Vibrational modes octahedral site

If a diffusional model with AHm < kT is appropriate, then the time th between electron hops must approach the period cor of the optical mode vibrations that trap or correlate the electrons. With an wj = 10" s, the hopping time Th would be short relative to the time scale of Mossbauer spectroscopy, ca. 10" s. We can therefore anticipate an isomer shift for the octahedral-site iron that is midway between the values typical for Fe ions and Fe " " ions. From Table 1 and Eq. (1), we can predict a room-temperature isomer shift of 6 0.75 mm/s wrt iron. Consistent with this prediction is the... 

Fig. 47. Normal vibrational modes Qi and Qi compatible with Jahn-Teller splitting of the degenerate ground state of an octahedral-site 3d4 and 3d cation, (a) Definition of modes for a free ion complex. (See following pages for Figs. 47(b) and 47(c).)...

In principle it is necessary to study the lattice dynamics of the whole crystal in order to understand the vibronic features in the luminescence spectra of a centre in a crystal. However, due to the fact that the uranate group can be regarded as an isolated unit in the NaF crystal, the vibronic features in the luminescence spectra of the octahedral uranate group will be mainly due to localized vibrations, and as a starting point we will discuss the luminescence spectra in this section in the site model For an A2 A) transition vibronic coupUng occurs only with the E components of the r 3, r 4, Ps and vibrational modes. For an E A x transition vibronic coupUng might be observed with all the vibrational modes of the UOg complex. 

A successful instance of empirical correlation was found for the electron-vibrational coupling, between 2Eg and 4A2g-states on Mn4+, entering substitutionally for M in the octahedral sites of Cs2MF6 (M = Si, Ge, Ti, Sn, Zr) and M2SiF6 (M = K, Rb, Cs)121 . The Huang-Rhys number S appears in the intensity of the n th vibronic sideband of a progression as exp (— S)Sn/n . From comparison with his emission data at 80 °K Paulusz found a quadratic dependence of S on the estimated Mn—F distance for both Alg and vibrational modes in the former series of hosts and a virtual constancy for die latter series. 

Such terms are equivalent to those obtained by Satten et al. (1983) in their study of the excitations of the T,u vibrational mode of the octahedral complex UCI5 at 260 cm L They were aware that their approach would work in a similar way for lanthanide complexes their choice of an actinide was partly determined by their familiarity with the UClj complex. Another important consideration was the high symmetry of the uranium site, which greatly reduces the number of intensity parameters required in the analysis. To assess the situation we note first that the possible pairs (k,t) in expression (94) are (1,2), (3,2), (3,4), (5,4), (5,6) and (7,6). The number of Ti representations of 0(, that occur in the representations of 0(3) are 1, 1,2 and 2 for /c = 1, 3, 5 and 7, so we expect 9 parameters in all. Satten et al. (1983) reduced that number to 6 by carrying out a complete closure over all virtual electronic states, which has the effect of fixing the ratio of the two operators (94) for which t = /c 1. They were able to account quite well for the relative intensities of some 20 or so transitions of the type Aig( H4)-> T, ( Lj), where is a... 

The emission spectra of the europium(III) ion in Cs2NaEuCl6 and in Cs2Na(EUxYi-x)Cl6 (x = 0.01 and 0.1) have recently been reported by Serra and Thompson (1976). In this compound the rare earth ion is in a site of perfect octahedral symmetry and as a result of the inversion symmetry only magnetic dipole transitions are allowed. The usually more intense electric dipole transitions are replaced by weak vibronic transitions. In the doped compound all possible magnetic dipole,transitions between the levels (J = 0, 1, 2, 3) and the Fj levels (J = 0,1,2,3,4) have been observed. Weak additional lines on the magnetic dipole transitions and the weak vibronic lines have been correlated with the various vibrational modes of the compound. The emission spectra complement the absorption spectra determined earlier by Schwartz (1975) and illustrate how the two types of spectra can be used to obtain a more complete picture of the energy levels. 

For each of the ionomer systems studies as well as for cations in zeolites, the cation-motion bands are easy to identify, because they vary in frequency approximately as M"1, where M is the mass of the cation. However, M-i 1 clearly is not the correct complete reduced mass for the vibration, since that would require the site to be of infinite mass. A better approximation to the proper reduced mass, p, can be obtained by considering at least the atoms immediately surrounding the cation. Typically, p is calculated from models in which the cation has either an octahedral surrounding (for the T mode) or a tetrahedral surrounding (for the T2 mode). With it and the band frequency, the force field element, (force constant), for the vibration can be calculated. 

The vibrational spectra of alkali fluorometallates have been examined in considerable detail. In the hexafluorometallates Li2ZrFe and M2MF6 (M = Rb or Cs M = Zr or Hf) the octahedral [MFe] " anion occupies a site of Dsd symmetry, and consequently the triply degenerate normal modes [V3 V4 V5 (f2g) and (t2u) in Oh] are split into a and e components. Vibrational frequencies (Table 19) have been assigned on the basis of polarized Raman and polarized IR reflectance spectra of single crystals, and assignments have been confirmed by normal coordinate analyses. 

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