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.     

Unified calculations of the optical and electron paramagnetic resonance spectral data for Ce ion in Y3Ga5O12 crystal

Seven crystal field energy levels (obtained from the optical spectra) and three g factors g_x, g_y and g_z (obtained from electron paramagnetic resonance (EPR) spectra) for Ce³⁺ ion in Y₃Ga₅O₁₂ crystal are calculated together by diagonalizing a complete energy matrix. The Hamiltonian of this energy matrix includes all the interactions for 4f¹ ion Ce³⁺ in rhombic crystal field and under an external magnetic field, and so the optical and EPR data can be studied in a unified way. The calculated crystal field energy levels are in better agreement with the experimental values than the calculated values in the previous paper, and the g factors (which have not been calculated previously) are explained reasonably. The results are discussed.     

Investigations of the optical band positions,EPR parameters and defect structure for the trigonal Cr3+–Li+ centre in CsMgCl3 crystal

A unified calculation of optical band positions and electron paramagnetic resonance (EPR) (or spin-Hamiltonian) parameters for the trigonal Cr³⁺–Li⁺ centre in CsMgCl₃ crystal is made by using the complete diagonalisation (of energy matrix) method based on the two-spin–orbit-parameter model. In this model, the contributions from the spin–orbit parameter of central dⁿ ion and that of ligand ion are included. From the calculation, the 11 observed optical and EPR data (eight optical band positions and three EPR parameters g_//, g_⊥, D) are reasonably explained with five adjustable parameters and the defect structure of the Cr³⁺–Li⁺ centre (which is consistent with the expectation based on the electrostatic interaction) in CsMgCl₃ is acquired. The results are discussed.     

Theoretical explanation of optical absorption spectra and covalent effect of Ni2+ ions in octahedral sites of Ca3Sc2Ge3O12 crystal

The optical absorption spectra (d-d transition bands) and covalent effect of Ni²⁺ ions in octahedral sites of Ca₃Sc₂Ge₃O₁₂ crystal have been investigated by the full energy matrix based on the two spin–orbit coupling parameters model. The bond length of octahedral site is R_i?=?2.19 Å, which can be determined by the cubic crystal-field parameter and optical spectral data. The lattice distortion of the Ni²⁺ center in Ca₃Sc₂Ge₃O₁₂ crystal is also obtained from the calculations. In addition, the result has shown that the covalent effect of Ni²⁺ ion in the octahedral site of Ga₃Sc₂Ge₃O₁₂ is obvious and cannot be ignored. The calculated d-d transition bands agree well with that of the experimental findings, suggesting that the present methods can explain reasonably the optical spectral data and covalent effect of 3d⁸ ions in octahedral lattices.     

Theoretical Studies of the Electron Paramagnetic Resonance and Optical Spectral Data for Vanadium(IV) Ion in Yttrium Aluminum Garnet Crystal

Four spin-Hamiltonian parameters (g factors g _// and g _⊥ and hyperfine structure constants A _// and A _⊥) and two optical spectral band positions for vanadium(IV) (V⁴⁺) ion in the tetrahedral Al³⁺ site of yttrium aluminum garnet (Y₃Al₅O₁₂) crystals are calculated from the (third-order) perturbation theory method (PTM) and complete diagonalization (of energy matrix) method (CDM). Both methods are based on the cluster approach. The calculated results from both methods coincide and reasonably agree with the experimental values. The defect structure of V⁴⁺ center (which is different from the corresponding structure in the host crystal) in Y₃Al₅O₁₂ crystal is also obtained from the calculation.     

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.     

Cr3+掺杂的Cd3Al2Ge3O12光谱特性及晶场参数计算

采用高温固相法合成了Cd₃Al₂Ge₃O₁₂：Cr³⁺多晶材料,利用X射线衍射对其结构进行了分析,通过Cr³⁺的室温吸收光谱、室温和77K发射光谱分别对其光谱特性和晶场参数进行了分析和计算.结果表明：在450 nm的蓝光激发下,Cd₃Al₂Ge₃O₁₂：Cr³⁺室温发 关键词： 3Al₂Ge₃O₁₂：Cr³⁺')" href="#">Cd₃Al₂Ge₃O₁₂：Cr³⁺ 荧光光谱 晶场参数 可调谐激光     

Investigations of the optical spectra and spin-Hamiltonian parameters for the rhombic Yb centers in garnets

Two complete diagonalization (of energy matrix) methods (CDM-I and CDM-II) are used to calculate the six optical spectral band positions and nine spin-Hamiltonian (SH) parameters (g factors g_i and hyperfine structure constants ¹⁷¹A_i, ¹⁷³A_i, where i=x, y, z) for Yb³⁺ ions in the rhombic dodecahedral sites of garnets Y₃Al₅O₁₂, Lu₃Al₅O₁₂ and Y₃Ga₅O₁₂. In CDM-I, the Hamiltonian concerning energy matrix does not contain the Zeeman and hyperfine interaction terms, whereas in CDM-II, it does. So, in CDM-I, the SH parameters are obtained by first-order perturbation method or the equivalence between SH and Zeeman term (or hyperfine interaction term) and in CDM-II, the SH parameters and optical spectral band positions are calculated together. The results obtained from both methods are not only close to each other, but also in reasonable agreement with the observed values. So the second-order perturbation formulas of SH parameters developed recently are incorrect and unnecessary.     

