Crystal-field levels

The arc and spark spectra of the individual lanthanides are exceedingly complex. Thousands of emission lines are observed. For the trivalent rare-earth ions in soUds, the absorption spectra are much better understood. However, the crystal fields of the neighboring atoms remove the degeneracy of some states and several levels exist where only one did before. Many of these crystal field levels exist very close to a base level. As the soUd is heated, a number of the lower levels become occupied. Some physical properties of rare-earth metals are thus very sensitive to temperature (7). 

K over the temperature range 6 to 40°K. Below 6°K, the deviation of the data from the straight line indicates lower crystal field levels. At higher temperatures, the magnetism becomes too weak to measure by the magnetometer. 

The electrostatic and spin-orbit parameters for Pu + which we have deduced are similar to those proposed by Conway some years ago (32). However, inclusion of the crystal-field interaction in the computation of the energy level structure, which was not done earlier, significantly modifies previous predictions. As an approximation, we have chosen to use the crystal-field parameters derived for CS2UCI6 (33), Table VII, which together with the free-ion parameters lead to the prediction of a distinct group of levels near 1100 cm-. Of course a weaker field would lead to crystal-field levels intermediate between 0 and 1000 cm-1. Similar model calculations have been indicated in Fig. 8 for Nplt+, Pu1 "1 and Amlt+ compared to the solution spectra of the ions. For Am t+ the reference is Am4" in 15 M NHhF solution (34). 

After determination of the quahtative schemes for the term splitting in the crystal fields, it is possible to go to a quantitative estimation of separation between the crystal field levels. All the electronic interaction stages can be represented quantitatively by means of the few parameters ... 

When the ion is embedded in a matrix, the crystal field splits the ground multiplet and the crystal field levels give rise to the same problem as the free ion multiplets, to be solved in the same way. If several crystal field levels are involved, a complete treatment using Eq. (13) is needed. 

The magnetic term is associated with changes in internal energy related to magnetic transitions. Its thermal dependence leads to the magnetic entropy and enthalpy determination. The Schottky term comes from the excitation of higher lying crystal field levels in compounds with locahzed 5 f levels. 

In tetrahedral and cubic symmetry, the crystal-field levels are inverted, giving a single orbital state lowest. For dl in an octahedral field, the 4F state also has the single orbital state lowest, so we would expect the d1 configuration in a tetrahedral or cubic field to behave in a similar fashion and fit the spin Hamiltonian given in Eq. (158) solved for S=f. For most of the examples listed in Table XV, the tetrahedral symmetry is not distorted so that D = E=0 and no fine structure is reported. The 5=f character of the spin state is revealed in these cases by the fact that Eq. (80) must be added to the spin Hamiltonian to explain the ESR results on d1 in tetrahedral and cubic fields (131). For Co2+ in Cs3CoCl5, D= —4.5 cm-1 (222) and in CdS, D > 2 cm-1 (223). 

Fig. 47. (a) Temperature dependence of the specific heat C as aC/T-vs.-T2 plot for TmNi2B2C. The maximum at 7"c indicates the transition to superconductivity and the low-temperature upturn is related to magnetic ordering. The solid line is calculated taking into account contributions from phonons and crystal field levels (b) specific heat of TmNi2B2C at low temperatures with a maximum at Tn (after Movshovich et al. 1994). 

Figure 86 Crystal field levels of regular stereometries in units of Dq Table 69 Theoretical Calculations of the Electronic Properties of CunX Chromophores...

The charge transfer spectrum below 50,000 cm.-1 is due to the promotion of an electron from the oxygen tt orbital (ej) to the crystal field levels ba and e,. Denoting the inner core [Pg.231]

Investigate the effect of spin-orbit coupling on the crystal-field levels of a Ce3+ ion substituting for Ca2 + in CaF2 with a nearest-neighbor O2 ion (see Problem 7.2). Is any further splitting of these levels to be expected if the site symmetry at Ce3+ is lowered to Cs by a further crystal-field perturbation that is weaker than //s.i. ... 

The experimental excess heat capacity thus obtained as the difference between measured Cp and Qat can then be compared to the values calculated from the crystal field levels. As an example, fig. 7 shows the good agreement of the experimental and calculated excess heat capacity of DyF3. 

If the energy of the crystal-field splitting AEcf produced by the Bq parameters is much smaller than the thermal energy (kT 200 cm-1 at 300 K), all the crystal-field levels of the ground state have comparable thermal populations and the T 2 term of the power series is adequate for modeling the magnetic anisotropy (Bleaney, 1972 Mironov et al 2002). Substitution of eqs. (35)-(37) into eq. (28) gives eq. (40) in terms of Aq2 r2) which can be transformed into eq. (41) with conventional B2 parameters... 

In the next section the rare-earth compounds that have been studied by optical means under pressure so far will be reviewed. Then, after a brief introduction of the most commonly used high pressure device, the diamond anvil cell, sect. 4 presents a discussion of the pressure-induced changes of the crystal-field levels and their interpretation. In sects. 5 and 6 some aspects of the dynamical effects under pressure are discussed. These include lifetime and intensity measurements, the influence due to excited configurations and charge transfer bands, and the electron-phonon coupling. 

In sect. 4.1 the one-electron crystal-field model for the f configurations was introduced. Though this model is very successful in providing a description of the crystal-field splittings, certain anomalous multiplets are poorly fitted. Prominent examples are the Di multiplet of Pr3+, the 2H(2)n/2 multiplet of Nd3+, and the 3Ks multiplet of Ho3+. Almost independent of the host crystal, the calculated crystal-field levels of these multiplets show a much larger deviation from the experimental ones than all the other levels. 

Fig. 10. Effect of pressure on the 4F3/2 crystal-field levels in YAIO3 and Y3AI5O12- The solid lines are polynomial fits to the data (from Hua and Vohra (1997)).

Gorller-Walrand and Binnemans (1996) have compiled the most complete listing of 4f-electron crystal field parameters across the lanthanide series. However, additional high quality crystal field level measurements for individual ions have been made since 1996 (see, for examples (De Leebeeck et al., 1999), for Nd LiYF4, or (Wegh et al., 2003), for Er LiYF4). 

Note Only partial crystal field levels were determined for 7F5 and 7F( -, because of the extremely weak intensity of the corresponding emission lines. 

One can assign the site symmetry by determining the number of crystal field levels of different electronic states, the polariza-... 

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