Theoretical investigation of the local lattice structure of Mn 2+ ion doped in tetragonal K 2ZnF 4 crystal

The complete energy matrices for a d⁵configuration ion in a tetragonal ligand-field has been constructed on the basis of the complete set of basis of d⁵configuration (252 dimension), and the relationship between the low-symmetry EPR parameters b₂ ⁰ ,b₄ ⁰ and the local distortion parameters has been established based on the complete energy matrices. As an application, we have studied the EPR parameters and the local lattice structure of Mn²⁺ ion doped in tetragonal K₂ZnF₄ system. The calculation indicated that the local lattice structure around a tetragonal Mn²⁺ ion center has an expansion distortion. Simultaneously, the local lattice structure parameters R₁ =2.0727 ?, R₂ =2.0801 ? at room temperature (295 K) and R₁ ^′ = 2.0439 ?, R₂ ^′ =2.05478 ? at low temperature (4.2 K) are determined.     

EPR and optical absorption studies of Cr ions in potassium sodium dl-tartrate tetrahydrate

EPR spectra of Cr³⁺ ions doped in potassium sodium dl-tartrate tetrahydrate single crystals are recorded at 77 K. The spin Hamiltonian and zero field parameters g, |D| and |E| are measured from the resonance lines obtained at various rotations of the magnetic field. The values obtained are: g_x=1.9257±0.0002, g_y=1.9720±0.0002, g_z=2.0102±0.0002, |D|=313±2 (×10⁻⁴) cm⁻¹ and |E|=101±2 (×10⁻⁴) cm⁻¹. From the results of EPR study, the site symmetry of Cr³⁺ ion in the crystal is discussed. The optical absorption at room temperature is also studied. From the observed band positions, the crystal field splitting parameter (D_q) and the Racah inter-electronic repulsion parameters (B and C) are evaluated. The bonding parameters are obtained by correlating optical and EPR data and the nature of bonding in the crystal is 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.     

An investigation on the defect structures and spin Hamiltonian parameters for the two orthorhombic Ti3+ centers in ZnWO4

By employing the perturbation formulae of the spin Hamiltonian parameters (SHPs) (g factors g_xx, g_yy, g_zz, hyperfine structure constants A_xx, A_yy, A_zz and superhyperfine parameters A_xx׳, A_yy׳, A_zz׳) for a 3d¹ ion in orthorhombically elongated octahedra and tetrahedra, the defect structures and the experimental EPR spectra are theoretically and systematically investigated for the two orthorhombic Ti³⁺ centers C₁ and C₂ in ZnWO₄. Center C₁ is ascribed to the impurity Ti³⁺ at host W⁶⁺ site associated with two nearest neighbor oxygen vacancies due to charge compensation. The resultant tetrahedral [TiO₄]^5– cluster is determined to undergo the local orthorhombic elongation distortion, characterized by the axial distortion angle Δθ (=θ–θ₀≈–6.84°) of the local impurity-ligand bond angle θ related to θ₀ (≈54.74°) and the perpendicular distortion angle Δε (=ε–ε₀≈2.5°) related to ε₀ (≈45°) of an ideal tetrahedron because of the Jahn–Teller effect. Center C₂ is attributed to Ti³⁺ on Zn²⁺ site, and this octahedral [TiO₆]^9– cluster may experience the local axial elongation ΔZ (≈0.001 Ǻ) and the planar bond angle variation Δφ (≈9.1°) due to the Jahn–Teller effect, resulting in a more regular oxygen octahedron. All the calculated SHPs (i.e., g factors for both centers, the hyperfine structure constants for center C₂ and superhyperfine parameters of next nearest neighbor ligand W for center C₁) show good agreement with the observed values. However, the theoretical results based on the previous assignment of center C₁ as Ti³⁺ on W⁶⁺ site with only one nearest planar oxygen vacancy (i.e., five-fold coordinated octahedral [TiO₅]^7– cluster) show much worse agreement with the experimental data. The defect structures and the SHPs (especially the g anisotropies) are discussed for both centers. The present studies on the superhyperfine parameters of ligand W⁶⁺ for center C₁ would be helpful to further investigations on the superhyperfine interactions of cation ligands which were rather scarcely treated before.     

