Crystal field interactions

Figure 9.7 Energy levels in (a) free and (b) Nd split by crystal field interactions...

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). 

The assumption of a large crystal-field interaction for Pu5+ spectra makes it necessary to conclude that while certain aspects of earlier free-ion estimates (37) are valid, the "assignment" of free-ion states to observed absorption bands was premature. Much of the structure must be due to crystal-field components of many free-ion groups that overlap in energy or to vibronic satellites similar to those encountered in CS2UCI6 (33). Thus, while the present computations would agree with earlier work in interpreting the levels observed in... 

S is the ionic spin and D, ID, and a are crystal field parameters describing the strength of the axial, the rhombohedral, and the cubic crystal field terms, respectively. The coordinate system of the cubic crystal field (ij, rj, g) may differ from that used to describe the axial and the rhombohedral crystal field interactions (x,y,z). 

The crystal field interaction gives rise to an energy splitting into a number of Kramers doublets. In the case of high-spin Fe " with spin S = 5/2, there are three Kramers doublets, each of which give rise to separate contributions in the Mossbauer spectra of samples with slow paramagnetic relaxation. For 1 = 0 and a = 0, they can be labeled l/2), 3/2) and 5/2). 

When the Zeeman energy is large compared to the crystal field interaction, the electronic wave functions are approximately the 5z) states with energy... 

In amorphous frozen solutions with only one type of species (e.g. [Fe(H20)g] ) the crystal field interaction of the Fe " ions may be similar, but the orientations of the crystal field axes in general differ. When magnetic fields are applied, this... 

The electron spin resonance (ESR) technique has been extensively used to study paramagnetic species that exist on various solid surfaces. These species may be supported metal ions, surface defects, or adsorbed molecules, ions, etc. Of course, each surface entity must have one or more unpaired electrons. In addition, other factors such as spin-spin interactions, the crystal field interaction, and the relaxation time will have a significant effect upon the spectrum. The extent of information obtainable from ESR data varies from a simple confirmation that an unknown paramagnetic species is present to a detailed description of the bonding and orientation of the surface complex. Of particular importance to the catalytic chemist... 

The crystal field interacts directly only with the orbital motion of the unpaired electrons and it has an effect on the electronic spins only through the spin orbit coupling. The strongest spin-lattice interaction will therefore occur for ions with ground states having an appreciable orbital character. 

If the atom or ion is situated in an environment of different atoms or ions, as, for instance, ions in a soUd, the surrounding hgands exert on it a further interaction, which is called the crystal field interaction Hcp and enters Eq. (9). One has to compare Hcf with Hi and H2, in order to decide whether it is or not a small perturbative term. In actinide solids, it is usually found that Hcf is of the same order of magnitude as Hi and H2, so that intermediate coupling schemes are necessary which include Hcf as well. (For a more exhaustive treatment of couplings in actinides, see Chap. D.)... 

The inclusion of the crystal field destroys the rotational symmetry of the ion and lifts the degeneracy of J levels (except of course Kramer s degeneracy) the only good quantum numbers will be T s, the irreducible representations of the point-group symmetry operation. If the crystal field interaction is comparable to J-J splitting (and we see from Table 2 that this is the case of actinides) it will also cause an admixture of different J multiplets. 

A further variation on the theme of emission is circularly polarized emission, where chiral interactions, for example between a lanthanide complex and a chiral ligand in solution, can be studied. Selection rules have been given619 based on S, L and / values for 4/states perturbed by spin-orbit coupling and 4/ electron-crystal field interactions, and four types of transition were predicted to be highly active chiroptically. These are given in Table 12. 

Fig. 9. Plot of the crystal-field interaction strength quantities ScF = g- +2X)m>0 l ml2]) f°r...

Recently, the 5-function model has also been employed to analyze high-pressure results on LaCl3 Pr3+ and LaCl3 Nd3+ (Burdick and Troster, 2003). This model assumes the dominant contributions to the correlation crystal field interactions arising from paired electrons within the same orbital. It has been shown that this model is capable to greatly improve the description of anomalous multiplets like the lT>2 multiplet of Pr3+ at ambient pressure (Burdick and Richardson, 1997). 

Since the 4F and 4f 15d configurations are of opposite parity, they are not mixed by the Coulomb interaction. However, these configurations can couple by means of the odd-parity crystal field interaction represented as... 

The crystal field interaction can be treated approximately as a point charge perturbation on the free-ion energy states, which have eigenfunctions constructed with the spherical harmonic functions, therefore, the effective operators of crystal field interaction may be defined with the tensor operators of the spherical harmonics Ck). Following Wyboume s formalism (Wyboume, 1965), the crystal field potential may be defined by ... 

For the 4f7 configuration of Eu2+, the host sensitive energy levels of the 4f65d states are not far from the metastable 4f7 6P7/2 multiplet near 27 000 cm-1. The strength of crystal field interaction determines whether the lowest 4f65d state is above or below the excited 4f7 multiplet, which is insensitive to host lattice. Because there is no 4f state below 6P7/2, strong blue luminescence arises from the parity allowed 4f55d-4f7 transition. The intensity of the... 

The f electrons within the 4fn configuration of the lanthanides have only weak interactions with the crystal field because they are shielded by outer 5s and 5p electrons. Consequently the spectra are dominated by transitions between the atomic states of the lanthanide ion. The left side of Figure 1 shows the ionic energy levels of Eu3+ in the gas phase. When the ion enters a crystal lattice, there will be additional crystal field interactions. The interactions cause small crystal field splittings on the order of 200 cm-1 that are superimposed on the atomic transitions and are easily observable. 

The d electrons within the dn electron configuration of the transition metals have much stronger interactions with the crystal field so crystal field interactions are comparable to the interactions within the atom. The spectral transitions can change more drastically to reflect the changes in the crystal field. The line-widths of the transitions are also much broader. Not all transition metals are useful as probe ions because the lines are too broad to allow one to resolve features in samples where there are multiple local environments about the ion. In fact, only some atomic states of the probe ions are useful because most states interact too strongly with the crystal field to give narrow enough lines. 

The 5fn electrons of the actinides represent an intermediate case where there is still shielding of the crystal fields but it is not as effective as in the lanthanides. The crystal field interactions are larger than the lanthanides but not as large as in the transition metals. The lines of most transitions are sharp and all the actinide ions could be used potentially as probes of the local environments of minerals. 

Energy level diagram for a octahedral complex, ignoring second-order crystal field interaction. 

For the weak field case, we have the situation where the crystal field interaction is much weaker than the electronic repulsion. In this approximation, the Russell-Saunders terms 3F, 3P, 1G, lD, and 5 for the d2 configuration are good basis functions. When the crystal field is turned on, these terms split according to the results given in Table 8.4.2 ... 

On the other hand, if spin-orbit coupling is larger than crystal field interaction, J is the quantum number that defines a state before the crystal field is turned on. For 4T>, we have J values of V2, IV2, 272, and 3 /2. In an octahedral crystal field, with the aid of Table 8.6.2, we can readily see that these states split into... 

Relative effects of spin-orbit coupbng and octahedral crystal field interaction on the electronic state 4D. 

One property of a transition metal ion that is particularly sensitive to crystal field interactions is the ionic radius and its influence on interatomic distances in a crystal structure. Within a row of elements in the periodic table in which cations possess completely filled or efficiently screened inner orbitals, there should be a decrease of interatomic distances with increasing atomic number for cations possessing the same valence. The ionic radii of trivalent cations of the lanthanide series for example, plotted in fig. 6.1, show a relatively smooth contraction from lanthanum to lutecium. Such a trend is determined by the... 

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