Theoretical study of the electron paramagnetic resonance parameters and local structure for the tetragonal Ir<Superscript>2+</Superscript> centre in NaCl

The electron paramagnetic resonance (EPR) parameters (the g factors, hyperfine structure constants and the superhyperfine parameters) for the tetragonal Ir²⁺ centre in NaCl are theoretically investigated from the perturbation formulas of these parameters for a 5d⁷ ion in tetragonally elongated octahedra. This impurity centre is attributed to the substitutional [IrCl₆]⁴⁻ cluster on host Na⁺ site, associated with the 4% relative elongation along the C ₄-axis due to the Jahn-Teller effect. Despite the ionicity of host NaCl, the [IrCl₆]⁴⁻ cluster still exhibits moderate covalency and then the ligand orbital and spin-orbit coupling contributions should be taken into account. In addition, the theoretical EPR parameters based on the Jahn-Teller elongation show good agreement with the observed values.     

Theoretical investigations of the spin Hamiltonian parameters and local tetragonal distortions for Cu2+ in crystalline and amorphous TeO2 and GeO2

The spin Hamiltonian parameters (i.e., anisotropic g factors and hyperfine structure constants) and local tetragonal distortions for Cu²⁺ in crystalline and amorphous TeO₂ and GeO₂ are theoretically investigated using the high-order perturbation formulas of these parameters for a tetragonally elongated octahedral 3d⁹ cluster. The impurity Cu²⁺ occupying the octahedral sites are found to experience the relative tetragonal elongation ratios of about 11.4% and 9.5% for crystalline TeO₂ and GeO₂ and 10.8% and 6.6% for amorphous TeO₂ and GeO₂, respectively, along the C₄ axis due to the Jahn–Teller effect. This reveals the larger tetragonal elongation distortions for the Cu²⁺ centres in crystalline than amorphous systems (especially TeO₂). The theoretical spin Hamiltonian parameters show good agreement with the experimental data. The results are discussed.     

Theoretical investigations of the EPR parameters and local structure for Cu2+ in BeO

The electron paramagnetic resonance (EPR) parameters (the anisotropic g factors, the hyperfine structure parameters and the quadrupole coupling constant Q) and local structure for Cu²⁺ in BeO are theoretically investigated from the perturbation formulas of these parameters for a 3d⁹ ion under trigonally distorted tetrahedra. The ligand orbital and spin-orbit coupling contributions are included in the basis of the cluster approach, in view of the strong covalency of the [CuO₄]^6? cluster. From the calculations, the impurity Cu²⁺ is suggested not to occupy exactly the ideal Be²⁺ site but to suffer a slight inward displacement (≈0.024 Å) toward the ligand triangle along the C₃ axis. The theoretical EPR parameters show good agreement with the experimental data.     

Defect Structure and EPR Parameters of the Cu2+Center in MNB Ternary Glasses

The electron paramagnetic resonance (EPR) parameters (g factors g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) for 15MgO-15Na₂O-69B₂O₃ (MNB):Cu²⁺ ternary glasses were calculated based on the high-order perturbation formulae of 3d⁹ ion in a tetragonal symmetry. From the calculations, the defect structures of MNB:Cu²⁺ ternary glasses were obtained and a negative sign for A _// and A_⊥ for the Cu²⁺ center is suggested in the discussion.     

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.     

Investigations on the local structure and the spin-Hamiltonian parameters for the tetragonal Cu<Superscript>2+</Superscript> centre in ZnGeF<Subscript>6</Subscript>⋅6H<Subscript>2</Subscript>O crystal

The spin-Hamiltonian parameters (g factors g_∥, g_⊥ and hyperfine structure constants A_∥, A_⊥) and the local structure for the tetragonal Cu²⁺ centre in trigonal ZnGeF₆?6H₂O crystal are theoretically studied using the perturbation formulae of these parameters for a 3 d⁹ ion in tetragonally elongated octahedra. In the calculations, the contributions to the spin-Hamiltonian parameters from ligand orbital and spin-orbit coupling are included on the basis of the cluster approach in view of moderate covalency of the studied systems, and the required crystal-field parameters are obtained using the superposition model and the local structures of the studied [Cu(H₂O)₆] ²⁺ cluster. According to the calculations, the ligand octahedra around Cu²⁺ suffer relative elongation τ (≈ 0.085 Å) along the [0 0 1] (or C₄) axis for the tetragonal Cu²⁺ centres in ZnGeF₆?6H₂O crystal, due to the Jahn–Teller effect. The calculated results show good agreement with the experimental data.     