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.     

Comparative analysis of crystal field effects and energy level scheme of six-fold coordinated Cr ion in the pyrochlores, Y2B2O7 (B=Ti, Sn)

The electronic energy levels of the six-fold coordinated Cr⁴⁺ ion in the pyrochlores Y₂B₂O₇ (B=Sn⁴⁺, Ti⁴⁺), have been computed using the exchange charge model of crystal field theory. The calculated Cr⁴⁺ energy levels and their trigonal splitting are in good agreement with experimental spectra. Calculations of the crystal field parameters show that the higher crystal field strength in Y₂Sn₂O₇ (in comparison with Y₂Ti₂O₇) arises from increased orbital overlap effects between the Cr⁴⁺ ion and the nearest oxygen ions, which are located at the 48f crystallographic position of the pyrochlore lattice. The increased overlap in Y₂Sn₂O₇ occurs despite the fact that the Cr⁴⁺-O^2- bond distance in Y₂Sn₂O₇ is longer than in Y₂Ti₂O₇. This is attributed to a lack of hybridization (covalent bonding) between the filled 2p orbital of oxygen ion occupying the 48f site of the pyrochlore lattice and the filled Sn⁴⁺ 4d¹⁰ orbital. As a result, a stronger crystal field is experienced by Cr⁴⁺ ions in Y₂Sn₂O₇, even if the Cr⁴⁺-O²⁻ distances are greater in this case, when compared to those in Y₂Ti₂O₇.     

Unified calculations of the optical band positions and spin-Hamiltonian parameters for V2+ ions in CdCl2 crystal

The eight optical spectral band positions and three spin-Hamiltonian parameters (g factors g_//, g_⊥ and zero-field splitting D) of V²⁺ ions in trigonal CdCl₂ crystal are calculated together from the complete diagonalisation (of energy matrix) method (CDM) based on the two-spin-orbit-parameter model (also called the cluster approach). In the model, differing from the usual one-spin-orbit-parameter model in the conventional crystal-field theory (where only the contribution to spin-Hamiltonian parameters due to the spin-orbit parameter of central dⁿ ion is considered), both the contributions from the spin-orbit parameter of central dⁿ ion and that of ligand ions are taken into account. The calculated results show reasonable agreement with the experimental values. The local lattice relaxation in the vicinity of V²⁺ ion due to the introduction of V²⁺ impurity is acquired from the calculations. The calculations of spin-Hamiltonian parameters from the CDM based on the one-spin-orbit-parameter and those from the perturbation theory method based on the two-spin-orbit-parameter model are also made for comparison. The results are discussed.     

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.     

Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Yb at the tetragonal Y site of KY3F10 crystal

The six optical band positions and six spin-Hamiltonian parameters [g factors g_∥, g_⊥ and hyperfine structure constants A_∥(¹⁷¹Yb³⁺), A_⊥(¹⁷¹Yb³⁺), A_∥(¹⁷³Yb³⁺), A_⊥(¹⁷³Yb³⁺)] for Yb³⁺ ion at the tetragonal Y³⁺ site of KY₃F₁₀ crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Hamiltonian of energy matrix contains the free-ion, crystal-field interaction, Zeeman (or magnetic) interaction and hyperfine interaction terms and so a 14×14 complete energy matrix for 4f¹³ ion in tetragonal crystal-field and under an external magnetic field is constructed. Diagonalizing the energy matrix, these optical and EPR spectral data are calculated together and the calculated results are in reasonable agreement with the experimental values. The signs of hyperfine structure constants A_∥, A_⊥ for the isotopes ¹⁷¹Yb³⁺ and ¹⁷³Yb³⁺ in KY₃F₁₀ are suggested. The results are discussed.     

Studies of the local compressibility of Cr 3+-centered octahedron in LiSc (WO 4)2 crystal from the pressure dependence of the optical spectra

The pressure-induced shifts of optical spectral bands ⁴T₂ and ²E for the preferential Cr³⁺-centered octahedron for Cr³⁺ at the Sc³⁺ site of the LiSc (WO ₄)₂ crystal have been calculated from crystal-field theory. From the calculation, the local linear compressibility d ln R/d p≈?3.3×10^?4 kbar^?1 for the Cr³⁺ center in a LiSc (WO ₄)₂ crystal is obtained. The result is discussed.     

