Diagonalization Of Energy Matrix Research Articles

Uniform explanation of the optical and electron paramagnetic resonance spectral data for La3Lu2Ga3O12: Cr3+ crystal

The optical and electron paramagnetic resonance (EPR) spectral data for Cr3+ ion in trigonal Lu3+ octahedral site of La3Lu2Ga3O12 (LLGG) crystal are computed in union from the complete diagonalization (of energy matrix) method based on the two-spin-orbit-parameter model. The model takes account of not only the contributions from the spin-orbit parameter of central dn ion in the conventional crystal-field theory, but also those of ligand ion via covalence effect. From the calculations, the observed three crystal-field energy levels (or optical bands) and three spin-Hamiltonian parameters (g factors g//, g⊥ and zero-field splitting D) are rationally explained in a unified way. The large angular distortion of Cr3+ impurity center in LLGG: Cr3+ crystal due to the great size mismatch is also acquired. The results are discussed.

Theoretical investigations of the optical and EPR spectra for trivalent cerium and ytterbium ions in orthorhombic YF3 crystal

The optical spectra and electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants A) for trivalent cerium and ytterbium ions in YF3 crystal with orthorhombic structure are investigated together by the complete diagonalization (of energy matrix) method (CDM). The obtained results are in reasonable agreement with the experimental ones. More importantly, two magnetically nonequivalent centers in YF3 crystal observed in EPR experiments are confirmed and ascribed to their specific positions in a unit cell by our calculations based on superposition model (SPM) analysis. Such identification of local sites with different magnetic properties would help us to understand not only the EPR spectra and magnetic susceptibility of other lanthanide ions doped in crystals with the same structure as YF3 but also the energy transfer scheme between two lanthanide ions occupying such two sites. All results are discussed carefully.

A Theoretical Study of Spectral Line Intensities of the Helium Atom in an Alternating Circular Electric Field

In this work, the behavior of the Stark component intensities of spectral lines in the emission spectrum of the helium atom excited by an alternating circularly polarized electric field is studied theoretically. The line intensities of an atom in the electric field are calculated within the framework of the method of energy matrix diagonalization. Based on the calculated results, a number of regularities have been revealed in the behavior of the Stark component intensities of the helium spectral lines with changes of the electric field strength.

Calculating Spectral Characteristics of the Helium Atom Excited by an Electric Field in Plasma of Current Sheets

In this work, the behavior of the energy spectrum and probabilities of transitions between the Stark states are studied theoretically for the helium spectrum emitted by plasma of current sheets. Calculations are performed by the method of the energy matrix diagonalization of an atom in the electric field. The results obtained have allowed us to reveal a number of regularities in the behavior of shifts and splitting of atomic levels and transition probabilities for the emission spectrum of the helium atom in a circularly polarized electric field arising in plasma of current sheets.

Unified research of the optical and EPR spectral data for the trigonal Cr3+ centers in emerald crystals

The complete diagonalization (of energy matrix) method founded on the two-spin–orbit-parameter model (where the contributions from both the spin–orbit parameter of central dn ion and that of ligand ions are contained) is adopted to calculate together the optical and EPR spectral data for the trigonal Cr3+ centers in emerald crystal. The computed 18 optical and EPR spectral data (15 optical band positions and three spin-Hamiltonian parameters) with only five adjustable parameters are in rational accordance with the experimental values. The calculations indicate that the above diagonalization method is able to explain unifiedly the optical and EPR spectral data for d3 ions in crystals.

Unified research on the optical and EPR spectral data for the Cr3+ion in the low-temperature trigonal phase of a LaAlO3crystal

The crystal field energy levels (or optical band positions) and EPR parameters ( g factor g// , g ⊥ and zero-field splitting D ) for the Cr 3+ ion in the trigonal phase of a LaAlO 3 crystal are calculated together through the complete diagonalization (of energy matrix) method. The method is founded on the two-spin-orbit-parameter model in which the contributions from both the spin-orbit parameter of the central d n ion and that of the ligand ion (the latter is ignored in the conventional crystal field theory) are considered. From the calculations, the observed seven optical band positions and three EPR parameters ( g// , g ⊥, D ) for LaAlO 3 :Cr 3+ at T ≈ 4.2 K are reasonably and unifiedly explained with only four adjustable parameters, and the impurity-induced local angular distortion of the Cr 3+ center in LaAlO 3 is estimated.

