Complete Diagonalization Research Articles

Trivalent europium-doped strontium molybdate red phosphors in white light-emitting diodes: Synthesis, photophysical properties and theoretical calculations

Eu3+-doped strontium molybdate red phosphors (Sr1−xMoO4:Eux (x=0.01–0.2)) for white light-emitting diodes (LED) were synthesized by the solid-state reaction method. The fluorescent intensities of the as-prepared phosphors were remarkably improved. The excitation and emission spectra demonstrate that these phosphors can be effectively excited by the near-UV light (395nm) and blue light (466nm). Their emitted red light peaks are located at 613nm, and the highest quantum yield value (η) of the as-grown red phosphor, which is 95.85%, is much higher than that of commercial red phosphor (77.53%). These red phosphors plus commercial yellow powers (1:10) were successfully packaged with the GaN-based blue chips on a piranha frame by epoxy resins. The encapsulated white LED lamps show high performance of the CIE chromaticity coordinates and color temperatures. Moreover, to explain the fluorescent spectra of these phosphors, a complete 3003×3003 energy matrix was successfully built by an effective operator Hamiltonian including free ion and crystal field interactions. For the first time, the fluorescent spectra for Eu3+ ion at the tetragonal (S4) Sr2+ site of SrMoO4 crystal were calculated from a complete diagonalization (of energy matrix) method. The fitting values are close to the experimental results.

Theoretical explanation for Raman and ESR spectra of V3+ ions in salt guanidinium vanadium sulfate hexahydrate

The Raman spectra and electronic spin resonance (ESR) parameters (spin-Hamiltonian parameter g factors, zero-field splitting parameter D, and hyperfine structure constant A) for the trigonal V3+ centers in salt guanidinium vanadium sulfate hexahydrate (GVSH) are calculated from the complete diagonalization (of energy matrix) method. The theoretical results are in agreement with the experimental findings and the trigonal crystal-field parameters are determined. The difficulty in explaining ESR parameters of V3+ in GVSH is removed.

Theoretical investigation of EPR and optical spectra of Mo(V) in [Mo6O19][N(C4H9)4]3 salt

The electron paramagnetic resonance (EPR) spectral data (the g factors and hyperfine structure constants) and d–d transition spectra for the tetragonal Mo5+ centre in [Mo6O19][N(C4H9)4]3 salt are theoretically investigated from the complete diagonalization method (CDM) for a 4d1 ion in tetragonally compressed octahedron. The theoretical results are in good agreement with the experimental data. The dependency of the g factors of the ground state on the R∥(MoO bond length) has been studied. It is shown that the g factors varied with the R∥ approximately in a linear way.

Calculations of EPR g factors for the isolated tetragonal Cu2+(II) centre in mechanically processed YBa2Cu3O7−δ superconductors

The g factors g∥ and g⊥ of the isolated tetragonal Cu(II)O5 cluster in YBa2Cu3O7−δ superconductors induced and suppressed by mechanical processing are calculated from the complete diagonalization (of the energy matrix) method (CDM) and the perturbation theory method (PTM). Both methods are based on the cluster approach where in addition to the contribution of the spin–orbit parameter of the central metal ion, the contribution of ligand ion via the covalence effect is taken into account. In the calculations, the structural data of the Cu(II)O5 cluster gained from x-ray diffraction are applied. The results from both the CDM and the PTM are similar and show reasonable agreement with the experimental values. It appears that both methods can be used to explain the EPR g factors for d9 ions in crystals.

