Hyperfine Structure Constants Ai Research Articles

A comparative study on the local structures of the V4+ and Cu2+ centers in WO3

Abstract The local structures and electron paramagnetic resonance (EPR) parameters (the g factors g i and the hyperfine structure constants A i , with i = x, y, z) of the V4+ and Cu2+ centers in WO3 were theoretically investigated based on the perturbation formulas of the EPR parameters for 3d1 and 3d9 ions under rhombically compressed and elongated octahedra, respectively. In these formulas, the adopted crystal-field parameters (CFPs) are obtained from the superposition model which enables connection of the CFPs and hence the EPR parameters to the rhombic distortion. Based on the calculations, the impurity-ligand distances of the studied [VO6]8− (or [CuO6]10−) cluster are found to suffer the axial compression (or elongation) δz of about 0.098 Å (or 0.132 Å) along the z-axis, and the additional planar bond length variation δr (≈0.052 or 0.047 Å) along x- and y-axis, respectively, due to the Jahn–Teller (JT) effect.

Studies on the EPR parameters and local angular distortion for the tetragonal Cu2+ center in CaWO4 crystal.

The electron paramagnetic resonance (EPR) parameters-g factors gi (i = || and ⊥) and hyperfine structure constants Ai (M) and Ai (N), with M and N belonging to isotopes 63 Cu2+ and 65 Cu2+ -and local structure of Cu2+ ion occupying W6+ site in CaWO4 crystal are theoretically studied based on the perturbation formulas of these parameters for a 3d9 ion under tetragonally elongated tetrahedra. In these formulas, the ligand orbital (LO) and spin-orbit coupling (SOC) contributions are included due to the shorter impurity-ligand distance R (≈1.83 Å) and hence the strong covalency of the studied [CuO4 ]6- cluster, and the related molecular orbital coefficients are quantitatively determined from the cluster approach in a uniform way; meanwhile, the required crystal field (CF) parameters for the tetragonally distorted tetrahedron (TDT) are estimated from the superposition model and the local structure of the impurity Cu2+ center. According to the calculation, the bond angle θ between the four equivalent Cu2+ -O2- bonds and the C4 axis in the CaWO4 :Cu2+ is found to be about 2.1° smaller than that (θ0 ≈ 54.74°) for an ideal tetrahedron due to the Jahn-Teller (JT) effect and the size mismatch. The fitted results agree well with the observed values, and the validity of the present assignment for the local structure of the Cu2+ center is also discussed.

Studies of local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) crystals

Abstract The electron paramagnetic resonance (EPR) parameters (g factor g i , and hyperfine structure constants A i , with i = x, y, z) and local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) are theoretically investigated using the high order perturbation formulas of these EPR parameters for a 3d 9 ion under orthorhombically elongated octahedra. In the calculations, contribution to these EPR parameters due to the admixture of d-orbitals in the ground state wave function of the Cu2+ ion are taken into account based on the cluster approach, and the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the studied EPR parameters with the local structures of the Cu2+ centers. Based on the calculations, the Cu–H2O bonds are found to suffer the axial elongation ratio δ of about 3 and 2.9% along the z-axis, meanwhile, the planar bond lengths may experience variation ratio τ (≈3.8 and 1%) along x- and y-axis for Cu2+ center in (NH4)2Zn(SO4)2·6H2O and Rb2Zn(SO4)2·6H2O, respectively. The theoretical results show good agreement with the observed values.

Studies of the EPR parameters and tetragonal distortion for the Cu2+ center in aluminium oxide

The electronic paramagnetic resonance (EPR) parameters (g factor gi , and hyperfine structure constants Ai , with i = || and ⊥) and tetragonal distortion of the Cu2+ center in Al2O3 are unified interpreted from the perturbation formulas for a 3d9 ion in tetragonally elongated octahedral. In the calculations, the impurity Cu2+ is found to occupy the host trigonally-distorted octahedral Al3+ site with the tetragonal elongation distortion due to the Jahn–Teller effect, despite the original trigonal distortion of the host cation site. The contributions to EPR parameters from both the spin–orbit coupling of the central ion and that of the ligands are taken into account. The defect structure of the Cu2+ center (characterized by the relative tetragonal elongation ratio η ≈ 4.3% along the C 4 axis) was determined from the calculation. Furthermore, the calculated results agree well with the experimental data and need fewer adjustable parameters than the previous studies.

