EPR theoretical study of local lattice structure in YAG:Mn system

By diagonalizing a set of complete energy matrices constructed for a d⁵ configuration ion in a trigonal ligand field, a reasonable interpretation is obtained for the EPR zero-field splitting of Mn²⁺ ions located at octahedral sites in yttrium aluminum garnet. It is shown that the local lattice structure around an octahedrally coordinated Mn²⁺ center has an expansion distortion, which may be attributed to the fact that the radius of Mn²⁺ ion is larger than that of Al³⁺ ion, and the Mn²⁺ ion will push the oxygen ligands outwards. Simultaneously, the local lattice structure distortion parameters ΔR=0.1825-0.2158 A and Δθ=1.220°-1.315° for the octahedral Mn²⁺ center in the crystal are determined, respectively. Meanwhile, we also demonstrated that the empirical impurity-ligand distance is not suitable for the YAG:Mn²⁺ system which has been approximately taken in previous works.     

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.     

Structural studies of Cr-doped mullite derived from single-phase precursors

Cr-doped mullites were prepared from single-phase precursors containing up to 9.60 wt% Cr₂O₃ using a sol-gel technique followed by thermal treatment. Particle induced X-ray emission spectroscopy and X-ray powder diffraction were used to characterize the samples. Mullites were orthorhombic, space group Pbam. Cr doping caused the increase of unit-cell parameters. Strongest expansion was noticed along c-axis followed by a and b (Δc/c=0.089, Δa/a=0.061, Δb/b=0.045% per mole Cr₂O₃). A second phase, namely θ-(Al,Cr)₂O₃, was revealed by XRD in the sample containing 9.60 wt% Cr₂O₃. The structure of mullites was refined by the Rietveld method, location of Cr³⁺ was performed by the EPR spectroscopy. At low chromium doping level (Cr₂O₃ content less than ∼5 wt%) Cr³⁺ ions were substituted for Al³⁺ in the AlO₆ octahedra of the mullite structure (M1 site). For higher doping level, Cr³⁺ ions were additionally substituted for Al³⁺ in the AlO₆ octahedra of the second phase [θ-(Al,Cr)₂O₃ at 1400 °C, or α-(Al,Cr)₂O₃ at 1600 °C] which segregated in the system. Substitution of Cr³⁺ for Al³⁺ on M1 site in the mullite structure resulted in increase of average distances in (M1)O₆ octahedron and decrease of average distances in T*O₄ tetrahedron, while average distances in TO₄ tetrahedron stayed almost constant.     

EPR theoretical study of local lattice structure in Al2O3:Fe system

By analyzing the EPR spectrum of transition-metal ion Fe³⁺ in Al₂O₃:Fe³⁺ system, the local lattice structure around impurity Fe³⁺ ion in the crystal has been studied by means of the diagonalization of the 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 two three-edge-pyramids elongated obviously along C₃ axis. The two distortion angles Δθ₁=−1.1±0.1°,Δθ₂=−1.8° as well as the two Fe-O bond lengths R₁=2.016 A, R₂=1.907 A are determined, respectively.     

Optical spectrum, local lattice structure and EPR g factors for Cr impurity ions in MgTiO3 and LiTaO3

On the basis of the 120×120 complete energy matrices for a d³ configuration ion in a trigonal ligand field, for Cr³⁺ ions doped in MgTiO₃ and LiTaO₃, the local structures and EPR g factors of the octahedral (CrO₆)⁹⁻ clusters have been studied, respectively. By simulating the calculated optical spectra and the EPR spectra data to the experimental results, local structure parameters are obtained. The calculated results show that although the local lattice structures around the M (M=Mg²⁺, Ta⁵⁺) ions are obviously different, after Cr³⁺ replacing the M, the local lattice structures around the Cr³⁺ ions are quite similar and close to those of the Cr₂O₃. This may be ascribed to the fact that the octahedral Cr³⁺ center in MgTiO₃:Cr³⁺ and LiTaO₃:Cr³⁺ systems and that in Cr₂O₃ exhibit similar octahedral (CrO₆)⁹⁻ clusters. Moreover, the corresponding theoretical values of the optical spectra have been reported. It is also found that the orbital reduction factor k is very important to understand the EPR g factors for Cr³⁺ ions doped in MgTiO₃ and LiTaO₃.     

