Fit Of Energy Levels Research Articles

Crystal field parameters of the C2 site in Eu2O3

We studied the energy levels of Eu3+ at the C2 lattice site of cubic Eu2O3. We identified 29 Lorentzian lines corresponding to 5D0 → 7F0-6 transitions obtained from photoluminescence spectra at 10 K. The levels were analyzed in terms of the 14 crystal field parameters corresponding to the site symmetry. The energy-level fit yielded a final standard deviation of 12.0 cm−1. The resulting crystal field strength parameter is Nv = 3869 ± 185. This value confirms the linear dependence on the host atomic radius predicted by the extended point charge electrostatic model (PCEM). The present study considered the highest number of transitions to date for Eu3+ in Eu2O3 to the authors’ knowledge.

Experimental and Theoretical Studies of the Vibrational and Electronic Spectra of a Lanthanide Ion at a Site of Th Symmetry: Pr3+ in Cs2NaPr(NO2)6

The Pr(3+) ion in Cs(2)NaPr(NO(2))(6) is situated at a site of T(h) symmetry with 12-coordination to O atoms of bidentate nitrito groups. First-principles calculations of the vibrational modes of the complex were carried out using the density functional theory with the generalized gradient approximation Perdew-Burke-Ernzerhof exchange-correlation functional. The calculations that treated the Pr(3+) 4f electrons as valence electrons showed better agreement with the experimental vibrational assignments compared with those treating the 4f electrons a part of the inner core. The (1)D(2) → (3)H(4) emission spectra of Cs(2)NaPr(NO(2))(6) at 7 K enabled assignments to be made for the crystal-field (CF) levels of the ground-state multiplet. The emission of the dilute system Cs(2)NaY(NO(2))(6):Pr(3+) was dominated by NO(2)(-) triplet emission, which was quenched at elevated temperatures by energy transfer to trace Eu(3+) impurity. From magnetic dipole calculations and the vibronic fingerprint, detailed assignments are given for the complex 10 K electronic absorption spectrum of Cs(2)NaPr(NO(2))(6) between 3940 and 18800 cm(-1), and the derived Pr(3+) 4f(2) energy-level data set has been fitted by calculation. By comparison with Cs(2)NaPrCl(6), the fourth-order CF parameter in Cs(2)NaPr(NO(2))(6) is relatively small so that interaction with a 4fnp configuration is not important. From the NO(2)(-) absorption bands above 20,000 cm(-1), the N-O bond length change upon excitation is small, whereas the angle O-N-O opens by more than 10° in the triplet state. By contrast to the NO(2)(-) internal vibration frequencies, which except for the wagging mode show only minor changes with the environment, the triplet-state energy shows a linear decrease with an increase of the lanthanide (Ln(3+)) ionic radius in Cs(2)NaLn(NO(2))(6). Using the eigenvectors from the energy-level fit, the variation of the inverse magnetic susceptibility with temperature has been calculated between 1 and 100 K and the values are somewhat lower than those from experiment.

