First-Principles Study on Self-Activated Luminescence and 4f → 5d Transitions of Ce³⁺ in M₅(PO₄)₃X (M = Sr, Ba; X =...

The origin of the self-activated luminescence in the apatite-type M₅(PO₄)₃X (MPOX; M = Sr or Ba; X = Cl or Br) samples and the spectral assignment for cerium-doped Sr₅(PO₄)₃Cl (SPOC) phosphors are determined from first-principles methods combined with hybrid density functional theory (DFT) calculations, using the standard PBE0 hybrid functional, with wave function-based embedded-cluster ab initio calculations (at the CASSCF/CASPT2/RASSI-SO level). Electronic structure calculations are performed in order to accurately derive the band gaps of the hosts, the locations of impurity states in the energy bands that are caused by native defects and doped Ce³⁺ ions, and the charge-compensation mechanisms of aliovalent doping. The calculations of defect formation energies under O-poor conditions demonstrate that the native defects are easily generated in the undoped MPOX samples prepared under reducing atmospheres, from which thermodynamic and optical transition energy levels, as well as the corresponding energies, are derived in order to interpret the luminescence mechanisms of the undoped MPOX as previously reported. Our calculations reveal that the self-activated luminescence is mainly attributed to the optical transitions of the excitons bound to the oxygen vacancies (V_O), along with their transformation of the charge states 0 ↔ 1+. Furthermore, the eight excitation bands observed in the synchrotron radiation excitation spectra of SPOC: Ce³⁺, Na⁺ phosphors are successfully assigned according to the ab initio calculated energies and relative oscillator strengths of the 4f₁ → 5d_1-5 transitions for the Ce³⁺ ions at both the Sr(1) and Sr(2) sites in the host. It is hoped that the feasible first-principles approaches in this work are applied in order to explore the origins of the luminescence in undoped and lanthanide-doped phosphors, complementing the experiments from the perspective of chemical compositions and the microstructures of materials.