Study on Local-Structure Symmetrization of K2XF6 Crystals Doped with Mn⁴⁺ Ions by First-Principles Calculations

The crystals of Mn⁴⁺-activated fluorides, such as those of the hexafluorometallate family, are widely known for their luminescence properties. The most commonly reported red phosphors are A₂XF₆: Mn⁴⁺ and BXF₆: Mn⁴⁺ fluorides, where A represents alkali metal ions such as Li, Na, K, Rb, Cs; X=Ti, Si, Ge, Zr, Sn, B = Ba and Zn; and X = Si, Ge, Zr, Sn, and Ti. Their performance is heavily influenced by the local structure around dopant ions. Many well-known research organizations have focused their attention on this area in recent years. However, there has been no report on the effect of local structural symmetrization on the luminescence properties of red phosphors. The purpose of this research was to investigate the effect of local structural symmetrization on the polytypes of K₂XF₆ crystals, namely O_h-K₂MnF₆, C_3v-K₂MnF₆, O_h-K₂SiF₆, C_3v-K₂SiF₆, D_3d-K₂GeF₆, and C_3v-K₂GeF₆. These crystal formations yielded seven-atom model clusters. Discrete Variational Xα (DV-Xα) and Discrete Variational Multi Electron (DVME) were the first principles methods used to compute the Molecular orbital energies, multiplet energy levels, and Coulomb integrals of these compounds. The multiplet energies of Mn⁴⁺ doped K₂XF₆ crystals were qualitatively reproduced by taking lattice relaxation, Configuration Dependent Correction (CDC), and Correlation Correction (CC) into account. The ⁴A_2g→⁴T_2g (⁴F) and ⁴A_2g→⁴T_1g (⁴F) energies increased when the Mn-F bond length decreased, but the ²E_g → ⁴A_2g energy decreased. Because of the low symmetry, the magnitude of the Coulomb integral became smaller. As a result, the decreasing trend in the R-line energy could be attributed to a decreased electron–electron repulsion.