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]     

Theoretical investigation of zero-field splitting and local structure distortion for a substitution of Fe ion in CdCl2 crystal

A theoretical method for studying the inter-relation between electron and molecule structure is proposed on the basis of the complete energy matrices of the electron-electron repulsion, the ligand-field and the spin-orbit coupling for d⁵ configuration ion in a trigonal ligand-field. As an application, the local distortion structure of (FeCl₆)^3- coordination complex for Fe³⁺ ions doped into CdCl₂ is investigated. Both the second-order zero-field splitting parameter and fourth-order zero-field splitting parameter are considered simultaneously in the structural investigation. By diagonalizing the complete energy matrices, the local structure distortion parameters ΔR=−0.24 Å, Δθ=2.137° at 26 K and ΔR=−0.203 Å, Δθ=2.515° at 225 K for Fe³⁺ ions in CdCl₂ are determined. These results elucidate a microscopic origin of various ligand-field parameters which are usually used empirically for the interpretation of electron paramagnetic resonance results. It is found that the theoretical results are in good agreement with the experimental values.     

Single crystal EPR and optical absorption study of Cr doped l-histidine hydrochloride monohydrate

EPR study of the Cr³⁺ ion doped l-histidine hydrochloride monohydrate single crystal is done at room temperature. Two magnetically inequivalent interstitial sites are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The zero field and spin Hamiltonian parameters are evaluated from the resonance lines obtained at different angular rotations and the parameters are: D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.9108±0.0002, g_y=1.9791±0.0002, g_z=2.0389±0.0002, A_x=(252±2)×10⁻⁴ cm⁻¹, A_y=(254±2)×10⁻⁴ cm⁻¹, A_z=(304±2)×10⁻⁴ cm⁻¹ for site I and D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.8543±0.0002, g_y=1.9897±0.0002, g_z=2.0793±0.0002, A_x=(251±2)×10⁻⁴ cm⁻¹, A_y=(257±2)×10⁻⁴ cm⁻¹, A_z=(309±2)×10⁻⁴ cm⁻¹ for site II, respectively. The optical absorption studies of single crystals are also carried out at room temperature in the wavelength range 195-925 nm. Using EPR and optical data, different bonding parameters are calculated and the nature of bonding in the crystal is discussed. The values of Racah parameters (B and C), crystal field parameter (Dq) and nephelauxetic parameters (h and k) are: B=636, C=3123, Dq=2039 cm⁻¹, h=1.46 and k=0.21, respectively.     

Theoretical investigations of the spin Hamiltonian parameters for LiF:Mn

The spin Hamiltonian (SH) parameters (g factor, the hyperfine structure constant A as well as the superhyperfine parameters A′ and B′) for LiF:Mn²⁺ are theoretically investigated from the perturbation formulas of these parameters for a 3d⁵ ion under ideal octahedra. The related molecular orbital coefficients and the unpaired spin densities of the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively determined from the cluster approach in a uniform way. The calculated SH parameters show good agreement with the experimental data. The results are discussed.     

EPR and optical studies of Cu doped ammonium dihydrogen phosphate single crystals

Electron paramagnetic resonance (EPR) spectra of Cu²⁺ ion in ammonium dihydrogen phosphate are studied at liquid nitrogen temperature (77 K). Four magnetically inequivalent Cu²⁺ sites in the lattice are identified. The angular variation spectra of the crystal in the three orthogonal planes indicate that the paramagnetic impurity, Cu²⁺ enters the lattice substitutionally in place of NH₄⁺ ions. The spin Hamiltonian parameters are determined with the fitting of spectra to rhombic symmetry crystalline field. The ground state wave function of Cu²⁺ ion is constructed and found to be predominantly |x²-y²〉. The cubic field parameter (Dq) and tetragonal parameters (Ds and Dt) are determined from optical spectra at room temperature. By correlating EPR and optical absorption spectra, the bonding coefficients are calculated and nature of bonding of metal ion with different ligands in the crystal is discussed.     

A semi-empirical analysis of ZFS parameters for transition metal (TM) ions (Cr3+ and Mn2+) centers in K2MgF4

The local structure around the transition metal (TM) ions (Cr³⁺ and Mn²⁺) centers in K₂MgF₄, namely tetragonal (TE) center I, monoclinic (MO) center II and orthorhombic (OR) centers III, have been explored by semi-empirical calculations in the frame of superposition model (SPM). We proposed the most appropriate structural model for each center by matching the theoretically predicted zero-field splitting parameters (ZFSPs) with the experimental ones obtained by EPR spectroscopy. It is shown that the tetragonality of MgF₆ octahedra increases with the substitution of both Cr³⁺ and Mn²⁺ for Mg²⁺ sites as well as with a rather higher value for the latter one. A tilt angle of 12.51° is found for MO Cr³⁺ center, which is comparatively small, as compared to the other A₂BF₄ crystals such as K₂ZnF₄ and Tl₂ZnF₄. Almost three times larger relaxation of intervening F-ligand than that of other equatorial F-ligands is also indicated for OR Cr³⁺ center.     

