Orbit-parameter Model Research Articles

Investigation on the EPR Parameters for Tetragonal VO2+ Centers in LiHSO4 Single Crystals

In this work, the electron paramagnetic resonance (EPR) parameters (g-factors and A-constants) of the tetragonal VO2+ centers in LiHSO4 single crystals are theoretically investigated by the high-order perturbation formulae for these parameters based on two-spin–orbit-parameter model. Since the spin–orbit coupling coefficient of the ligand O2− is close to that of the central ion V4+ for the present system with strong covalence, the contributions to the EPR parameters from the ligand p- and s-orbitals as well as the spin–orbit coupling coefficient of the O2− ligand should be considered. The requirements of the crystal-field parameters are determined from the optical spectrum. The calculated results show good agreement with the experimental values. The signs of A-constants are ascertained in the discussion.

Analysis of the optical band positions for manganese (IV) ions in trigonal barium titanium hexafluoride and barium silicon hexafluoride crystals

The optical band positions (or crystal field energy levels) of manganese (IV) ions in trigonal barium titanium hexafluoride and barium silicon hexafluoride crystals are computed from the full diagonalization (of energy matrix) method founded on the two-spin–orbit-parameter model which consists of the effects from both the spin–orbit parameters of dn ion and ligand ions. The computed results are in rational agreement with the experimental values. It is found that the large difference of first excited state splitting ΔE (2E) between the manganese (IV)-doped barium titanium hexafluoride and barium silicon hexafluoride crystals is owing mainly to the great difference of trigonal distortion between the fluorine octahedral clusters in the two host crystals.

Trigonal Distortions of the Cr3+ Octahedral Centers in Cr3+-Doped ABO3 (A = Sc, In, Lu) Crystals Obtained by Analyzing EPR Data

The spin-Hamiltonian parameters (g factors g//, g⊥ and zero-field splitting D) of the trigonal Cr3+ centers in Cr3+-doped ABO3 (A = Sc, In, Lu) borate crystals are computed from both the complete diagonalization (of energy matrix) method and also the perturbation method based on the two-spin–orbit-parameter model, where the contributions to spin-Hamiltonian parameters due to both the spin–orbit parameter of central d n ion and that of ligands via covalence effect are considered. The calculated results are compatible with those available in experiments. The defect structures of the trigonal (CrO6)9− octahedral centers are also evaluated from the calculations. It is found that the trigonal (MO6)9− octahedra change from the elongation in the host crystals to the compression in the impurity centers because of the large size and nature mismatch substitution in these Cr3+-doped ABO3 crystals. The results are discussed.

Uniform calculation of the optical and EPR spectral data for the trigonal (CrO6)9− octahedral clusters in Y3Al5O12 crystal

The complete diagonalization (of the energy matrix) method is applied in this paper for the unified calculation of optical and EPR spectral data of the trigonal (CrO6)9− octahedral clusters in Y3Al5O12 (YAG) crystal. The method is based on the two-spin–orbit-parameter model where, besides the contributions from the spin–orbit parameter of central dn ion in the traditional crystal-field theory, those from the spin–orbit parameter of ligand ions via the covalence effect are considered. The computed 32 spectroscopic data values (29 crystal field energy levels and three spin-Hamiltonian parameters, namely the g factors g// and g⊥, and the zero-field splitting D) are in reasonable agreement with the experimental values, despite using only four adjustable parameters. This suggests that the method is valid in the uniform calculation of optical and EPR spectral data for d3 ions in crystals. The impurity-induced angular distortion of the (CrO6)9− clusters in YAG crystal was also evaluated.

Unified research of the optical and EPR spectral data for the trigonal Cr3+ centers in emerald crystals

The complete diagonalization (of energy matrix) method founded on the two-spin–orbit-parameter model (where the contributions from both the spin–orbit parameter of central dn ion and that of ligand ions are contained) is adopted to calculate together the optical and EPR spectral data for the trigonal Cr3+ centers in emerald crystal. The computed 18 optical and EPR spectral data (15 optical band positions and three spin-Hamiltonian parameters) with only five adjustable parameters are in rational accordance with the experimental values. The calculations indicate that the above diagonalization method is able to explain unifiedly the optical and EPR spectral data for d3 ions in crystals.

Theoretical explanation of optical absorption spectra for nickel ion at the interstitial site of zinc borate nanopowder

ABSTRACTZinc borates have been used in a variety of applications, including cellulose fibers, textiles, optical materials, and intumescent systems. They have also received many experimental investigations, including metallic ions doping. However, the relevant theoretical studies are absent, especially for the optical spectra and microstructures of zinc borates contained metallic impurities. In this work, as a typical example, the absorption spectra for nickel ions at the interstitial sites in the zinc borate nanopowders are theoretically investigated from the complete energy matrix method based on the two-spin–orbit parameter model and the suggested local defect model for nickel ion in octahedral symmetry. The theoretical results are in good agreement with the experimental values. The local lattice distortion induced by the impurity nickel at the interstitial site of zinc borate nanopowder is also estimated from the calculations. These results are discussed.

