EPR and optical spectra of Ni2+-VAg in silver chloride and silver bromide

The optical absorption and EPR spectra of Ni²⁺-V_Ag centres in the AgCl:Ni²⁺ and AgBr:Ni²⁺ systems have been investigated theoretically on the basis of the complete energy matrices including the electron–electron repulsion interaction, the ligand field interaction, the spin–orbit coupling interaction, and Zeeman interaction. Because the charge compensation forms a silver ion vacancy (V_Ag) which makes the attractive force acted on the each ligand ion different, it was determined that the Ni–X (X = Cl, Br) distance next to V_Ag is shorter than others for both AgCl:Ni²⁺ and AgBr:Ni²⁺ systems in the tetragonal symmetry. Besides, it was found that the local lattice structure of (NiX₆)^4? clusters in AgCl and AgBr crystals exhibit a compression distortion. This compression distortion may be ascribed to the fact that the Ni²⁺ ion has a smaller ionic radius and more effective charge than the Ag⁺ ion.     

Investigation of local lattice structure around Cr3+ ions at the trigonal and tetragonal sites in RbCdF3: Cr3+ crystal

The local lattice structure and EPR, optical spectra for Cr³⁺ doped in RbCdF₃ crystal have been studied by diagonalizing the complete energy matrices. The results show that the local structure of the Cr³⁺ ions in RbCdF₃ exhibits a compressed distortion at the trigonal and tetragonal sites. The compressed distortion can be ascribed to the fact that the radius of Cr³⁺ ion is smaller than that of Cd²⁺ ion, and therefore Cr³⁺ ion will draw the fluorin ligands inwards. The variational ranges of the local structural parameters for Cr³⁺ doped in RbCdF₃ crystal R =?1.9491 Å ～?1.9814 Å, θ?= 55.234° ～?55.286° at the trigonal site and R ₁ =?1.8617 Å ～?1.8928 Å, R ₂ =?1.9527 Å ～?1.9851 Å at tetragonal site are obtained respectively, and the EPR and optical spectra agree well with the experimental results.     

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.     

EPR parameters and defect structure of the tetrahedral Ti3+ defect center in beryl crystal

The EPR parameters (g factors g _i and hyperfine structure constants A _i , where i=x, y, z) of Ti³⁺ ion at the tetrahedral Si⁴⁺ site of beryl crystals are calculated within the rhombic symmetry approximation from the high-order perturbation formulas based on the two-spin-orbit (SO)-parameter model. In these formulas both the contribution due to the SO coupling parameter of the central 3d¹ ion and that of ligand ions are considered. From the calculations, the defect structure of the Ti³⁺ defect center in beryl crystal is estimated and the EPR parameters g _x , g _y , g _z and A _y are reasonably explained. The values of the parameters A _x and A _z (which were not reported) are suggested and remain to be checked by the further experimental studies.     

Effect of local structure on electron paramagnetic resonance spectra for trigonal [Cr(H2O)6]3+coordination complex in the sulfate alums series: a ligand field theory study

A simple theoretical method is introduced for studying the interrelation between electronic and molecular structures.By diagonalizing the 120 × 120 complete energy matrices,the relationships between zero-field splitting(ZFS) parameter D and local distortion parameter △θ for Cr 3+ ions doped,separately,in α-and β-alums are investigated.Our results indicate that there exists an approximately linear relationship between D and △θ in a temperature range 4.2-297 K and the signs of D and △θ are opposite to each other.Moreover,in order to understand the contribution of spin-orbit coupling coefficient ζ to ZFS parameter D,the relation between D and ζ is also discussed.     

