Crystal splitting effects

In principle this crystal splitting effect occurs for every vibration when there is more than one molecule per unit cell but frequently the amount of splitting is too small to be noticed because of the weak coupling between nonbonded atoms in different molecules in the unit cell. 

Crystal field effects are of the order of the free ion interaction thus they cannot be treated as a small perturbation as in the lanthanides. Whereas the crystal field splitting in the oxidation state +3 is comparable to that for the lanthanides, it is significantly increased in the progression... 

All lanthanide ions, with the exception of gadolinium(III) and europium(II), are likely to be relaxed by Orbach-type processes at room temperature. In fact, the f" configurations n l) of lanthanides(III) give rise to several free-ion terms that upon strong spin-orbit coupling, provide several closely spaced energy levels. Table III reports the multiplicity of the ground levels, which varies from 6 to 17, and is further split by crystal field effects. 

An appreciation of the crystal field effect on the vibrations of the Bravais cell which is repeated to build the crystal is extremely important when interpreting the vibrational spectra of many substances, since in the presence of a crystal field influence the number of observed bands in the spectrum cannot be directly determined from the formula unit which goes to make up the unit cell. In other words, there is almost always a larger number of bands to account for when investigating solid state samples. The solid state effects often cause degenerate bands to split in the same degree as symmetric and antisymmetric stretching modes split. 

The point symmetry of the octahedral sites in the spinel-structure is Dsd- While the octahedra are perfect for an oxygen parameter u of 3/8, they are compressed along a threefold axis for u < 3/8, and expanded for u > 3/8. In the case of MgCr204 ( a0,385) and MgAl204 (21 = 0,387) ( normal spinels with Mg + in tetrahedral and Cr +, Al + in octahedral sites), the expansion is of the magnitude of about 4 to 5%. The corresponding splitting effects of the second absorption band in the remission spectra of the mixed-crystal powders (Mg)( > (Cr jAL-x) O4 (13) are about... 

In a later study, Wang and Lunsford (263) used the alkaline-earth zeolites to determine whether any systematic change in the crystal field effect on the adsorbed Oj species could be detected as the cation is varied from Mg2 + to Ba2 +. The results show that three or more different adsorption sites are present on each of the cationic zeolites and that there is no significant trend in the energy splitting of the nt levels of the Oj ion as one goes from Mg2 + to Ba2+. 

A general model for electronic relaxation of the Gd3+ S = 7/2 ion in various complexes in solution was presented by Rast el al. [86]. Contrary to the usual assumption, the electronic relaxation in their model is not only due to the effects of the transient zero field splitting, but is also strongly influenced by the static crystal field effect which is modulated by the random Brownian rotation of the complex. Experimental peak-to-peak widths of three gadolinium complexes could be well interpreted as a function of temperature and frequency using three static and one transient crystal field parameters. Moreover, their interpretation of experimental data did not require the addition of any field independent contribution to the line width like the spin-rotation mechanism. 

ESR detects a splitting of the Lande factor below 140 K, as is represented in Fig. 6 at T=40 K, consistent with a static JTD [13]. The largest value of the 0-tensor (gzz) was not found parallel to the tetragonal c-axis,suggesting that the direction of elongation is dictated by molecular symmetry and not crystal field effects. The two other values of the 0-tensor are similar, as expected for axial symmetry, but not strictly equal, leading Bietsch et al. [13] to conclude in favor of a D2h distortion. 

Several theories have been developed to explain how energy absorbed by one molecule is transferred to a second acceptor molecule of the same or a different species. At first sight exciton theory,20 66 which accounts for excitation transfer in molecular aggregates or crystals and the Davydov splitting effects connected with it, appears to bear little relationship to the treatment of long-range resonance transfer as developed, for example, by Forster.81-32 However, these theories can be shown to arise from the same general considerations treated at different well-defined mathematical limits.33-79... 

Today, we do not know the physical reason why there may be more than one asymmetric unit in the unit cell, nor do we have definite answer to the question When is the symmetry of the free molecule reduced by the condensation into a solid and when is this symmetry preserved Typical examples are the substituted 2,4,6-trichloro-l-X-benzenes. The symmetry of the gaseous molecule is preserved in the solid in so far as the Cl atoms in positions 2 and 6 are crystallographically equivalent for X = N02 and X = Br. Sites 2 and 6 of the molecule, however, are inequivalent in the solid for X = I, Cl, OH, and all other compounds for which the NQR spectrum is known. In the vast majority of molecules, the symmetry is reduced by condensation. We shall take the frequency splitting of NQR resonances due to this breakdown of symmetry as a qualitative measure of the crystal field effect. 

We have already considered the multiplicity of asymmetric units and shall now discuss the positioning of chemically equivalent atoms at different point positions. Table III.4 shows the splitting of the 3SC1 NQR frequencies at 77 °K in benzene derivatives 126>. Only substances with one asymmetric unit in the unit cell are considered. One recognizes the spread of the frequencies for chemically equivalent chlorine atoms. The crystal field effect Av is within the limit of Av % 500 kHz. 

Muller et al. (206) have been concerned with the Lii ni white lines for Ca, Ti, Cr, Co, and Cu and LHi white lines for Sr, Zr, Nb, Ru, Rh, and Pd. In the latter series the shape of the white lines with increasing atomic number is determined by (i) the narrowing and increase of the 4d density of states and (ii) progressive filling of the 4d band. Crystal structure effects are much less conspicuous in the L-edge spectra than in the K-edge spectra. The shapes of the individual L, white lines of the 3d elements Ca, Ti, Cr, Co, Ni, and Cu are similar to those encountered in the 4d series, but the 2p1/2-2p3/2 spin-orbit splitting here is so small (from 6 eV for Ca to 20 eV for Cu) that the Lji and LfH spectra are superimposed. The relative size of the Lm and L white lines follows approximately the multiplicity ratio 2 to 1 of the 2p3/2 and 2pi/2 core states. 

The symmetry around the dimer is, however, usually low in crystals. The degeneracy of configurations (a) and (b) in Fig. 9, therefore, is removed by an environmental effect, which is sometimes called a site-splitting effect. The presence of two non-equivalent configurations in crystals has been confirmed by X-ray and neutron diffraction experiments. Although the... 

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