Research on the optical spectra, g factors and defect structures for two tetragonal Y2+ centers in the irradiated CaF2: Y crystal

Based on the defect models that the tetragonal Y2+ (1) center in the irradiated CaF2: Y crystal is due to Y2+ at Ca2+ site associated with a nearest interstitial F− ion along C4 axis and the tetragonal Y2+ (2) center is Y2+ at Ca2+ site where the tetragonal distortion is caused by the static Jahn–Teller effect, the two optical spectral bands and anisotropic g factors for both tetragonal Y2+ centers are calculated. The calculations are made by using two methods based on the cluster approach, one is the complete diagonalization (of energy matrix) method (CDM) and another is the perturbation theory method (PTM). The calculated results for each Y2+ center from CDM and PTM coincide and show reasonable agreement with the experimental values. The calculated isotropic g factor for Y2+ (2) center at higher temperature owing to the dynamical Jahn–Teller effect is also consistent with the observed value. The defect structures (i.e., tetragonal distortion) of the two Y2+ centers are obtained from the calculation. It appears that both theoretical methods can be applied to explain the optical and EPR data, to study the defect model and to determine the defect structures for d1 ions in crystals.

Theoretical explanation of absorption spectra and ESR parameters of Cu2+ in shattuckite

The optical absorption spectra and electronic spin resonance parameters (ESR g factors g(parallel to), g(perpendicular to) and hyperfine structure constants A(parallel to), A(perpendicular to)) for Cu2+ in shattuckite crystal are calculated from the two spin-orbital coupling parameters model, high-order perturbation formulas and complete diagonalization (of energy matrix) method (CDM) of 3d(9) ion in tetragonal symmetry. The calculated results are in good agreement with the observed values. Since the ESR parameters are sensitive to the local structure of a paramagnetic impurity center, the defect structure of Cu2+ center in shattuckite crystal is estimated. The results are discussed. (C) 2012 Elsevier B.V. All rights reserved.

Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Cr3+ ions in Y2Ti2O7 crystal

The optical band positions and spin-Hamiltonian parameters (g factors g(parallel to) g(perpendicular to) and zero-field splitting D) for the trigonal Cr3+ centers in Y2Ti2O7 crystal are calculated from the complete diagonalization (of energy matrix) method based on the two-spin-orbit-parameter model. In the calculations, the contributions to spectral data from both the spin-orbit parameter of central d(n) ion and that of ligand ion are considered and the crystal field parameters used are estimated from the superposition model. The calculated results are in reasonable agreement with the experimental values. The defect structures of Cr3+ center is suggested. (C) 2012 Elsevier B.V. All rights reserved.

Investigations of EPR g Factors and Rhombic Distortion for the Rhombic Cu2+ Centers in K2Zn1−x Cu x F4 Crystals at Low Temperature

The electron paramagnetic resonance g factors g (i) (i = x, y, z) of two rhombic Cu2+ centers, Cu2+(II) and Cu2+(III), in K2Zn1-x Cu (x) F-4 crystals found at low temperature are calculated from the complete diagonalization (of energy matrix) method based on the cluster approach. The calculations show that the ground state wave function of the two rhombically compressed Cu2+ centers is with a small admixture of . The rhombic distortions for both Cu2+ centers are obtained from the calculations. The results are discussed.

Investigations of the g factors and crystal field parameters for Ce3+ in CaYAlO4 crystal

The EPR g factors g|| and g⊥ for Ce3+ at the tetragonal Y3+/Ca2+ site of CaYAlO4 crystal are calculated from a complete diagonalization (of energy matrix) method. In the method, the contributions to g factors of ground Kramers doublet due to all the rest doublets within the ground and excited multiplets 2F5/2 and 2F7/2 (rather than the doublets within only the ground multiplet 2F5/2 in the previous paper) are considered. The crystal field parameters Bkq in the energy matrix are obtained from the superposition model with the structural data of CaYAlO4 crystal. The calculated g factors are in much better agreement with the experimental values than those from the simple method in the previous paper. The calculated crystal field parameters Bkq are comparable with those of other trivalent rare earth ions in the isomorphous ABCO4 crystals and can be regarded as reasonable. The calculations suggest that the crystal field parameter B20 is positive in Ce3+:CaYAlO4 crystal. The opinion that the parameter B20 must be negative and the simple calculation method of g factors resulting in this opinion are unreliable. It appears that for the reasonable and exact calculations of g factors for 4f1 ion in crystals, the complete diagonalization (of energy matrix) method should be applied.