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.     

Tetragonal distortions of the octahedral environments of Cr3+, Fe3+ and Gd3+ ions in A2CdF4 (A = Rb,Cs) and ACdF3 crystals

Abstract

The tetragonal distortions of local octahedral environments of Cr³⁺, Fe³⁺ and Gd³⁺ ions in Rb₂CdF₄, Cs₂CdF₄, RbCdF₃ and CsCdF₃ crystals have been studied by analyzing their EPR spectra. From the studies, it is found that the tetragonal distortions for Cr³⁺ and Fe³⁺ impurity ions, which substitute Cd²⁺ and have nearly the same ionic radius, are close to each other, whereas that for Gd³⁺ impurity ion, having a larger ionic radius, is larger than those for Cr³⁺ and Fe³⁺ ions in the same crystal. It appears that not only the impurity-ligand distance, but also the tetragonal distortions of impurity centres in crystals are closely related to the size of impurity.     

Absorption and EPR spectra of Cr3+ ions in a LaBeAl11O19 crystal

Electron spectra of optical absorption and EPR of Cr³⁺ ions in a LaBeAl₁₁O₁₉ crystal are investigated. It is shown that the Cr³⁺ ions occupy, three different octahedral positions of Al³⁺ in the LaBeAl₁₁O₁₉ structure, namely, 12k, 2a, and 4f₂; the ratio of their intensitites is 1∶2∶30, respectively. Parameters of the Cr³⁺ centers are determined and its is shown that the optical absorption spectra in the visible region are practically determined by the Cr³⁺ (III) occupying the 4f₂-positions. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 2, pp. 275–277, March–April, 1999.     

Electron paramagnetic resonance parameters of Mn<Superscript>4+</Superscript> ion in h-BaTiO<Subscript>3</Subscript> crystal from a two-mechanism model

The EPR parameters (g factors g _‖, g _⊥ and zero-field splitting D) of Mn⁴⁺ ion in h-BaTiO₃ crystal are calculated from the complete high-order perturbation formulas based on a two-mechanism model for the EPR parameters of 3d ³ ions in trigonal symmetry. In the model, not only the widely used crystal-field mechanism, but also the charge-transfer mechanism (which is not considered in crystal-field theory) are included. The calculated results are in reasonable agreement with the experimental values. The relative importance of charge-transfer mechanism to EPR parameters and the defect structure of Mn⁴⁺ centre in h-BaTiO₃ crystal obtained from the calculations are discussed.      

Theoretical investigation of optical spectra and covalent effect of Cr in Y2Ti2O7 and Y2Sn2O7

In this work, the complete matrix of optical spectral levels in trigonal symmetry of 3d² (3d⁸) ions are established on basis of strong field coupling mechanism by using two spin–orbit coupling parameters model. The contribution of the spin–orbit coupling of ligand to the optical spectra has been included in these formulas. As an application, the optical spectra of Cr⁴⁺ in Y₂Ti₂O₇ and Y₂Sn₂O₇ have been studied by the complete diagonalization (energy matrix) method. The covalent effect has been studied and the difficulty about Dq parameter in explanation of optical spectra of Cr-doped Y₂Ti₂O₇ and Y₂Sn₂O₇ is removed. The theoretical results are in good agreement with observed data.     

Effect of Eu,Tb codoping on the luminescent properties of Y2O3 nanorods

Red-emitting Y₂O₃:Eu³⁺ and green-emitting Y₂O₃:Tb³⁺ and Y₂O₃:Eu³⁺, Tb³⁺ nanorods were synthesized by hydrothermal method. Their structure and micromorphology have been analyzed by X-ray powder diffraction (XRD) and transmission electron microscopy (TEM). The photoluminescence (PL) property of Y₂O₃:Eu³⁺,Tb³⁺ phosphor was investigated. In the same host (Y₂O₃), upon excitation with ultraviolet (UV) irradiation, it is shown that there are strong emissions at around 610 and 545 nm corresponding to the forced electric dipole ⁵D₀-⁷F₂ transition of Eu³⁺ and ⁵D₄-⁷F₅ transition of Tb³⁺, respectively. Different qualities of Eu³⁺and Tb³⁺ ions are induced into the Y₂O₃ lattice. From the excitation spectrum, we speculate that there exists energy transfer from Tb³⁺ to Eu³⁺ ions .The emission color of powders reveals regular change in the separation of light emission. These powders can meet with the request of optical display material for different colors or can be potentially used as labels for biological molecules.