Investigation of the Local Structure and Electron Paramagnetic Resonance Parameters of Tetragonal Cu2+ Centers in Sodium Fluoride–Sodium Borate Glasses

Based on the defect model that the impurity Cu2+ in TiO2 on the octahedral Ti4+ site is associated with one oxygen vacancy VO along the C 2 axis, the electron paramagnetic resonance (EPR) parameters, i. e., the g factors gi (i = x;y; z) and the hyperfine structure constants At, of the Cu2+-VOcenter in TiO2 are calculated by using the perturbation formulas of these parameters for a 3d9 ion in a rhombically elongated octahedra. From this study, the impurity Cu2+ is found to be away from VO by a distance Dz (≈ 0:33 Å) along the C2 axis, meanwhile the four O2- ions in the plane perpendicular to the C2 axis may be shifted by Dx (≈ 0:28 Å) towards VO due to the electrostatic interaction between these ions and VO. The theoretical results based on the above local structure distortions show good agreement with the experimental data.

EPR parameters and local lattice structure study of V 2+ ions in CdCl 2 and CsMgCl 3 crystals

Local structure and electron paramagnetic resonance (EPR) parameters for Cu2+ center in [Co(nicotinamide)2(H2O)4](saccharinate)2 (CoNAS) crystal are theoretically investigated using high-order perturbation formulas for 3d9 ions in rhombically elongated octahedra. In the calculated formulas, the related molecular orbital coefficients are acquired from the superposition model which enables to correlate the crystal field parameters and hence the EPR parameters with the studied Cu2+ center, the admixtures of d-orbitals in the ground state wave function as well as the ligand orbital and spin–orbit coupling contributions are taken into account. Based on the studies, the [CuO4N2]12− cluster of the studied Cu2+ center are found to suffer the axial and perpendicular bond length variations Δz (≈ 0.0612 Å) along z-axis and δr (≈ 0.0360 Å) along x- and y-axes, respectively, due to the Jahn–Teller effect.

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.

Theoretical study of EPR spectra for Mn 2+ ion in [Mg(H 2O) 6]SnCl 6 single crystal

The electron paramagnetic resonance (EPR) parameters (zero-field splitting D, and g-factors g ∥, g ⊥) for d 8 Ni2+ ions in tetragonal ligand fields KZnF3 : Ni2+ or in trigonal ligand fields CdCl2(CdBr2 and CsMgI3) : Ni2+ complexes have been systematically studied on the basis of the 45 × 45 complete energy matrices. The local structural distortion parameters of the crystals obtained are ΔR 1 = 0.0355 Å, ΔR 2 = 0.0296 Å for KZnF3 : Ni2+, ΔR = −0.1730 Å, Δθ = −1.5695○ for CdCl2 : Ni2+, Å, Δθ = −2.6236○ for CdBr2 : Ni2+ and ΔR = −0.0267 Å, Δθ = −1.8967○ for CsMgI3 : Ni2+. The calculated results show that the local structures exhibit elongation distortion for KZnF3 : Ni2+ and compression distortions for Ni2+ : CdCl2 (CdBr2 and CsMgI3) systems. Further, the relationships between ZFS parameter D and structural parameters (θ, R) are studied and the influence of the orbit reduction factor k on g-factors (Δg, g) are discussed.

Theoretical investigation of local lattice structure of the tetragonal FeF 5O cluster in KMgF 3:Fe 3+ crystal

Theoretical studies of the local structures and EPR parameters for various Rh 2+ centers in AgCl

A simple theoretical method is introduced for studying the local molecular structure of the (MnO6)10– coordination complex. By diagonalizing the complete energy matrices of the electron–electron repulsion, the ligand field and the spin–orbit coupling for a d5 configuration ion in a trigonal ligand field, the local distortion structure of the (MnO6)10– coordination complex for Mn2+ ions in A–PCC:Mn2+ (PCC = {[(CH3)2N]2OPOPO[N(CH3)2]2}(ClO4)2, A = Mg, Zn) complex systems is investigated. Both the second‐order zero‐field splitting parameter b20 and the fourth‐order zero‐field splitting parameter b40 are taken simultaneously in the structural investigation. From electron paramagnetic resonance (EPR) calculations, the local structure parameters R = 2.18 Å, θ = 56.38° for Mn2+ ions in Mg–PCC:Mn2+ and R = 2.20 Å, θ = 56.52° for Mn2+ ions in Zn–PCC:Mn2+ complex systems are determined, respectively. It is found that the theoretical calculation results of the EPR spectra for Mn2+ ions in A–PCC:Mn2+ complex systems are in good agreement with the experimental values. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper systematically investigates the local distortion and electron paramagnetic resonance (EPR) parameter for CdCl2:V2+ and CsMgX3:V2+ (X = Cl, Br) systems on the basis of the complete energy matrix, in which not only the contributions due to the spin–orbit coupling of the central ions but also that of the ligands are considered. To describe the difference of overlapping between d-orbits and p orbit, two spin–orbit coupling coefficients are introduced. By simulating the crystal field parameter and EPR parameter, the local distortion parameters are studied and the relationships between the EPR parameter and the spin–orbit coupling coefficients as well as divergent parameter are discussed. These results show that the local structures exhibit compression distortion for CdCl2:V2+ and elongation distortions for CsMgX3:V2+ (X = Cl, Br), respectively. It notes that the empirical formula R ≈ RH + (ri – rb)/2 is not suitable for CdCl2:V2+ and CsMgX3:V2+ (X = Cl, Br) systems. The contributions of ligand to spin–orbit coupling interaction cannot be neglected for strong covalent systems, especially for V2+ doped in CsMgBr3:V2+.