Site symmetry of Mn(II) and Co(II) in zinc phosphate glass

Optical absorption and EPR spectra of Mn(II) and Co(II) doped zinc phosphate glasses have been investigated. Crystal filed parameters and g values are determined. For Mn(II) doped glass the values are Dq=850, B=850, and g values are around 2 at room temperature (RT). For Co(II) doped glass, Dq=890, B=700, and g=4.45 and 2.06 at liquid nitrogen temperature. The optical and EPR data has been correlated.     

Examination on the electron paramagnetic resonance spectra and the photoluminescence spectra of the Cr ions in the KMgF3 crystal

In this paper, the photoluminescence spectra and the electron paramagnetic resonance spectra of the Cr³⁺ ions in the KMgF₃ crystal are explained based on the complete energy matrix diagonalization procedure and a crystal-field like model. The results agree well with the experimental data. It is also shown that the nearest neighbor F⁻ ions deviate 1.3981 and −0.486° from their original position because of the K⁺ vacancy.     

EPR, optical absorption and superposition model study of Fe³(+) doped strontium nitrate single crystals

Electron paramagnetic resonance (EPR) study of Fe3(+) ions doped strontium nitrate (SN) single crystals is performed at liquid nitrogen temperature and at X band frequency. The spin Hamiltonian (SH) parameters are determined from the resonance lines observed at different angular rotations. The crystal field parameters (CFPs) are evaluated using superposition model of Newman. The Zeeman g-factor and zero-field splitting parameters (ZFSPs) of Fe3(+) ion in SN (truncated SH considered) are: g=1.9989 ± 0.002 and ∣D∣=(338 ± 5) × 10?? cm?1, ∣E∣=(10 ± 5)× 10?? cm?1, a=(458 ± 5)× 10?? cm?1, respectively. The Fe3(+) ion enters the lattice substitutionally replacing the Sr2(+) sites of cubic symmetry. The local site symmetry of Fe3(+) ion in the crystal is orthorhombic (lower than that of the host). The optical absorption study of the crystal is also done at room temperature in the wavelength range 195-925 nm. The energy values of different orbital levels are determined. The observed bands are assigned as transitions from the (6)A?(g)(S) ground state to various excited states of Fe3(+) ion in a cubic crystal field approximation. The observed band positions are fitted with four parameters, the Racah interelectronic repulsion parameters (B and C), the cubic crystal field splitting parameter (Dq) and the Trees correction (α) yielding: B=934, C=2059, Dq=1450, and α=90 (in cm?1). On the basis of EPR and optical data, the nature of metal-ligand bonding in this crystal is discussed. The ZFSPs are also determined theoretically using microscopic SH theory based on perturbation theory and CFPs, B(kq) obtained from superposition model. The values of ZFSPs thus obtained are ∣D∣=(340 ± 5) × 10?? cm?1 and ∣E∣=(15 ± 5) × 10?? cm?1.     

Single crystal EPR investigation on Mn(II) doped biomineral: cobalt potassium phosphate hexahydrate

Single crystal EPR study of Mn(II) doped in cobalt potassium phosphate hexahydrate has been carried out at room temperature. The impurity shows a 30 line pattern EPR spectra along a particular crystallographic axis suggesting the existence of only one type of impurity in place of Co(II) ion in the host lattice. The spin Hamiltonian parameters have been estimated as: g₁₁=2.011, g₂₂=1.998, g₃₃=1.991, and A₁₁=−8.9, A₂₂=−8.8, A₃₃=−8.4 mT and D₁₁=−15.2, D₂₂=−9.4, D₃₃=24.6 mT, respectively. The sign of A is designated as negative and D as positive. The covalency of metal-oxygen bond has been estimated. The relaxation times, calculated as a function of temperature, indicate spin-lattice relaxation narrowing at room temperature.     

