Racah Parameters and Tanabe-Sugano Energy-Level Diagram for X ₃ Sc ₂ Ga ₃ O ₁₂ :Cr

The Racah parameters, B and C , in conjunction with the Tanabe-Sugano (T-S) energy-level diagram are widely used as a means of fundamentally understanding the effects of electron-electron repulsion within the transition metal complexes. In a TS diagram, the Racah parameter ratio of r  =  C / B is assumed and then the excited-state transition energies are plotted on its diagram as a function of the crystal-field strength parameter Dq . Once the Racah parameter ratio r is determined, more refined comparison between theory and experiment will be made with deducing more reliable Racah and related parameter determination. The present study focuses on the effects of r value on the T-S diagrams of some X 3 Sc 2 Ga 3 O 12 :Cr 3+ garnet phosphors with X = Lu, Y, Gd, and La. Our newly proposed analysis model is comparatively discussed with the generally accepted model. Results suggest that an assumption of r = 8.0 explains the luminescent properties of the Cr 3+ -activated garnet phosphors very well. Because of the common best-fit determined value of r ∼ 8.0, the various excited-state energies, such as 2 E g , 4 T 2 g , 4 T 1 g ,a , 2 A 1 g ,a , and 4 T 1 g ,b , for these garnet phosphors can be plotted on the same T-S diagram. This makes possible to deeply understanding a group of X 3 Sc 2 Ga 3 O 12 :Cr 3+ garnet phosphors.