Investigations of EPR parameters and local lattice distortions for both Co2+ centers in La2Mg3(NO3)12.24H2O crystal

The EPR g factors, g parallel and g perpendicular, of Co2+ and hyperfine structure constants (A parallel, A perpendicular) of 59Co2+ and 60Co2+ isotopes in both trigonal Mg2+ sites of La2Mg3(NO3)12.24H2O crystal are calculated from the high-order perturbation formulas of EPR parameters based on the cluster approach for 3d7 ion. It is found that to explain reasonably all these EPR parameters, the local relaxation effects (particularly, those related to the trigonal distortion angles thetai) in the vicinity of both Co2+ impurities should be considered. The local angles thetai are obtained from the calculations and the results are discussed.     

EPR parameters and defect structures for the Co2+ ions in LiNbO3 and LiTaO3 crystals

The electron paramagnetic resonance (EPR) parameters (g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) for Co2+ ions in LiNbO3 and LiTaO3 crystals are calculated from the second-order perturbation formulas based on the cluster approach for 3d7 ions in trigonal octahedral clusters. The calculated results are in reasonable agreement with the experimental values. From the calculations, the negative sign of A parallel for Co2+ in the two crystals and the more exact and rational values of A parallel for Co2+ in LiTaO3 are suggested. The defect structures (characterized by the Co2+ displacement DeltaZ along C3 axis and the O(2-) displacement DeltaX in an oxygen triangle towards the center of the triangle) for the Co2+ centers in both crystals are estimated. The results are discussed.     

Theoretical study of local structure for Ni2+ ions at tetragonal sites in K2ZnF4:Ni2+ system

A theoretical method for studying the local lattice structure of Ni2+ ions in (NiF6)(4-) coordination complex is presented. Using the ligand-field model, the formulas relating the microscopic spin Hamiltonian parameters with the crystal structure parameters are derived. Based on the theoretical formulas, the 45 x 45 complete energy matrices for d8 (d2) configuration ions in a tetragonal ligand-field are constructed. By diagonalizing the complete energy matrices, the local distortion structure parameters (R perpendicular and R || ) of Ni2+ ions in K2ZnF4:Ni2+ system have been investigated. The theoretical results are accorded well with the experimental values. Moreover, to understand the detailed physical and chemical properties of the fluoroperovskite crystals, the theoretical values of the g factor of K2ZnF4:Ni2+ system at 78 and 290 K are reported first.     

Investigation of EPR parameters and the local structure of the rhombic Cu2+ center in zinc fluoride

Based on a cluster approach, the local structure of the rhombic Cu²⁺ center in a ZnF₂ crystal is investigated by using the high-order perturbation formulas of electron paramagnetic resonance (EPR) parameters g factors g _i (i = x, y, z) and hyperfine structure constants A _i in rhombically compressed octahedral symmetry. According to the studies, the local axial distortion angle Δα′(≈ 2.9°) in the impurity center is found to be by ～2.5° larger than the host value, which is characterized as a contraction and stretching of the parallel and perpendicular bond lengths by about 0.116 Å and 0.058 Å respectively. This results in a more compressed ligand octahedron because of the Jahn-Teller effect via the interaction of the vibrations of impurity-ligand bonds in the Cu²⁺ center. The reasonableness of the results is also discussed.     

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.     

Theoretical investigations of the EPR g factors and the local structure for Er3+ in BaWO4

The electron paramagnetic resonance (EPR) parameters g factors g(parallel) and g(perpendicular) as well as the local structure for Er3+ in scheelite-type BaWO4 are theoretically investigated by using the perturbation formulas of the EPR parameters for a 4f11 ion under tetragonal symmetry. In these formulas, the contributions to the EPR parameters arising from the second-order perturbation terms and the admixture of different states are included. It is found that the impurity-ligand bonding angles (or the polar angles) related to the fourfold axis in the tetragonal Er3+ center are about 1.5 degrees smaller than those in pure crystal. The calculated EPR parameters are in agreement with the observed values. The validity of the results is discussed.     