EPR parameters and defect structures of the off-center Ti ion on the Sr site in neutron-irradiated SrTiO3 crystal

The EPR parameters (g factors and hyperfine structure constants A) for the tetragonal Ti³⁺ center in cubic phase and the rhombic Ti³⁺ center in tetragonal phase in the neutron-irradiated SrTiO₃ crystals are calculated from the third-order perturbation formulas of EPR parameters for d¹ ions. These low-symmetry Ti³⁺ centers in both phases of SrTiO₃ are due to the Ti³⁺ ion at “off center” on the Sr²⁺ site. From the calculation, the defect models (including the direction and magnitude of the Ti³⁺ off-center displacement) of the two Ti³⁺ centers in SrTiO₃ are estimated and the EPR parameters of both Ti³⁺ centers are reasonably explained on the basis of the defect models. The results are discussed.     

Investigations of the spin-Hamiltonian parameters,optical absorption bands,and local structure for the tetragonal Cu2+ center in Cu2+-doped ZnCdO nanopowder

The spin-Hamiltonian (or EPR) parameters of tetragonal Cu²⁺ octahedral centers in ZnCdO nanopowders are calculated from the high-order perturbation formulas based on the cluster approach. In these formulas, the contributions to spin-Hamiltonian parameters due to the admixture between the d orbitals of dⁿ ion and the p orbitals of ligand ions via covalence effect are considered. The crystal field parameters are calculated from the superposition model and so the optical absorption bands (related to the crystal field energy levels) and local structure of Cu²⁺ octahedral centers in ZnCdO nanopowder are also studied. The calculated spin-Hamiltonian parameters and optical absorption bands are in reasonable agreement with the experimental values. The tetragonal elongation ΔR (=R_//−R_⊥) of Cu²⁺ octahedron in ZnCdO nanopowder due to Jahn–Teller effect is acquired from the calculations. The results are discussed.     

Theoretical studies of the dependence of EPR g-factors on local structure for the trigonal Er3+–VK centres in KMgF3 and KZnF3

The dependence of the EPR g-factors on the local structural parameter for a 4f¹¹ configuration ion Er³⁺ in a trigonal crystal-field has been studied by diagonalizing the 364×364 complete energy matrices. Our studies indicate that the EPR spectra of the trigonal Er³⁺–V_K centers in KMgF₃ and KZnF₃ may be attributed to the translation of the cubic Kramers doublet Γ₇. Furthermore, the EPR g-factors of the trigonal Er³⁺–V_K centers may be interpreted reasonably by the shifts ΔZ≈0.340 Å and ΔZ≈0.303 Å of the Er³⁺ ions toward the charge compensator V_K along the C₃ axis for the KMgF₃:Er³⁺ and the KZnF₃:Er³⁺ systems respectively.     

Studies of the spin-Hamiltonian parameters and defect structures for the trigonal Mo 3+ centers in Y 3Al 5O 12 and Lu 3Al 5O 12 crystals

The complete diagonalization (of energy matrix) method (CDM) and the perturbation theory method (PTM) are applied to calculate the spin-Hamiltonian (SH) parameters (electron paramagnetic resonance g factors g _//, g _⊥ and zero-field splitting D) of the trigonal Mo ³⁺ centers in Y ₃Al ₅O ₁₂ and Lu ₃Al ₅O ₁₂ crystals. Both methods are based on the cluster approach in which the covalence effect due to the admixture between the d orbitals of central d ⁿ ion and p orbitals of ligands is considered. The g factors calculated by both methods are close to each other and agree with the experimental values. However, the calculated zero-field splittings D from PTM for both crystals are about 84% those from CDM. The reasons that the CDM is preferable to the PTM in the calculations of SH parameters are discussed. The angular distortions of Mo ³⁺ centers in both garnet crystals are predicted.     

EPR parameters and local lattice structure study of V ions in CdCl2 and CsMgCl3 crystals

The local lattice structure and EPR parameters (D, g_‖, g_⊥) have been studied systematically on the basis of the complete energy matrix for a d³ configuration ion in a trigonal ligand field. By simulating the calculated optical and EPR spectra data to the experimental results, the local distortion parameters (ΔR, Δθ) are determined for V²⁺ ions in CdCl₂ and CsMgCl₃ crystals, respectively. The results show that the local lattice structure of CdCl₂:V²⁺ system exhibits a compression distortion (ΔR=−0.0868 Å) while that of CsMgCl₃:V²⁺ system exists an elongation distortion (ΔR=0.0165 Å). The different distortion may be ascribed to the fact that the radius of V²⁺ ion is smaller than that of Cd²⁺ ion or larger than that of Mg²⁺ ion. Moreover, the relationships between EPR parameter D and local structure parameters (R, θ) as well as the orbital reduction factor k and g‐factors (g_‖, g_⊥) are discussed.