Optical Spectroscopy of Rare Earth Ion-Doped TiO2 Nanophosphors

Trivalent rare-earth (RE3+) ion-doped TiO2 nanophosphors belong to one kind of novel optical materials and have attracted increasing attention. The luminescence properties of different RE3+ ions in various TiO2 nanomaterials have been reviewed. Much attention is paid to our recent progresses on the luminescence properties of RE3+ (RE = Eu, Er, Sm, Nd) ions in anatase TiO2 nanoparticles prepared by a sol-gel-solvothermal method. Using Eu3+ as a sensitive optical probe, three significantly different luminescence centers of Eu3+ in TiO2 nanoparticles were detected by means of site-selective spectroscopy at 10 K. Based on the crystal-field (CF) splitting of Eu3+ at each site, C2v and D2 symmetries were proposed for Eu3+ incorporated at two lattice sites. A structural model for the formation of multiple sites was proposed based on the optical behaviors of Eu3+ at different sites. Similar multi-site luminescence was observed in Sm(3+)- or Nd(3+)-doped TiO2 nanoparticles. In Eu(3+)-doped TiO2 nanoparticles, only weak energy transfer from the TiO2 host to the Eu3+ ions was observed at 10 K due to the mismatch of energy between the TiO2 band-gap and the Eu3+ excited states. On the contrary, efficient host-sensitized luminescences were realized in Sm(3+)- or Nd(3+)-doped anatase TiO2 nanoparticles due to the match of energy between TiO2 band-gap and the Sm3+ and Nd3+ excited states. The excitation spectra of both Sm(3+)- and Nd(3+)-doped samples exhibit a dominant broad peak centered at approximately 340 nm, which is associated with the band-gap of TiO2, indicating that sensitized emission is much more efficient than direct excitation of the Sm3+ and Nd3+ ions. Single lattice site emission of Er3+ in TiO2 nanocrystals can be achieved by modifying the experimental conditions. Upon excitation by a Ti: sapphire laser at 978 nm, intense green upconverted luminescence was observed. The characteristic emission of Er3+ ions was obtained both in the ultraviolet-visible (UV-vis) and near-infrared regions through the high-resolution experiments at 10 K. The CF experienced by Er3+ in TiO2 nanocrystal was systematically studied by means of the energy level fitting.

Crystal field energy-levels of Nd3+:Gd3Sc2Al3O12 and fitting

Nd3+ :GSAG, a laser crystal of 942 nm with good performance, was grown by Czochralski method successfully, and its transmission spectra at room temperature were studied. Sixty-eight crystal field splitting levels of Nd3+ with the maximum up to 29967 cm-1 were identified, to which the Hamiltonian parameters of free-ion and crystal field were fitted, and the root-mean-square deviation of energy level fitting is 16.7 cm-1, which indicated that the experimental and calculated energy levels are well consistent. The obtained Hamiltonian parameters can be used to calculate the wavefunctions of Nd3+ in GSAG, predict its energy level splitting, study the luminescent properties and so on.

Energy levels, fluorescence lifetime and Judd–Ofelt parameters ofEu3+ inGd2O3 nanocrystals

Crystal-field (CF) levels below 36 000 cm−1 of Eu3+ atthe C2 site of Gd2O3 nanorods are experimentally determined from the excitation and emissionspectra at 10 K. The levels are analysed in terms of 20 freely varied free-ionand CF parameters, and energy-level fit yields a final standard deviation of12.9 cm−1, showing very good agreement between the observed and thecalculated values. The Judd–Ofelt (JO) intensity parametersΩ2,4,6 are determined to be 12.39, 2.02 and 0.19 (in10−20 cm2) which takes J-mixing into account. For the first time the absolute value of theΩ6 parameteris reliably determined. The calculated radiative transition rates and branching ratios for the transitionsfrom 5D0 agree well with the experiments. The size dependence of the JO intensity parameters ofEu3+ inRE2O3 (RE = Y, Gd, Lu) nanocrystals is clarified. The fluorescence lifetime of5D0 ofEu3+ inGd2O3 nanorods is observed to be significantly affected by the surrounding media, giving rise to afilling factor of 0.58 for the nanoparticles.

Experimental study and crystal-field modeling ofNd3+(4f3)energy levels inBi4Ge3O12andBi4Si3O12