Local structure and the electron paramagnetic resonance parameters for the Cr3+ ions at K+-vacancy site in Cr3+:KZnF3 laser crystal

The quantitative relationship between the electron paramagnetic resonance (EPR) parameters D,g_∥,g_⊥ and the local structure parameters of Cr³⁺ ion in KZnF₃ crystals is established. The local structure for Cr³⁺ paramagnetic center in KZnF₃:Cr³⁺ crystal has been determined from EPR parameters of Cr³⁺ ion. This work shows that the trigonal crystal field of Cr³⁺ ion in KZnF₃ crystals comes from following two origins: (1) the nearest-neighbor K⁺ vacancy caused by the charge compensation in the [1 1 1]-axis direction; and (2) the lattice distortions of the nearest-neighbor fluorine coordination caused by the K⁺ vacancy and the differences in mass, charge, and radius between Cr³⁺ ion and Zn²⁺ ion. The unified calculation of the EPR zero-field splitting and g factors, taking into account the K⁺ vacancy and the lattice distortions, has been carried out on the basis of the complete diagonalization procedure and the superposition crystal-field model, all calculation results are in excellent agreement with the experimental data. Although the main source of the trigonal crystal field comes from the K⁺ vacancy caused by the charge compensation, the contribution of the lattice distortion cannot be neglected.     

Theoretical study of local crystal structure in KZnF3:Fe system

An analysis of the relationship between the EPR trigonal-field parameters and the local crystal structure of KZnF₃:Fe³⁺system is presented by diagonalizing the complete energy matrices for a d⁵ configuration ion in a trigonal crystal field. We propose a two-layer-ligand model, in which the ligands consist of six nearest-neighbor F⁻ ions in the first layer and eight next nearest-neighbor K⁺ ions in the second layer. The calculation indicates that the local structure distortion of KZnF₃:Fe³⁺system is due to the displacement of a K⁺ ion along C₃ axis towards the Fe³⁺ ion, which leads to the shift of the F⁻ ions away from C₃ axis. By simulating the EPR low-symmetry parameters D and (a−F), the distorted angles between the Fe³⁺-F⁻ bonds and C₃ axis are determined, Δθ₁=2.58°, Δθ₂=−1.4° at room temperature (300 K) and Δθ₁=2.84°, Δθ₂=−1.4° at low temperature (77 K). Those results are in good agreement with the experimental findings Δθ₁=2.8±0.3°and Δθ₂=−1.1±0.3°.     

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.     

EPR spectra of Fe centers in layered TlGaSe2 single crystal

A single-crystal TlGaSe₂ doped by paramagnetic Fe ions has been studied at room temperature by electron paramagnetic resonance (EPR) technique. The fine structure of EPR spectra of paramagnetic Fe³⁺ ions was observed. The spectra were interpreted to correspond to the transitions among spin multiplet (S=5/2, L=0) of Fe³⁺ ion, which are splitted by the local ligand crystal field (CF) of orthorhombic symmetry. Four equivalent Fe³⁺ centers have been observed in the EPR spectra and the local symmetry of crystal field at the Fe³⁺ site and CF parameters were determined. Experimental results indicate that the Fe ions substitute Ga at the center of GaSe₄ tetrahedrons, and the rhombic distortion of the CF is caused by the Tl ions located in the trigonal cavities between the tetrahedral complexes.     

Theoretical investigations of the local structure distortion and the spin Hamiltonian parameters of Cr ions at tetragonal charge-compensation defect CrF5O site in Cr: KMgF3 crystals

The local structure distortion and the spin Hamiltonian (SH) parameters, including the zero-field splitting (ZFS) parameter D and the Zeeman g-factors g_‖ and g_⊥, are theoretically investigated by means of complete diagonalization method (CDM) and the microscopic spin Hamiltonian theory for tetragonal charge compensation CrF₅O defect center in Cr³⁺:KMgF₃ crystals. The superposition model (SPM) calculations are carried out to provide the crystal field (CF) parameters. This investigation reveals that the replacement of O²⁻ for F⁻ and its induced lattice relaxation Δ₁(O²⁻) combined with an inward relaxation of the nearest five fluorine Δ₂(F⁻) give rise to a strong tetragonal crystal field, which in turn results in the large ZFS and large anisotropic g-factor Δg. The experimental SH parameters D and Δg can be reproduced well by assuming that O²⁻ moves towards the central ion Cr³⁺ by Δ₁(O²⁻)=0.172R₀ and the five F⁻ ions towards the central ion Cr³⁺ by Δ₂(F⁻)=0.022R₀. Our approach takes into account the spin-orbit (SO) interaction as well as the spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions omitted in previous studies. This shows that although the SO interaction is the most important one, the contributions to the SH parameters from other three magnetic interactions are appreciable and should not be omitted, especially for the ZFS parameter D.     

