Study on Local-Structure Symmetrization of K(2)XF(6) Crystals Doped with Mn(4+) Ions by First-Principles Calculations

The crystals of Mn(4+)-activated fluorides, such as those of the hexafluorometallate family, are widely known for their luminescence properties. The most commonly reported red phosphors are A(2)XF(6): Mn(4+) and BXF(6): Mn(4+) 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 K(2)XF(6) crystals, namely O(h)-K(2)MnF(6), C(3v)-K(2)MnF(6), O(h)-K(2)SiF(6), C(3v)-K(2)SiF(6), D(3d)-K(2)GeF(6), and C(3v)-K(2)GeF(6). 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 Mn(4+) doped K(2)XF(6) crystals were qualitatively reproduced by taking lattice relaxation, Configuration Dependent Correction (CDC), and Correlation Correction (CC) into account. The (4)A(2g)→(4)T(2g) ((4)F) and (4)A(2g)→(4)T(1g) ((4)F) energies increased when the Mn-F bond length decreased, but the (2)E(g) → (4)A(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.