Most of the $^{2S+1}L_{J}$ multiplets of the ${\mathrm{Nd}}^{3+}$ ion $(4{f}^{3})$ in ${\mathrm{Bi}}_{4}{\mathrm{Ge}}_{3}{\mathrm{O}}_{12}$ and ${\mathrm{Bi}}_{4}{\mathrm{Si}}_{3}{\mathrm{O}}_{12}$ single crystals have been experimentally observed in the UV, visible, and NIR spectroscopic regions. The majority of the Stark energy levels were identified for each multiplet, including some recently identified. In these crystals, the ${\mathrm{Nd}}^{3+}$ ions substitute ${\mathrm{Bi}}^{3+}$ ions at sites of ${C}_{3}$ point group symmetry. A Hamiltonian including the Coulomb, spin-orbit, interconfigurational interaction terms of the ${\mathrm{Nd}}^{3+}(4{f}^{3})$ configuration, and trigonal crystal-field terms was used to fit these energy levels. The Hamiltonian was diagonalized in the $\ensuremath{\mid}{\mathrm{SLJM}}_{J}⟩$ complete $4{f}^{3}$ basis that includes 364 states. A least-squares fit was carried out for all the observed energy levels. Previously obtained ${B}_{kq}$ crystal-field parameters did not reproduce all of the observed ${\mathrm{Nd}}^{3+}$ energy levels. The ${B}_{kq}$ parameters obtained in this work allow a good energy level fitting for both lattices. The obtained crystal-field parameters produced an average standard deviation of about $20\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. Although the intensity of the crystal field experimented by the neodymium ions in both lattices is quite similar, an analysis of the nephelauxetic ratio shows a larger wave-function overlap in bismuth silicate than in bismuth germanate. Also, the spectroscopic electron paramagnetic resonance Land\'e $g$ factors were calculated for both lattices, obtaining excellent agreement with the experimental values.

Electronic Spectra and Crystal Field Analysis of Er3+ in Cs2NaErF6

The optical electronic spectra of Cs2NaErF6, Cs2NaY0.9Er0.1F6, and Cs2NaM0.5Er0.5F6 (M Sc, Ga) have been investigated at temperatures down to 10 K. The absorption spectra span the range from 6000 to 41 000 cm-1, whereas emission has been observed from the 4S3/2, 4F9/2, 4I9/2, and 4I11/2 multiplet terms in the spectral range from 25 000 to 9000 cm-1. Each transition between crystal field levels comprises extensive, well-resolved vibronic structure. From the detailed vibronic analyses, 39 crystal field levels have been assigned from 0 to 27 642 cm-1. A configuration interaction assisted crystal field (CIACF) calculation provides a good energy level fit with reasonable energy parameters. The mean deviation of the standard 4f112p6 fit to the energy levels (23 cm-1) exceeded that for the 4f112p6/4f122p5 CIACF fitting (6.4 cm-1), which provides 4f112p6/4f122p5 further evidence for the importance of the charge-transfer configuration interaction.

Electronic Spectra of Cs2NaYbF6 and Crystal Field Analyses of YbX63- (X = F, Cl, Br)

Detailed analysis of the vibronic structure in the electronic absorption spectrum of Cs2NaYbF6 at temperatures between 10 and 300 K enables the crystal field energy level diagram of Yb3+ in this cubic host to be deduced. Ultraviolet and visible laser excitation of Cs2NaYbF6, Cs2NaY(0.9)Yb(0.1)F6, and Cs2NaHo(0.99)Yb(0.01)F6 give spectral features mainly due to Yb3+ being situated at a range of defect sites. The 4f13 crystal field analyses of octahedral YbX6(3-) (X = F, Cl, Br) systems show the expected trends in parameter values, but the energy level fits are poor. Inclusion of the interaction with the charge-transfer configuration 4f14np5 provides an exact fitting of energy levels for YbX6(3-), and a smooth variation of ff and fp crystal field parameters for Cs2NaLnCl6 (Ln = Er, Tm, Yb) is observed.