Theoretical study of trigonal Fe center in SrCl2:Fesystem

The presence of Fe³⁺ centers with trigonal symmetry in chlorinated SrCl₂ crystal is an interesting phenomenon. By diagonalizing the complete energy matrices for a d⁵ configuration ion in a trigonal ligand-field and simulating the EPR low-symmetry parameters D and (a−F) simultaneously, the local lattice structure around trigonal Fe³⁺ center in SrCl₂:Fe³⁺ system has been studied. It is shown that Nistor et al.'s viewpoint about replacement is right, but the Cl⁻ ion along 〈111〉 axis around the Fe³⁺ center is replaced not by an O²⁻ ion but by some negative ion with effective charge to be less than that of Cl⁻ ion. Our results indicate that when the ratio of the effective charge of the negative ion to that of Cl⁻ ion is 0.8 as well as the distortion angle of the upper triangle is Δθ=−4.682°, the EPR parameters D and (a−F) can be explained satisfactorily.     

Spin Hamiltonian parameters and structural disorder analysis for Cr ion in YGG crystals

A new crystalline lattice distortion model has been proposed, on the basis of it, the relations between spin Hamiltonian parameters and crystal micro structure have been established. By taking into account slight magnetic interactions, including spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions, the local structure of Cr³⁺ ion in YGG crystal has been studied using complete diagonalization method (CDM). The studies show that the local structure in the YGG:Cr³⁺ crystal is of the compressed trigonal distortion. The ligand oxygen plane moved 0.0138 nm toward Cr³⁺ ion along C₃-axis. Accordingly, the SH parameters in YGG:Cr³⁺ crystal are explained successfully.     

EPR and optical absorption study of Cr-doped tetramethyl ammonium cadmium chloride single crystals

EPR study of Cr³⁺-doped tetramethyl cadmium chloride (TMCC) single crystals is carried out at room temperature. The crystal field and spin-Hamiltonian parameters are evaluated from the resonance line positions of different lines observed in the EPR spectra. The g and D parameter values are found to be g=1.9741±0.0002 and D=553±2×10⁻⁴ cm⁻¹, respectively. EPR data indicate that the site symmetry of Cr³⁺ ion in the crystal is distorted octahedron. Cr³⁺ ions enter the lattice substitutionally replacing Cd²⁺ sites and bind to the neighboring extra Cd vacancies necessary for charge compensation. The optical absorption spectra are measured in 195–925 nm wavelength range at room temperature. From optical study the energy values of different orbital levels are estimated. Further, the bonding parameters are obtained by correlating optical and EPR data 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 obtained to be B=722, C=2845, Dq=2043 cm⁻¹, h=1.015 and k=0.21.     

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.     

Theoretical study of EPR spectra and local structure for (NiO6) cluster in LiNbO3:Ni and Al2O3:Ni systems

For a d⁸ configuration ion, the 45×45 complete energy matrix, which contains the electron-electron repulsion interaction, the ligand-field interaction, the spin-orbit coupling interaction as well as the Zeeman interaction, has been established. By diagonalizing the complete energy matrix, the local lattice structure, EPR parameters (D, g_//, g_⊥) and optical absorption spectra for Ni²⁺ ions doped in LiNbO₃ and Al₂O₃ have been investigated. The local structure distortion parameters ΔR, Δθ₁ and Δθ₂ are determined for LiNbO₃:Ni²⁺ and Al₂O₃:Ni²⁺ systems, simultaneously. These results show that local structure of (NiO₆)¹⁰⁻ cluster exhibits an elongation distortion in both LiNbO₃:Ni²⁺ and Al₂O₃:Ni²⁺ systems, in spite of the different reasons of the elongation in both systems. In addition, we have found that the orbit reduction effect is very important to understand the anisotropic g-factors for Ni²⁺ ions doped in LiNbO₃ and Al₂O₃ crystals.     