Spin Hamiltonian parameters and local structures for tetragonal and orthorhombic Ir2+ centers in AgCl

The perturbation formulae of the spin Hamiltonian parameters (the anisotropic g factors, hyperfine structure constants and superhyperfine parameters) are established for a 5d⁷ ion in an orthorhombically elongated octahedron based on the cluster approach. These formulae are applied to the theoretical studies of the EPR spectra and the local structures for the tetragonal and orthorhombic Ir²⁺ centers in AgCl. For the tetragonal Ir²⁺ center, the uncompensated substitutional [IrCl₆]⁴ cluster is found to experience a relative elongation of about 0.08 Å along the C ₄ axis due to the Jahn–Teller effect. For the orthorhombic center, the ligand octahedron also suffers Jahn–Teller elongation (by about 0.08 Å) along the [001] (or Z) axis. Meanwhile, the ligand Cl intervening in the impurity Ir²⁺ and the next nearest neighbor silver vacancy V_Ag along the [100] (or X) axis may undergo an inward displacement of 0.004 Å towards the center of the octahedron due to electrostatic repulsion of the V_Ag. The calculated spin Hamiltonian parameters based on the above local structures show good agreement with experimental data for both centers.     

Theoretical investigations on the g factors and local structures for Cu2+ in the ZnX (X= O,S and Se) nanocrystals

ABSTRACT

The g factors and local structures for Cu²⁺ in the ZnX (X = O, S and Se) nanocrystals at room temperature are theoretically investigated by the perturbation calculations for a tetragonally distorted tetrahedral 3d⁹ cluster in a consistent way, and the isotropic g factor is predicted for the ZnS:Cu²⁺ nanocrystals at room temperature. The bond angles θ between the four equivalent Cu²⁺?X^2? bonds and the C₄ axis are found to be about 1.26°, 1.24° and 1.07°, respectively, larger in the ZnO, ZnS and ZnSe nanocrystals than that (θ₀ ≈ 54.74°) for an ideal tetrahedron, inducing tetragonally compressed tetrahedra. The declining tendency (ZnO > ZnS > ZnSe) of the tetragonal angular distortion Δθ (= θ ? θ₀) can be ascribed to the decreasing strength of the dynamic Jahn–Teller effect via the vibration interactions of the [CuX₄]^6? groups due to the weakening Cu²⁺?X^2? bonding. The isotropic g factors are attributable to the appropriate Δθ due to the dynamic Jahn–Teller effect and the internal stress. The slightly increasing (ZnO < ZnS < ZnSe) g factors can be illustrated by the declining cubic field parameter Dq, angular distortion Δθ and covalency factor N of the systems.     

EPR and optical absorption studies on VO ions in zinc lactate trihydrate

EPR and optical absorption studies of VO²⁺-doped zinc lactate trihydrate single crystals are done at room temperature. The EPR spectra of VO²⁺ are characteristic of tetragonally compressed octahedral site. The angular variation of the EPR spectra shows single site occupying interstitial position in the lattice. The spin Hamiltonian parameters are evaluated as g_x=1.9771, g_y=2.0229, g_z=1.9236 and A_x=76, A_y=104, A_z=197 (×10⁻⁴) cm⁻¹. Using these parameters and optical absorption data various bonding parameters are determined and the nature of bonding in the complex is 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.     

EPR studies of Cu2+ and V4+ ions in phosphate glasses

Two lead-phosphate glass systems doped with both copper and vanadium ions in different ratios were studied by EPR (electron paramagnetic resonance) method. EPR spectra and parameters (g_‖ = 2.44, g_⊥ = 2.08 andA _‖ = 117.6 · 10⁻⁴ cm⁻¹) obtained for x(CuO · V₂O₅)(l−x)[2P₂O₅ · PbO] glasses withx ≤ 10 mol% suggest a tetrahedral (Td) coordination of Cu²⁺ ions and not a tetragonally elongated octahedron as has been assumed in previous works. The ground state of the paramagnetic electron is thed _xy copper orbital with a 4p_z contribution of 6%. For 20 ≤x ≤ 40 mol% a broad line (ΔB = 307 G) characteristic for clustered ions appears atg = 2.18. The V⁴⁺ ions are evidenced only in the spectra of x(CuO · 2V₂O₅)(1 −x)[2P₂O₅ · PbO] glasses and the resonance parameters suggest a pentacoordinated C_4v local symmetry for these ions. The hyperfine structures characteristic for Cu²⁺ and V⁴⁺ ions disappear for 10 ≤x ≤ 40 mol% due to the mixed exchange Cu²⁺−V⁴⁺ pair formation in these glasses.     

