Defect structure of Cu2+ center in K2SO4‒Na2SO4‒ZnSO4 glasses

The spin Hamiltonian parameters (g factors g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) of Cu²⁺ in K₂SO₄?Na₂SO₄?ZnSO₄ glasses are calculated from the high-order perturbation formulas of 3d⁹ ion in tetragonal octahedral sites. The calculated results are in agreement with the observed values. Since the EPR parameters are sensitive to the local structure of a paramagnetic impurity center, the defect structure of Cu²⁺ center in K₂SO₄?Na₂SO₄?ZnSO₄ glasses is estimated. The validity of results is discussed.     

Spin-Hamiltonian parameters and tetragonal distortion due to the Jahn–Teller effect for Cu2+ centres in trigonal Zn(BrO3)·6H2O crystal

The spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants ⁶⁵A_// and ⁶⁵A_⊥) for the tetragonal Cu²⁺ centres in trigonal Zn(BrO₃)·6H₂O crystal are calculated from the complete diagonalization (of energy matrix) method (CDM) based on the cluster approach. In the CDM, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM and the contributions to the spin-Hamiltonian parameters from both the spin-orbit coupling parameter of central d⁹ ion and that of ligand ion are included. The calculated spin-Hamiltonian parameters of Zn(BrO₃)·6H₂O: Cu²⁺ show good agreement with the experimental values and the tetragonal elongation (characterized by ΔR=R_// ? R _⊥, where R_// and R _⊥ represent the metal-ligand distances parallel with and perpendicular to the C₄ axis) due to the static Jahn–Teller effect is obtained from the calculations. The results are discussed.     

Investigation of the local structure of Cu2+ ions doped in alkali lead tetraborate glasses by their electron paramagnetic resonance and optical spectra

The local structure of the Cu²⁺ centers in alkali lead tetraborate glasses was theoretically studied based on the optical spectra data and high-order perturbation formulas of the spin Hamiltonian parameters (electron paramagnetic resonance g factors g_∥, g_⊥ and hyperfine structure constants A_∥, A_⊥) for a 3d⁹ ion in a tetragonally elongated octahedron. In these formulas, the relative axial elongation of the ligand O^2? octahedron around the Cu²⁺ due to the Jahn–Teller effect is taken into account by considering the contributions to the g factors from the tetragonal distortion which is characterized by the tetragonal crystal-field parameters Ds and Dt. From the calculations, the ligand O^2? octahedral around Cu²⁺ is determined to suffer about 19.2% relative elongation along the C₄ axis of the alkali lead tetraborate glass system, and a negative sign for A_∥ and a positive sign for A_⊥ for these Cu²⁺ centers are suggested in the discussion.     

Theoretical calculations of spin-Hamiltonian parameters and defect structures for Cu2+ in trigonally-distorted tetrahedral sites of ZnO and GaN crystals

The spin-Hamiltonian (SH) parameters (g factors g _//, g ⊥ and hyperfine structure constants ⁶³ A _//, ⁶³ A ⊥, ⁶⁵ A _//, ⁶⁵ A ⊥) for Cu²⁺ ions in the trigonally-distorted tetrahedral sites of ZnO and GaN crystals are calculated from a complete diagonalization (of energy matrix) method (CDM) based on a two spin-orbit parameter model for d ⁹ ions in trigonal symmetry. In the method, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM. The calculated results are in good agreement with the experimental values. The calculated SH parameters are also compared with those using the traditional diagonalization method or perturbation method only within the ² T ₂ term. It appears that, for exact calculations of SH parameters of d ⁹ ions in trigonal tetrahedral clusters in crystals, the present CDM is preferable to the traditional diagonalization method or perturbation method within the ² T ₂ term. The local structures of Cu²⁺ centers (which differ from the corresponding structure in the host crystal) in ZnO : Cu²⁺ and GaN : Cu²⁺ are obtained from the calculations. The results are discussed.     

Theoretical investigation of the spin-Hamiltonian parameters and optical spectra for the doped Cu2+ in ZnCdO nanopowder

The spin-Hamiltonian (SH) parameters (g factors g_||, g_⊥ and hyperfine structure constants A_||, A_⊥) and d–d transitions for ZnCdO:Cu²⁺ are calculated based on the perturbation formulas for a 3d⁹ ion in tetragonally elongated octahedra. Good agreement between the calculated results (four SH parameters and three optical absorption bands) and the experimental results can be obtained. Since the SH parameters are sensitive to the local structure of a paramagnetic impurity center, the tetragonal distortion (characterized by the relative elongation ratio ρ ≈ 3.5% along the C₄ axis) of the impurity center due to the Jahn–Teller effect is also acquired from the calculations. The negative and positive signs of hyperfine structure constants A_|| and A_⊥ for ZnCdO:Cu²⁺, respectively, are also suggested in the discussions.     

