Studies of the g factors and the local structure of the orthorhombic Ni center in KTaO3 crystal

The local structure and the g factor (g_x, g_y, and g_z) of the Ni⁺ center in KTaO₃ are theoretically studied using the perturbation formulas of the g factors for a 3d⁹ ion in orthorhombically elongated octahedra. The orthorhombic field parameters are determined from the superposition model and the local geometry of the system. In view of the covalency, the contributions from the ligand orbital and spin–orbit coupling interactions are taken into account from the cluster approach. In the calculations, the orthorhombic center is attributed to Ni⁺ occupying the host Ta⁵⁺ site, associated with the nearest-neighboring oxygen vacancy V_O along the c-axis. Furthermore, the planar Ni⁺–O²⁻ bonds are found to experience the relative variation ΔR (≈0.076 Å) along the a- and b-axis, respectively, due to the Jahn–Teller effect and the size mismatching substitution of Ta⁵⁺ by Ni⁺. Meanwhile, the effectively positive V_O can make the central Ni⁺ displace away from V_O along the c-axis by about 0.20 Å. The calculated g factors based on the above local distortions show good agreement with the experimental data.     

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

The spin Hamiltonian parameters, g factors g_i (i = x, y, z) and the hyperfine structure constants A_i 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 δ?′ (≈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 optical and EPR spectra for Fe ion in the MF3:Fe (M=Al, Ga) systems

By analyzing the EPR spectra of Fe³⁺ ion in the fluorinde glasses, the local lattice structures around impurity Fe³⁺ ion in MF₃:Fe³⁺ (M=Al, Ga) systems have been studied by means of 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. Both the second-order and fourth-order EPR parameters D and (a−F) are taken simultaneously in the structural investigation. The results indicate that the local lattice structure around octahedral Fe³⁺ center has an expansion distortion for Fe³⁺ in MF₃:Fe³⁺ (M=Al, Ga). The expansion distortion may be ascribed to the fact that the radius of Fe³⁺ ion is larger than that of Al³⁺ ion and Ga³⁺ ion, and the Fe³⁺ ion will push the fluoride ligands upwards and downwards, respectively. The local lattice structure parameters R=1.927 A, θ=55.538° for Fe³⁺ in AlF₃:Fe³⁺ and R=1.931 A, θ=56.09° for Fe³⁺ in GaF₃:Fe³⁺ are determined, respectively, and the EPR spectra of the MF₃:Fe³⁺ (M=Al, Ga) systems are satisfactorily explained.     

Theoretical explanation of absorption spectra and ESR parameters of Cu in shattuckite

The optical absorption spectra and electronic spin resonance parameters (ESR g factors g_‖, g_⊥ and hyperfine structure constants A_‖, A_⊥) for Cu²⁺ in shattuckite crystal are calculated from the two spin–orbital coupling parameters model, high-order perturbation formulas and complete diagonalization (of energy matrix) method (CDM) of 3d⁹ ion in tetragonal symmetry. The calculated results are in good agreement with the observed values. Since the ESR parameters are sensitive to the local structure of a paramagnetic impurity center, the defect structure of Cu²⁺ center in shattuckite crystal is estimated. The results are discussed.     

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.     

Theoretical investigations of the spin Hamiltonian parameters for the tetragonal [Rh(CN)4Cl2] complex in KCl

The spin Hamiltonian parameters (g factors, hyperfine structure constants and superhyperfine parameters) for the tetragonal [Rh(CN)₄Cl₂]⁴⁻ complex in KCl are theoretically investigated from the perturbation formulas of these parameters for a 4d⁷ ion in a tetragonally elongated octahedron. This center can be assigned to the substitutional Rh²⁺ on host K⁺ site reduced from Rh³⁺ by capturing one electron during the electron irradiation, associated with the two axial ligands CN⁻ replaced by two Cl⁻. The crystal-fields of the two axial Cl⁻ are weaker than those of the four planar CN⁻, yielding the tetragonal elongation distortion. This system belongs to the case of low spin (S = 1/2) under strong crystal-fields, different from that of high spin (S = 3/2) under weak and intermediate crystal-fields (e.g., 3d⁷ ions such as Fe⁺ and Co²⁺ in conventional chlorides). The calculated spin Hamiltonian parameters show good agreement with the experimental data. The above [Rh(CN)₄Cl₂]⁴⁻ complex due to the different axial and perpendicular ligands is unlike the tetragonally elongated [RhCl₆]⁴⁻ complex due to the Jahn–Teller effect in the similar NaCl:Rh²⁺ crystals.     

