Optical Band Positions Research Articles

Theoretical Explanations of the Optical Band Positions and Local Structure for Cu2+Centers in ZnO-Bi2O3-B2O3-CuO Glasses

The local structure, two optical band positions and three electronic spin resonance parameters for Cu centers at the tetragonally-distorted octahedral sites in ZnO-Bi2O3-B2O3-CuO glasses are calculated from the high-order perturbation method based on the two-spin-orbit-parameter model, where the contributions from both the spin orbit coupling parameters of central d ion and ligand ion are included. The theoretical results are in good agreement with the experimental values. The calculations show that the high-order perturbation method based on the two-spin-orbit-parameter model is e ective in the explanations of optical spectra, electronic spin resonance parameters and local distortion structure for d ions in glasses.

Unified calculations of optical and EPR data for Cu3+ ion in Al2O3 crystal

The optical band positions and EPR parameters ( g factors g ∥ , g ⊥ and zero-field splitting D ) for Cu 3+ ion in Al 2 O 3 crystal are calculated by using the complete diagonalization (of energy matrix) method based on the two-spin–orbit-parameter model. In the model, both the contribution to the spectral data from the spin-orbit parameter of central 3d n ion and that of ligand ion are contained. The calculated results show reasonable agreement with the experimental values. The defect structure of Cu 3+ impurity center is estimated from the calculations. • Unified calculation for the optical and EPR spectral data of Cu 3+ in Al 2 O 3 is made. • The complete diagonalization (of energy matrix) method is used in the calculation. • The diagonalization method is based on the two-spin–orbit-parameter model. • The defect structural data is obtained from the calculation.

Investigations of the optical spectral bands, g factors and local structure for the tetragonal Cr5+ tetrahedral clusters in Cr-doped silica glasses

In this paper, the weaknesses and mistakes in the assignments of some optical absorption bands and the theoretical calculations of g factors (g//<g⊥) in the previous papers for the tetragonally-elongated (CrO4)3− clusters in Cr-doped silica glasses prepared with sol–gel method are pointed out and corrected. On the basis of these, the g factors g// and g⊥ for this Cr5+ cluster are calculated from the high-order perturbation formulas based on the two-mechanism model (where the contributions to g factors due to both the crystal field (CF) mechanism in the widely-used CF theory and the charge-transfer (CT) mechanism are included) for the tetragonally-elongated d1 tetrahedral clusters with the ground state |dx2−y2〉. From the calculated values and by considering the small admixture between the ground state |dx2−y2〉 and the first excited state |dz2〉 owing to the vibrational motion of ligands (note: this dynamic effect leads the elongated (CrO4)3− cluster to become the twinkling compressed one), the calculated g// and g⊥ are in reasonable agreement with the experimental values. In the calculations, the needed CF energy levels (corresponding to the optical spectral bands) are obtained from CF theory in which the CF parameters are estimated from the superposition model. Thus, the optical band positions of (CrO4)3− cluster in silica glassed are explained and the local structure of static (CrO4)3− cluster is obtained. By considering the dynamic effect, the isotropic g factors (g//=g⊥) at room temperature for another (CrO4)3− cluster in silica glasses and the anisotropic g factors (g//>g⊥) for the tetragonally-compressed (CrO4)3− cluster in barium aluminophosphate glasses are also explained in a unified way. The results are discussed.

Investigations of the Optical Band Positions and Spin-Hamiltonian Parameters for the Rhombic VO2+Complex in CsCl Crystal

The optical band positions and spin-Hamiltonian parameters (g factors g(i) and hyperfine structure constants A(i), where i = x, y, z) of the rhombic VO2+ complex in CsCl crystal are calculated together from two theoretical methods. One is the complete diagonalization (of energy matrix) method and another is the perturbation theory method. The calculated results from the two methods coincide and are in reasonable agreement with the experimental values. So, both methods are effective in the explanations of optical and electron paramagnetic resonance (EPR) data for d(1) ions in crystals. The calculations also suggest that in d(1) rhombic octahedra the ground state is almost a pure vertical bar d(xy)>) state. This point is different from that of conjugate d(9) (e.g., Cu2+) ions in rhombic octahedra where the ground state should be an admixture of ground and first excited states.

Unified calculations of the optical band positions and EPR g factors for NaCrS2 crystal

Six optical band positions and EPR g factors g, g⊥ for the trigonal Cr3+ octahedral clusters in NaCrS2 crystal are calculated together through the complete diagonalization (of energy matrix) method based on the two-spin–orbit-parameter model, where besides the contribution due to the spin–orbit parameter of central dn ion in the conventional crystal-field theory, the contribution due to the spin–orbit parameter of ligand ion via the covalence effect is also considered. In the calculations, the crystal-field parameters Bkl are obtained from the superposition model with the structural data of Cr3+ octahedral clusters in NaCrS2 crystal measured exactly by the X-ray diffraction method. The calculated optical and EPR spectral data are in a reasonable agreement with the observed values. So, the reliability of the superposition model in the studies of crystal-field parameters for dn ions in crystals is confirmed, and the complete diagonalization (of energy matrix) method based on the two-spin–orbit-model is effective in the unified calculations of optical and EPR spectral data for dn ions in crystals.

