Studies of EPR g factors of the isoelectronic 3d series Cr, Mn and Fe in SrTiO3 crystals

The g-shifts Δg(=g−g_s, where g_s≈2.0023 is the free-ion value) of the isoelectronic 3d³ series Cr³⁺, Mn⁴⁺ and Fe⁵⁺ in SrTiO₃ crystals are calculated from the high-order perturbation formula based on the cluster approach for 3d³ ion in cubic octahedral site. The formula includes not only the contribution from the crystal-field (CF) mechanism, but also that from the charge-transfer (CT) mechanism (which is omitted in the CF theory). From the calculations, it is found that the contribution Δg_CT from the CT mechanism in sign is contrary to the corresponding Δg_CF from the CF mechanism and the relative importance of CT mechanism (characterized by |Δg_CT/Δg_CF|) increases with the increasing valence state (and hence the atomic number) of 3d³ ion. The positive g-shift Δg of SrTiO₃:Fe⁵⁺ is due mainly to the contribution of CT mechanism. So, for the explanations of g factors of the high valence state 3dⁿ ions (e.g. Mn⁴⁺ and Fe⁵⁺) in crystals, the contributions from both CF and CT mechanisms should be taken into account.     

Investigations of the electron paramagnetic resonance parameters and defect structures for Ni ions in CdX2 (X=Cl,Br) crystals

The high-order perturbation formulas of electron paramagnetic resonance (EPR) parameters (g factors g_∥,g_⊥ and zero-field splitting D) for 3d⁸ ions in trigonal octahedral clusters are established. These formulas contain the contributions not only from the crystal-field (CF) mechanism, but also from the charge-transfer (CT) mechanism (which is not considered in the widely used CF theory). From these formulas, the EPR parameters and the impurity-induced defect structures for Ni²⁺ ions in CdX₂ (X=Cl, Br) crystals are studied. The calculated EPR parameters are coincident with the experimental values, and the defect structure of Ni²⁺ impurity center obtained from the calculation is different from the corresponding structure in the host crystal. The sign of Q^CT (Q=Δg_∥, Δg_⊥, or D) due to CT mechanism agrees with that of the corresponding Q^CF due to CF mechanism and the relative importance of CT mechanism (characterized by Q^CT/Q^CF) increases with increasing covalence of 3d⁸ clusters and hence with raising atomic number of ligand X. So, in the explanations of the EPR parameters of 3d⁸ (or other 3dⁿ) ions in crystals with the heavy-element ligand ion (e.g., Br⁻), the calculated formulas based on the two-mechanism (CF and CT mechanisms) model are preferable to those based on only the CF mechanism in the CF theory.     

Investigation of the EPR g factors and defect structure for the Cu-VNa center in the X-irradiated NaCl: Cu crystal

The g factors of a tetragonally-compressed Cu²⁺ center in NaCl: Cu⁺ crystal X-irradiated at room temperature are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, the contribution to g factors from both crystal-field (CF) and charge-transfer (CT) mechanisms are included. The calculations are based on the defect model that the tetragonally-compressed Cu²⁺center is assigned to the Cu²⁺ ion (which is caused by Cu⁺ ion (at the Na⁺ site) irradiated by X-ray) associated with a nearest Na⁺ ion vacancy V_Na along C₄ axis due to charge compensation. From the calculations, the g factors g_|| and g_⊥ are explained and the defect structure (charactering by the displacement ΔZ of the Cl⁻ ion intervening in Cu²⁺ and V_Na) of the Cu²⁺ (or Cu²⁺-V_Na) center is obtained. The results are discussed.     

Investigations of the g factors for the trigonal [Ti(H2O)6] clusters in frozen solution from two microscopic spin Hamiltonian methods

The spin Hamiltonian parameters (SH) (g factors g_∥ and g_⊥) for the trigonal [Ti(H₂O)₆]³⁺ clusters in the rapidly frozen solutions of Ti³⁺ 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 3dⁿ 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 3dⁿ 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.     

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.     

Electron paramagnetic resonance parameters of Mn<Superscript>4+</Superscript> ion in h-BaTiO<Subscript>3</Subscript> crystal from a two-mechanism model

The EPR parameters (g factors g _‖, g _⊥ and zero-field splitting D) of Mn⁴⁺ ion in h-BaTiO₃ crystal are calculated from the complete high-order perturbation formulas based on a two-mechanism model for the EPR parameters of 3d ³ ions in trigonal symmetry. In the model, not only the widely used crystal-field mechanism, but also the charge-transfer mechanism (which is not considered in crystal-field theory) are included. The calculated results are in reasonable agreement with the experimental values. The relative importance of charge-transfer mechanism to EPR parameters and the defect structure of Mn⁴⁺ centre in h-BaTiO₃ crystal obtained from the calculations are discussed.      