The structural parameters, electron localization functions, electron paramagnetic resonance (EPR) parameters, formation energies, and thermodynamic transition levels of various oxygen vacancy defects in amorphous silica are comprehensively and integrally investigated by using density functional theory. The trends of changes in the oxygen vacancy defect structure and electron localization induced by the increase in distance between defective silicon atoms are clearly identified. It is shown that the dimer configuration may be the potential structure of the Eδ' center. For the back-projected unpuckered configuration and the puckered configuration, whose EPR parameters are more consistent with the experimental values of the Eγ' center, the unpaired electron localized on the sp3 hybridized silicon atom is a common feature. Due to the three-coordinated oxygen atom in the forward-oriented configuration, the EPR parameters are closest to those of the Eα' center. Transformations of oxygen vacancy defects under different charge states are studied by sequentially adding and removing electrons. The thermodynamic transition level analysis reveals that the dimer and forward configurations may behave as deep traps for electron accumulation. The back-projected puckered fourfold-coordinated and fivefold-coordinated configurations are comparatively stable and may be able to function as shallow traps for electron transport. The neutral double unpuckered, neutral back-projected puckered fourfold-coordinated, and neutral back-projected unpuckered configurations are more likely to lose electrons during hole trapping. As the bias voltage is repeatedly changed, the defect density of the puckered configuration may reduce, while that of the dimer and unpuckered configuration may take an opposite trend.

Theoretical study of spin singlets contributions to zero-field splitting and local lattice structure of Cr 2+ in CdGa 2S 4

On the basis of the perturbation formulas for a $d^{1}$ configuration ion in a tetragonal crystal field, the three optical absorption bands and electron paramagnetic resonance (EPR) parameters ($g$ factors $g_{i}$ and hyperfine structure constants $A_{i}$ for $i = \|$ and $\perp$, respectively) of VO$^{2+}$ in Na$_{3}$C$_{6}$H$_{5}$O$_{7}\cdot2$H$_{2}$O single crystals were studied using the perturbation theory method. By simulating the calculated optical and EPR spectra to the observed values, local structure parameters and negative signs of the hyperfine structure constants $A_{i}$ of the octahedral (VO$_{6}$)$^{8-}$ cluster in trisodium citrate dehydrate single crystal can be obtained.

A novel structure‐based drag model was proposed to study the hydrodynamics of bubbling fluidized beds (BFBs) operated with ultrafine cohesive particles by considering local heterogeneous flow structures. Firstly, a local structure parameters model capturing the internal flow structures of the studied system was built by balance equations and empirical formulas and the solutions (i.e. local structure parameters) of this model solved by global search algorithm were evaluated in terms of hydrodynamics, energy consumption, and voidage. Then the local structure parameters were employed to derive the structure‐based drag model. Lastly, three drag models (i.e. the structure‐based drag model, Gidaspow model, and Syamlal‐O'Brien model) were investigated and incorporated separately into the two‐fluid model, where the simulation results were also separately compared with available experimental data. The comparison shows that Gidaspow and Syamlal‐O'Brien drag models failed to predict the solid volume fraction profiles. However, the error analysis results of the structure‐based drag model indicate the average absolute relative error of solid volume fraction in the radial direction is 7.04 % and 5.64 % at the height of 0.1 m and 0.2 m respectively, which exhibits promising predictions. Thus, it is feasible to simulate the BFBs with cohesive particles through the combination of the structure‐based drag model with the two‐fluid model.

We conduct a high-resolution large-eddy simulation (LES) case study in order to investigate the effects of surface heterogeneity on the (local) structure parameters of potential temperature \(C_T^2\) and specific humidity \(C_q^2\) in the convective boundary layer (CBL). The kilometre-scale heterogeneous land-use distribution as observed during the LITFASS-2003 experiment was prescribed at the surface of the LES model in order to simulate a realistic CBL development from the early morning until early afternoon. The surface patches are irregularly distributed and represent different land-use types that exhibit different roughness conditions as well as near-surface fluxes of sensible and latent heat. In the analysis, particular attention is given to the Monin–Obukhov similarity theory (MOST) relationships and local free convection (LFC) scaling for structure parameters in the surface layer, relating \(C_T^2\) and \(C_q^2\) to the surface fluxes of sensible and latent heat, respectively. Moreover we study possible effects of surface heterogeneity on scintillometer measurements that are usually performed in the surface layer. The LES data show that the local structure parameters reflect the surface heterogeneity pattern up to heights of 100–200 m. The assumption of a blending height, i.e. the height above the surface where the surface heterogeneity pattern is no longer visible in the structure parameters, is studied by means of a two-dimensional correlation analysis. We show that no such blending height is found at typical heights of scintillometer measurements for the studied case. Moreover, \(C_q^2\) does not follow MOST, which is ascribed to the entrainment of dry air at the top of the boundary layer. The application of MOST and LFC scaling to elevated \(C_T^2\) data still gives reliable estimates of the surface sensible heat flux. We show, however, that this flux, derived from scintillometer data, is only representative of the footprint area of the scintillometer, whose size depends strongly on the synoptic conditions.