Unified calculations of optical and EPR spectral data for two tetragonal Cu2+ centers in Cu2+-doped ZnO nanocrystals

Three optical band positions and four spin-Hamiltonian (or EPR) parameters (g factors g//, g⊥ and hyperfine structure constants A//, A⊥) of two tetragonal Cu2+ centers in Cu2+-doped ZnO nanocrystals synthesized at room temperature by mild and simple solution method are calculated from the complete diagonalization (or energy matrix) method based on the cluster approach (where the covalence effect due to the admixture between the orbitals of dn ion and ligands is considered). The calculations rest on the defect models suggested in the previous paper that both Cu2+ centers are Cu2+ on the interstitial octahedral sites in ZnO nanocrystals and the tetragonal elongations of octahedra are due to the static Jahn–Teller effect. The calculated results are in reasonable agreement with the experimental values. The defect models of both Cu2+ centers are therefore confirmed and their defect structures (i.e., the tetragonal elongations R//−R⊥) are acquired. The results are discussed.

Theoretical calculations of the optical band positions and zero-field splitting 2D for Cr3+ ions in fluoride garnet Na3Li3In2F12

Five optical band positions and one EPR zero-field splitting 2D for Cr3+ ions at the trigonally-distorted octahedral In3+ site in fluoride garnet Na3Li3In2F12 are calculated together from the complete diagonalization (of energy matrix) method based on the two-spin–orbit-parameter model, where the contributions from both the spin–orbit parameters of central dn ion and ligand ion are contained. The calculated results are in reasonable agreement with the experimental values. The calculations show that similar to the bonding length (i. e., metal-ligand distance) R, the bonding angle θ (between the direction of R and C3 axis) is different from the corresponding one in the host crystal Na3Li3In2F12 because of the size mismatching substitution. It appears that the complete diagonalization (of energy matrix) method based on the two-spin–orbit-parameter model is effective in the unified calculation of optical spectra and EPR zero-field splitting for d3 ions in crystals.

Unified calculations of the optical band positions and spin-Hamiltonian parameters for V2+ ions in CdCl2 crystal

The eight optical spectral band positions and three spin-Hamiltonian parameters (g factors g//, g⊥ and zero-field splitting D) of V2+ ions in trigonal CdCl2 crystal are calculated together from the complete diagonalisation (of energy matrix) method (CDM) based on the two-spin-orbit-parameter model (also called the cluster approach). In the model, differing from the usual one-spin-orbit-parameter model in the conventional crystal-field theory (where only the contribution to spin-Hamiltonian parameters due to the spin-orbit parameter of central dn ion is considered), both the contributions from the spin-orbit parameter of central dn ion and that of ligand ions are taken into account. The calculated results show reasonable agreement with the experimental values. The local lattice relaxation in the vicinity of V2+ ion due to the introduction of V2+ impurity is acquired from the calculations. The calculations of spin-Hamiltonian parameters from the CDM based on the one-spin-orbit-parameter and those from the perturbation theory method based on the two-spin-orbit-parameter model are also made for comparison. The results are discussed.

Investigations of the g factors and optical spectral band positions for Cr5+ in Sr2(VO4)Cl crystal

The EPR g factors gx, gy, gz and the optical spectral band positions for Cr5+ at the rhombically distorted tetrahedral V5+ site in Sr2(VO4)Cl crystal are calculated from the high-order perturbation formulas based on the two-mechanism model. In the calculations the optical band positions are obtained from the crystal-field energy levels used and the contributions to g factors from both the crystal field mechanism and charge transfer mechanism (which is omitted in the widely used crystal field theory) are included. The calculated results are in reasonable agreement with the experimental values. The calculations suggest that for the high valent state d1 ion (e.g., Cr5+ considered) in crystals, the exact theoretical calculations of g factors should take both crystal field and charge transfer mechanisms into account.