EPR g factors and tetragonal distortion for the isoelectronic Ni and Cu centers in the CuGaSe2 crystal

The EPR g factors, g_|| and g_⊥, for the isoelectronic 3d⁹ ions Ni⁺ and Cu²⁺ at the tetragonal Cu⁺ site of the CuGaSe₂ crystal are calculated from the high-order perturbation formulas based on a two-spin-orbit-parameter model. In the model, both the contributions to g factors from the spin-orbit parameter of central 3d⁹ ion and that of ligand ion are contained. The calculated results appear to be consistent with the experimental values. The tetragonal distortions (characterized by θ−θ₀, where θ is the angle between the metal-ligand bond and C₄ axis, and θ₀≈54.74° is the same angle in cubic symmetry) of Ni⁺ and Cu²⁺ centers, which are different from the corresponding angle in the host CuGaSe₂ crystal and from impurity to impurity, are obtained from the calculations. The difference of the sign of g_||−g_⊥ between the isoelectronic Ni⁺ and Cu²⁺ centers is found to be due to the different tetragonal distortions of both centers in the CuGaSe₂ crystal.     

Theoretical investigations of the local structure and the g factors for the tetragonal Ru3+ center in PbTiO3

The local structure and the g factors for the tetragonal Ru³⁺ center in PbTiO₃ are theoretically studied from the perturbation formulas of the g factors for a 4d⁵ ion in tetragonally distorted octahedra. From the studies, the distance between the impurity Ru³⁺ and the center of the oxygen octahedron is found to be about 0.283 Å, which is smaller than that (≈0.3 Å) for the host Ti⁴⁺ site. It appears that the impurity may not occupy exactly the host Ti⁴⁺ site but suffer a slight inward shift toward the center of the oxygen octahedron. The calculated g factors based on the above local structure show good agreement with the experimental values.     

Investigations on the local structure and g factors for the interstitial Ti3+ in TiO2

The EPR g factors gi (i = x, y, z) for the interstitial Ti³⁺ in rutile are theoretically studied from the perturbation formulas of these parameters for a 3d¹ ion in rhombically compressed octahedra. The ligand octahedron in the impurity center is found to be less compressed than that on the host interstitial site due to the Jahn-Teller effect. The local compression parameter (≈0.026) and the rhombic distortion angle δϕ′ (≈0.7°) around the impurity Ti³⁺ are smaller than the host values (≈0.091 and 3.5°). The theoretical g factors based on the above local structural parameters are in good agreement with the experimental data. In addition, the g factors for a tetragonal interstitial Ti³⁺ center are also reasonably interpreted.      

Spin-Hamiltonian parameters and local rotational order parameters for Gd ion in the tetragonal phase of SrTiO3 crystal

Using a diagonalization method, the spin-Hamiltonian parameters (g factors g_||, g_⊥ and zero-field splittings b₂⁰, b₄⁰, b₂⁴, b₆⁰, b₆⁴) for Gd³⁺ ion at the 12-fold coordinated Sr²⁺ site in the tetragonal phase of SrTiO₃ at T≈4.2 and 77 K are calculated in a unified way. The calculated results are in reasonable agreement with the experimental values. The local rotational order parameters ?_l of Gd³⁺ center at the two temperatures are also obtained from the calculations. It is found that the local rotational order parameters ?_l of Gd³⁺ impurity center at both temperatures are different from the corresponding parameters ?_h in the host SrTiO₃ crystal and the changes of spin-Hamiltonian parameters with temperature are caused by the change of local rotational order parameter?_l with temperature. The results are discussed.     

Structural and electrical transport properties of ZnxFe3−xO4 thin film deposited on Si (1 1 1) by pulsed-laser deposition

Polycrystalline thin films of Fe_3−xZn_xO₄ (x = 0.0, 0.01 and 0.02) were prepared by pulsed-laser deposition technique on Si (1 1 1) substrate. X-ray diffraction studies of parent as well as Zn doped magnetite show the spinel cubic structure of film with (1 1 1) orientation. The order–disorder transition temperature for Fe₃O₄ thin film with thickness of 150 nm are at 123 K (Si). Zn doping leads to enhancement of resistivity by Zn²⁺ substitution originates from a decrease of the carrier concentration, which do not show the Verwey transition. The Raman spectra for parent Fe₃O₄ on Si (1 1 1) substrate shows all Raman active modes for thin films at energies of T_2g¹, T_2g³, T_2g², and A_1g at 193, 304, 531 and 668 cm⁻¹. It is noticed that the frequency positions of the strongest A_1g mode are at 668.3 cm⁻¹, for all parent Fe₃O₄ thin film shifted at lower wave number as 663.7 for Fe_2.98Zn_0.02O₄ thin film on Si (1 1 1) substrate. The integral intensity at 668 cm⁻¹ increased significantly with decreasing doping concentration and highest for the parent sample, which is due to residual stress stored in the surface.     