Ultravioletf→femission and crystal field analysis forEr3+inCs2NaErCl6

Luminescence is reported from the ${}^{2}{\mathrm{I}}_{11/2}$ level of ${\mathrm{Er}}^{3+},$ in the cubic elpasolite lattices ${\mathrm{Cs}}_{2}{\mathrm{NaErCl}}_{6}$ and ${\mathrm{Cs}}_{2}{\mathrm{NaYCl}}_{6}.$ Altogether, with the use of ultraviolet laser excitation, 11 transitions from ${}^{2}{\mathrm{I}}_{11/2}$ ${\ensuremath{\Gamma}}_{7}$ (at 40 668 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) to lower term multiplets have been observed and assigned. Transitions are also reported from the ${}^{2}{\mathrm{K}}_{13/2}$ ${\ensuremath{\Gamma}}_{6}$ level at 32 613 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The absence of emission from ${}^{2}{\mathrm{P}}_{3/2}$ (at 31 367 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) under the experimental conditions is rationalized. Up-conversion to ${}^{2}\mathrm{H}{(2)}_{9/2},$ which is not due to two-photon absorption, is reported for ${\mathrm{Cs}}_{2}{\mathrm{NaErCl}}_{6}$ under blue pulsed laser excitation. Trap emission from ${}^{2}{\mathrm{G}}_{9/2}$ defect sites has been observed under ultraviolet excitation. A preliminary investigation has been made of the electronic absorption spectra of ${\mathrm{Cs}}_{2}{\mathrm{NaErCl}}_{6}$ and 58 Kramers quartet and doublet levels have been assigned, with a further 18 levels uncertain. The energy-level fit to 58 levels with total degeneracy 180 has been performed with a mean deviation of 20.4 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, which is improved to 16.8 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ if an empirical correction to the diagonal reduced matrix element of ${\mathrm{U}}^{4}$ for ${\mathrm{the}}^{2}$H(2) term is included. The average error is similar for the 18 uncertain levels (total degeneracy 52). A comparison is included with the energy-level parametrizations of other ${\mathrm{Er}}^{3+}$ systems.

A spectroscopic investigation of Y 3 Al 5 O 12 :Pr 3 + in translucent ceramic form: Crystal field analysis assisted by configuration-interaction

This paper presents an investigation of Pr3+ doped in the D2 site of Y3Al5O12 (YAG), for the first time on a translucent ceramic sample free of spurious phases, impurity or pair sites. The optical study is carried out by optical absorption, excitation, and emission by selective excitation into 1D2 and 3P0, at different temperatures between 20 K and 60 K, in the 4 300-23 000 cm-1 range. A detailed account of the line assignments is given. 67 over 91 levels of the 4f2 configuration are determined. Several crystal field calculations within the ground configuration 4f2 and the larger matrix 4f2+4f6p are carried out. The energy level fit is slightly improved by configuration interaction. The 3P2 and 1I6 levels are strongly mixed together by the large 6th order crystal field parameters. In sintered samples with different Pr3+ concentrations, satellite lines with intensities increasing quadratically with the concentration are observed. A few weak lines forbidden in D2 site symmetry are observed.

4f5d–4f 2 emission transitions of Pr 3+

The first well-resolved, high-resolution d–f emission spectra are reported for a lanthanide ion. Numerous transitions are observed and assigned for Pr 3+ at a crystal site of octahedral symmetry. The symmetry representation of the lowest f 1d 1 state is deduced and the eigenvectors from the 4f 15d 1 energy level fit are utilized to model the experimentally observed intensities.

Configuration interaction of Pr3+ in PrCl63−

The low-temperature electronic spectra of Pr3+ at an octahedral site of symmetry in the PrCl63− moiety, in crystals of Cs2NaPrCl6, Cs2LiPrCl6, and Cs2NaMCl6:Pr(M=Gd, Y) have been measured and interpreted. Together with the results from d–f emission spectra and resonance electronic Raman spectra, these new data permitted the assignment of symmetry representations of up to 39 out the possible 40 crystal field levels of the 4f2 configuration. The inclusion of configuration interaction with the next highest even parity configuration, 4f6p, into the energy level parametrization reduced the mean deviation of the energy level fit using the single 4f2 configuration model alone, by a factor of 2.9 (i.e., from 32.7 to 11.6 cm−1). In particular, the interaction mechanism for the “anomalous” multiplets D21 and G41 was shown to arise from crystal field mixing with 4f6p states. This leads to the inclusion of up to about 0.5% of fp-orbital character for these 4f2 eigenvectors. In the 4f2 single-configuration fits to triplet levels alone, the fourth-degree crystal field parameter turned out to be larger than in the fits to singlet terms, which is the reverse of the expected order if correlation crystal field effects are important.