Theoretical studies on the Spin Hamiltonian parameters and the local structure for Cu2+ in rutile

The spin Hamiltonian parameters (SHPs) (the g factors gi and the hyperfine structure constants Ai, i = x, y, z) and the local structure of the substitutional Cu2+ center in rutile (TiO2) are theoretically studied from the perturbation formulas of these parameters for a 3d9 ion in rhombically elongated distorted octahedra. The related molecular orbital coefficients are quantitatively determined from the cluster approach in a uniform way, and the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the studied SHPs with the local structure of the Cu2+ center. Based on the studies, the Cu–O bond lengths parallel and perpendicular to the C2-axis are found to be R||’ ≈ 2.030 Å and R⊥’ ≈ 1.924 Å, respectively, with the planar bond angle θ ≈ 87.21°. The calculated SHPs are in agreement with the experimental data and the results are discussed.

Spin-Hamiltonian parameters, defect model and defect structure for the tetragonal Mo5+ center in x-ray-irradiated α-ZnMoO4 crystals

ABSTRACTThe spin-Hamiltonian parameters (g factors gi, hyperfine structure constants Ai (95Mo5+) and Ai (97Mo5+), i = // and ⊥) assigned to the tetragonal Mo5+ (4d1) tetrahedral center in α-ZnMoO4 crystal caused by a Mo6+(1) ion trapping an electron after x-ray irradiation are calculated from the high-order perturbation formulas resting on the two-mechanism model. The model takes account of both the effects of crystal-field (CF) mechanism concerning the CF excited states in the CF theory and that of the charge-transfer (CT) mechanism related to CT excited states. The calculated results are reasonably consistent with the experimental values, confirming this assignment (or defect model). The calculations also indicate that the effect of CT mechanism cannot be neglected. The defect structure (particularly, the angular distortion) and signs of constants Ai (95Mo5+) and Ai (97Mo5+) of this Mo5+ defect center are also decided from the calculations. The outcomes are discussed.

Investigations of the electron paramagnetic resonance parameters and defect structures for Cu2+ ions in BeO crystal with trigonally distorted tetrahedral symmetry

Abstract The electron paramagnetic resonance(EPR) parameters (g factors gi and hyperfine structure constants Ai, where i = x, z) for Cu2+ ions embedded in beryllium oxide (BeO) crystal at Be2+ sites with C3v local symmetry have been calculated by the complete diagonalization method (CDM) and high-order perturbation theory method (PTM). The calculated results from the two methods are in reasonable agreement with the observed data available. The defect structural data of the trigonal Cu2+ center in beryllium oxide are determined from the calculations and analyses. The calculated results show that the Be2+ ions are replaced by Cu2+ ions in BeO crystal and the ligands undergo outward movement.

Theoretical research of the spin-Hamiltonian parameters for two rhombic W5+ centers in KTiOPO4 (KTP) crystal through a two-mechanism model

The high-order perturbation formulas based on the two-mechanism model are employed to calculate the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, where i=x, y, z) for two approximately rhombic W5+ centers in KTiOPO4 (KTP) crystal. In the model, both the widely-applied crystal-field (CF) mechanism concerning the interactions of CF excited states with the ground state and the generally-neglected charge-transfer (CT) mechanism concerning the interactions of CT excited states with the ground state are included. The calculated results agree with the experimental values, and the signs of constants Ai are suggested. The calculations indicate that (i) for the high valence state dn ions in crystals, the contributions to spin-Hamiltonian parameters should take into account both the CF and CT mechanisms and (ii) the large g-shifts |Δgi | (=|gi−ge |, where ge≈ 2.0023) for W5+ centers in crystals are due to the large spin–orbit parameter of free W5+ ion.

Investigations of the EPR Parameters and Local Lattice Structure for the Rhombic Cu2+ Centre in TZSH Crystal

Abstract The electron paramagnetic resonance (EPR) parameters [i.e. g factors g i (i=x, y, z) and hyperfine structure constants A i ] and the local lattice structure for the Cu2+ centre in Tl2Zn(SO4)2·6H2O (TZSH) crystal were theoretically investigated by utilising the perturbation formulae of these parameters for a 3d9 ion under rhombically elongated octahedra. In the calculations, the admixture of d orbitals in the ground state and the ligand orbital and spin-orbit coupling interactions are taken into account based on the cluster approach. The theoretical EPR parameters show good agreement with the observed values, and the Cu2+–H2O bond lengths are obtained as follows: R x ≈1.98 Å, R y ≈2.09 Å, R z ≈2.32 Å. The results are discussed.

