Theoretical investigations on the spin Hamiltonian parameters and local structures for the trigonal Ni2+ centers in CsMgX3 (X=Cl,Br, I)

The spin Hamiltonian parameters (zero-field splitting and the anisotropic g factors) and the local structures for the trigonal Ni²⁺ centers in CsMgX₃ (X=Cl, Br, I) are theoretically investigated from the perturbation formulas of these parameters for a 3d⁸ ion in trigonally distorted octahedra, by including the ligand s-orbital contributions. Based on the studies, the local impurity-ligand bond angles β related to the C ₃ axis in the Ni²⁺ centers are found to be about 2° larger than the corresponding angles, β_H, in the hosts, due to the size mismatching substitution of Mg²⁺ by Ni²⁺. The theoretical results based on the inclusion of the ligand s-orbital contributions show an improvement when compared with those in the absence of the above contributions, especially for the ligand I^?.     

Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Cr ions in Y2Ti2O7 crystal

The optical band positions and spin-Hamiltonian parameters (g factors g_g_? and zero-field splitting D) for the trigonal Cr³⁺ centers in Y₂Ti₂O₇ crystal are calculated from the complete diagonalization (of energy matrix) method based on the two-spin-orbit-parameter model. In the calculations, the contributions to spectral data from both the spin-orbit parameter of central dⁿ ion and that of ligand ion are considered and the crystal field parameters used are estimated from the superposition model. The calculated results are in reasonable agreement with the experimental values. The defect structures of Cr³⁺ center is suggested.     

Studies of the g factors and the local structure for Ni3+ in LaAl0.9Ni0.1O3, La0.75Y0.25Al0.99Ni0.01O3 and YAl0.9Ni0.1O3

The electron paramagnetic resonance g factors and the local structure for Ni³⁺ in LaAl_0.9Ni_0.1O₃ (LAN), La_0.75Y_0.25Al_0.99Ni_0.01O₃ (LYAN) and YAl_0.9Ni_0.1O₃ (YAN) are theoretically studied from the perturbation formulas of the g factors for a 3d⁷ ion of low spin (S = 1/2) in tetragonally elongated octahedra. In these formulas, the contributions to the g factors from the tetragonal distortion, characterized by the tetragonal field parameters Ds and Dt are taken into account. According to the calculations, the ligand octahedra around Ni³⁺ are suggested to suffer 2% relative elongation along the [001] (or C₄) axis due to the Jahn-Teller effect.     

Interaction Between Pr3☎ Pairs and Excitons in CsCdBr3

CsCdBr₃ consists of linear chains of [CdBr₆]^4- octahedra separated by Cs^? ions. The excited states of the covalently bound [CdBr₆]^4- octahedra form the lowest excitonic states of the crystal lattice. The trivalent Pr ions substitute for the divalent Cd ions. For reasons of charge compensation in the linear Cd^2? chains, pair centers of the form Pr^3?-(Cd vacancy)-Pr^3? are predominantly formed. In CsCdBr₃ the optical band gap is wider than the electronic one. This allows to study the interaction between Pr^3? ions and excitons by means of optical spectroscopy. The interaction leads to quantum up- and down-conversion generating one photon from two lower ones in energy and vice versa. Related experiments are discussed.     

Spin Hamiltonian parameters and local structures for tetragonal and orthorhombic Ir2+ centers in AgCl

The perturbation formulae of the spin Hamiltonian parameters (the anisotropic g factors, hyperfine structure constants and superhyperfine parameters) are established for a 5d⁷ ion in an orthorhombically elongated octahedron based on the cluster approach. These formulae are applied to the theoretical studies of the EPR spectra and the local structures for the tetragonal and orthorhombic Ir²⁺ centers in AgCl. For the tetragonal Ir²⁺ center, the uncompensated substitutional [IrCl₆]⁴ cluster is found to experience a relative elongation of about 0.08 Å along the C ₄ axis due to the Jahn–Teller effect. For the orthorhombic center, the ligand octahedron also suffers Jahn–Teller elongation (by about 0.08 Å) along the [001] (or Z) axis. Meanwhile, the ligand Cl intervening in the impurity Ir²⁺ and the next nearest neighbor silver vacancy V_Ag along the [100] (or X) axis may undergo an inward displacement of 0.004 Å towards the center of the octahedron due to electrostatic repulsion of the V_Ag. The calculated spin Hamiltonian parameters based on the above local structures show good agreement with experimental data for both centers.     

Spin-Hamiltonian Parameters and Defect Structure of the Copper (2+) Center in Lithium Borate

The spin-Hamiltonian parameters (the anisotropic g factors g _|| and g _⊥ and the hyperfine structure constants A _|| and A _⊥) for the impurity Cu²⁺ in Li₂B₄O₇ are theoretically investigated using the high-order perturbation formulas of these parameters for a 3d ⁹ ion in tetragonally elongated octahedra. In the calculation formulas, the tetragonal field parameters D_s and D_t are determined from the superposition model, by considering the relative axial elongation of the oxygen octahedron around Cu²⁺ due to the Jahn-Teller effect. Based on the calculations, the relative axial elongation of about 0.21 Å for the tetragonal Cu²⁺ center was found.     