Covalent bonding and J–J mixing effects on the EPR parameters of Er~(3+) ions in GaN crystal

The EPR parameters of trivalent Er~(3+) ions doped in hexagonal Ga N crystal have been studied by diagonalizing the 364×364 complete energy matrices. The results indicate that the resonance ground states may be derived from the Kramers doublet Γ_6. The EPR g-factors may be ascribed to the stronger covalent bonding and nephelauxetic effects compared with other rare-earth doped complexes, as a result of the mismatch of ionic radii of the impurity Er~(3+)ion and the replaced Ga~(3+) ion apart from the intrinsic covalency of host Ga N. Furthermore, the J–J mixing effects on the EPR parameters from the high-lying manifolds have been evaluated. It is found that the dominant J–J mixing contribution is from the manifold ~2K_(15/2), which accounts for about 2.5%. The next important J–J contribution arises from the crystal–field mixture between the ground state ~4I_(15/2) and the first excited state~4I_(13/2), and is usually less than 0.2%. The contributions from the rest states may be ignored.     

Theoretical study of the dependence of EPR spectra on local structure for octahedral Cr3+ centres in oxides and fluorides series

A theoretical method for investigating the inter-relation between the EPR parameters and local structure has been established on the basis of the complete energy matrices for 3d³ configuration ions in both the trigonal and tetragonal ligand fields. By means of this method, the local structure of the octahedral Cr³⁺ centres in double molybdates series and spinels series as well as the perovskite-type fluorides series has been studied systematically. Furthermore, the dependence of the EPR zero-field splitting parameter D on the local structure parameters in both trigonal and tetragonal ligand-fields has been revealed, simultaneously. The inter-relation between the EPR parameters D and Δg(g _// ??g _⊥) is also elucidated.     

Investigations of the spin-Hamiltonian parameters for Er3+ ions in AlN crystal

The spin-Hamiltonian parameters (g factor g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) for Er³⁺ ion at the trigonal Al³⁺ site of AlN crystal are calculated by diagonalising the 52 × 52 energy matrix. The matrix are related to the ground mutiplet ⁴I_15/2 and the first to third excited multiplets ⁴I_13/2, ⁴I_11/2 and ⁴I_9/2 for 4f¹¹ ions in trigonal crystal field under an external magnetic field. The crystal-field parameters used in the matrix are obtained from the superposition model and the local lattice relaxation due to the substitution of Er³⁺ for Al³⁺ is considered. The calculated spin-Hamiltonian parameters are in reasonable agreement with the experimental values and the signs of hyperfine structure constants are suggested. The results are discussed.     

Investigations of the electron paramagnetic resonance parameters and the tetragonal local structure for (VCl6)4- coordination complex in MCl:V2+ (M=Na, K, Rb) systems

By simulating the electron paramagnetic resonance (EPR) and optical spectra on the basis of the 120×120 complete energy matrix, this paper determines the local lattice structure parameters R1 and R2 for MCl:V2+ (M=Na, K, Rb) systems at 77 K, 195 K and RT (room temperature 295 K or 302 K), respectively. The theoretical results indicate that there exists a compressed distortion in MCl:V2+ systems. Meanwhile, it finds that the structure parameters R1, R2 and |△R| (= R1-R2) increase with the rising temperature. Subsequently, from the analysis it concludes that the relation of EPR parameter D vs.△R is approximately linear. Finally, the effects of orbital reduction factor k on the g factors for the three systems have been discussed.     

Al2O3:Fe3+体系晶格局域结构的EPR理论研究

本文通过分析Al2O3∶Fe3+体系中Fe3+离子的EPR谱,研究Fe3+的局域晶体结构结果表明Al2O3∶Fe3+的局域结构存在各向异性膨胀.用拟合EPR谱的低对称参量D和(a-F)实验值的方法,求得两个三棱锥的棱与C3轴的夹角分别为θ1=46.54°和θ2=61.26°,相对于原Al2O3结构的畸变角分别是Δθ1=-1.1°±0.1°,Δθ2=-1.8°.两畸变角同时均小于0说明Al2O3∶Fe3+体系中含Fe3+离子的晶格主要产生沿C3轴的伸长畸变.     