Synthesis, Structure, and Spectroscopy of Rare Earth Hypophosphites. 1. Anhydrous and Monohydrated Lanthanide Hypophosphites.

The lanthanide hypophosphite complexes Ln(H(2)PO(2))(3) (Ln = La, Pr, Nd) and Ln(H(2)PO(2))(3).H(2)O (Ln = La, Pr) crystallize in the space group P&onemacr; (No. 2), Z = 2. The lattice constants for La(H(2)PO(2))(3) are a = 6.7912(6) Å, b = 7.0801(8) Å, c = 8.863(1) Å, alpha = 82.64(1) degrees, beta = 74.43(1)( o), gamma = 71.91(1) degrees; for La(H(2)PO(2))(3).H(2)O, a = 7.2291(4) Å, b = 7.983(1) Å, c = 8.934(1) Å, alpha =110.57(1) degrees, beta = 98.26(1) degrees, gamma = 104.35(1) degrees. In both structures hypophosphite ions bridge adjacent 8-coordinate lanthanide ions to give infinite chains. Infrared and Raman spectra (300-20 K) are shown to be consistent with the crystallographic data, with 52 of the 54 fundamental hypophosphite modes of vibration assigned. The electronic spectra of the anhydrous compounds consist mainly of bands due to pure electronic electric dipole transitions. Two-center vibronic transitions observed in the (3)H(4) --> (1)D(2) spectrum of Pr(H(2)PO(2))(3) are not well-simulated by a model with dipole-dipole interaction terms between the two centers. The energy level scheme of Pr(3+) in Pr(H(2)PO(2))(3) was fitted to a model Hamiltonian for a C(2)(v)() site symmetry Pr(3+) ion, including configuration interaction of 4f(2) with 4f6p. Theoretical crystal field parameters were in reasonable agreement with those derived from the energy level fitting. The results highlight the C(2)(v)() (k even) and C(1) (k odd) distortions from the ideal D(4)(d)() antiprismal structure, which slightly modify the 4f(2) energy level scheme, and largely determine the spectral intensities in Pr(H(2)PO(2))(3), respectively. The derived energy level scheme of Nd(H(2)PO(2))(3) is similar to that for 8-coordinated Nd(3+) in NdCl(3).6H(2)O.

Group-chain scheme analysis of the energy levels and magnetic properties of Nd 3+ in LiYF 4 crystal

Based on the analysis of group-chain scheme, the crystal-field-level fitting of Nd3+:LiYF4 has been carried out, in which the Nd3+ ions occupy positions with site symmetry S4. The RMS deviation of energy-level fitting is 12.8 cm-1. Using the obtained wave functions, g-factors of the ground state are calculated, which are g||?=?2.067 and g??=?2.631, in good agreement with the experimental values (g|| = 1.987 and g??=?2.554). The method proposed turns out to be effective in the study of spectral properties of localized centres in laser crystals.

An analysis of neutron scattering spectroscopy in UO 2

A calculation has been performed to analyse neutron scattering spectrum of an ion with f 2 configuration in a cubic crystal field. The present analysis, using a six-interaction Hamiltonian, gives an energy-level fit which has a rms σ=15.1 relative to the experimentally observed crystal field excitations. The wave functions thus obtained were used to calculate the effective magnetic moment of UO 2. The final values of interaction parameters (in cm −1) are F 2=230.84, F 4=39.22, F 6=3.77, ζ 5f=1968, α=34.87, β=−565.68, γ=799.07, M 0=0.570, M 2=0.318, M 4=0.222, A 4〈 r 4〉=−900.6, A 6〈 r 6〉=195.4.