Calculations of the electronic levels, spin-Hamiltonian parameters and vibrational spectra for the CrCl3 layered crystals

Calculations of the Cr3+ energy levels, spin-Hamiltonian parameters and vibrational spectra for the layered CrCl3 crystals are reported for the first time. The crystal field parameters and the energy level scheme were calculated in the framework of the Exchange Charge Model of crystal field. The spin-Hamiltonian parameters (zero-field splitting parameter D and g-factors) for Cr3+ ion in CrCl3 crystals were obtained using two independent techniques: i) semi-empirical crystal field theory and ii) density functional theory (DFT)-based model. In the first approach, the spin-Hamiltonian parameters were calculated from the perturbation theory method and the complete diagonalization (of energy matrix) method. The infrared (IR) and Raman frequencies were calculated for both experimental and fully optimized geometry of the crystal structure, using CRYSTAL09 software. The obtained results are discussed and compared with the experimental available data.

Investigations of the spin-Hamiltonian parameters and defect structure due to Jahn–Teller effect for the tetragonal Nb4+ center in cubic Cs2ZrCl6 crystal

The spin-Hamiltonian parameters (g factors g//, , and hyperfine structure constants A//, ) of the tetragonally compressed Nb4+ center in cubic Cs2ZrCl6 crystal are calculated from two theoretical methods: one is the complete diagonalization (of energy matrix) method and another is the perturbation theory method. Both methods are based on the two-spin–orbit-parameter model where the contributions to spin-Hamiltonian parameters from the spin–orbit parameter of central dn ion (in the conventional crystal field theory) and that of ligand ion via covalence effect are contained. The calculated results from the two methods are in reasonable agreement with the experimental values. The tetragonal distortion of (NbCl6)2− octahedral cluster due to the Jahn–Teller effect for Nb4+ at the cubic Zr4+ site in Cs2ZrCl6 is also acquired. The results are discussed.

Theoretical spectra identification and fluorescent properties of reddish orange Sm-doped BaTiO3 phosphors

The reddish orange Sm3+-doped tetragonal perovskite BaTiO3 (BTO) phosphors for white LEDs were synthesized by the simple solid state reaction method. These phosphors, which can be effectively excited by the near ultraviolet light 409nm (6P3/2 (Γ7)→6H5/2 (Γ7)), produces the emitted reddish orange light peaks locate at about 561nm, 595nm and 643nm originated from the transitions of 4G5/2 (Γ7)→6H5/2 (Γ7), 4G5/2 (Γ7)→6H7/2 (Γ7) and 4G5/2 (Γ7)→6H9/2 (Γ7). Moreover, in order to calculate the fluorescent spectra of these phosphors, the complete 2002×2002 energy matrix was successfully constructed by an effective operator Hamiltonian including the free ion and crystal field interactions. Sixteen experimental fluorescent spectra in visible light range for Sm3+ ion at the tetragonal (C4v) Ba2+ site of BTO crystal, firstly, were accurately and quantitatively indentified from a complete diagonalization (of energy matrix) method (CDM) through only five crystal field parameters. The fitting values are very close to the experimental results, evidently proving the capability of CDM to investigate the luminescent phosphors alike in kind for w-LEDs.

Research on the optical band positions, spin-Hamiltonian parameters and atom-position parameter of Co2+ ion in CdSe crystal

The optical band positions and EPR (or spin-Hamiltonian) parameters (g factors g//, g⊥ and zero-field splitting D) of Co2+ ion in the trigonally-distorted tetrahedral Cd2+ site of CdSe crystal are calculated simultaneously from the complete diagonalization (of energy matrix) method (CDM) based on the two-spin–orbit-parameter model. This model contains the contributions to the spectral data from both the spin–orbit parameters of central dn ion (i.e., one-spin–orbit-parameter model) in the conventional crystal-field theory and that of ligand ions via covalence effect. The calculated 12 optical band positions and three spin-Hamiltonian parameters using four adjustable parameters show reasonable agreement with the experimental values. The local atom-position parameter uloc (where the corresponding parameter u in the host CdSe crystal is unlikely) in the Co2+ center is also estimated from the calculations. The calculations of these spectral data from the CDM based on the conventional one-spin–orbit parameter model are also made for comparison. It is found that the calculated optical band positions are also close to the experimental values, but the calculated spin-Hamiltonian parameters are in poor agreement with the observed values. So, for the unified and reasonable calculations of optical and EPR data of dn ions in crystals (in particular, in the cases of ligand with large spin–orbit parameter), the CDM based on the two-spin–orbit-parameter model should be applied.