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 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.     

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.     

EPR,optical and superposition model study of Mn2+ doped L+ glutamic acid

Electron paramagnetic resonance (EPR) study of Mn²⁺ doped L+ glutamic acid single crystal is done at room temperature. Four interstitial sites are observed and the spin Hamiltonian parameters are calculated with the help of large number of resonant lines for various angular positions of external magnetic field. The optical absorption study is also done at room temperature. The energy values for different orbital levels are calculated, and observed bands are assigned as transitions from ⁶A_1g(s) ground state to various excited states. With the help of these assigned bands, Racah inter–electronic repulsion parameters B = 869 cm^?1, C = 2080 cm^?1 and cubic crystal field splitting parameter Dq = 730 cm^?1 are calculated. Zero field splitting (ZFS) parameters D and E are calculated by the perturbation formulae and crystal field parameters obtained using superposition model. The calculated values of ZFS parameters are in good agreement with the experimental values obtained by EPR.     

Theory studies of the local lattice distortions and the EPR parameters for Cu2+, Mn2+ and Fe3+ centres in ZnWO4

The local lattice distortions and the electron paramagnetic resonance (EPR) parameters (g factors, hyperfine structure constants and zero-field splittings) for Cu²⁺, Mn²⁺ and Fe³⁺ in ZnWO₄ are theoretically studied based on the perturbation calculations for rhombically elongated octahedral 3d⁹ and 3d⁵ complexes. The impurity centres on Zn²⁺ sites undergo the local elongations of 0.01, 0.002 and 0.013 Å along the C₂ axis and the planar bond angle variations of 8.1°, 8.0° and 8.6° for Cu²⁺, Mn²⁺ and Fe³⁺, respectively, due to the Jahn–Teller effect and size and charge mismatch. In contrast to the host Zn²⁺ site with obvious axial elongation (～0.31 Å) and perpendicular (angular) rhombic distortion, all the impurity centres demonstrate more regular octahedral due to the above local lattice distortions. The copper centre exhibits significant Jahn–Teller reductions for the spin-orbit coupling and orbital angular momentum interactions, characterised by the Jahn–Teller reduction factor J (≈0.29 ? 1). The calculated EPR parameters agree well with the experimental results. The local structures of the impurity centres are analysed in view of the corresponding lattice distortions.     

Theoretical analysis of spin-Hamiltonian parameters for the rhombic Cu2+ centres in CuGaSe2 crystals

The spin-Hamiltonian parameters (g factors g_i and hyperfine structure constants A_i, where i = x, y, z) of the rhombic Cu²⁺ centres in the CuGaSe₂ crystal are determined from the high-order perturbation formulae based on the cluster approach (sometimes also called two-spin-orbit parameter model). In the studies, some parameters in the analysis of g factors for the same centre within the tetragonal symmetry approximation in the previous paper are used, and the parameter due to the perturbation of rhombic crystal field caused by a charge compensator at, e.g., [110] direction are considered. As the result of a fitting process, the determined spin-Hamiltonian parameters are in reasonable agreement with the experimental values. The results are discussed.     

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.     

EPR of Cu2+-doped tris-sarcosine calcium chloride

The EPR study of the Cu²⁺-doped tris-sarcosine calcium chloride (TSCC) at room temperature is reported. Two magnetically inequivalent sites for Cu²⁺ were observed. The rhombic spin Hamiltonian parameters are determined by fitting the EPR spectra for two centres: Cu²⁺(I) g₁ = 2.0276, g₂ = 2.0517, g₃ = 2.4019, A₁ = 82, A₂ = 128, A₃ = 152 [G] and Cu²⁺(II) g₁ = 2.0231, g₂ = 2.0368, g₃ = 2.5294, A₁ = 76, A₂ = 92, A₃ = 156 [G]. The ground state wave function is also determined. The g-anisotropy is evaluated and compared with the experimental value. Further, the optical study of the crystal at room temperature is carried out and the nature of bonding in the complex is discussed.