Investigations of EPR Parameters of MgTiO3:Cr3+, SrTiO3:Cr3+, and SrTiO3:Mn4+ Crystals

Complete high-order perturbation formulas are established based on charge-transfer (CT) and crystal-field (CF) mechanisms. The electron paramagnetic resonance (EPR) g-factors of MgTiO₃:Cr³⁺, SrTiO₃:Cr³⁺, and SrTiO₃:Mn⁴⁺ crystals are calculated from the formulas. The calculations of the EPR g-factors agree well with the experimental values. The contribution rate of the CT mechanism to EPR parameters increases with increasing valence state of the 3d ⁿ ions in the crystals. For the higher-valence state 3d ³ Mn⁴⁺ ion in the crystals, the elucidation of the EPR parameters rationally involves both CF and CT mechanisms.     

Theoretical explanation of g factors for Ti ions in LiNbO3 and LiTaO3 crystals

The EPR g factors g_// and g_⊥ for Ti³⁺ ions at the trigonal octahedral Li⁺ sites of LiNbO₃ and LiTaO₃ crystals are calculated from the third-order perturbation formulas of g factors for 3d¹ ion in trigonal symmetry. In the calculations, the crystal-field parameters are obtained from the structural data by using the superposition model. The calculated values are in reasonable agreement with the observed values. The results are discussed.     

Investigations of the Spin-Hamiltonian Parameters for the Rhombic Mo5+ Centers in Ca1−x Y x MoO4 Crystal

The spin-Hamiltonian parameters (g factors g _i and hyperfine structure constants A _i , where i = x, y, z) of the rhombic Mo⁵⁺ center in Ca_1?x Y _x MoO₄ crystal are calculated from the high-order perturbation formulas based on the two-mechanism model for the rhombic d¹ tetrahedral clusters with the ground state |d _z 2〉. In these formulas, besides the contributions due to the widely applied crystal-field (CF) mechanism concerning CF excited states, those due to the charge-transfer (CT) mechanism (which is omitted in CF theory) concerning CT excited states are considered. The calculated results are in reasonable agreement with the experimental values. The calculations show that because of the great relative importance of CT mechanism for the components of spin-Hamiltonian parameter along x and y axes, the accurate and complete calculations of spin-Hamiltonian parameters for Mo⁵⁺ and other high valence state dⁿ ions in crystals should take account of both the CF and CT mechanisms. The defect model of the rhombic Mo⁵⁺ center is also confirmed from the calculations.     

Optical investigation of charge-transfer transitions in spinel Co3O4

Optical transitions in normal-spinel Co₃O₄ have been identified by investigating the variation of its optical absorption spectrum with the replacement of Co by Zn. Three optical-transition structures were located at about 1.65, 2.4, and 2.8 eV from the measured dielectric function of Co₃O₄ by spectroscopic ellipsometry. The variation of the absorption structures with the Zn substitution (Zn_xCo_3−xO₄) can be explained in terms of charge-transfer transitions involving d states of Co ions. The 1.65 eV structure is assigned to a d-d charge-transfer transition between the t_2g states of octahedral Co³⁺ ion and t₂ states of tetrahedral Co²⁺ ion, t_2g(Co³⁺)→t₂(Co²⁺). The 2.4 and 2.8 eV structures are interpreted as due to charge-transfer transitions involving the p states of O²⁻ ion: p(O²⁻)→t₂(Co²⁺) for the 2.4 eV absorption and p(O²⁻)→e_g(Co³⁺) for the 2.8 eV absorption. The observed gradual reduction of the 1.65 and 2.4 eV absorption strength with the increase of the Zn composition for Zn_xCo_3−xO₄ can be explained in terms of the substitution of the tetrahedral Co²⁺ sites by Zn²⁺ ions. The crystal-field splitting Δ_Oh between the e_g and the t_2g states of the octahedral Co³⁺ ion is estimated to be 2 eV.     

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 g_i and hyperfine structure constants A_i, 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 calculations of the optical band positions and spin-Hamiltonian parameters for Yb at the tetragonal Y site of KY3F10 crystal

The six optical band positions and six spin-Hamiltonian parameters [g factors g_∥, g_⊥ and hyperfine structure constants A_∥(¹⁷¹Yb³⁺), A_⊥(¹⁷¹Yb³⁺), A_∥(¹⁷³Yb³⁺), A_⊥(¹⁷³Yb³⁺)] for Yb³⁺ ion at the tetragonal Y³⁺ site of KY₃F₁₀ crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Hamiltonian of energy matrix contains the free-ion, crystal-field interaction, Zeeman (or magnetic) interaction and hyperfine interaction terms and so a 14×14 complete energy matrix for 4f¹³ ion in tetragonal crystal-field and under an external magnetic field is constructed. Diagonalizing the energy matrix, these optical and EPR spectral data are calculated together and the calculated results are in reasonable agreement with the experimental values. The signs of hyperfine structure constants A_∥, A_⊥ for the isotopes ¹⁷¹Yb³⁺ and ¹⁷³Yb³⁺ in KY₃F₁₀ are suggested. The results are discussed.     