Complete Diagonalization Calculation of the Optical and EPR Data for the Tetragonal Cu2+Center in Cu2+-Doped ZnSe Nanocrystals

By using the complete diagonalization (of energy matrix) method based on the cluster approach (where the admixture between the d orbitals of d ion and p orbitals of ligands due to covalence e ect is considered), the optical and electron paramagnetic resonance data (three optical band positions and four EPR parameters g‖, g⊥, A‖, A⊥) are calculated for the tetragonal Cu 2+ center in Cu-doped poly vinyl alcohol (PVA) passivated ZnSe nanocrystals with the defect model of Cu in the interstitial octahedral site in ZnSe. The calculated results are near the experimental values. The tetragonal elongation of the Cu octahedral cluster in ZnSe nanocrystals is obtained. The results are discussed.

Crystal field analyses for the optical spectra of Mn4+ion in Y3Al5O12crystal

The optical peaks of Mn 4+ ions in Y 3 Al 5 O 12 crystal are analyzed by calculating the crystal field energy levels through the complete diagonalization (of energy matrix) method based on the two-spin-orbit-parameter model. In the model, the contributions from both the spin-orbit parameter of central d n ion and that of ligand ion are considered. From the calculations, the eleven observed optical peaks are assigned and explained reasonably with three adjustable parameters, and the defect structure of Mn 4+ center in Y 3 Al 5 O 12 crystal is estimated.

Regularities in the Behaviour of Transition Probabilities in the Emission Spectrum of Argon in An Alternating Electric Field

In this work, a study of the influence of an alternating electric field on transition probabilities in the emission spectrum of the Ar atom is performed. Calculations are carried out by the method of the energy matrix diagonalization of an atom in the electric field, free from limitations of perturbation theory. Within the framework of this method, regularities in the behavior of transition probabilities under changes in the frequency and strength of the electric field are revealed. It is established that the behavior of the considered probabilities depends on the electronic structure of the Stark states participating in the transition.

Experimental and theoretical spectroscopic study of praseodymium(III) doped strontium aluminate phosphors

SrAl2O4: Pr3+ phosphors were successfully prepared by the high-temperature solid-phase method. The structure and photoluminescence properties of different Pr3+ concentrations doped SrAl2O4: Pr3+ were investigated by X-ray diffraction (XRD) and fluorescence spectrophotometer, respectively. Moreover, the role of Li+ ions as charge compensation for SrAl2O4: Pr3+ was also studied in detail. To better understand the fluorescent mechanism of SrAl2O4: Pr3+ phosphors, a complete 91×91 Hamiltonian energy matrix was built by an effective operator Hamiltonian including free ion and crystal-field interactions. The fluorescent spectrum for Pr3+ ions at Sr2+ sites of SrAl2O4 crystal was successfully studied from a complete diagonalization (of energy matrix) method of 4f2 electron configurations. The theoretical values are in agreement with the observed data.

Unified calculation of optical and EPR spectral data for Cr3+-doped KAl(MoO4)2 crystal

This paper reports an unified calculation of optical and EPR spectral data for Cr3+ ion at the trigonal Al3+ site of KAl(MoO4)2 crystal from the complete diagonalization (of energy matrix) method based on the two-spin–orbit-parameter model. In this model, differing from that in the conventional crystal-field theory, not only the contributions from the spin–orbit parameter of central dn ion, but also those from the spin–orbit parameter of ligand ion via covalence effect are taken into account. The calculation shows that by using only three adjustable parameters, the observed twelve optical and EPR spectral data (nine optical band positions and three EPR parameters g||, g⊥ and D) are reasonably explained in a unified way with this method. The results are discussed.