Studies of the optical band positions, spin-Hamiltonian parameters and defect structure for Cr3+ in CdIn2S4 crystal

The calculations of optical band positions and spin-Hamiltonian parameters (g factors g//, g⊥ and zero-field splitting D) for Cr3+ ion at the trigonal octahedral In3+ site in semiconducting spinel CdIn2S4 have been carried out by using the complete diagonalization (of energy matrix) method based on the two-spin–orbit-parameter model. In the model, differing from the conversional one-spin–orbit-parameter in the widely-used crystal-field theory, both the contribution to spin-Hamiltonian parameters from the spin–orbit parameter of central dn ion and that of ligand are contained. The calculated results are in reasonable agreement with the experimental values. It is found from the calculations that the MO6 octahedral cluster in CdIn2S4:Cr3+ changes from the trigonal elongation in the host crystal to the trigonal compression in the Cr3+ impurity center owing to the impurity-induced local lattice relaxation. The results are discussed.

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.

Investigation of the optical spectra and spin-Hamiltonian parameters for the rhombic Cu2+ center in β-Ca3(PO4)2

The four optical band positions and six spin-Hamiltonian parameters (the g factors gi and the hyperfine structure constants Ai, i=x, y, z) for the rhombic Cu2+ center in β-Ca3(PO4)2 are calculated by two theoretical methods: the complete diagonalization (of energy matrix) method and the perturbation theory method (PTM). Both methods are based on the cluster approach, in which the covalence due to admixture of ligands to the central metal ion is considered. The calculated results of the two methods are close to each other and agree with the experimental values. This suggests that both methods are effective in explaining the optical and electron paramagnetic resonance data for d9 ions in crystals. The calculations also show that although the admixture of |dz2⟩ to the ground state wave function is small, it should not be neglected in calculations of spin-Hamiltonian parameters. So, in PTM, the high-order perturbation formulae of spin-Hamiltonian parameters based on the cluster approach for d9 ion in rhombic symmetry should be derived by taking into account the admixture of the |dz2⟩ state to the |dx2−y2⟩ ground state.

Studies of the optical band positions and EPR g factors for Cu(H 2O) 62+ centers in Tutton salt crystals

The optical band positions and EPR g factors g i ( i = x, y, z) of Cu(H 2O) 6 2+ clusters in pure Tutton salts M 2Cu(SO 4) 2·6H 2O (M = NH 4, Rb) are calculated from the complete diagonalization (of energy matrix) method based on the cluster approach. In the calculation, the superposition model with the structural data is used to obtain the crystal-field parameters. The calculated results are in reasonable agreement with the experimental values, suggesting that the complete diagonalization method and superposition model are effective in the studies of optical and EPR data. The g factors g i of Cu(H 2O) 6 2+ clusters in Cu 2+-doped isomorphous diamagnetic Tutton salts M 2Zn(SO 4) 2·6H 2O are also studied from the same method. It is found that the approximately tetragonally compressed Zn(H 2O) 6 2+ octahedra in the host crystals change to the approximately tetragonally elongated Cu(H 2O) 6 2+ octahedra in the impurity centers. The causes concerning the Jahn–Teller effect are discussed. It appears that in some cases the octahedral environment of an impurity M I in crystals differs from that of the replaced host ion, but is close to the one in the isomorphous pure crystals where M I is the host ion rather than the impurity ion.

Crystal field parameters for Yb 3+ ions at orthorhombic centers in garnets—Revisited

The major purpose of this paper is to clarify the deficiencies identified in the recent paper by Liu et al. (J. Lumin. 130 (2010) 103) as well as to reanalyze the available data and provide corrected results for the orthorhombic crystal field parameters (CFPs) for selected rare-earth ions in garnets. It appears that Liu et al., when utilizing the computer package for standardization of CFPs, have inadvertently confused the properties of CFPs expressed in the Wybourne notation with those in the extended Stevens operator notation. This confusion has led to misinterpretations concerning the orthorhombic standardization transformations and incorrect labeling of the CFP sets as supposedly ‘standardized’ for Yb 3+, Pr 3+, Nd 3+, and Er 3+ ions in various garnets. These deficiencies have prompted us to reconsider the CFP sets determined earlier by matching the experimental data, i.e. the orthorhombic spin Hamiltonian parameters ( g factors, g i , and hyperfine structure constants, A i ; i=x, y, z) and available optical spectral band positions, with the theoretical data calculated using the complete diagonalization method. To further verify the correctness of the present results the CFPs for orthorhombic Yb 3+ centers in Yb 3Al 5O 12 and Yb 3Ga 5O 12 garnets are calculated using the superposition model (SPM), which requires adoption of a well-defined symmetry-adapted axis system (SAAS). Hence, the SPM calculations enable reanalysis of available CFP sets based on the correct standardization procedure and establishing the correspondence between the SAAS and the ‘ nominal’ axis systems assigned to fitted CFP sets. Using the proper SAAS and general transformations of the axis systems, the relations between the calculated g i and/or A i values and the respective principal values determined by EPR experiments can be established. The consistent methodology utilized here may be helpful for proper reanalysis of spectroscopic data for rare-earth and transition-metal ions at orthorhombic symmetry sites in various crystals.