New analysis of the Comet-Tail (AΠi − XΣ) system in the CO isotopic molecule

The emission spectra of the 0-2, 4-2, and 6-1 bands of the Comet-Tail (A²Π_i − X²Σ⁺) system in the ¹⁴C¹⁶O⁺ isotopic molecule, comprising nearly 600 lines, have been recorded and analyzed for the first time. The spectra have been photographed under high resolution by using conventional spectroscopy, and it was possible to separate and observe most of the lines of all the 12 branches of this transition. The reduction of the individual bands’ spectra has been performed by nonlinear least-squares procedure and by means of effective Hamiltonians of Brown et al. the rovibronic structure parameters have been obtained. The currently investigated bands of the Comet-Tail system and the earlier analyzed bands of the A − X and B − A systems in the ¹⁴C¹⁶O⁺ molecule have been merged together. The results of this global fit made it possible to derive a new set of the equilibrium molecular constants for the A and X states. Then the RKR potential curve parameters for both A and X states and Franck-Condon factors as well as r-centroids for the A − X transition have been calculated for the ¹⁴C¹⁶O⁺ molecule.     

High-resolution infrared spectra of OOO ozone isotopomer in the range 900-5000 cm: line positions

Continuing the systematic study of ozone high-resolution infrared spectra, we present in this paper the measurements and analyses of line positions for the ¹⁸O¹⁶O¹⁸O isotopomer. In the range 900-5000 cm⁻¹, corresponding to the observed spectra, 15 bands are analysed: ν₁, ν₃, ν₂+ν₃, ν₁+ν₂, 2ν₃, ν₁+ν₃, 2ν₁, ν₂+2ν₃, ν₁+ν₂+ν₃, 3ν₃, 2ν₁+ν₃, ν₂+3ν₃, ν₁+3ν₃, ν₁+ν₂+3ν₃, and 5ν₃. As in the case of ¹⁶O₃, ¹⁸O₃, and ¹⁶O¹⁸O¹⁶O, the analysis of these bands is performed using effective rovibrational Hamiltonians for nine polyads of interacting upper vibrational states. To correctly reproduce all observed transitions, we have to account for resonance perturbations due to 13 “Dark” states: (0 3 0), (0 4 0), (2 1 0), (0 3 1), (1 0 2), (0 4 1), (1 1 2), (3 1 0), (0 3 2), (0 0 4), (3 2 0), (0 1 4), and (0 4 2). We present the range of observed transitions, the results for spectroscopic parameters (vibrational energy levels, rotational and centrifugal distortion constants, and resonance coupling parameters), as well as the statistics for rovibrational energy levels, calculations and measurements. A comparison of observed band centres with those predicted from an isotopically invariant potential function is discussed. The RMS deviation between predicted and directly observed band centres is ≈0.03 cm⁻¹ up to 3000 and ≈0.25 cm⁻¹ for all 16 bands up to 5000 cm⁻¹.     

Spectroscopic properties of the rubidium and cesium aluminum double molybdate crystals

Infrared, Raman, electron absorption, excitation and emission spectra were measured for RbCr_xAl_1−x(MoO₄)₂ and CsCr_xAl_1−x(MoO₄)₂ crystals (x=0-2%) at the temperatures ranging from 7 to 300 K. A very rich vibronic structure of the emission band was explained and assigned to the respective vibrational modes. One Cr³⁺ center characterized by 2.35 ms lifetimes for rubidium derivative and 1.3 ms for cesium one at 7 K for the ²E→⁴A₂ transition was identified for both crystals. The local structure of the Cr³⁺ surrounding is discussed in terms of the spectroscopic results and the crystal field parameters are derived for both materials.     

Electron paramagnetic resonance and the thermoluminescence emission mechanism of the 280 °C peak in natural andalusite crystal

Samples of natural andalusite (Al₂SiO₅) crystal have been investigated in terms of thermoluminescence (TL) and electron paramagnetic resonance (EPR) measurements. The TL glow curves of samples previously annealed at 600 °C for 30 min and subsequently gamma-irradiated gave rise to four glow peaks at 150, 210, 280 and 350 °C. The EPR spectra of natural samples heat-treated at 600 °C for 30 min show signals at g=5.94 and 2.014 that do not change after gamma irradiation and thermal treatments. However, it was observed that the appearance of a paramagnetic center at g=1.882 for the samples annealed at 600 °C for 30 min followed gamma irradiation. This line was attributed to Ti³⁺ centers. The EPR signals observed at g=5.94 and 2.014 are due to Fe³⁺. Correlations between EPR and TL results of these crystals show that the EPR line at g=1.882 and the TL peak at 280 °C can be attributed to the same defect center.     

Investigations on the local structure and EPR parameters for the trigonal Nd3+ centre in CdS

The local structure and the electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants) for the trigonal Nd³⁺ centre in CdS are theoretically investigated by considering the local lattice relaxation. The impurity Nd³⁺ is found not to occupy exactly the host Cd²⁺ site, but to suffer a shift of about 0.31 Å away from the sulphide triangle along the C₃ axis due to size and charge mismatch. The theoretical EPR parameters based on the above impurity axial displacement are in good agreement with the observed values. The local structure and the EPR parameters are discussed for this centre.     