Theoretical investigations of EPR g factors for Ce3+ ion at monoclinic Cs site in YAlO3 crystal

Three EPR principal g values (gx, gy and gz) for monoclinic (Cs) Ce3+ center in YAlO3 crystal are calculated by the complete diagonalization (of energy matrix) method (CDM) based on the superposition model (SPM) analysis. The calculated g factors are more reasonably closer to experimental results reported by Asatryan et al. (2002) than their same work in 1997. The reliability of fitted crystal-field parameters of YAP:Ce3+ crystal is also analyzed. In SPM calculations, the seeming abnormal negative power-law exponent t6 is found to be actually reasonable and its underlying cause may be explained by future ab initio studies.

Spin-Hamiltonian Parameters of Gd3+ Ion in the Room Temperature Tetragonal Phase of BaTiO3

Abstract The spin-Hamiltonian parameters (g factors g||, g⊥, and zero-field splittings b0 2 , b0 4 , b4 4 , b0 6 , b4 6 ) of the 4f7 Gd3+ ion in the tetragonal phase of a BaTiO3 crystal are calculated through the diagonalization (of energy matrix) method based on the one-electron crystal field mechanism. In the calculations, the crystal field parameters are estimated from the superposition model with the structural data of the studied crystal. It is found that by using three adjustable intrinsic parameters Āk(R0) (k=2, 4, 6) in the superposition model, the seven calculated spin-Hamiltonian parameters are in good agreement with the experimental values, suggesting that the diagonalization method based on one-electron crystal field mechanism is effective in the studies of spin-Hamiltonian parameters for 4f7 ions in crystals.

Unified calculations of optical and EPR data for Cu3+ ion in Al2O3 crystal

The optical band positions and EPR parameters ( g factors g ∥ , g ⊥ and zero-field splitting D ) for Cu 3+ ion in Al 2 O 3 crystal are calculated by using the complete diagonalization (of energy matrix) method based on the two-spin–orbit-parameter model. In the model, both the contribution to the spectral data from the spin-orbit parameter of central 3d n ion and that of ligand ion are contained. The calculated results show reasonable agreement with the experimental values. The defect structure of Cu 3+ impurity center is estimated from the calculations. • Unified calculation for the optical and EPR spectral data of Cu 3+ in Al 2 O 3 is made. • The complete diagonalization (of energy matrix) method is used in the calculation. • The diagonalization method is based on the two-spin–orbit-parameter model. • The defect structural data is obtained from the calculation.

Investigations of the Optical Band Positions and Spin-Hamiltonian Parameters for the Rhombic VO2+Complex in CsCl Crystal

The optical band positions and spin-Hamiltonian parameters (g factors g(i) and hyperfine structure constants A(i), where i = x, y, z) of the rhombic VO2+ complex in CsCl crystal are calculated together from two theoretical methods. One is the complete diagonalization (of energy matrix) method and another is the perturbation theory method. The calculated results from the two methods coincide and are in reasonable agreement with the experimental values. So, both methods are effective in the explanations of optical and electron paramagnetic resonance (EPR) data for d(1) ions in crystals. The calculations also suggest that in d(1) rhombic octahedra the ground state is almost a pure vertical bar d(xy)>) state. This point is different from that of conjugate d(9) (e.g., Cu2+) ions in rhombic octahedra where the ground state should be an admixture of ground and first excited states.

Investigations of defect structure and EPR parameters for tetragonal Nd3+ centers in AWO4 (A=Ca, Sr, Pb) crystals by superposition model analysis

The characteristics of the local environment around the paramagnetic centers formed by the Nd3+ ions doped into three tungstate crystals (CaWO4, SrWO4 and PbWO4) are investigated by using superposition model analysis. The inter-relation between the electronic and molecular structures of Nd3+ ion in a tetragonal (S4 symmetry) ligand field has been established by a complete diagonalization (of energy matrix) method. The local lattice distortions in the vicinity of the impurity ion Nd3+ have been derived and the local distortion angles Δθ=−1.69°, −1.13°, and −1.48° are obtained for Nd3+ in CaWO4, SrWO4 and PbWO4, respectively. The calculated EPR parameters are in good agreement with the experimental values. On the basis of this, the links between EPR g-factors and the local structure as well as crystal field parameters are studied.