Theoretical investigation of optical spectra and covalent effect of Cr4+ in Y2Ti2O7 and Y2Sn2O7

In this work, the complete matrix of optical spectral levels in trigonal symmetry of 3d2 (3d8) ions are established on basis of strong field coupling mechanism by using two spin–orbit coupling parameters model. The contribution of the spin–orbit coupling of ligand to the optical spectra has been included in these formulas. As an application, the optical spectra of Cr4+ in Y2Ti2O7 and Y2Sn2O7 have been studied by the complete diagonalization (energy matrix) method. The covalent effect has been studied and the difficulty about Dq parameter in explanation of optical spectra of Cr-doped Y2Ti2O7 and Y2Sn2O7 is removed. The theoretical results are in good agreement with observed data.

Investigation of the g factors and defect structures for the tetragonal Ti3+ and Ti3+–Nb5+ centers in the low-temperature rhombohedral phase of BaTiO3

In this study, the electron paramagnetic resonance g factors g // and g ⊥ of two tetragonal Ti3+ defect centers, the isolated Ti3+ center and the Ti3+–Nb5+ center, in the low-temperature rhombohedral phase of BaTiO3 are calculated from the complete diagonalization (of energy matrix) method and the perturbation theory method. Both the methods are based on the two-spin–orbit (SO)-parameter model. In the model, the contributions to the g factors due to both the SO parameters of the central 3d1 ion and the ligand ion are included. The calculations are related to the defect models and defect structures of the two tetragonal Ti3+ centers. In the isolated Ti3+ center, the Ti3+ ion is assumed to occupy the approximately cubic octahedral Ti4+ site. The octahedron surrounding the Ti3+ undergoes a static Jahn–Teller distortion (characterized by the ligand displacement a) from approximately cubic to tetragonally compressed. In the Ti3+–Nb5+ center, the substitutional Ti3+ is charge compensated by an Nb5+ ion at the nearest neighboring Ti4+ site along the C 4-axis. The O2− ion intervening Ti3+ and Nb5+ has an additional displacement Δ z toward Nb5+ owing to the electrostatic interaction. From the calculations, the g factors of the two tetragonal Ti3+ centers are reasonably explained by either method. Also, the defect models of both the Ti3+ centers are confirmed and their defect structures (characterized by the ligand displacements a and Δ z) are obtained. The results are discussed.

Reinvestigations of the optical spectra and EPR parameters for Yb3+ ions in AWO4 (A=Ca, Sr, Pb, Ba) scheelite crystals

The optical spectra and electron paramagnetic resonance parameters (g factors g‖, g⊥ and hyperfine structure constants 171A‖, 171A⊥, 173A‖ and 173A⊥) for the tetragonal (D2d) Yb3+ centers in AWO4 (A=Ca, Sr, Pb and Ba) scheelite crystals are reinvestigated using a complete diagonalization (of energy matrix) method. The calculated results are in good agreement with the experimental values. The new crystal-field parameters (CFPs) obtained by fitting procedures are compared with those in the literature and the more reliable sets of CFPs for the Yb3+ ion in four scheelite crystals in this work are confirmed. The trends of the crystal-field interaction between the Yb3+ ion and its environment are studied, and the results are discussed.

Studies on the spin-Hamiltonian parameters of two Cu2+ centers and their defect structures due to Jahn–Teller effect for Cu2+-doped ZnGa2O4 spinel

A complete diagonalization (of energy matrix) method based on the cluster approach (where the covalence effect due to the admixture between the orbitals of the central d n ion and that of ligands is considered) was applied to calculate the spin-Hamiltonian parameters (g factors, g | and g ⊥, and hyperfine structure constants, A | and A ⊥) for two Cu2+ centers in ZnGa2O4 spinel at the temperature T ≈ 110 K. In both Cu2+ centers, Cu2+ ions occupy the trigonally-distorted octahedral sites 16d and the octahedrons undergo the static Jahn–Teller distortions from trigonal to tetragonally-elongated and tetragonally-compressed, respectively. The calculated spin-Hamiltonian parameters of the elongated Cu2+ center show good agreement with the experimental values and those of the compressed Cu2+ center are close to the observed values. The better agreement of spin-Hamiltonian parameter between calculation and experiment for the compressed Cu2+ center can be acquired by considering a small admixture of state to the ground state due to the vibrational motion of ligands. The defect structures of both Cu2+ centers (characterized by the ligand displacements a 1 and a 2, respectively) in ZnGa2O4 spinel were also determined from the calculation.

