Analysis of crystal-field effect on luminescence spectra of Mn⁴⁺ (3d³) ion-doped double perovskite La₂ZnTiO₆ phosphor by semiempirical computations: exchange charge model and superposition model

Abstract

Herein, a systematic microscopic investigation of the crystal-field (CF) effects on the Mn4+ ions doped at triclinic site in double perovskite La2ZnTiO6 crystal has were performed using two independent modelling...

Effects of distortions in ion-host systems on optical spectra, crystal-field and spin-Hamiltonian parameters of Cr3+ ions doped pyrochlores Y2Ti2O7 and Y2Sn2O7: exchange charge model and superposition model calculations

“…Both SPM/ZFSPs and ECM/CFPs were calculated using the same crystal structure data and atomic coordinates of ions expressed in SAAS defined above. To take into account of the long-range nature of the electrostatic contributions to the ECM/CFPs, 8,39 a large cluster of 74 250 ions was considered, including ions located at distances up to ∼61 Å from the metal site. The SPM/CFPs were calculated using the spherical polar coordinates of only six ligands surrounding the central metal ion that described radial and angular distortions of trigonally distorted Ti/Sn/Cr–O 6 polyhedra.…”

“…, ref. 7, 8, 17, 18, 31, 33, 35 and references therein. For the sake of clarity, here we provide only a brief outline of key notions and notations.…”

“…The B S kq parameters are modelled considering only ions within the ML n polyhedra, since the overlapping integrals decrease exponentially with increase in metal–ligand distances. 8,32 The Cr 3+ –O 2− overlap integrals are calculated numerically using the Slater-type atomic 3d orbitals of Cr 3+ ions, 51 and the s- and p-orbitals of the O 2− ligands. 52 These integrals are approximated by the following expressions: S ( s ) = 〈 d 0| s 0〉 = −0.73 376 exp(−0.3361 R 1.49077 ), S ( σ ) = 〈 d 0| p 0〉 = 0.18 exp(−0.03 994 R 2.404 ) and S (π) = 〈 d 1| p 1〉 = 7.21 162 exp(−2.01 893 R 0.68326 ), where R is the metal–ligand distance within the range of 3.5 a.u.…”

“…Substituting ( θ i , ϕ i ) in eqn (11) yields only three non-zero values of the SPM/CFPs: B 20 , B 40 and B 43 , as expected for the actual trigonal D 3d site symmetry 47 of the Cr 3+ ion. Due to the mismatch of the ionic radii, electrical charges and electronegativities of the host ion (Ti 4+ ) and dopant ion (Cr 3+ ), 6,8,36 and depending on the concentration of Cr 3+ ions, the degree of distortion of the CrO 6 octahedron differs from that for the host TiO 6 octahedron. The dopant ion-induced structural distortion can be optimized by the ab initio calculations 24,25 based on DFT and the molecular dynamics simulations.…”

“…Therefore for simplicity, we have considered two independent structural distortions within the CrO 6 polyhedron: (i) radial distortion, Δ R (change in the metal–ligand bond distance R i ), and (ii) angular distortion, Δ θ (change in angular positions). 7,8 Therefore, incorporating the distortions for the CrO 6 octahedron, the radial distance of the ligand becomes R i = R h + Δ R , where R h is the Ti–O bond distance, whereas the angular position becomes θ i = θ h + Δ θ , where θ h = 59.2898° is the angle between the Ti–O bond and the Z axis (trigonal D 3d axis) of the host TiO 6 structure. Including these distortions, eqn (11), yields explicit expressions for SPM/CFPs as:To consider the effects of these dopant-induced distortions, the SPM/CFPs were calculated by varying four parameters: Ā 2 , Ā 4 , Δ R and Δ θ , by matching the computed SHPs and energy levels of Cr 3+ ions with the available experimental data.…”