Theoretical research on the spin-Hamiltonian parameters of the rhombic W5+ centers in CaWO4:Y3+ crystal

Detailed theoretical calculations for the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, where i=x, y, z) of the rhombic W5+ center in CaWO4:Y3+ crystal are performed by using the high-order perturbation formulas for d1 ions in rhombic tetrahedral clusters with the ground state |dz2〉. These formulas consist of the contributions from two mechanisms, the crystal-field (CF) mechanism connected with CF excited states in the vastly-used CF theory and the frequently-neglected charge-transfer (CT) mechanism related to CT excited states. The calculated results agree well with the experimental values. The calculations indicate that for W5+ ion (or other high valence state dn ions) in crystals, the model calculations of spin-Hamiltonian parameters should take both the CF and CT mechanisms into account. The signs of hyperfine structure constants Ai are suggested and the forming (or defect model) of rhombic W5+ center in CaWO4:Y3+ crystal is confirmed from the calculations.

Theoretical studies of the EPR parameters and local structures for Cu2+-doped cobalt ammonium phosphate hexahydrate

High-order perturbation formulas for a 3d9 ion in rhombically elongated octahedral was applied to calculate the electron paramagnetic resonance (EPR) parameters (the g factors, gi, and the hyperfine structure constants Ai, i = x, y, z) of the rhombic Cu2+ center in CoNH4PO4·6H2O. In the calculations, the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the EPR parameters with the local structure of the rhombic Cu2+ center. Based on the calculations, the ligand octahedral (i.e. [Cu(H2O)6]2+ cluster) are found to experience the local bond length variations ΔZ (≈0.213 Å) and δr (≈0.132 Å) along axial and perpendicular directions due to the Jahn–Teller effect. Theoretical EPR parameters based on the above local structure are in good agreement with the observed values; the results are discussed.

Theoretical explanation of spin-Hamiltonian parameters for the rhombic Mo5+ octahedral clusters in molybdenum phosphate glasses

The high-order perturbation formulas based on the two-mechanism model are used to calculate the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, where i = x, y, z) of the rhombic Mo5+ oxygen octahedral clusters in molybdenum phosphate glasses. These formulas consist of the crystal-field mechanism in the extensively applied crystal-field theory and of the charge-transfer mechanism (which is often neglected). In the calculations, only three adjustable parameters are applied and the six calculated spin-Hamiltonian parameters are reasonably coincident with the experimental values. The results are discussed.

Theoretical Studies of the Local Structure and Electron Paramagnetic Resonance Parameters for Tetragonal VO2+ in C6H7KO7

Abstract The optical spectra, electron paramagnetic resonance parameters (i.e., the spin Hamiltonian parameters, including paramagnetic g factors and the hyperfine structure constants Ai) and the local distortion structure for the tetragonal VO2+ in C6H7KO7 are theoretically studied based on the crystal-field theory and three-order perturbation formulas of a 3d1 centre in tetragonal site. The magnitude of orbital reduction factor, core polarisation constant κ, and local structure parameters are obtained by fitting the calculated optical spectra and electron paramagnetic resonance parameters to the experimental values. The theoretical results are in reasonable agreement with the experimental values.

Assignments of the optical band positions and theoretical calculations of the spin-Hamiltonian parameters for the tetragonal W5+ octahedral clusters in tungsten oxide (WO3)-based glasses

The optical band positions of W5+ octahedral clusters (WO6)7− in tungsten oxide (WO3)-based glasses are reassigned and suggested. Based on this, the spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants A//, A⊥) of these W5+ clusters are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, besides the contributions due to crystal-field (CF) mechanism in the extensively-used CF theory, the contributions owing to charge-transfer (CT) mechanism (which are often omitted) are also included. The calculated results are in reasonable agreement with the experimental values and the signs of hyperfine structure constants Ai are suggested. The results are discussed.

