New Analysis Model for the Determination of Racah and Crystal-Field Splitting Parameters: Verification and Case Studies

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 3d 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.

Broadband photoluminescence in a ceramic (Mg2SnO4–SnO2):Cr3+ system

“…From this method, the Dq/B ratio was 2.32, located close to the crossing level region. The Dq, B and Dq/B values were relatively close to the values determined using the Adachi model [46,47]. Figure 5 displays an energy level diagram, showing the energy levels involved in the Cr 3+ excitation and emission processes in the Mg 2 SnO 4 -SnO 2 system.…”

“…The Dq value (1600 cm −1 ) is compatible with Cr 3+ introduced into an octahedral environment, and the Dq/B ratio obtained from the Tanabe-Sugano diagram and the Adachi model [46,47] indicates that the Cr 3+ cations are subjected to an intermediate crystal field [36,52]. The Racah B value is lower than the free-ion value (918 cm −1 [43]), which indicates the covalent character of the Cr 3+ -O 2− bond.…”

“…For the same reason, this transition was used in the Adachi model described previously. Among the crystal field-dependent transitions, the energy determination of the 4 A 2 ( 4 F) → 4 T 2 ( 4 F) transition is more accurate than that of 4 A 2 ( 4 F) → 4 T 1 ( 4 F), where the last transition is found in a higher-lying energy position [46,47]. The 4 T 2 ( 4 F)/ 2 E( 2 G) energy ratio was obtained using the observed energies of the 4 T 2 ( 4 F) and 2 E( 2 G) levels, considering 4 A 2 ( 4 F) as the ground level.…”

“…Adachi [46,47] recently proposed a model for the calculation of the Dq and B parameters, starting from the energies of the 2 E( 2 G) and 4 T 2 ( 4 F) states and the C/B ratio. Assuming C/B = 4.8 (a reasonable value for d 3 systems [43]) and using the energies of the 4 A 2 ( 4 F) → 4 T 2 ( 4 F) transition (band at 15,998 cm −1 in the excitation spectrum) and the 2 E( 2 G) → 4 A 2 ( 4 F) transition (structure at 695 nm (14,388 cm −1 ) in the emission spectrum)) observed in the present work, the found values of the parameters from the Adachi model were Dq = 1,600 cm −1 and B = 691 cm −1 , with Dq/B = 2.32.…”

“…This Dq/B value obtained from the Adachi model is distinct from the Dq/B ratio obtained using Eqs. (1) and (2), probably due to energy deviations between the observed and expected energies since the energies related to the 4 T 1 ( 4 F) and 4 T 2 ( 4 F) states are both used in the B calculation using the energy matrices [46,47]. The energy of the 4 A 2 ( 4 F) → 4 T 1 ( 4 F) transition estimated by the Adachi model was 22,771 cm −1 , which gives a difference close to 5% of the observed value (21,746 cm −1 ), which can be considered a good result.…”