The Best Approximate Racah Parameter Ratios of r = C/B for the Cr³⁺-Activated Fluoride and Oxide Phosphors

The Racah parameters B and C in conjunction with the Tanabe−Sugano (T–S) energy-level diagram are widely used as a means of fundamental understanding the effects of electron−electron repulsion within the transition metal complexes in coordination chemistry. In a T–S diagram, the Racah parameter ratio r = C/B is assumed and the excited-state transition energies are plotted as a function of the crystal-field strength parameter Dq. Once the Racah parameters are determined, more refined comparison is made between theory and experiment and more accurate Racah and related parameters are then deduced. The present investigation focuses on the effects of r = C/B ratio on the T–S diagram pictures for some Cr³⁺-activated fluoride and oxide phosphors. Our newly proposed analysis model is comparatively discussed with the popularly used model. Results suggest that an assumption of r = 8.0 can successfully explain the luminescence properties of various Cr³⁺-activated phosphors. The present study further provides the ever-unknown relationships between the Racah parameters and T–S diagram that are important for more fundamental understanding the 3d ³ (Cr³⁺)-ion-activated phosphor properties and are, therefore, of both scientific and technological interests.