Theoretical Analysis of Electron Paramagnetic Resonance and Optical Spectra of Copper(II) Doped Bis(L-asparaginato)Zn(II)

ABSTRACT In this paper, a complete diagonalization (of energy matrix) procedure (CDP) is proposed to calculate the spin-Hamiltonian parameters [g-factors g∥, g⊥ and hyperfine structure constants A∥, A⊥, which can be obtained from electron spin resonance (ESR) spectra] and d-d transitions (optical spectra) for d9 ions in an orthorhombic field with D2h symmetry. The calculated spin-Hamiltonian parameters and d-d transitions of ZnC8H14N4O6: Cu2+ crystal from the CDP are in reasonable agreement with the experimental values. This suggests that the method is effective for the theoretical analysis of ESR and optical spectral data for 3d9 ions with ground state 2B2() in a D2h symmetry.

Zero-field splitting of the ground state and local lattice distortions for Fe3+ ions at the tetragonal FeF5O cluster center in Fe3+:KMgF3 crystals

The relations between the zero-field splitting (ZFS) parameters and the structural parameters of the tetragonal FeF5O cluster center in Fe3+:KMgF3 crystals have been established by means of the microscopic spin Hamiltonian theory and the superposition model (SPM). On the basis of this, the local structure distortions, the second-order ZFS parameter D, the fourth-order one (a+2F/3), and the energy level separations Δ1 and Δ2 of the ground spin state for Fe3+ ion doped in Fe3+:KMgF3 crystals are theoretically investigated. We use complete diagonalization method (CDM) and take into account the electronic magnetic interactions, i.e. the spin–spin (SS), the spin-other-orbit (SOO), and the orbit–orbit (OO) interactions, besides the well-known spin–orbit (SO) interaction. This investigation reveals that the replacement of O2− for F− and the induced lattice relaxation ΔR2(O), combined with an inward relaxation of the nearest five fluorine ions ΔR1(F) give rise to a strong tetragonal crystal field, which yields the large ZFS of the ground state. The theoretically calculated parameters D, (a+2F/3), Δ1, and Δ2 for Fe3+:KMgF3 crystals are in good agreement with experimental ones when the five F− ions move toward Fe3+ by |ΔR1(F)|=6.40×10−4nm and the O2− ion toward Fe3+ by |ΔR2(O)|=10.55×10−3nm.

Spin-Hamiltonian parameters and defect structures for the trigonal Yb3+ centers in wurtzite-type ZnS and CdS crystals

A complete diagonalization (of the energy matrix, where the corresponding Hamiltonian consists of free-ion, crystal-field, Zeeman and hyperfine interaction terms) method is applied to calculate the spin-Hamiltonian parameters (g factors g||, g⊥ and hyperfine structure constants A∥, A⊥) for the trigonal Yb3+ centers in wurtzite-type ZnS and CdS crystals. The calculated results are in reasonable agreement with the experimental values. In the calculations, the crystal-field parameters are obtained from the superposition model, which enables correlation of the spin-Hamiltonian parameters with the defect structure of the studied impurity center. The defect structures of Yb3+ centers (characterized by the local atom-position parameters uloc, which differ from the corresponding parameter in the host crystal) in both crystals are therefore estimated from the calculations. The results are discussed.

