Tuning Emission Energy by Atomic Substitution in Cr ³⁺ -Doped K ₂ ABF ₆ (A = Li, Na; B = Al, Ga, In) Fluorides

We present results of the first-principles calculations within a density functional theory (DFT) framework of the electronic structure and parameters of the ²E → ⁴A₂ and ⁴T₂ → ⁴A₂ optical transitions of Cr³⁺ ions in a series of fluorides with the general chemical formula K₂ABF₆ (A = Li, Na; B = Al, Ga, In). Calculations for the undoped fluorides reveal that the energy band gap gradually decreases in the K₂AAlF₆ → K₂AGaF₆ → K₂AInF₆ sequence. The theoretical data reveal for the Cr³⁺-doped K₂ABF₆ fluorides new spin-up and spin-down electronic states related to the Cr³⁺ 3<i>d</i>-orbitals appearing in the host's energy band gaps. The formation of the Cr-F chemical bonds due to the hybridization of the Cr³⁺ 3<i>d</i>- and F 2<i>p</i>-states is characteristic of the K₂ABF₆:Cr³⁺ phosphors. The emission energy, <i>E</i>_em(²E → ⁴A₂), of the spin-forbidden transition increases with increased Cr-F bond lengths, while the crystal field strength 10<i>D</i>q(⁴T₂ → ⁴A₂) parameter decreases in the K₂AAlF₆:Cr³⁺ → K₂AGaF₆:Cr³⁺ → K₂AInF₆:Cr³⁺ sequence. Such theoretical attempts for the K₂ABF₆:Cr³⁺ phosphors were performed for the first time, and these data provide a solid background for better understanding the physical properties of nondoped and Cr³⁺-doped K₂ABF₆ fluorides, which are perspective phosphor materials. The calculations indicate also that in such a family of Cr³⁺-doped fluorides the emission energy can be successfully tuned by substitution of some kinds of atoms by their counterparts that can be useful also for exploring other related compounds as promising phosphors. From a practical point of view, the obtained relationships will allow obtaining the expected emission parameters through targeted optimization of the chemical composition. The presented computational approach can readily be applied to other optical materials without any restrictions related to the symmetry and chemical composition, providing an opportunity for precise determination of luminescent properties and allowing the targeted synthesis of efficient phosphors with expected properties and desired emission spectral distribution.