Lattice modes

The normal modes for solid Ceo can be clearly subdivided into two main categories intramolecular and intermolecular modes, because of the weak coupling between molecules. The former vibrations are often simply called molecular modes, since their frequencies and eigenvectors closely resemble those of an isolated molecule. The latter are also called lattice modes or phonons, and can be further subdivided into librational, acoustic and optic modes. The frequencies for the intermolecular modes are low, reflecting, the... 

The Raman and infrared spectra for C70 are much more complicated than for Cfio because of the lower symmetry and the large number of Raman-active modes (53) and infrared active modes (31) out of a total of 122 possible vibrational mode frequencies. Nevertheless, well-resolved infrared spectra [88, 103] and Raman spectra have been observed [95, 103, 104]. Using polarization studies and a force constant model calculation [103, 105], an attempt has been made to assign mode symmetries to all the intramolecular modes. Making use of a force constant model based on Ceo and a small perturbation to account for the weakening of the force constants for the belt atoms around the equator, reasonable consistency between the model calculation and the experimentally determined lattice modes [103, 105] has been achieved. 

The Raman spectroscopic work of Ja-covitz [31], Cornilsen et al. [32, 33], and Audemer et al. [34] is the most direct spectroscopic evidence that the discharge product in battery electrodes, operating of the pi ji cycle, is different from well-crystallized / -Ni(OH)2. The O-H stretching modes and the lattice modes in the Raman spectra are different from those found for well-crystallized Ni(OH)2, prepared by recrystallization from the ammonia complex, and are more similar to those... 

Figures 4 and 5 show the Raman and IR spectra of ce-Ss in the range up to about 100 cm A comparison of these spectra with those presented in Figs. 2 and 3 reveals that the linewidths are much smaller at low temperatures (ca. 0.02-0.2 cm ). The wavenumbers and assignments of the external and torsional modes as reported by Gautier and Debeau [106] and Becucci et al. [107] are listed in Table 3. The spectra in Figs. 4 and 5 clearly demonstrate that there is no gap between the external vibrations and the crystal components of the lowest internal vibration Vg. Moreover, at about 76 cm an IR active lattice mode appears between two components of the fundamental Vg at 74 cm and 79 cm respectively.

Fig. 20 Raman spectrum of solid 85 at -90 °C. The lines at 84 and 106 cm represent lattice modes [151]...

The intense yellow rodlike crystals of S14 contain molecules of approximate Cs symmetry on sites of Ci symmetry [165]. Their Raman spectra recorded at -100 °C exhibit the expected pattern Stretching modes give rise to lines between 440 and 485 cm. This rather narrow region reflects the very narrow bond distance distribution in S14 molecules (204.7-206.1 pm). As usual, the bending, torsional and lattice modes show up below 300 cm (see Table 11 and Fig. 26). 

Experimental studies of liquid crystals have been used for many years to probe the dynamics of these complex molecules [12]. These experiments are usually divided into high and low-frequency spectral regions [80]. This distinction is very important in the study of liquid crystalline phases because, in principle, it can discriminate between inter- and intramolecular dynamics. For many organic materials vibrations above about 150 cm are traditionally assigned to internal vibrations and those below this value to so-called lattice modes . However, the distinction is not absolute and coupling between inter- and intramolecular modes is possible. 

Fig. 19. Low-temperature (20 K) resonance Raman spectra of dithionite-reduced P. furiosus 3Fe Fd as a function of excitation wavelength (.191). The asterisk indicates a lattice mode of ice.

Spectral Region Probed Limited to 4000-1200 cm" from Absorption by Lattice Modes of Solid 4000-400 cm"" Only Spectral Limitations are Imposed by Spectrometer... 

The infrared spectra for various aluminum oxides and hydroxides are shown in Figure 3. Figure 3a is a-alumina (Harshaw A13980), ground to a fine powder with a surface area of 4 m /g. The absorption between 550 and 900 cm is due to two overlapping lattice modes, and the low frequency band at 400 cm is due to another set of lattice vibrations. These results are similar to those obtained by reflection measurements, except that the powder does not show as... 

In the condensed phase the sum is over all 3n frequencies, but in the ideal vapor phase the six external (zero) frequencies do not contribute to the IE s, the sum is over the remaining 3n — 6 internals. For condensed rare gases the harmonic assumption is highly approximate, and this is also true for the lattice modes of polyatomics. However as molecular size increases the relative contribution of the external modes becomes less and less important relative to internals. 

Figure 5.4. Resonance Raman spectra of [Fe2S2] centers in A. vinelandii. A, NifU as isolated. B, D37A NifU-1 as isolated. C, NifU-1 repnrified after NifS-mediated cluster assembly. D, IscU containing two [Fc2S2] clnsters per dimer pnrified fraction after IscS-mediated clnster assembly. All spectra were recorded nsing 457-nm excitation at 17 K and with 6cm resolntion. Vibrational modes resnlting from lattice modes of ice have been snbtracted.

On the other hand however, the cluster-anions P7 and Pii are thermally remarkably stable. In the condensed state (in the crystal as well as in melts), the characteristic vibrations can be observed both in i.r. spectra and in Raman spectra upto temperatures of 900 K (25, 26,27). As an example, the Raman spectra of Ha3P7 in Figure 7 clearly show that the typical cluster-vibrations of the P7 -anion are maintained up to the region of the plastic phase, although the absorption bands become increasingly broader and less distinct with temperature. The lattice vibrations at 50-100 cm " behave completely differently. As expected they disappear at the transition to the plastic phase. Completely unexpected however, they remain sharply resolved up to the critical temperature Tc. This effect can be connected with the presence of two undamped lattice modes (25). 

Quenching of narrow-line emissions (as observed for many Ln3+ ions) has been explained by phonon emission to the lattice modes. Moos and co-workers (60) and others (67) have given many examples. Usually the nonradiative rate is described by Kiel s formula (62) for a single-frequency p-phonon process,... 

In many cases it is possible to differentiate between the so called internal vibrations, those vibrations within the coordination polyhedron, and the external vibrations or lattice modes. The lattice modes can be of either the hbrational or translational type. 

The vibrational spectra of inorganic molecular crystals of binary compounds of the type AB and AB2, as well as ionic crystals of complex anions and cations, have been studied recently under pressures up to 70 Kbar (217—219). By this technique it is possible to differentiate between internal and lattice vibrations (220) since lattice modes have a greater dependence on pressure. 

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