Theoretical and comparative investigations of Yb ion in MWO4 and M′MoO4 scheelites crystals (M=Sr, Pb, Ca, Ba) and (M′=Sr, Pb, Ca, Cd)

The crystal-field model is applied to a series of scheelites crystals (CaWO₄, SrWO₄, PbWO₄, BaWO₄, CdMoO₄, CaMoO₄, SrMoO₄ and PbMoO₄) doped with the Yb³⁺ ion. The calculated crystal-field parameters present a general trend of variation with M²⁺ ionic radius of the host cation. The maximum splitting ΔE of the ²F_7/2 manifold of the Yb³⁺ ion is then obtained as a function of N_V crystal-field strength parameters. The agreement between experimental results and theoretical predictions for all investigated systems is very satisfactory. The crystal-field effects are very important for the prediction of emission energies of the Yb³⁺ ion in different scheelites.     

Research of the Spin-Hamiltonian Parameters and Defect Structure for the Trigonal Mn<Superscript>4+</Superscript> Centers in Y<Subscript>2</Subscript>Ti<Subscript>2</Subscript>O<Subscript>7</Subscript>:Mn<Superscript>4+</Superscript> Crystal

The high-order perturbation formulas founded on the two-mechanism model are applied in this paper to compute the spin-Hamiltonian parameters (g factors g _//, g _⊥ and zero-field splitting D) of the trigonal Mn⁴⁺ centers in Y₂Ti₂O₇:Mn⁴⁺ crystal. In this model, besides the contributions from the traditional crystal-field (CF) mechanism (in the CF theory) related to CF excited states, those from the charge-transfer (CT) mechanism connected with CT excited states are contained. The calculated results are reasonably coincident with the observed values. The calculations show that the contributions of CT mechanism to spin-Hamiltonian parameters (in particular, the g factors) for (MnO₆)^8? clusters are large and cannot be neglected. The defect structure of trigonal (MnO₆)^8? clusters in Y₂Ti₂O₇:Mn⁴⁺ crystals is also evaluated. The results are discussed.     

Crystal-field hamiltonian and spin-orbit interaction for d and d ions at low C3 symmetry sites: V:Al2O3 and Ni:LiNbO3

The experimental studies have provided evidence of the occurrence of transitions from the ³T_1g(³F) ground state to the crystal-field levels ³T_2g(³F), ³T_1g(³P) and ³A_2g(³F) for the V³⁺ centres in Al₂O₃ crystal; and from the ³A_2g(³F) ground state to the crystal-field levels ³T_2g(³F), ³T_1g(³F) and ³T_1g(³P) for the Ni²⁺ centres in LiNbO₃ crystal (levels are assigned to irreps of the O_h point symmetry group). Using the experimental spectroscopic data, theoretical calculations of the crystal-field levels of V³⁺:Al₂O₃ and Ni²⁺:LiNbO₃ are carried out based on the Racah theory. The observed crystalline-field splittings of the V³⁺ and Ni²⁺ terms were accounted for using a C₃ symmetry Hamiltonian. The spin-orbit interaction was taken into account in this work. The Racah, crystal-field and spin-orbit parameters, which fit experimental and theoretical energy levels, have been reliably obtained. A good agreement between the theoretical and experimental results for the energy levels of V³⁺:Al₂O₃ and Ni²⁺:LiNbO₃ has been obtained.     

Crystal-field analysis for d ions at D4h symmetry sites: Electronic states in trans-NiCl2(H2O)4 complex

The polarized absorption spectra of trans-NiCl₂(H₂O)₄ complex were measured by Bussière et al. [Coord. Chem. Rev. 219-221 (2001) 509-543] at low-temperature. Using the experimental spectroscopic data, semiempirical calculations of the crystal-field levels of trans-NiCl₂(H₂O)₄ chromophore are carried out, based on the Racah theory. We used idealized D_4h point group symmetry to analyse the observed crystalline-field splitting of this chromophore. As a result, Racah and crystal-field parameters have been reliably obtained. A good agreement between the theoretical and experimental energy levels of trans-NiCl₂(H₂O)₄ complex has been obtained. The region of ³T_1g/¹E_g(O_h) bands is of great interest and it is useful to use the tetragonal symmetry to understand the features of this spectral region.     