Theoretical studies of absorption spectra and microstructure of Ni2+ at the octahedral site of the NiFe2O4 nanoparticle

The optical absorption spectra, microstructure and electronic spin resonance parameters (electronic spin resonance (ESR) g factor) for Ni2+ ions at octahedral centers of nickel ferrite nanoparticles are calculated from the two-spin–orbit-parameter model. The effect of spin–orbital coupling of the central metal 3d8 ions and ligand oxygen ions has been taken into account in the full energy matrix and ESR g formula. The calculated results are in good agreement with the observed values. In addition, the microstructures of Ni2+ ions at octahedral centers in NiFe2O4 are reasonably determined from the calculations.

Investigations of the optical band positions, EPR parameters and defect structure for the trigonal Cr3+–Li+ centre in CsMgCl3 crystal

A unified calculation of optical band positions and electron paramagnetic resonance (EPR) (or spin-Hamiltonian) parameters for the trigonal Cr3+–Li+ centre in CsMgCl3 crystal is made by using the complete diagonalisation (of energy matrix) method based on the two-spin–orbit-parameter model. In this model, the contributions from the spin–orbit parameter of central dn ion and that of ligand ion are included. From the calculation, the 11 observed optical and EPR data (eight optical band positions and three EPR parameters g//, g⊥, D) are reasonably explained with five adjustable parameters and the defect structure of the Cr3+–Li+ centre (which is consistent with the expectation based on the electrostatic interaction) in CsMgCl3 is acquired. The results are discussed.

Investigations of the spin-Hamiltonian parameters and defect structure due to Jahn–Teller effect for the tetragonal Nb4+ center in cubic Cs2ZrCl6 crystal

The spin-Hamiltonian parameters (g factors g//, , and hyperfine structure constants A//, ) of the tetragonally compressed Nb4+ center in cubic Cs2ZrCl6 crystal are calculated from two theoretical methods: one is the complete diagonalization (of energy matrix) method and another is the perturbation theory method. Both methods are based on the two-spin–orbit-parameter model where the contributions to spin-Hamiltonian parameters from the spin–orbit parameter of central dn ion (in the conventional crystal field theory) and that of ligand ion via covalence effect are contained. The calculated results from the two methods are in reasonable agreement with the experimental values. The tetragonal distortion of (NbCl6)2− octahedral cluster due to the Jahn–Teller effect for Nb4+ at the cubic Zr4+ site in Cs2ZrCl6 is also acquired. The results are discussed.

Research on the optical band positions, spin-Hamiltonian parameters and atom-position parameter of Co2+ ion in CdSe crystal

The optical band positions and EPR (or spin-Hamiltonian) parameters (g factors g//, g⊥ and zero-field splitting D) of Co2+ ion in the trigonally-distorted tetrahedral Cd2+ site of CdSe crystal are calculated simultaneously from the complete diagonalization (of energy matrix) method (CDM) based on the two-spin–orbit-parameter model. This model contains the contributions to the spectral data from both the spin–orbit parameters of central dn ion (i.e., one-spin–orbit-parameter model) in the conventional crystal-field theory and that of ligand ions via covalence effect. The calculated 12 optical band positions and three spin-Hamiltonian parameters using four adjustable parameters show reasonable agreement with the experimental values. The local atom-position parameter uloc (where the corresponding parameter u in the host CdSe crystal is unlikely) in the Co2+ center is also estimated from the calculations. The calculations of these spectral data from the CDM based on the conventional one-spin–orbit parameter model are also made for comparison. It is found that the calculated optical band positions are also close to the experimental values, but the calculated spin-Hamiltonian parameters are in poor agreement with the observed values. So, for the unified and reasonable calculations of optical and EPR data of dn ions in crystals (in particular, in the cases of ligand with large spin–orbit parameter), the CDM based on the two-spin–orbit-parameter model should be applied.

Unified calculation of optical and EPR spectral data for Cr3+-doped KAl(MoO4)2 crystal

This paper reports an unified calculation of optical and EPR spectral data for Cr3+ ion at the trigonal Al3+ site of KAl(MoO4)2 crystal from the complete diagonalization (of energy matrix) method based on the two-spin–orbit-parameter model. In this model, differing from that in the conventional crystal-field theory, not only the contributions from the spin–orbit parameter of central dn ion, but also those from the spin–orbit parameter of ligand ion via covalence effect are taken into account. The calculation shows that by using only three adjustable parameters, the observed twelve optical and EPR spectral data (nine optical band positions and three EPR parameters g||, g⊥ and D) are reasonably explained in a unified way with this method. The results are discussed.