Spectral studies on metal-ligand bonding of novel rhodanine azodye sulphadrugs

A series of novel complexes with 5-sulphadiazineazo-3-phenyl-2-thioxo-4-thiazolidinone (H2L1) and 5-sulphamethazineazo-3-phenyl-2-thioxo-4-thiazolidinone (H2L2) and various anions were prepared. Their structures and properties were characterized by elemental analyses, IR, UV-vis, EPR spectroscopy and magnetic measurements. The visible and EPR spectral studies indicated that the Cu(II) complexes have distorted octahedral. From the electron paramagnetic resonance and spectral data, the orbital reduction factors k(parallel) and k(perpendicular) were calculated. In all cases k(perpendicular) > k(parallel) indicates a 2B1g ground state. The crystal field parameters for Co(II) and Ni(II) complexes were calculated. The electronic absorption and a g(parallel)/A(parallel) values are indicative for the beginning of tetragonal distortion. The complexes, however, have lower symmetries and the amount of distortion in terms of DT/Dp, applying NSH 'Hamiltonian Theory' has been evaluated which indicate that the complexes are moderately distorted.     

Theoretical studies of the spin Hamiltonian parameters and the local structures for M2+ (M=Co, Mn, V and Ni) ions in CsMgCl3

The spin Hamiltonian parameters (zero-field splitting D, g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) for M2+ (M=Co, Mn, V and Ni) ions in CsMgCl3 are studied by using the perturbation formulas of the spin Hamiltonian parameters for 3dn (n=7, 5, 3, 8) ions in trigonal symmetry based on the cluster approach. In these formulas, the contributions to the spin Hamiltonian parameters from the admixture of d orbitals of the central ions with the p orbitals of the ligands and from the trigonal distortion are included and the parameters related to these effects can be obtained from the optical spectra and the local structures of the studied systems. Based on the studies, it is found that the local trigonal distortion angle beta in the M2+ impurity center is unlike that betaH (approximately 51.71 degrees) in the host CsMgCl3. The spin Hamiltonian parameters for these divalent ions in CsMgCl3 are also satisfactorily explained by using the local angle beta. The validity of the results is discussed.     

Studies of EPR parameters for Mn5+ -doped Li3PO4 and Li3VO4 crystals

The EPR parameters (zero-field splitting D and g factors g parallel, g perpendicular) of Mn5+ -doped Li3PO4 and Li3VO4 crystals are calculated from the complete high-order perturbation formulas based on a molecular orbital scheme for a 3d2 ion in tetragonal MX4 clusters. These formulas include not only the contribution coming from crystal-field excitations, but also that arising from charge-transfer excitations (which is discarded in crystal field theory). The calculated results are in reasonable agreement with the observed values. The contributions to EPR parameters coming from the charge-transfer excitations are comparable with those arising from the crystal-field excitations. It appears that for a high valence state 3dn ion in crystals, the reasonable explanations of EPR parameters should take the contributions due to both crystal-field and charge-transfer excitations into account.     

Investigations of the g factors and hyperfine structure parameters for Er3+ ion in zircon-type compounds

The electron paramagnetic resonance (EPR) g factors g(parallel), g(perpendicular) and hyperfine structure parameters A(parallel), A(perpendicular) of the tetragonal Er3+ centers in zircon-type compounds YXO4 (X = As, P, V), ScVO4 and RSiO4 (R = Zr, Hf, Th) are calculated from the perturbation formulas of EPR parameters for 4f11 ion in tetragonal symmetry. In these formulas, the second-order perturbation contributions are included in addition to the first-order perturbation contributions considered in the previous papers. The crystal-field parameters used in the calculations are obtained by analyzing the optical spectral data from the superposition model. Although the superposition model intrinsic parameters An(R0) used in this paper for Er3+ in various zircon-type compounds are not as scattered as those in the previous paper, the calculated results of both the optical spectra and EPR parameters show better agreement than those in the previous paper with the observed values, suggesting that the above calculation method and parameters are more reasonable. The contributions of the second-order perturbation terms to EPR parameters are also discussed.     