Theoretical Studies of the Electron Paramagnetic Resonance and Optical Spectral Data for Vanadium(IV) Ion in Yttrium Aluminum Garnet Crystal

ABSTRACT Four spin-Hamiltonian parameters (g factors g // and g ⊥ and hyperfine structure constants A // and A ⊥) and two optical spectral band positions for vanadium(IV) (V4+) ion in the tetrahedral Al3+ site of yttrium aluminum garnet (Y3Al5O12) crystals are calculated from the (third-order) perturbation theory method (PTM) and complete diagonalization (of energy matrix) method (CDM). Both methods are based on the cluster approach. The calculated results from both methods coincide and reasonably agree with the experimental values. The defect structure of V4+ center (which is different from the corresponding structure in the host crystal) in Y3Al5O12 crystal is also obtained from the calculation.

Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Yb3+ at the tetragonal Y3+ site of KY3F10 crystal

The six optical band positions and six spin-Hamiltonian parameters [g factors g∥, g⊥ and hyperfine structure constants A∥(171Yb3+), A⊥(171Yb3+), A∥(173Yb3+), A⊥(173Yb3+)] for Yb3+ ion at the tetragonal Y3+ site of KY3F10 crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Hamiltonian of energy matrix contains the free-ion, crystal-field interaction, Zeeman (or magnetic) interaction and hyperfine interaction terms and so a 14×14 complete energy matrix for 4f13 ion in tetragonal crystal-field and under an external magnetic field is constructed. Diagonalizing the energy matrix, these optical and EPR spectral data are calculated together and the calculated results are in reasonable agreement with the experimental values. The signs of hyperfine structure constants A∥, A⊥ for the isotopes 171Yb3+ and 173Yb3+ in KY3F10 are suggested. The results are discussed.

A unified calculation of the optical spectral band positions and electron paramagnetic resonance spectral data for Yb 3+ in InP semiconductor

The complete energy matrix for a 4 f 13 ion in cubic crystals and under an external magnetic field is established by means of the irreducible tensor operator and/or equivalent operator methods. By diagonalizing the energy matrix, four optical spectrum band positions and three spin-Hamiltonian parameters [ g factor and hyperfine structure constants A( 171Yb 3+) and A( 173Yb 3+)] for Yb 3+ in InP semiconductor are calculated together. The calculated results are in good agreement with the experimental values. The signs of hyperfine structure constants A( 171Yb 3+) and A( 173Yb 3+) are determined from the calculations. The results are discussed.

Resonant Raman scattering in ultrafine CdSxSe1−x colloidal particles

Vibrational spectra of ultrafine (∼1.8 nm) CdSxSe1−x colloidal nanoparticles (NPs) are studied by resonant Raman scattering (RRS). The detected difference of the shape and spectral position of the longitudinal optical vibration band in comparison with the spectrum of slightly larger NPs (≥ 2 nm) is explained by the dominance of surface atoms as their fraction increases above 50%. The correlation of experimental results with ab initio calculated vibrational spectra and with vibration anharmonicity enhancement as the NP size decreases is discussed.

Studies of the optical spectrum band positions and spin-Hamiltonian parameters for Pa4+ ion in ThX4 (X=Cl, Br) crystals

The optical spectrum band positions and spin-Hamiltonian (SH) parameters ( g factors g ∥ and g ⊥ and hyperfine structure constants A ∥ and A ⊥ ) for 5f 1 ion Pa 4+ at the tetragonal Th 4+ site of ThX 4 (X=Cl, Br) crystals are calculated from a complete diagonalization (of energy matrix) method (CDM). In the CDM, the magnetic (or Zeeman) interaction and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM and so the optical and EPR spectra data can be studied in a unified way. The calculated results are in reasonable agreement with experimental values. The possible misprints or small errors in the experimental g factors for Pa 4+ in Th X 4 crystals are pointed out. The results are discussed.

Investigations of the optical spectra and EPR g factors for the tetragonal Cu2+ centers in trigonal ZnCO3 crystal

Two distinctive theoretical methods, the complete diagonalization (of energy matrix) method (CDM) and the perturbation theory method (PTM), are employed to calculate the optical band positions and EPR g factors g(||), g(perpendicular) for the tetragonal Cu(2+) centers in trigonal ZnCO(3) crystal. The results from the two methods coincide and are also in good agreement with the experimental values. So both the CDM and PTM are adequate for the investigations of optical and EPR data for d(9) ions in crystals. The tetragonal distortion due to the static Jahn-Teller effect for the tetragonal Cu(2+) centers in trigonal Zn(2+) site of ZnCO(3) is also acquired from the calculations. The results are discussed.