Investigations of the spin-Hamiltonian parameters for Er3+ ions in AlN crystal

The spin-Hamiltonian parameters (g factor g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) for Er³⁺ ion at the trigonal Al³⁺ site of AlN crystal are calculated by diagonalising the 52 × 52 energy matrix. The matrix are related to the ground mutiplet ⁴I_15/2 and the first to third excited multiplets ⁴I_13/2, ⁴I_11/2 and ⁴I_9/2 for 4f¹¹ ions in trigonal crystal field under an external magnetic field. The crystal-field parameters used in the matrix are obtained from the superposition model and the local lattice relaxation due to the substitution of Er³⁺ for Al³⁺ is considered. The calculated spin-Hamiltonian parameters are in reasonable agreement with the experimental values and the signs of hyperfine structure constants are suggested. The results are discussed.     

Substitutional site of Co2+ ion in RbMgF3 crystal

The spin-Hamiltonian (SH) parameters (g factors g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) for Co²⁺ ions at the trigonal Mg²⁺ (I) and Mg²⁺ (II) sites of RbMgF₃ crystal are calculated from the second-order perturbation formulas based on the cluster approach for 3d⁷ ions in trigonal symmetry. From the calculations, it is found that the calculated SH parameters for Co²⁺ ion at the Mg²⁺ (I) site are in poor agreement with, but those for Co²⁺ at the Mg²⁺ (II) site are close to, the experimental values. Therefore, we suggest that Co²⁺ in RbMgF₃ crystal substitutes for Mg²⁺ (II) ion. The results are discussed.     

Theoretical studies of the Spin Hamiltonian parameters and local structures for Cu2+ centers in MNB ternary glasses

ABSTRACT

The spin Hamiltonian parameters (g factors g_|| and g_⊥ and the hyperfine structure constants A_|| and A_⊥) for the doped Cu²⁺ ion (in the form of CuO) in ternary glasses (i.e. xMgO·(30-x)Na₂O·69B₂O₃·CuO, with 5?<?x < 17?mol%) are theoretically investigated based on the high-order perturbation formulas for a tetragonally elongated octahedral 3d⁹ complex. In these formulas, the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the spin Hamiltonian parameters with the tetragonal distortion (characterized by relative tetragonal elongation δ along the C₄ axis due to the Jahn–Teller effect) of [CuO₆]^10? cluster. The concentration dependences of the spin Hamiltonian parameters are illustrated by the approximately linear increases of the cubic field parameter D_q and the covalency factor N as well as the relative elongation δ with increasing the MgO concentration x. Based on the calculation, the [CuO₆]^10? clusters in the MNB glasses are found to suffer the relative elongations of about δ (≈ 0.125?Å) along the tetragonal axis due to the Jahn–Teller effect. The theoretical results show good agreement with the experimental data. And the improvement is also achieved in present work with respect to the previous theoretical analysis based on the conventional crystal-field model formulas by including the ligand orbital and spin–orbit coupling contributions.     

Theoretical investigation of the optical spectra and g factors for Cu2+ in dioptase

The optical spectra of Cu²⁺ in dioptase are calculated using crystal-field theory. Good agreement between measured and calculated energy values is obtained under D _4h point-symmetry approximation. The electron paramagnetic resonance g factors, g _// and g _⊥, are also investigated from high-order perturbation formulae. The local structure of Cu²⁺ in dioptase is obtained using these formulae. Theoretical results are in perfect agreement with experimental findings.     

Theoretical research on the spin-Hamiltonian parameters of the square-planar CuS46− clusters in Cu(II)–dithiophosphonate complexes

The spin-Hamiltonian parameters (g-factors g_//, g_⊥ and hyperfine structure constants A_//, A_⊥) of the square-planar CuS^{6 ?}₄ clusters in Cu(II)–bis [4-ethoxphenyl-O-alkyl]-dithiophosphonate complexes are computed with the high-order perturbation formulas based on the two-mechanism model. The model includes the contributions to spin-Hamiltonian parameters from the vastly-utilised crystal-field (CF) mechanism concerning the CF excited states and the generally-omitted charge-transfer (CT) mechanism due to CT excited states. The energy levels of CF and CT excited states needed in the calculation are obtained from the observed optical spectra. The calculated results are in rational accordance with the experimental values. The signs of constants A_// and A_⊥ are suggested and the reasons of the very small g-shifts |?g_i| (= | g_i ? g_e |, where g_e ≈ 2.0023 and i = // or ⊥) are discussed.     

Spin-Hamiltonian Parameters and Defect Structure of the Copper (2+) Center in Lithium Borate

The spin-Hamiltonian parameters (the anisotropic g factors g _|| and g _⊥ and the hyperfine structure constants A _|| and A _⊥) for the impurity Cu²⁺ in Li₂B₄O₇ are theoretically investigated using the high-order perturbation formulas of these parameters for a 3d ⁹ ion in tetragonally elongated octahedra. In the calculation formulas, the tetragonal field parameters D_s and D_t are determined from the superposition model, by considering the relative axial elongation of the oxygen octahedron around Cu²⁺ due to the Jahn-Teller effect. Based on the calculations, the relative axial elongation of about 0.21 Å for the tetragonal Cu²⁺ center was found.     

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

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.     

