Racah parameters and Tanabe−Sugano energy-level diagram: Effects of the different host-lattice cation species on the crystal-field strength parameters

The Racah parameters in conjunction with the Tanabe−Sugano (T−S) energy-level diagram are widely used as a means of explaining the effects of electron−electron repulsion within the metal complexes in coordination chemistry. For the determination of the Racah parameters (B, C) and crystal-field splitting parameter (Dq), the three excited-state zero-phonon line (ZPL) energies, E(²E_g)_ZPL, E(⁴T_2g)_ZPL, and E(⁴T_1g,a)_ZPL, are required. However, it is very difficult to accurately determine such excited-state ZPL energies from optical spectra. Although a revised model [J. Lumin. 218 (2020) 116,829] was proposed to overcome this by properly assuming the Racah parameter ratio of r = C/B and demonstrated its effectiveness, no detailed discussion has been paid to its validation. The present study focuses on this problem and analyzes some representative data of the Mn⁴⁺ and Cr³⁺-activated phosphors, such as K₂−IV−F₆:Mn⁴⁺ and Na₃−IV−F₆:Cr³⁺ with IV = Si, Ge, and Sn. The effects of different r values on the 3d³−ligand characteristics are discussed in detail. The non-dimensional Racah parameter β₁ is introduced to examine in more detail the acceptability and superiority of the revised models. Our proposed model reveals the ever-unknown relationships between the Racah parameters and T−S diagram that are important for deeply understanding the various 3d³-ion-activated phosphor properties and their potential applications.