Defect model and EPR parameters for the tetragonal Yb3+ center in KTaO3 crystal

The defect model of the tetragonal Yb3+ (at K+ site) center in KTaO3 crystal is suggested, i.e., Yb3+ ion does not occupy the ideal K+ site, but is displaced by an amount DeltaZ along one of 100 axes because of the much smaller ionic radius of Yb3+ compared with that of the replaced K+. Based on the defect model, the EPR parameters (g factors g(parallel), g(perpendicular) and hyperfine structure constants 171A parallel, 171A perpendicular, 173A parallel, 173A perpendicular) are calculated by diagonalizing the 14 x 14 complete energy matrix. The calculated values are in agreement with the observed values and the off-center displacement DeltaZ (approximately 0.2 angstroms) is estimated from the calculations. These results are discussed.     

Theoretical investigation of the EPR parameters and local structure for trigonal Yb3+ ion in Bi4Ge3O12 crystal

Bi4Ge3O12 single crystals are of great interest for science research and engineering applications. In this paper, the electron paramagnetic resonance (EPR) g factors g||, gperpendicular of Yb3+ and hyperfine structure constants A||, Aperpendicular of 171Yb3+ and 173Yb3+ isotopes in Bi4Ge3O12 crystal are calculated from the perturbation formulas of these parameters. The crystal-field parameters are obtained from the superposition model and the crystal structure data. The EPR parameters for trigonal Yb3+ centers in Bi4Ge3O12 are reasonably explained by involving the defect structures of impurity Yb3+ centers. Based on the calculations, Yb3+ ion is found not to occupy exactly the host Bi3+ site, but to shift away from the center of oxygen octahedron by a distance DeltaZ approximately 0.317 A along C3 axis. The results are discussed.     

Investigations of the optical spectra and EPR parameters in CaWO4:Yb3+

In this paper, we calculate the optical spectra data (crystal-field energy levels), the electron paramagnetic resonance (EPR) g factors gparallel, gperpendicular of Yb3+ and hyperfine structure constants Aparallel, Aperpendicular of 171Yb3+ and 173Yb3+ isotopes in CaWO4 crystal in a unified way from the crystal-field theory. All the calculated results are in good agreement with the experimental values. The signs of Aparallel and Aperpendicular for both isotopes 171Yb3+ and 173Yb3+ are suggested.     

Investigations of EPR parameters for the trigonal Ti3+-Ti3+ pair in beryl crystal

By using the complete diagonalization of energy matrix of 3d1 ions in trigonal symmetry, the EPR parameters (g factors g( parallel), g( perpendicular) and zero-field splitting D) of the trigonal Ti3+-Ti3+ pair in beryl crystal are calculated. In the calculations, the exchange interaction in the Ti3+-Ti3+ pair is taken as the perturbation and the local trigonal distortion in the defect center is considered. The results (which are in agreement with the experimental values) are discussed.     

Investigations of the optical spectra and EPR g factors for the tetragonal Cu2+ centers in trigonal ZnCO3 crystal

Two distinctive theoretical methods, the complete diagonalization (of energy matrix) method (CDM) and the perturbation theory method (PTM), are employed to calculate the optical band positions and EPR g factors g_//, g_⊥ for the tetragonal Cu²⁺ centers in trigonal ZnCO₃ crystal. The results from the two methods coincide and are also in good agreement with the experimental values. So both the CDM and PTM are adequate for the investigations of optical and EPR data for d⁹ ions in crystals. The tetragonal distortion due to the static Jahn–Teller effect for the tetragonal Cu²⁺ centers in trigonal Zn²⁺ site of ZnCO₃ is also acquired from the calculations. The results are discussed.     

Theoretical studies of the local structure for the trigonal Ti(3+) center in LiF crystal

The local structure of the trigonal Ti(3+) center in LiF crystal is theoretically investigated by using the perturbation formulas of the anisotropic g factors and g(//) and g(/_) for a 3d(1) ion in trigonally distorted octahedra based on the cluster approach. From the studies on the basis of various possible structure models, the local structure of the trigonal Ti(3+) center may be characterized as [TiF(3)O(3)](6-) cluster (or model I). In this model, the impurity Ti(3+) is expected to substitute for the host Li(+) ion and shift away from its regular lattice site along the [111] (or C(3)) axis by about 0.19 A due to the strong electrostatic attraction of the O(2-) triangle replacing the original F(-) triangle. The magnitude of the above displacement obtained in this work is comparable with that ( approximately 0.2-0.3A) given by ENDOR experiment. Moreover, the cubic field parameter Dq (approximately 1497 cm(-1)) based on the above structure model is also in agreement with that (approximately 1500 cm(-1)) obtained from the experimental optical spectra of the studied system. The theoretical investigations of the local structure in this work may be useful to understand optical properties of Ti-doped LiF.     