Local tetragonal distortions of the (CrF6)3− and (FeF6)3− octahedral clusters in Cr3+- and Fe3+-doped tetragonal Rb2KGaF6 crystals

The local tetragonal distortions (α???α₀) (where α is the angle defined as tgα?=?R_⊥/R_//, R_⊥ and R_// are the metal–ligand distances parallel with and normal to the C₄ axis, α₀?=?45° is the same angle in cubic symmetry) of (CrF₆)^3? and (FeF₆)^3? octahedral clusters in the tetragonal Rb₂KGaF₆ crystals are estimated by analyzing their electron paramagnetic resonance (EPR) zero-field splittings D. The results indicate that the two impurity octahedra and hence the host (GaF₆)^3? octahedra are tetragonally elongated. The distortion (α???α₀) in magnitude differs from impurity to impurity because of the different sizes and natures of these impurities. These results are analogous to those in ABX₃ and doped ABX₃ perovskite crystals where the cubic-to-tetragonal phase transition is due to the rotation of BX₆ octahedra associated with the release or elongation of B–X bond along the C₄ rotational axis.     

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 investigation of the optical spectra and local lattice structure for Mn5+ in a Sr10(VO4)6F2 crystal

In this paper, the relationships between the optical spectra and local lattice structure for Mn⁵⁺ in a Sr₁₀(VO₄)₆F₂ crystal are established by the crystal- and ligand-field theory. The effect of spin–orbital coupling between the central 3d² ions and ligand ions has been considered in the full energy matrix. Using the matrix and superposition model formula, we have calculated the optical spectra and local lattice structure parameters of Mn⁵⁺ in Sr₁₀(VO₄)₆F₂ with a C_3v system. The calculated results are in good agreement with the observed values. In addition, the trigonal compressed distortions of the (MnO₄)^3? centers in Sr₁₀(VO₄)₆F₂ crystals are also obtained from the calculations.     

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.     

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 investigations of the spin Hamiltonian parameters and local tetragonal distortions for Cu2+ in crystalline and amorphous TeO2 and GeO2

The spin Hamiltonian parameters (i.e., anisotropic g factors and hyperfine structure constants) and local tetragonal distortions for Cu²⁺ in crystalline and amorphous TeO₂ and GeO₂ are theoretically investigated using the high-order perturbation formulas of these parameters for a tetragonally elongated octahedral 3d⁹ cluster. The impurity Cu²⁺ occupying the octahedral sites are found to experience the relative tetragonal elongation ratios of about 11.4% and 9.5% for crystalline TeO₂ and GeO₂ and 10.8% and 6.6% for amorphous TeO₂ and GeO₂, respectively, along the C₄ axis due to the Jahn–Teller effect. This reveals the larger tetragonal elongation distortions for the Cu²⁺ centres in crystalline than amorphous systems (especially TeO₂). The theoretical spin Hamiltonian parameters show good agreement with the experimental data. The results are discussed.     

Theoretical studies on the EPR parameters of the interstitial V4+ in rutile

The electron paramagnetic resonance (EPR) parameters g-factors g _i (i=x, y, z) and the hyperfine structure constants A _i for the interstitial V⁴⁺ in rutile are theoretically studied from the perturbation formulas of these parameters for a 3d¹ ion in rhombically distorted octahedra. On the basis of the studies, the local axial distortion angle Δα′ in the impurity center is found to be about 2° smaller than the host value, characterized as stretching and contraction of the parallel and perpendicular bonding lengths by about 0.28 and 0.14 Å,respectively. This results in the less compressed ligand octahedron because of the Jahn–Teller effect and space effect arising from occupation of the impurity V⁴⁺ at the interstitial site. The theoretical EPR parameters based on the above local structural parameters of this work are in better agreement with the experimental data than those of the previous studies in the absence of the local angular distortion and the ligand orbital contributions. The two experimental optical absorption bands are also reasonably analyzed.     

Studies of the spin-Hamiltonian parameters, d–d transitions and defect structures for two tetragonal Cu centers in Ba2ZnF6:Cu crystal

Two theoretical methods, the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM), are applied to calculate the spin-Hamiltonian parameters (g-factors g, g and hyperfine structure constants A, A, obtained from electron paramagnetic resonance (EPR) spectra) and d–d transitions (obtained from optical spectra) for two tetragonal Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ crystals. The Cu²⁺(I) ion replaces the Zn²⁺ ion at tetragonally compressed octahedral coordination and has the ground state ²A₁(|d_z²), whereas the Cu²⁺(II) ion is at an interstitial site with a square-planar F⁻coordination and has the ground state ²B₂(|d_x²-y²). The calculated spin-Hamiltonian parameters and d–d transitions from the PTM and CDM coincide and are in reasonable agreement with the experimental values. This suggests that both methods are effective for the theoretical studies of EPR and optical spectral data for 3d⁹ ions in tetragonal symmetry with different ground states. The defect structures of the two Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ are also estimated.     