Theoretical studies of the EPR parameters and local structures for Cu2+ centres in a (CH3)2NH2Al(SO4)2·6H2O crystal

Local structure and electron paramagnetic resonance (EPR) parameters (the g factors, g i , and the hyperfine structure constants A i , i = x, y, z) for the impurity Cu2+ centres in a (CH3)2NH2Al(SO4)2·6H2O (DMAAS) crystal are theoretically investigated by using the high-order perturbation formulas of these parameters for a 3d 9 ion in an orthorhombically elongated octahedron. The related molecular orbital coefficients are quantitatively determined from the cluster approach in a uniform way. From the studies, the four planar Cu2+-O2− bond lengths are found to experience the relative variation δR ( ≈0.033 and 0.063 A) along the X- and Y-axes, while the two parallel bond lengths may undergo relative elongation ΔZ (≈0.058 and 0.052 A) along the C 2 axis for the studied Cu2+ centres I and II, respectively, due to the Jahn-Teller effect. The theoretical EPR parameters based on the above local lattice distortions agree well with the experimental data. The results are discussed.

Investigations on the spin Hamiltonian parameters and defect structure for the interstitial Mo5+ centre in TiO2

The spin Hamiltonian parameters, g factors gi (i=x, y, z) and the hyperfine structure constants Ai for the interstitial Mo5+ centre in rutile TiO2 are quantitatively investigated from the perturbation formulas of these parameters for a 4d1 ion in rhombically compressed octahedra. From the studies, the local compression parameter τ′ (≈0.024) and the rhombic distortion angle δϕ′ (≈1.74°) around the impurity Mo5+ are smaller than the host values (≈0.091 and 3.5°). This means that the oxygen octahedron in the impurity centre has less rhombic distortion than that on the host interstitial site due to the Jahn–Teller effect and occupation of the impurity. The above local lattice distortion of the studied impurity centre is also discussed.

Theoretical studies of the spin-Hamiltonian parameters for the rhombic Mo5+ tetrahedral centres in ZrSiO4 crystal from a two-mechanism model

The high-order perturbation formulas of spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, i = x, y, z) based on the two-mechanism model for d1 ions in rhombic tetrahedral clusters with the ground state are derived in this paper. In the model, besides the contributions to spin-Hamiltonian parameters due to the crystal-field (CF) mechanism in the widely applied CF theory, those due to the charge-transfer (CT) mechanism are taken into account. From these formulas, the six spin-Hamiltonian parameters gi and Ai for the rhombic Mo5+ tetrahedral centres in ZrSiO4 crystal are calculated with four adjustable parameters. The calculated results are in reasonable agreement with the experimental values. The calculations show that for the exact and complete calculations of spin-Hamiltonian parameters of the high valence state dn ions in crystals, the contributions due to CT mechanism should not be neglected. Some information on the defect structure of Mo5+ impurity centres in ZrSiO4 crystal is also acquired from the calculations. The results are discussed.

Crystal-field study for Yb3+ doped KY(WO4)2 crystal – Revisited based on superposition model

The optical spectra and electron paramagnetic resonance (EPR) parameters (gi and hyperfine structure constants Ai, i=x, y, z) for Yb3+:KY(WO4)2 crystal have been simultaneously explained by a crystal-field study based on superposition model (SPM). The deficiencies in a recent paper by Trabelsi et al. (2010) have been clarified and solved in the present work. The more reliable fitted phenomenological crystal-field parameters (CFPs) have been confirmed and monoclinic standardization of the obtained CFPs for Yb3+:KY(WO4)2 crystal is performed to ensure direct comparison with other rare earth ion doped potassium rare-earth double tungstates. By SPM calculations in this work, two individual EPR experiments with greatly different y-directional principal g factors for Yb3+:KY(WO4)2 crystal have been analyzed and possible reason for this large difference is also given. It indicates that magnetic dipolar and exchange interactions among different rare earth ions will play an important role in determining their magnetic properties in crystal under low temperature and more investigations should be carried out. The present procedures for SPM analysis can be applied to other crystal field environment with low site symmetry.

Theoretical calculations of spin-Hamiltonian parameters for the rhombic-like Mo5+ centers in KTiOPO4 crystal

The spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, were i=x, y and z) for Mo5+ ion occupying the Ti(1) site with approximately rhombic symmetry in KTiOPO4 crystal are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, not only the contribution due to the conventional crystal-field (CF) mechanism, but also those due to the charge-transfer (CT) mechanism are included. The six calculated spin-Hamiltonian parameters with four adjustable parameters are in reasonable agreement with the experimental values. The calculations show that for more accurate calculations of spin-Hamiltonian parameters of the high valence dn ions (e.g., Mo5+ considered here) in crystals, the contribution from CT mechanism, which is ignored in the conventional crystal field theory, should be taken into account. The reasonable crystal field energy levels of Mo5+ in KTiOPO4 are also predicted from calculations.

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

The spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, 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.