Studies of the defect structures of the trigonal Cr3+-Vc centers in fluoroperovskites from EPR and optical spectra

The EPR parameters (zero-field splitting D and g factors g(parallel), g(perpendicular)) and the first excited state splitting Delta(2E) of the trigonal Cr3+-Vc centers (Vc denotes the cation vacancy in a C3 axis) in Cr3+-doped fluoroperovskites KMgF3, KZnF3, CsCdF3, CsCaF3, RbCdF3 and BaLiF3 are studied from the high-order perturbation formulas. From the studies, the defect structures (characterized by the vacancy-induced displacements Delta x1 of Cr3+ ion and Delta x2 of the three F- ion between Cr3+ and Vc) of these trigonal Cr3+-Vc centers are determined. It is found that the signs of displacements Delta x1 and Delta x2 are consistent with the expectations based on the electrostatic interactions, and the magnitudes of Delta x1 and Delta x2 for Cr3+ in the inverse perovskite BaLiF3 are larger than those for Cr3+ in the classical perovskites. The results are discussed.     

Theoretical investigation on the optical and EPR spectra for Cu2+-doped ZnO-CdS nanocomposites

The three optical absorption bands and EPR parameters of the [CuO₆]¹⁰⁻ center in the ZnO-CdS composite nanopowders are theoretically studied from the perturbation formulas based on the cluster approach. In the formulas, the contributions to EPR parameters arising from the ligand orbital and spin–orbit coupling interactions via covalence effect are considered. For the studied [CuO₆]¹⁰⁻ cluster, the Cu–O bond lengths are suggested to show a relative elongation ratio ρ (≈ 4.1%) along the z-axis due to Jahn–Teller effect. The defect models suggested in this work are different from the previous assumption that the impurity Cu²⁺ can replace the host Zn²⁺ site when it enters the lattices of the ΖnO and ΖnS nanocrystals, forming the tetrahedral [CuΧ₄]⁶⁻ clusters (Χ = O, S). The validity of the proposed model is discussed. The differences between the present calculations and the previous ones for the interstitial Cu²⁺ center in ZnO nanocrystals are analyzed in view of the dissimilar impurity behaviors due to the new composition CdS and distinct preparation conditions.     

Spin-Hamiltonian parameters and angular distortion for the trigonal Nd3+ center in congruent LiNbO3

The 52 × 52 energy matrix related to the ground multiplet ⁴I_9/2 and the first to third excited multiplets ⁴I_11/2, ⁴I_13/2 and ⁴I_15/2 for 4f³ ions in trigonal crystal field under an external magnetic field is established. By diagonalizing the energy matrix, the spin-Hamiltonian parameters (g factor g_//, g_⊥ and hyperfine structure constants ¹⁴³A_//, ¹⁴³A_⊥, ¹⁴⁵A_//, ¹⁴⁵A_⊥) of the trigonal Nd³⁺ center in congruent LiNbO₃ crystal are calculated. The calculated results are in reasonable agreement with the experimental values. From the calculations, the negative signs of hyperfine structure constants are suggested and the angular distortion of the trigonal Nd³⁺ center in LiNbO₃, which is unable to be determined by EXAFS measurement, is obtained. The results are discussed.     

EPR g factors of trigonal Dy(3+) center in ThO(2) crystal

The perturbation formulas of EPR g factors g(parallel) and g( perpendicular ) for the lowest Kramers doublet of 6H(15/2) of a 4f(9) ion in trigonal symmetry are established in this paper. In these formulas, besides the contribution due to the interaction within the lowest 6H(15/2) manifolds considered in the previous papers, the contributions due to the J-mixing among the 6H(15/2), 6H(13/2) (first excited state) and 6H(11/2) (second excited state) via crystal-field interaction, the admixtures among the states with the same J value via spin-orbit coupling interaction and those between the lowest Kramers doublet Gammagamma and other Kramers doublets Gamma(X) within the states 6H(J) (J=15/2,13/2,11/2) via crystal-field and orbital angular momentum interactions are included. From these formulas, the g factors g(parallel) and g( perpendicular ) for the trigonal Dy(3+) center in ThO(2) crystal are calculated. The results are discussed.     