Studies of the spin-Hamiltonian parameters and defect structures for the tetragonal and cubic Yb 3+ centers in AgCl crystal

The spin-Hamiltonian parameters, g factors and hyperfine structure constants, for the tetragonal and cubic Yb 3+ centers in AgCl crystal are calculated from the complete diagonalization (of energy matrix) method. The calculations are based on the defect models that the tetragonal Yb 3+ center is formed by the substitutional Yb 3+ associated with two nearest Ag + vacancy ( V Ag) along <001> and < 00 1 ¯ > axes (i.e., C 4 axis) owing to charge compensation and in cubic Yb 3+ center the two compensators V Ag are remote. From the calculations, the spin-Hamiltonian parameters of both Yb 3+ centers in AgCl are explained reasonably, the signs of hyperfine structure constants A i ( 171Yb 3+) and A i ( 173Yb 3+) are suggested, the above defect models of both Yb 3+ centers are confirmed and their defect structures are determined.

Study of the Electron Paramagnetic Resonance Parameters for Copper Ions in Lead Titanate Crystal

Abstract The electron paramagnetic resonance parameters (g factors g||, g⊥ and hyperfine structure constants A&gt;||, A⊥) of PbTiO3: Cu2+ are calculated from the complete diagonalization method and the perturbation theory method. The calculated results obtained by the complete diagonalization method are close to that obtained by the perturbation theory method, and in good agreement with the experimental values. In the complete diagonalization method, the complete diagonalization procedure is established based on the 3d9 electron system in tetragonal field. From the calculation of the electron paramagnetic resonance parameters, the local defect structure of the [CuO6]-10 cluster can be determined as D4h with Rx = Ry = 0:1952 nm, Rz = 0:2076 nm.

Local structure distortion and spin Hamiltonian parameters for Cr3+−VZn tetragonal defect centre in Cr3+ doped KZnF3 crystal

The quantitative relationship between the spin Hamiltonian parameters (D, g‖, Δg) and the crystal structure parameters for the Cr3+−VZn tetragonal defect centre in a Cr3+:KZnF3 crystal is established by using the superposition model. On the above basis, the local structure distortion and the spin Hamiltonian parameter for the Cr3+−VZn tetragonal defect centre in the KZnF3 crystal are systematically investigated using the complete diagonalization method. It is found that the VZn vacancy and the differences in mass, radius and charge between the Cr3+ and the Zn2+ ions induce the local lattice distortion of the Cr3+ centre ions in the KZnF3 crystal. The local lattice distortion is shown to give rise to the tetragonal crystal field, which in turn results in the tetragonal zero-field splitting parameter D and the anisotropic g factor Δg. We find that the ligand F− ion along [001] and the other five F− ions move towards the central Cr3+ by distances of Δ1 = 0.0121 nm and Δ2 = 0.0026 nm, respectively. Our approach takes into account the spin—orbit interaction as well as the spin—spin, spin—other-orbit, and orbit—orbit interactions omitted in the previous studies. It is found that for the Cr3+ ions in the Cr3+:KZnF3 crystal, although the spin—orbit mechanism is the most important one, the contribution to the spin Hamiltonian parameters from the other three mechanisms, including spin—spin, spin—other-orbit, and orbit—orbit magnetic interactions, is appreciable and should not be omitted, especially for the zero-field splitting (ZFS) parameter D.

Investigation of energy levels and local lattice for LuLiF4: Yb3+ laser crystal

The complete energy matrix of 4f1/4f13 electronic configuration has been established by using the complete (energy matrix) diagonalization method and superposition model. The calculated energy levels agree well with experimental findings. The structure parameters have been determined in the present work and given as follows: R1≈0.23nm, R2≈0.24nm, θ1≈127.58°, θ2≈31.85°. Comparing with the host crystal structure data, the varieties of bond lengths and angles are, respectively, ΔR1=ΔR2=0.0004 nm, Δθ1=1.5° and Δθ2=−0.5°. Thus, there is slightly tetragonal distortion. What is more, the intrinsic parameters are given in A¯2(R0)>A¯4(R0)>A¯6(R0) which are agreement with the results of many studies.