Preparation and luminescent properties of cubic Eu:Y2O3 nanocrystals and comparison to bulk Eu:Y2O3

Y₂O₃:Eu³⁺ nanocrystals were prepared by combustion synthesis. The particle size estimated by X-ray powder diffraction (XRD) was about 10 nm. A blue-shift of the charge-transfer (CT) band in excitation spectra was observed in Y₂O₃:Eu³⁺ nanocrystals compared with bulk Y₂O₃:Eu³⁺. The electronic structure of Y₂O₃ is calculated by density functional method and exchange and correlation have been treated by the generalized gradient approximation (GGA) within the scheme due to Perdew-Burke-Ernzerhof (PBE). The calculated results show that the energy centroid of 5d orbital in nanocrystal has increasing trend compared with that in the bulk material. The bond length and bond covalency are calculated by chemical bond theory. The bond lengths of Y₂O₃:Eu³⁺ nanocrystal are shorter than those of the bulk counterpart and the bond covalency of Y₂O₃:Eu³⁺ nanocrystal also has an increasing trend. By combining centroid shift and crystal-field splitting, the blue-shift of the CT band is interpreted.     

Theoretical examination of optical and EPR spectra for Cu ion in K2PdCl4 crystal

In this work, two d-d transition spectra and four EPR parameters g_∥, g_⊥, A_∥, A_⊥ of K₂PdCl₄/Cu²⁺ are uniformly interpreted based on Zhao's crystal-field model. The calculation result is in good agreement with the experiment findings. The ligand spin-orbit coupling is neglected on the calculation, which is consistent with the ab initio result by Hillier et al. [J. Am. Chem. Soc. 98 (1976) 95]     

Calculations of the Spin-Hamiltonian Parameters for the Trigonal Cr3+ and Mn4+ Centers in Ca3Ga2Ge3O12 (CGGG) Garnet Crystal

The spin-Hamiltonian parameters (zero-field splitting D, g-factors g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) of Cr³⁺ and Mn⁴⁺ ions at the trigonal Ga³⁺ site of Ca₃Ga₂Ge₃O₁₂ (CGGG) garnet crystals are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, besides the contributions to spin-Hamiltonian parameters from the crystal-field (CF) mechanism in the frequently applied CF theory, those from the charge-transfer (CT) mechanism (which is neglected in CF theory) are taken into account. The calculated results are in reasonable agreement with the experimental values. The defect structures of Cr³⁺ and Mn⁴⁺ impurity centers in CGGG crystals are also obtained from the calculations. The calculations show that the relative importance of CF mechanism (characterized by $ \left| {{{Q^{\text{CT}} } \mathord{\left/ {\vphantom {{Q^{\text{CT}} } {Q^{\text{CF}} }}} \right. \kern-0pt} {Q^{\text{CF}} }}} \right| $ , where $ Q = D,\;\Delta g_{\rm{//}} ,\;\Delta g_{ \bot } ,\;A_{\rm{//}}^{(2)} or\;A_{ \bot }^{(2)} $ ) for Mn⁴⁺ center in CGGG is larger than that for Cr³⁺ center. So, for the high valence state dⁿ ions in crystals, the reasonable calculations of spin-Hamiltonian parameters should consider the contributions due to both the CF and CT mechanisms.     

Preparation of activated carbon from a renewable bio-plant of Euphorbia rigida by H2SO4 activation and its adsorption behavior in aqueous solutions

The use of activated carbon obtained from Euphorbia rigida for the removal of a basic textile dye, which is methylene blue, from aqueous solutions at various contact times, pHs and temperatures was investigated. The plant material was chemically modified with H₂SO₄. The surface area of chemically modified activated carbon was 741.2 m² g⁻¹. The surface characterization of both plant- and activated carbon was undertaken using FTIR spectroscopic technique. The adsorption process attains equilibrium within 60 min. The experimental data indicated that the adsorption isotherms are well described by the Langmuir equilibrium isotherm equation and the calculated adsorption capacity of activated carbon was 114.45 mg g⁻¹ at 40° C. The adsorption kinetics of methylene blue obeys the pseudo-second-order kinetic model and also followed by the intraparticle diffusion model up to 60 min. The thermodynamic parameters such as ΔG°, ΔH° and ΔS° were calculated to estimate the nature of adsorption. The activation energy of the system was calculated as 55.51 kJ mol⁻¹. According to these results, prepared activated carbon could be used as a low-cost adsorbent to compare with the commercial activated carbon for the removal textile dyes from textile wastewater processes.