New Analysis Model for the Determination of Racah and Crystal-Field Splitting Parameters: Verification and Case Studies
Sadao Adachi
Abstract
The Racah parameters in conjunction with the Tanabe—Sugano energy-level diagram are widely used as a means of describing the effects of electron—electron repulsion within the metal complexes in coordination chemistry. A determination of the excitation energy levels in the 3 d 3 -configuration ions (Mn 4+ , Cr 3+ , etc.) is possible from a set of Racah parameters ( B and C ) and crystal-field splitting parameter ( Dq ), and vice versa. The Tanabe—Sugano diagram promises that the zero-phonon line 2 E g energies, E ( 2 E g ) ZPL , over B of the Mn 4+ and Cr 3+ ions should be nearly crystal field independent, since they are practically parallel to the horizontal axis in the whole range of Dq / B variation. However, the experimental E ( 2 E g ) ZPL plots showed a gradual increase with increasing Dq / B , in disagreement with the Tanabe—Sugano diagram. Therefore, a new analysis model assuming the Racah parameter ratio of C / B ∼ 4.7 has been recently proposed [ ECS J. Solid State Sci. Technol. , 8 , R164 (2019); 8 , R183 (2019)]. However, the new model has been used without rigorous validation. The present study focused on this problem and analyzed the luminescence properties of LiBaF 3 :Cr 3+ and LaGaO 3 :Mn 4+ phosphors. More generalized expressions were proposed for analyzing the various kinds of phosphors at an optional ratio of C / B = r .