Theoretical investigations of the EPR parameters and local structure for Cu2+ in BeO

The electron paramagnetic resonance (EPR) parameters (the anisotropic g factors, the hyperfine structure parameters and the quadrupole coupling constant Q) and local structure for Cu²⁺ in BeO are theoretically investigated from the perturbation formulas of these parameters for a 3d⁹ ion under trigonally distorted tetrahedra. The ligand orbital and spin-orbit coupling contributions are included in the basis of the cluster approach, in view of the strong covalency of the [CuO₄]^6? cluster. From the calculations, the impurity Cu²⁺ is suggested not to occupy exactly the ideal Be²⁺ site but to suffer a slight inward displacement (≈0.024 Å) toward the ligand triangle along the C₃ axis. The theoretical EPR parameters show good agreement with the experimental data.     

Investigations of the defect structures and the EPR parameters for the substitutional Mo5+ centers in rutile type crystals

The defect structures and the electron paramagnetic resonance parameters for the substitutional Mo⁵⁺ centers in rutile type SnO₂, TiO₂ and GeO₂ crystals are theoretically investigated from the perturbation formulas of these parameters for a 4d¹ ion in rhombically compressed octahedra. The [MoO₆]^7? clusters suffer the Jahn–Teller effect and transform the ligand octahedra from original elongation on host tetravalent sites to compression in the impurity centers, with additional smaller rhombic (perpendicular) distortions when compared with those in the hosts. The defect structures and the importance of the ligand contributions are discussed.     

Stark structure of the energy spectrum of the Am3+ ion in LaCl3

We have analyzed the structure of the energy spectrum of the Am³⁺ ion in LaCl₃ in the weak and intermediate configuration interaction approximation. We have established that in the intermediate configuration interaction approximation, the mean-square deviation of the calculated values of the Stark level energies from the experimental values is 53% smaller than in the weak configuration interaction approximation. We have determined the even and odd crystal field parameters and the covalency parameters. We conclude that based on analysis of the Stark structure of the energy spectrum, we can make quantitative estimates of the intensity characteristics. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 637–640, September–October, 2006.     

Investigations on the EPR parameters and tetragonal distortions for Cu2+ in alkali lead tetraborate glasses

The electron paramagnetic resonance parameters (g factors and hyperfine structure constants) and local structures are theoretically investigated for Cu²⁺ in alkali lead tetraborate 90R₂B₄O₇·9PbO·CuO (R = Li, Na and K) glasses based on the high-order perturbation calculations for a tetragonally elongated octahedral 3d⁹ complex. The [CuO₆]^10? complexes are found to experience the relative tetragonal elongation ratios 18%, 23% and 30% for R = Li, Na and K, respectively, due to the Jahn–Teller effect, much larger than those for similar ARbB₄O₇ (A = Li, Na and K) glasses. This point is attributed to the lattice expansion (longer A–O bond lengths) with doped PbO, yielding lower force constants and more intense Jahn–Teller elongations in the 90R₂B₄O₇·9PbO·CuO glasses. The increasing tendency (Li > Na > K) of the relative elongation ratio λ, covalency and the ratio Δg_///Δg_⊥ for g-shifts are systematically analysed in a uniform way.     

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.     

Effect on the EPR and local lattice structure distortion of V3+ ion doping corundum crystal: three models studied

This paper reports on the application of conventional models (the displacement model and the elongation model) and the four-parameter model in detecting the local molecular structure of a coordination complex. By diagonalizing the complete energy matrices, the EPR parameters and optical spectra as well as the local distortion structure for V³⁺ ion in the Al₂O₃ : V³⁺ system have been studied using the three models. The four-parameter model is shown to provide a significant improvement over the conventional models. Based on these calculations, it was found that when V³⁺ is doped in Al₂O₃, the distance between upper and lower ligand oxygen plane increases by 0.16097 Å and the shifts of O^2? ions in the upper and lower ligand oxygen planes expand by 0.07076 Å and 0.004066 Å, respectively. To understand the detailed physical and chemical properties of the doped Al₂O₃, the contributions of the spin-orbit coupling to the zero-field splitting for V³⁺ ion are investigated.     

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.