Geometry and Electronic Structure of CuCl(6)(4-) Polyhedra Doped into (3-Chloroanilinium)(8)[CdCl(6)]Cl(4)-An EPR and Structural Investigation

The EPR single-crystal and powder spectra of mixed crystals of (3-chloroanilinium)(8)(Cd(1-x)Cu(x)Cl(6))Cl(4) are measured as a function of temperature and x and analyzed with respect to the geometry and bonding properties of the CuCl(6) polyhedra. These undergo strong distortions due to vibronic Jahn-Teller coupling, with the resulting tetragonal elongation being superimposed by a considerable orthorhombic symmetry component induced by a host site strain acting as a compression along the crystallographic a axis. This strain becomes apparent in the cadmium compound (x = 0), whose crystal structure is also reported [a = 8.701(2) ?, b = 13.975(2) ?, c = 14.173(2) ?, alpha = 81.62(1) degrees, beta = 72.92(1) degrees, gamma = 77.57(1) degrees, triclinic P&onemacr;, Z = 1]. A calculation of the ground state potential surface and its vibronic structure nicely reproduces the g values, Cu-Cl spacings, and ligand field data. At high copper concentrations (including x = 1), the CuCl(6) polyhedra are coupled elastically, with the long axes of neighboring polyhedra having perpendicular orientations. The elastic correlation presumably is not of the long-range antiferrodistortive type, however. Above about 55 K, the angular Jahn-Teller distortion component becomes dynamically averaged within the time scale of the EPR experiment, leading to local tetragonally compressed CuCl(6) octahedra.     

High pressure synthesis,crystal growth and magnetic properties of TiOF

Polycrystalline samples of TiOF have been prepared at 1300 °C and 8 GPa, with small single crystals grown at the same conditions. The crystal structure remains tetragonal rutile-type down to at least 90 K (space group P4₂/mnm, a = 4.6533 (2) Å and c = 3.0143 (2) Å at 90 K) and the Ti(O,F)₆ octahedra are slightly compressed, consistent with Jahn-Teller distortion of 3d¹ Ti³⁺. Diffuse scattering reveals disordered structural correlations that may arise from local cis-order of oxide anions driven by covalency. TiOF is paramagnetic down to 5 K and observation of a small paramagnetic moment and a substantial Pauli term indicates that the d-electrons are partially delocalised.     

Investigations of the spin-Hamiltonian parameters for Er3+ at the Th4+ site in ThGeO4

The spin-Hamiltonian (SH) parameters g factors g(parallel), g(perpendicular) and the hyperfine structure parameters A(parallel) and A(perpendicular) for Er3+ at the tetragonally distorted dodecahedral Th4+ site in ThGeO4 are theoretically investigated by using the perturbation formulas of the SH parameters for a 4f11 ion in tetragonal symmetry. In these formulas, the contributions to the SH parameters from the second-order perturbation terms and the admixture of various energy levels are taken into account. The related crystal-field parameters are calculated from the geometrical relationship of the impurity center and the superposition model. Based on the studies, the lowest Kramers doublet is found to be Gamma7, rather than Gamma6 suggested in the previous work. The calculated SH parameters for Gamma7 doublet in this work are smaller than those obtained for Gamma6 doublet in the previous work and in good agreement with the observed values. The various contributions to the SH parameters are discussed.     