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.     

Combustion synthesized MgAl2O4:Cr phosphors—An EPR and optical study

Magnesium aluminate (MgAl₂O₄) doped with trivalent chromium (Cr³⁺) was synthesized by the combustion method. The prepared sample was characterized by X-ray powder diffraction, Brunauer-Emmet-Teller (BET) adsorption isotherms and diffuse-reflectance UV-vis spectroscopy techniques. Electron paramagnetic resonance (EPR) and photoluminescence (PL) studies have been performed at room temperature and at 110 K. The EPR spectrum exhibit resonance signals at g=5.37, 4.53, 3.82, 2.26 and 1.96 characteristic of Cr³⁺ ions. The luminescence of Cr³⁺-activated MgAl₂O₄ exhibits a red emission peak around 686 nm from the synthesized phosphor particles upon 551 nm excitation. The luminescence is assigned to a transition from the upper ²E_g→⁴A_2g ground state of Cr³⁺ ions. By correlating EPR and optical data the crystal field splitting parameter (D_q), Racah inter-electronic repulsion parameter (B) and the bonding parameters have been evaluated and discussed. The bonding parameters suggests that the ionic nature of Cr³⁺ ions with the ligands and the Cr³⁺ ions are in distorted octrahedral environment.     

Studies of the zero-field splitting and g-factor for the defect model of Cr in α-LiIO3 crystals at low temperature

The EPR zero-field splitting parameters D and g-factors for Cr³⁺ in α-LiIO₃ single crystal, taking into account both the effect of lattice distortion and two Li⁺ vacancies, have been investigated using a complete diagonalization method (CDM) for 3d³ ions in a trigonal symmetry crystal field. The theoretical results (D=−0.60876 cm⁻¹, g_∥=1.9641, g_⊥=1.9682) are in excellent agreement with experimental results (D=−0.6099(3) cm⁻¹g_∥=1.965±0.001, g_⊥=1.971±0.002). In addition, Macfarlane's perturbation expressions lead to results almost identical with the CDM for Cr³⁺ in an α-LiIO₃ single crystal.     

Spectral studies on Cr ions doped in sodium-lead borophosphate glasses

Electron paramagnetic resonance (EPR), optical absorption and emission spectra of Cr³⁺ ions doped in (30−x) (NaPO₃)₆+30PbO+40B₂O₃+xCr₂O₃ (x=0.5, 2.0, 3.0, 4.0 and 5.0 mol%) glasses have been studied. The EPR spectra exhibit resonance signals with effective g values at g≈4.55 and g≈1.97. The EPR spectra of x=3.0 mol% of Cr₂O₃ in sodium-lead borophosphate glass sample were studied at various temperatures (295-123 K). The intensity of the resonance signals increases with decrease in temperature. The optical absorption spectrum exhibits four bands characteristic of Cr³⁺ ions in octahedral symmetry. From the analysis of the bands, the crystal-field parameter Dq and the Racah interelectronic repulsion parameters B and C have been evaluated. The emission spectrum exhibit one broad band characteristic of Cr³⁺ ions in octahedral symmetry. This band has been assigned to the transition ⁴T_2g (F)→⁴A_2g (F). Correlating EPR and optical data, the molecular bonding coefficient (α) has been evaluated.     

Variable temperature EPR spectra of Copper (II) ions in kainite crystals

X-band electron paramagnetic resonance (EPR) studies on divalent copper ions embedded in KMgClSO₄·3H₂O single crystals have been performed at low temperature (123 K). The angular variation of the EPR spectra reveals the presence of two Cu²⁺ sites, which have different orientations. The spin-Hamiltonian parameters of this six-coordinated cupric ion have been evaluated from the EPR spectra at 123 K. The forbidden lines due to Δm_I=±1 transitions are observed in between allowed transitions. The temperature variation EPR studies have also been performed both for a single crystal and a polycrystalline sample. The ground state wavefunction of Cu²⁺ ions has been estimated and is found to be an admixture of d_3z²−r² and d_x²−y². The temperature variation of the EPR spectra reveals that Cu²⁺ ions exhibit dynamic Jahn-Teller effect. From the polycrystalline EPR data, the temperature dependent magnetic susceptibilities are evaluated and discussed.