The Best Approximate Racah Parameter Ratio: <i>r</i> = <i>C/B</i> = 3.7 (free-ion value), 4.7 or 8.0 for the Mn⁴⁺-Activated Phosphors?

The 3 d 3 -configuration ions, such as Mn 4+ and Cr 3+ , are very important for use in the warm white-LED lighting and indoor plant cultivation applications. The Racah parameters in conjunction with the Tanabe−Sugano (T−S) energy-level diagram are widely used as a means of deep understanding the effects of electron−electron repulsion within the transition metal complexes in coordination chemistry. In a T−S diagram, the Racah parameter ratio of 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 Racha and related parameter values are deduced. The present investigation examines the effects of r = C / B ratio on the T−S diagram analysis results for some Mn 4+ -activated phosphors. A newly proposed analysis model is comparatively discussed with the popularly used model. Results suggest that an assumption of r = 8.0 successfully explains the luminescence properties at least for the Mn 4+ -activated fluoride phosphors examined in the present study. Contrarily, no large difference in the analysis results of the Mn 4+ -activated oxide phosphors can be obtained between r = 4.7 and 8.0 though, if anything, the latter value of 8.0 seems to be slightly better.