) for the tetragonally-compressed (CrO₄)³⁻ cluster in barium aluminophosphate glasses are also explained in a unified way. The results are discussed