Investigations on the g factors of the ground and excited states for Cu2+ ions in ZnO crystal

The g factors g _// and g _⊥ of the ground Γ₆(² T ₂) and excited Γ_4,5(² E), Γ₆(² E) states for trigonal Cu²⁺ centres in ZnO crystals are calculated from three theoretical methods, the complete diagonalization (of the energy matrix) method, the second-order perturbation method (PTM-I) and the simplified second-order perturbation method (PTM-II, this method was described in an earlier paper). These methods are based on the cluster approach in which the spin-orbit coupling parameters ζ, ζ′ and the orbital reduction factors k, k′ are calculated from a semi-empirical molecular orbital method. The crystal-field parameters used in the calculations are obtained from the superposition model and so the defect structure of Cu²⁺ centres in ZnO can be acquired. The calculated g factors from the three methods are in reasonable agreement with the experimental values and the defect structure of Cu²⁺ centres in ZnO is acquired. It appears that in some cases the approximate PTM can be applied in the studies of g factors of various states. The conditions that the PTM are ineffective are discussed.     

Investigations on the EPR parameters and tetragonal distortions for Cu2+ in alkali lead tetraborate glasses

The electron paramagnetic resonance parameters (g factors and hyperfine structure constants) and local structures are theoretically investigated for Cu²⁺ in alkali lead tetraborate 90R₂B₄O₇·9PbO·CuO (R = Li, Na and K) glasses based on the high-order perturbation calculations for a tetragonally elongated octahedral 3d⁹ complex. The [CuO₆]^10? complexes are found to experience the relative tetragonal elongation ratios 18%, 23% and 30% for R = Li, Na and K, respectively, due to the Jahn–Teller effect, much larger than those for similar ARbB₄O₇ (A = Li, Na and K) glasses. This point is attributed to the lattice expansion (longer A–O bond lengths) with doped PbO, yielding lower force constants and more intense Jahn–Teller elongations in the 90R₂B₄O₇·9PbO·CuO glasses. The increasing tendency (Li > Na > K) of the relative elongation ratio λ, covalency and the ratio Δg_///Δg_⊥ for g-shifts are systematically analysed in a uniform way.     

Unified calculations of spin-Hamiltonian parameters and optical band positions for Ni+ ion in AgGaSe2 crystal

The complete diagonalisation (of energy matrix) method based on the two-spin-orbit-parameter model is applied to unifiedly calculate the spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants A_//, A_⊥) and optical band positions for Ni⁺ ion in silver gallium selenide (AgGaSe₂) crystal. In the model, besides the contribution due to the spin-orbit parameter of central dⁿ ion (i.e., the one-spin-orbit-parameter model in the traditional crystal-field theory), that of ligand ions are taken into account. The calculated results are reasonably consistent with the experimental values. The local structure of Ni⁺ centre in AgGaSe₂ is estimated through the calculation. The complete diagonalisation method based on the one-spin-orbit-parameter model is also applied to calculate these electron paramagnetic resonance and optical data. It is found that although the calculated optical band positions are close to those based on the two-spin-orbit-parameter model and hence to the experimental values, the calculated spin-Hamiltonian parameters (in particular, the g factors) are in disagreement with the experimental values. The latter point is further confirmed from the calculations with the perturbation method. So, for the rational calculations of spin-Hamiltonian parameters of dⁿ clusters with ligand having large spin-orbit parameter, the contributions due to spin-orbit parameters of both the central dⁿ ion and ligand ion should be contained.     

Research of the g factors,optical band positions and local structure for the tetragonal octahedral (CrO6)7− clusters in glasses

The electron paramagnetic resonance g factors g_//, g_⊥ and also the optical band positions of the tetragonal (CrO₆)^7? octahedral clusters in glasses are calculated from the high-order perturbation formulas (in which the needed crystal-field (CF) energy levels correspond to the optical band positions). The formulas are founded on the two-mechanism model which takes account of both the contribution to g factors from the widely used CF mechanism and that from the frequently neglected charge-transfer (CT) mechanism. The calculated results are in rational agreement with the experimental values, suggesting that the contribution to g factors from CT mechanism should be considered. The local structure of (CrO₆)^7? clusters in glasses is also acquired from the calculation. The results are discussed.     

Theoretical studies of the local structures and electron paramagnetic resonance parameters for Cu2+ center in Zn(C3H3O4)2(H2O)2 single crystal

The electron paramagnetic resonance (EPR) parameters (g factors g_xx, g_yy, g_zz and hyperfine structure constants A_xx, A_yy, A_zz) are interpreted by taking account of the admixture of d-orbitals in the ground state wave function of the Cu²⁺ ion in a Zn(C₃H₃O₄)₂(H₂O)₂ (DABMZ) single crystal. Based on the calculation, local structural parameters of the impurity Cu²⁺ center were obtained (i.e. R_a≈1.92 Å, R_b≈1.96 Å, R_c≈1.99 Å). The theoretical EPR parameters based on the above Cu²⁺?O^2? bond lengths in the DABMZ crystal show good agreement with the observed values and some improvements have been made as compared with those in the previous studies.