Investigations of the EPR g factors and hyperfine structure constants for two trigonal Co2+ centers in Al2O3 crystals

The EPR g factors gparallel, gperpendicular and the hyperfine structure constants Aparallel, Aperpendicular for two trigonal Co2+ centers (i.e. Co2+(I) center at the substitutional site and Co2+(II) center at the interstitial site) in Al2O3 crystals are calculated from the second-order perturbation formulas based on the cluster approach. In these formulas, the contributions to EPR parameters from both the spin-orbit coupling parameter of central 3dn ion and that of ligand are included. The calculated results are in reasonable agreement with the observed values. Based on the calculations, the defect structures of both Co2+ centers in Al2O3 crystals are obtained and the negative sign of Aparallel for Co2+(I) center is suggested. The results are discussed.     

Investigations of the EPR parameters for Sm3+ ions in KY3F10 and LiYF4 crystals

In this paper, we calculate the EPR parameters (g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) of rare earth ion Sm3+ in fluoride crystals KY3F10 and LiYF4 from the perturbation formulas of EPR parameters for a 4f5 ion in tetragonal symmetry. In these formulas, the crystal-field J-mixing of the first and second excited-state multiplets 6H(7/2) and 6H(9/2) into the ground state multiplet 6H(5/2), the mixtures among the states with the same J value via spin-orbit coupling interaction and the interactions between the ground Kramers doublet Gammagamma and the same irreducible representation as Gammagamma in other 11 Kramers doublets Gammax within 6HJ (J=5/2, 7/2, 9/2) states via crystal-field and orbital angular momentum (or hyperfine structure) are considered. The calculated results (which are in agreement with the observed values) are discussed.     

Local tilting angles tau for Fe+ in Cd2+ site and Fe3+ in Si4+ site of CdSiP2 semiconductor

The EPR parameters (g factors, g(parallel), g(perdendicular) and zero-field splitting D) for Fe+ in Cd2+ site and Fe3+ in Si4+ site of CdSiP2 semiconductor are calculated from the distinct high-order perturbation formulas. From the calculations, the local tetragonal distortions and hence the local tilting angles tau (which are different from the corresponding host values) for both paramagnetic centers are estimated. The results are discussed.     

Evolution of cobalt spin states and magnetic coupling along the SrCo(1-x)Sb(x)O(3-δ) system: correlation with the crystal structure

The oxides of the SrCo(1-x)Sb(x)O(3-δ) perovskite family have been recently designed, characterized and described as cathode materials for solid-oxide fuel cells with competitive power performance in the temperature range 750-850 °C. They feature a number of interesting properties including a good electronic conductivity, low electrode polarization resistance and adequate thermal expansion; the crystal structure adopts a 3C corner-linked perovskite network with a considerable number of oxygen vacancies. This paper reports on the effects of Sb-doping on the crystal structure features, the Co oxidation state and magnetic properties related to the presence of spin-state transitions in the Co cations. A phase transition was observed from the tetragonal P4/mmm space group for x≤ 0.15 to the cubic Pm ?3m space group in the x = 0.2 composition from neutron powder diffraction data. For the tetragonal phases the oxygen vacancies were found to be ordered and localized in the axial O2 and equatorial O3 atoms surrounding the Co2 positions. A noticeable distortion of CoO(6) octahedra is observed for x = 0.05 and 0.1, exhibiting a charge-ordering with a mixed oxidation state of Co(3+/4+) at Co1 sites and Co(3+) at Co2 positions: the Jahn-Teller Co(3+) in an intermediate-spin configuration is responsible for the octahedral distortion. Increasing Sb contents promotes a higher average oxidation state of cobalt, from a valence of 3.2+ for x = 0.05 to 3.4+ for x = 0.2, inducing a decrease of the oxygen vacancies and favouring a random distribution over a Pm ?3m cubic symmetry. All the samples present an antiferromagnetic behaviour with a G-type (k = 0) magnetic structure. The increase of the Sb content induces the weakening of the crystal field (Δ(cf)) in the octahedral environment promoting the Co spin-transition from the intermediate-spin to the high-spin configuration, as evidenced by the decrease of the octahedral distortion, increment of the unit-cell volume and enhancement of the ordered magnetic moment.     