Theoretical investigations of the spin Hamiltonian parameters for the CoCl(PPh3)3 molecules

The perturbation formulas of the spin Hamiltonian parameters (zero-field splitting and g factor g_// and g_⊥) are established for a 3d⁸ ion in trigonally distorted tetrahedra for the first time. In the theoretical treatments, the contributions from the Jahn–Teller effect, the ligand orbital and spin–orbit coupling interactions and configuration interactions are taken into account from the cluster approach in a uniform way. The above formulas are applied to the studies of the spin Hamiltonian parameters for the three CoCl(PPh₃)₃ molecules, and the experimental electron paramagnetic resonance spectra of all the molecules are satisfactorily explained. The significant compressions of the ligand tetrahedra with mixed chlorine and PPh₃ groups around Co⁺ are analysed for three distinct CoCl(PPh₃)₃ compounds, characterised by the Cl–Co–P bond angles θ larger than the tetrahedral angle of 109.47°. The local trigonal distortions are discussed in view of the Jahn–Teller effect.     

Unified calculations of spin-Hamiltonian parameters and optical band positions for Ni+ ion in AgGaSe2 crystal

The complete diagonalisation (of energy matrix) method based on the two-spin-orbit-parameter model is applied to unifiedly calculate the spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants A_//, A_⊥) and optical band positions for Ni⁺ ion in silver gallium selenide (AgGaSe₂) crystal. In the model, besides the contribution due to the spin-orbit parameter of central dⁿ ion (i.e., the one-spin-orbit-parameter model in the traditional crystal-field theory), that of ligand ions are taken into account. The calculated results are reasonably consistent with the experimental values. The local structure of Ni⁺ centre in AgGaSe₂ is estimated through the calculation. The complete diagonalisation method based on the one-spin-orbit-parameter model is also applied to calculate these electron paramagnetic resonance and optical data. It is found that although the calculated optical band positions are close to those based on the two-spin-orbit-parameter model and hence to the experimental values, the calculated spin-Hamiltonian parameters (in particular, the g factors) are in disagreement with the experimental values. The latter point is further confirmed from the calculations with the perturbation method. So, for the rational calculations of spin-Hamiltonian parameters of dⁿ clusters with ligand having large spin-orbit parameter, the contributions due to spin-orbit parameters of both the central dⁿ ion and ligand ion should be contained.     

Theoretical studies of absorption spectra and microstructure of Ni2+ at the octahedral site of the NiFe2O4 nanoparticle

The optical absorption spectra, microstructure and electronic spin resonance parameters (electronic spin resonance (ESR) g factor) for Ni²⁺ ions at octahedral centers of nickel ferrite nanoparticles are calculated from the two-spin–orbit-parameter model. The effect of spin–orbital coupling of the central metal 3d⁸ ions and ligand oxygen ions has been taken into account in the full energy matrix and ESR g formula. The calculated results are in good agreement with the observed values. In addition, the microstructures of Ni²⁺ ions at octahedral centers in NiFe₂O₄ are reasonably determined from the calculations.     

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.     

Investigation of the local structure of Cu2+ ions doped in alkali lead tetraborate glasses by their electron paramagnetic resonance and optical spectra

The local structure of the Cu²⁺ centers in alkali lead tetraborate glasses was theoretically studied based on the optical spectra data and high-order perturbation formulas of the spin Hamiltonian parameters (electron paramagnetic resonance g factors g_∥, g_⊥ and hyperfine structure constants A_∥, A_⊥) for a 3d⁹ ion in a tetragonally elongated octahedron. In these formulas, the relative axial elongation of the ligand O^2? octahedron around the Cu²⁺ due to the Jahn–Teller effect is taken into account by considering the contributions to the g factors from the tetragonal distortion which is characterized by the tetragonal crystal-field parameters Ds and Dt. From the calculations, the ligand O^2? octahedral around Cu²⁺ is determined to suffer about 19.2% relative elongation along the C₄ axis of the alkali lead tetraborate glass system, and a negative sign for A_∥ and a positive sign for A_⊥ for these Cu²⁺ centers are suggested in the discussion.     

Strong Visible and Near-Infrared Cathodoluminescence in Alkali Feldspar

In this study, cathodoluminescence (CL) spectroscopy at direct current and alternating current under the sample temperature condition of 40–293 K using different modulation frequencies is presented for alkali feldspar from the Dartmoor granite (UK). These feldspars contain strain-controlled lamellar crypto- and microperthites that are cross-cut by strain-free deuteric microperthites. The CL spectra of the alkali feldspar at room and low temperature confirm that the observed emission peaked at ～460 nm could be associated with Al-O^?-Al or Ti impurity centers, yellow emission ～560 nm could be associated with the presence of the centers such as radiation-induced defect centers, and ～756 nm emission could be associated with the Fe³⁺ impurity center on T₁ and T₂ sites. The consequence of their association is to produce different luminescence properties such as intensity, peak wavelength, and band shape.