Crystal-field analysis of the energy levels and spectroscopic characteristics of in crystal

On the basis of the analysis of the group-chain scheme ), the crystal-field-level fitting has been carried out for , in which the ions occupy site symmetry positions. The RMS value of the energy-level fitting is and the group character of each Stark level compares well to the experimental assignment on the whole. The wavefunctions obtained were used in the study of the Zeeman interaction and the fluorescence spectra. The calculated g-factors obey Karayianis's partial g-sum rule, and the g-factor of the ground state of is predicted. According to the Judd-Ofelt theory, the odd crystal-field parameters have been quantitatively determined by the fit to the experimental transition rates from . The line-to-line transition rates and thus the fluorescence spectra from at room temperature have been calculated, which are in agreement with the experiment by and large.

The millimeter wave spectrum of CH3 18OH in the 119–165 GHz spectral range

The rotational millimeter-wave spectrum of CH318OH has been revisited, and 162 transitions of both a- and b-types have been measured in the 119-165 GHz spectral range. The spectrum was recorded using the frequency-modulated millimeter-wave spectrometer at the/ustus-LiebigUniversit~it in Giegen. The CH318OH transition assignments were based on energy levels obtained from the far-infrared analysis of S. Zhao (Ph.D. thesis, University of New Brunswick, 1993) using the "Ritz" program of G. Moruzzi et al. (J. Mol. Spectrosc. 167, 156 (1994)) for direct energy level fitting. The relatively low residuals between calculated and observed frequencies highlight the good quality of the results from this program. The newly measured transitions combined with those existent in the literature have been included in least-squares fits to improve the set of rotational, torsional and centrifugal distortion constants for O-18 methanol.

Spectroscopic characteristics, magnetic properties and fluorescence dynamics of in crystal

Based on the analysis of the group-chain scheme, the crystal-field-level fitting has been carried out for :, in which the ions occupy site symmetry positions. The RMS of energy-level fitting is . The wavefunctions obtained were used to the study of magnetic, thermal and spectroscopic properties of the crystal. The calculated g-factors confirm Karayianis' partial g-sum rule. The temperature dependence of Schottky specific heat and magnetic susceptibility agrees well with the experimental data. Using the Judd - Ofelt parameter analysis, the parameters are fitted to the absorption spectra with , and (in ). Considering the radiative, nonradiative transition and cross-relaxation in , one set of rate equations is established to study the fluorescence dynamics. The relation between the ion's population density in the excited state and the doped ion concentration is discussed, and some useful inferences are drawn.

Configuration interaction in PrCl3

A program for the resolution of two-electron configurations defined on a multi-configuration |SLJMJ〉 basis is described. It is utilized for the resolution of the electronic structure of Pr3+ in PrCl3. General formulas for the calculation of the electrostatic, spin-orbit and crystal field interactions are given. Results involving 4f2 + 4f5d + 4f6p interaction are compared with calculations involving 4f2 + 4f5d or 4f2 + 4f6p only. All things being considered, the diagonalisation of the 4f2 + 4f6p matrix is the “cheapest” solution leading to an improved experimental/calculated energy level fit.

Crystal-field analysis of the spectroscopic characteristics and magnetic properties of in crystal

On the basis of the analysis of a group-chain scheme and with the use of the constraint condition determined by the ratios of crystal-field parameters calculated using the point-charge model, a crystal-field-level fitting has been carried out for , in which the ions are assumed to occupy positions with point symmetry . The RMS value of the energy-level fitting is . The wavefunctions obtained were used in the study of the magnetic, thermal, and spectroscopic properties of the crystal. The calculated g-factors obey Karayianis's partial g-sum rule. The temperature dependences of the Schottky specific heat and magnetic susceptibility agree well with data published by others. The line shown by calculation to be the strongest is -polarized at 450.4 nm, which corresponds to blue upconversion lasing in the experiment. The method proposed turns out to be effective in the study of the spectroscopic and magnetic properties of localized centres in crystals.