EPR paramaters and defect structure of the trigonal Ti2+ center in ZnS

The axial Ti2+ center in a nearly wholly cubic ZnS crystal is assigned to the Ti2+ ion on the hexagonal site of wurtzite structure caused by stacking faults. On the ground of the assignment, the EPR parameters (zero-field splitting D, g factor g( parallel) and g-anisotropy Deltag=g( parallel)-g( perpendicular)) of the axial Ti2+ center are calculated from the high-order perturbation formulas based on the cluster approach for the EPR parameters of 3d2 ion in trigonal symmetry. From the calculations, the local atom-position parameter u(loc) (which is different from the corresponding parameter u in the host wurtzite structure) and hence the defect structure of the Ti2+ center are estimated. The results (the calculated EPR parameters and the defect structure) are discussed.     

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 g_i (i = || and ⊥) and hyperfine structure constants A_i (M) and A_i(N), with M and N belonging to isotopes ⁶³Cu²⁺ and ⁶⁵Cu²⁺—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.     

Single crystal EPR and optical absorption studies of Cu2+ ion in L-arginine sulphophosphate monohydrate--a nonlinear optical crystal

The EPR spectra of Cu2+ ion in L-arginine sulphophosphate monohydrate (LASP), a nonlinear optical material (NLO) have been studied at room temperature. Two magnetically inequivalent interstitial Cu2+ sites in the lattice were identified. The principal values of g- and A-tensors indicate that the symmetry of the electrostatic field around the Cu2+ ion is rhombic. Bonding parameters have been evaluated and the ground state wave function of Cu2+ ion is constructed. The ground state is found to be an admixure of x2 - y2 and 3z2 - r2 orbitals. By correlating EPR and optical absorption spectra the crystal field parameters have been evaluated.     

Theoretical investigations of the EPR parameters for Cr3+ and Mn4+ ions in PbTiO3 crystals

The complete high-order perturbation formulas of EPR parameters (g factors g( parallel), g( perpendicular) and zero-field splitting D), containing the crystal-field (CF) mechanism and charge-transfer (CT) mechanism (the latter is omitted in crystal-field theory which is often used to study the EPR parameters), are established from a cluster approach for 3d3 ions in tetragonal octahedral sites. According to the calculations based on these formulas, the EPR parameters g( parallel), g( perpendicular) and zero-field splitting D for Cr3+ and Mn4+ ions in PbTiO3 crystals are explained reasonably. The calculations show that (i) the sign of g-shift Deltag(i)(CT) (=g(i)-g(s), where g(s)=2.0023 is free-electron value and i= parallel and perpendicular) in CT mechanism is opposite to, but that of D(CT) is the same as, the corresponding signs in the CF mechanism and (ii) the relative importance of CT mechanism for the high valence state 3d3 ion (e.g., Mn4+) is large and so the contributions to EPR parameters from CT mechanism should be taken into account. The different sign of splitting D and the different defect structure for Cr3+ and Mn4+ impurity centers in PbTiO3 crystals are also suggested from the calculations. The results are discussed.     

Spin-Hamiltonian parameters and defect structure for the rhombic Dy3+ center in AgCl crystal

Based on the defect model that the rhombic Dy(3+) center in AgCl crystal is formed by substitutional Dy3+ ion associated with two nearest Ag+ vacancies (VAg) along the <110> and <110> axes owing to charge compensation, the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants 161Ai and 163Ai, where i=x, y, z) of this rhombic Dy3+ center are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman (or magnetic) and hyperfine interaction terms are attached to the classical Hamiltonian used in the calculation of crystal-field energy levels and a 66×66 energy matrix concerning this Hamiltonian is constructed by taking all the ground-term multiplets 6HJ (J=15/2, 13/2, 11/2, 9/2, 7/2, 5/2) into account. The calculated results (g factors gi and average |A(161Dy3+)| and |A(163Dy3+)|) are in reasonable agreement with the experimental values. From the calculations, the above defect model of rhombic Dy3+ center is confirmed, the defect structure of this Dy3+ center (characterized by the displacement of Cl- ligand caused by VAg) is obtained and the components of hyperfine structure constants Ai(161Dy3+) and Ai(163Dy3+) are predicted. The results are discussed.     