Spectroscopic studies on Fe and Mn doped SrB4O7 glasses

EPR and optical absorption studies on Fe³⁺ and Mn²⁺ doped strontium tetraborate (SrB₄O₇) glasses are carried out at room temperature. The EPR spectrum of the Fe³⁺ doped glass consists of signals with g-values 9.04, 4.22 and 2.04, whereas the EPR spectrum of Mn²⁺ doped glass exhibits a characteristic hyperfine sextet around g=2.0. The spectroscopic analyses of the obtained results confirmed distorted octahedral site symmetry for the Fe³⁺ and Mn²⁺ impurity ions. Crystal field and Racah parameters evaluated from optical absorption spectra are: Dq=790, B=700 and C=3000 cm⁻¹ for Fe³⁺doped glass and Dq=880, B=700 and C=2975 cm⁻¹ for Mn²⁺ doped glass.     

Defect model and spin-Hamiltonian parameters for the tetragonal Nd center in the tetragonal phase of SrTiO3 crystal

The spin-Hamiltonian parameters (g factors g_∥, g_⊥ and hyperfine structure constants ¹⁴³A_∥, ¹⁴³A_⊥, ¹⁴⁵A_∥ and ¹⁴⁵A_⊥) of the tetragonal Nd³⁺ center in the low-temperature (T≈4.2 K) tetragonal phase of SrTiO₃ are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are attached to the conventional Hamiltonian and a 52×52 energy matrix concerning the ground term ⁴H_J (J=9/2, 11/2, 13/2, 15/2) is constructed. The Nd³⁺ center is attributed to Nd³⁺ occupying the 12-fold coordinated Sr²⁺ site in SrTiO₃. Differing from the defect model assumed in the previous paper that the tetragonal distortion of this Nd³⁺ center is due to the association of one interstitial oxygen ion at a nearest neighborhood of Nd³⁺ and the Nd³⁺ displacement Δz along C₄ axis, we suggest that it is due to the distortion of SrTiO₃ lattice in the tetragonal phase. The calculated g factors g_∥ and g_⊥ show good agreement with the experimental values, suggesting that our defect model of Nd³⁺ center in SrTiO₃ is reasonable. The experimental hyperfine structure constants were not reported and so our calculated results remain to be checked by EPR experiment.     

Theoretical evaluation of the electron paramagnetic resonance spin Hamiltonian parameters for the impurity displacements for Fe3+ and Ru3+ in corundum

The impurity displacements for Fe³⁺ and Ru³⁺ in corundum (Al₂O₃) are theoretically studied using the perturbation formulas of the spin Hamiltonian parameters (zero-field splitting and anisotropic g factors) for a 3d⁵ (with high spin S = 5/2) and a 4d⁵ (with low spin S = 1/2) ion in trigonal symmetry, respectively. According to the investigations, the nd⁵ (n = 3 and 4) impurity ions may not locate at the ideal Al³⁺ site but undergo axial displacements by about 0.132 Å and 0.170 Å for Fe³⁺ and Ru³⁺, respectively, away from the center of the ligand octahedron along the C₃ axis. The calculated spin Hamiltonian parameters based on the above axial displacements show good agreement with the observed values. The validity of the results is discussed.     

Theory studies of the local lattice distortions and the EPR parameters for Cu2+, Mn2+ and Fe3+ centres in ZnWO4

The local lattice distortions and the electron paramagnetic resonance (EPR) parameters (g factors, hyperfine structure constants and zero-field splittings) for Cu²⁺, Mn²⁺ and Fe³⁺ in ZnWO₄ are theoretically studied based on the perturbation calculations for rhombically elongated octahedral 3d⁹ and 3d⁵ complexes. The impurity centres on Zn²⁺ sites undergo the local elongations of 0.01, 0.002 and 0.013 Å along the C₂ axis and the planar bond angle variations of 8.1°, 8.0° and 8.6° for Cu²⁺, Mn²⁺ and Fe³⁺, respectively, due to the Jahn–Teller effect and size and charge mismatch. In contrast to the host Zn²⁺ site with obvious axial elongation (～0.31 Å) and perpendicular (angular) rhombic distortion, all the impurity centres demonstrate more regular octahedral due to the above local lattice distortions. The copper centre exhibits significant Jahn–Teller reductions for the spin-orbit coupling and orbital angular momentum interactions, characterised by the Jahn–Teller reduction factor J (≈0.29 ? 1). The calculated EPR parameters agree well with the experimental results. The local structures of the impurity centres are analysed in view of the corresponding lattice distortions.