On the origin of the metallic and anisotropic magnetic properties of NaxCoO2 (x approximately equal to 0.75)

Nonstoichiometric Na(x)CoO2 (0.5 < x < 1) consists of CoO2 layers made up of edge-sharing CoO6 octahedra and exhibits strongly anisotropic magnetic susceptibilities as well as metallic properties. A modified Curie-Weiss law was proposed for systems containing anisotropic magnetic ions to analyze the magnetic susceptibilities of Na(x)CoO2 (x approximately 0.75), and implications of this analysis were explored. Our study shows that the low-spin Co4+ (S = 1/2) ions of Na(x)CoO2 generated by the Na vacancies cause the anisotropic magnetic properties of Na(x)CoO2 and suggests that the six nearest-neighbor Co3+ ions of each Co4+ ion adopt the intermediate-spin electron configuration, thereby behaving magnetically like low-spin Co4+ ions. The Weiss temperature of Na(x)CoO2 is more negative along the direction of the lower g factor (i.e., theta|| < theta(perpendicular) < 0 and g|| < g(perpendicular)). The occurrence of intermediate-spin Co3+ ions surrounding each Co4+ ion accounts for the apparently puzzling magnetic properties of Na(x)CoO2 (x approximately 0.75), i.e., the large negative Weiss temperature, the three-dimensional antiferromagnetic ordering below approximately 22 K, and the metallic properties. The picture of the magnetic structure derived from neutron scattering studies below approximately 22 K is in apparent conflict with that deduced from magnetic susceptibility measurements between approximately 50 and 300 K. These conflicting pictures are resolved by noting that the spin exchange between Co3+ ions is more strongly antiferromagnetic than that between Co4+ and Co3+ ions.     

Theoretical calculations of spin-Hamiltonian parameters for CsCdX(3):Ni(2+) (X=Cl, Br) crystals from the two-mechanism model

The high-order perturbation formulas of spin-Hamiltonian (SH) parameters (g factors g( parallel), g( perpendicular) and zero-field splitting D) for 3d(8) ions in trigonal octahedral sites of crystals are derived considering not only the crystal-field (CF) mechanism, but also the charge-transfer (CT) mechanism (which is neglected in the extensively used CF theory). From these formulas and by considering the suitable impurity-induced local lattice relaxation, the SH parameters of CsCdX(3):Ni(2+) (X=Cl, Br) crystals are calculated. The results are in reasonable agreement with the experimental values. The sign of Q(CT) (Q=Deltag( parallel), Deltag( perpendicular) or D, where the g-shift Deltag(i)=g(i)-g(e), g(e) approximately 2.0023 is the free-electron value) due to CT mechanism is the same as that of the corresponding Q(CF) due to CF mechanism. The relative importance of CT mechanism (characterized by Q(CT)/Q(CF)) increases with the increasing atomic number of ligand X. So, for 3d(n) ion clusters in crystals with heavy element ligand ion (e.g., Br(-)), the reasonable explanations of SH parameters should contain the contributions from both CF and CT mechanisms.     

Studies of the trigonal field parameters and g factors for magnetic semiconductor NaCrS2

The trigonal field parameters v and v' of magnetic semiconductor NaCrS2 are calculated from the superposition model, and its g factors g parallel and g perpendicular are calculated from the high-order perturbation formulas of 3d3 ions in trigonal symmetry obtained by the one and two spin-orbit coupling parameter models. These calculations are based on the structural data of NaCrS2 crystal. The calculated results suggest that the superposition model is effective to the analyses of the low-symmetry field parameters of 3dn ions in crystals and that the two spin-orbit coupling parameter model (where the contributions from both the spin-orbit coupling parameter of 3dn ion and that of ligand are considered) is preferable to the one spin-orbit coupling parameter model (in which the contribution from only the spin-orbit coupling parameter of 3dn ion is considered) in the explanations of g factors in the cases that ligands have large spin-orbit coupling parameter in 3dn clusters.