CsCdBr3晶体中Nd3+离子的晶体场能级计算

在C3v点群对称场中,运用双层点电荷和点电荷配位场模型计算了CscdBR3晶体中Nd3+离子的65个配位场能级,与实验能级值相比,它们的均方根偏差分别为29.27和36.25cm-1.结果表明:双层点电荷模型引入键电荷q是成功的,它能够更准确地反映中心离子与配体之间相互作用的真实情况,对研究C3v对称场中稀土离子的光谱特性具有非常重要的意义.     

A novel nonlinear optical crystal for the IR region: noncentrosymmetrically crystalline CsCdBr3 and its properties

A noncentrosymmetric crystal structure of CsCdBr(3) has been successfully observed with X-ray single-crystal structure analysis. It crystallizes in the hexagonal space group P6(3)mc, with a = 7.7281(14) A, b = 7.7281(14) A, c = 6.742(2) A, alpha = 90 degrees, beta = 90 degrees, gamma = 120 degrees, Z = 2. It was obtained by a new preparation procedure different from that reported in the literature that gave a centrosymmetric structure. The structure contains Cd-Br octahedrons, which are connected in a plane-sharing way to form one-dimensional long chains. Each octahedron is slightly distorted, as the three Cd-Br bond lengths are 2.774 A, while the other three Cd-Br bond lengths are 2.804 A. The distortion directions of all of the octahedrons are almost parallel and give rise to the accumulation of the microcosmic nonlinear optical (NLO) coefficient. The Kurtz powder technique shows that CsCdBr(3) has a powder second harmonic generation of about 2 times as large as that of potassium dihydrogen phosphate (KDP). It shows excellent transparency in the visible and infrared regions. The thermal stability is also good. Therefore it may be utilized as a potential nonlinear optical crystal for the IR region.     

Investigations of the optical and EPR spectra for VO2+ in LiKSO4 crystals

The optical spectra and EPR spectra (characterized by the spin-Hamiltonian parameters g(//), g(perpendicular), A(//) and A(perpendicular)) for the molecular ion VO2+ in LiKSO4 crystals are calculated from two microscopic theory methods, one of which is the complete diagonalization (of energy matrix) method (CDM) and the other is the perturbation theory method (PTM). The calculated three optical absorption bands and four spin-Hamiltonian parameters from the two methods are not only close to each other, but also in reasonable agreement with the experimental values. It appears that both theoretical methods are effective in the explanation of optical and EPR spectra for 3d1 ions in crystals. The negative signs of hyperfine structure constants A(//) and A(perpendicular) for VO2+ in LiKSO4 crystals are also suggested from the calculations.     

Studies of the spin-Hamiltonian parameters and defect structures for the tetragonal and cubic Yb3+ centers in AgCl crystal

The spin-Hamiltonian parameters, g factors and hyperfine structure constants, for the tetragonal and cubic Yb(3+) centers in AgCl crystal are calculated from the complete diagonalization (of energy matrix) method. The calculations are based on the defect models that the tetragonal Yb(3+) center is formed by the substitutional Yb(3+) associated with two nearest Ag(+) vacancy (V(Ag)) along <001> and <001ˉ> axes (i.e., C(4) axis) owing to charge compensation and in cubic Yb(3+) center the two compensators V(Ag) are remote. From the calculations, the spin-Hamiltonian parameters of both Yb(3+) centers in AgCl are explained reasonably, the signs of hyperfine structure constants A(i)((171)Yb(3+)) and A(i)((173)Yb(3+)) are suggested, the above defect models of both Yb(3+) centers are confirmed and their defect structures are determined.     

Theoretical investigations of zero-field splitting of excited states for 3d3 ions in trigonal crystal fields

By taking into account slight interactions, i.e. spin-spin, spin-other-orbit and orbit-orbit interactions, in addition to spin-orbit interaction, the zero-field splitting of ground state and low excited states and g factors of ZnGa2O4:Cr3+ crystal have been interpreted systematically. And the contributions to zero-field splitting arising from slight magnetic interaction and trigonal crystal field are investigated. It is found that there exist combined mechanism between magnetic interactions and trigonal crystal field.