Free-ion energy levels

Lcted free-ion energy levels in the 5f -configuration, vf + through Am + and the overlapping range of the f- 5fN ld transitions. 

When an f-element ion is embedded in a crystal, the free-ion energy levels, characterized by the total angular momentum J, are affected in two different ways. On one hand the energy... 

An array of charges in a crystal produces an electric field at any one ion, the so-called crystalline electric field. The presence of this field causes a Stark splitting of the free ion energy levels which results in a substantial modification of magnetic, electrical and thermal properties of the material. The theory of the crystal field and its interpretation in terms of group theory are originally due to Bethe (16). 

The field of lathanide lasers is mature but not exhausted. Additional laser schemes and materials will undoubtedly be exploited. There are 1639 free-ion energy levels associated with the 4fn electronic configurations of the thirteen trivalent lanthanides. Yet, of the 192,177 possible transitions between pairs of levels, by mid-1979 only 41 had been used for lasers. It is certain that given suitable pump sources and materials, stimulated emission involving many... 

Bethe ( 4) pointed out that when the free-ion is put into a crystal the electric fields distort the isotropy of free space. This causes a splitting in the free-ion energy levels, with any residual degeneracy determined by the symmetry of the crystal. 

This basic parameterization scheme, used at the time of the last A.C.S. symposium on lanthanide and actinide chemistry ( 5), has been discussed in detail by Wybourne 06). In applying the scheme, the free-ion Hamiltonian was first diagonalized and then the crystal-field interaction was treated as a perturbation. This procedure yielded free-ion energy levels that frequently deviated by several hundred cm from the observed energy levels.a In addition, the derived parameters such as the Slater radial integral, f(2), and the spin-orbit radial integral did not follow an expected systematic pattern across the lanthanide or actinide series ( 7). ... 

The free-ion energy levels up to approximately 30000 cm for all of the tripositive lanthanide ions in LaCl3 single crystals are shown in Figure 1. Crosswhite (16) has recently tabulated and discussed the free-ion and crystal-field parameters needed to describe the lanthanide data. The tripositive actinide levels are shown in Figure 2. Table I summarizes the free-ion parameters for the actinides which have been studied in detail. The detailed analyses of the U3+ and Np3+ ions have recently been completed (17, 18). The analyses presented in Table I for Pu3+, Am3+, and Cm3+ are based on published spectra (19, 20, 21, 22) obtained by Conway and coworkers. 

The wave functions used in the expressions for the line strengths are precisely those deduced by an analysis of the free-ion energy level structure. Therefore, only three new parameters, the s, have been introduced to account for the line strengths. This scheme has been remarkably successful in modeling experimental observations in both crystal and solution environments. It also accommodates the existence of the "hypersensitive" transitions. Peacock (30) has recently reviewed the field with regard to lanthanide f-f transitions. The simplicity of this scheme has been utilized by Krupke (31) and Caird (32) to predict potential laser transitions in the lanthanides. 

Figure 3. Intraconfiguration absorption spectra of the heavier tripositive actinide ions in aqueous solution. The vertical lines are the calculated positions of the free-ion energy levels. A broad background absorption has been subtracted from the data. No measurements have been obtained for fermium.

Excitation of these ions using 40,000 cm i energy results in various excited states for each ion. Each state relaxes by phonon processes until the terminal excited state is reached, from which emission of a visible photon results. But we need to remember that any time we put a trivalent rare earth ion into a host crystal to form a phosphor, we will modify its free-ion energy levels, depending upon the site symmetry and crystal field strength. 

Examine the diagram, given as 6.8.40 above, showing calculated free-ion energy levels again. For the most part, the energy levels are rather closely spaced. When an upper ener level of a rare earth ion in a crystal is excited, it may decay to a lower state by ... 

It drops off in relation to l/r3, the radius of the ion in the crystal. A three-body exchange process has too low a probability to be of practical value in an Anti-Stokes phosphor. If we reexamine the calculated free-ion energy level diagram, we notice that Yb3+ has a single energy level with no adjacent levels to which relaxation could occur. Therefore, if we add this ion to our material, we should be able to obtain a phosphor which functions as an Anti-Stokes material. The energy level of Yb3+ lies at 10,300 cm-i (9710 A). It just happens that the output of a GaAsrSi laser diode occurs at 9500 500 A. 

Fig. 1.5 Dieke s diagram free-ion energy levels of trivalent rare earth ions. Reproduced from Ref. [22] by permission of John Wiley Sons Ltd...

Kotzian (1991) and Kotzian et al. (1995) reported INDO/S-CI results for transition energies and relative oscillator strengths of the 4f—>4f excitations in the [R(H20) ] (R=Pr, Nd, Tm, n=8,9) complexes. These excitations are parity-forbidden for the free ion (Laporte selection rule), but may gain intensity due to admixture of opposite-parity character in a non-centrosymmetric environment The field of the water ligands leads only to a small perturbation of the free ion energy levels (Pr 4f, Nd 4f, Tm 4f ). Due... 

Comparison of energy-level model parameters (in cra ) used in calculating 3+ lanthanide and actinide free-ion energy levels for f through f configurations. Lanthanide parameters are from Carnall et al. (1989) and actinide parameters are from Carnall (1992), n denotes the number of 4f or 5f electrons. 

Only two studies of transcurium-ion fluorescence in solution have been published. Carnall etal. (1984) measured the absorption spectrum of Bk ", interpreted its energy-level structure in terms of a free-ion energy-level model, analyzed its absorption band intensities in terms of Judd-Ofelt theory, and reported luminescence lifetime data for aquated Bk in DjO. Beitz et al. (1983) carried out LIF studies on Es " in HjO and DjO solutions as well as complexed Es " in an organic phase. No luminescence studies have been reported for actinide elements heavier than Es. 

Fig. 16.7 Free-ion energy level structurefar An. The approximate extent of the crystal field splitting for certain low-lying levels is indicated.

Fig. 16.15 Absorption spectra of the quadrivalent actinide ions. Aquo-ion spectra are indicated for U, Np, and Pu, while the spectra of Am, Cm, and Bk are of solid AnF samples [112]. Estimated free-ion energy level structure is shown for first few excited states. See discussion in Section 16.4.3.)...

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