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.

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.

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.

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.

An optional explanation for nickel sites of nickel–zinc phosphate glasses by their optical spectra and EPR g factor

In this paper, the nickel site, optical spectra and electron paramagnetic resonance (EPR) g factor of nickel–zinc phosphate glasses have been studied by ligand-field theory. The orbital mixing effect between p and d orbits has been included in the calculation by two-spin–orbit parameter model. The present study shows that nickel occupies the tetrahedral zinc site with cubic symmetry in nickel–zinc phosphate glasses. Unlike the result of previous study that assigns nickel to an octahedral interstitial site, it is an optional explanation for nickel sites in nickel–zinc phosphate glasses by analysing the optical absorption spectra and EPR g factor.

EPR g factors and tetragonal distortion for the isoelectronic Ni + and Cu 2+ centers in the CuGaSe 2 crystal

The EPR g factors, g || and g ⊥, for the isoelectronic 3d 9 ions Ni + and Cu 2+ at the tetragonal Cu + site of the CuGaSe 2 crystal are calculated from the high-order perturbation formulas based on a two-spin–orbit-parameter model. In the model, both the contributions to g factors from the spin–orbit parameter of central 3d 9 ion and that of ligand ion are contained. The calculated results appear to be consistent with the experimental values. The tetragonal distortions (characterized by θ− θ 0 , where θ is the angle between the metal–ligand bond and C 4 axis, and θ 0 ≈54.74° is the same angle in cubic symmetry) of Ni + and Cu 2+ centers, which are different from the corresponding angle in the host CuGaSe 2 crystal and from impurity to impurity, are obtained from the calculations. The difference of the sign of g ||− g ⊥ between the isoelectronic Ni + and Cu 2+ centers is found to be due to the different tetragonal distortions of both centers in the CuGaSe 2 crystal.

A theoretical study of EPR g factors for the rhombic CuCl 64− clusters in (3-chloroanilinium) 8[CdCl 6]Cl 4:Cu 2+ crystal

In this paper, the third-order perturbation formulas of EPR g factors g i ( i= x, y, z) for d 9 ions in rhombic symmetry where the ground state being an admixture of ∣d x 2 − y 2 〉 and ∣d z 2 〉 states are derived. These formulas are based on a two-spin–orbit-parameter model in which the contributions to g factors due to both the spin–orbit parameter of the central 3d n ion and that of ligand ion are included. From these formulas, the g factors g i for the rhombic CuCl 6 4− clusters in (3-chloroanilinium) 8[CdCl 6]Cl 4:Cu 2+ crystal are calculated. The calculated values are in good agreement with those obtained by the complete diagonalization (of energy matrix) method and experimental values. Results are discussed.

Investigations of the g factors for the trigonal [Ti(H 2O) 6] 3+ clusters in frozen solution from two microscopic spin Hamiltonian methods

The spin Hamiltonian parameters (SH) ( g factors g ∥ and g ⊥) for the trigonal [Ti(H 2O) 6] 3+ clusters in the rapidly frozen solutions of Ti 3+ are calculated from the complete diagonalization (of energy matrix) method (CDM, which is established in this paper) and the perturbation theory method (PTM). The two methods are based on the two-spin–orbit-parameter model (where both the contribution due to the spin–orbit (SO) coupling parameter of central 3 d n ion and that of ligand are included) rather than the one-SO-parameter model in the conventional crystal-field theory (where only the contribution due to the SO coupling parameter of 3 d n ion is considered). The calculated results from both methods are not only consistent with the observed values, but also close to each other. This suggests that both methods can be effective in the studies of SH parameters.

Studies of the local structures for the two tetragonal centers in AgCl : Cr 3+ crystals from EPR parameters

The local structural parameters for the tetragonal Cr 3+-V M and V M-Cr 3+-V M centers in AgCl : Cr 3+ crystals have been estimated by calculating their EPR zero-field splitting and g factors from two theoretical models. One is the two spin–orbit (SO) parameter model in which not only the contribution due to the SO coupling of central d 3 ion, but also that of the ligands are included, and another is the conventional one-SO-parameter model where only the contribution due to the SO coupling of the central d 3 ion is considered. The estimated tetragonal distortion Δ R based on the two-SO-parameter model is about 2.2 that based on the one-SO-parameter model for both centers and the reasonableness of the former is discussed. It appears that for the d n clusters with ligands having a large SO coupling coefficient ζ p, the contribution of SO coupling of ligands to the EPR parameters cannot be neglected and so the two-SO-parameter model should be used to explain the EPR parameters, or, conversely, to study the local structures of these clusters from EPR data.