Lattice-mode vibrations

The sensitivity of lattice modes to structural changes is illustrated by the recent study of Mueller and Connor [25] on the effects of cyclohexane adsorption on the structure of MFI zeolites. The adsorption of molecules such as paraxylene and benzene into MFI zeolites causes a structural transition from monoclinic to orthorhombic symmetry, which has been characterized by X-ray powder diffraction and 29 si NMR spectroscopy [26]. Cyclohexane has a slightly larger kinetic diameter than benzene or paraxylene (0.60 nm compared with 0.585nm), but does not cause the same structural transition. Cyclohexane adsorption does however affect the zeolite lattice mode vibrational frequencies. Figure 7 shows spectra taken from reference 25 before and after (upper spectrum) adsorption of cyclohexane in a low aluminium MFI zeolite. 

One can also wonder, which is the original cause of the ferroelectric-para-electric phase transitions in KDP-type crystals the H-hopping or the vibrations (rotations) of the H-bonded molecules. It has been shown that the angular displacements and the H-sites are coupled, thus the vibrations of molecules destabilize and facilitate the H-hopping. This coupling is essential for understanding the interactions between the lattice-mode vibrations in crystals, and the transformations in hydrogen bonds. Also other features of the KDP crystals, like the existence of soft modes, can be explained in this way. 

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. 

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.

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. 

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... 

Summary. Coherent optical phonons are the lattice atoms vibrating in phase with each other over a macroscopic spatial region. With sub-10 fs laser pulses, one can impulsively excite the coherent phonons of a frequency up to 50THz, and detect them optically as a periodic modulation of electric susceptibility. The generation and relaxation processes depend critically on the coupling of the phonon mode to photoexcited electrons. Real-time observation of coherent phonons can thus offer crucial insight into the dynamic nature of the coupling, especially in extremely nonequilibrium conditions under intense photoexcitation. 

Figure 5.15 A two-dimensional center, showing a mode vibration destroying the inversion symmetry of the static lattice. The black circle represents the central ion (A), while the other circles represent the ligand (B) ions.

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). 

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. 

The vibration bands relative to phosphate groups in the apatite structure differ from the normal modes of the P04 isolated ion, due to distortions of the PO4 tetrahedra in the apatite lattice and vibrational coupling [4]. Therefore, site-group and factor-group analyses were applied [15,16,18,21] to elucidate the vibrational spectra observed (Fig. 5) and band assignments of infrared (IR) and Raman bands have been given (Table 3). 

Remarkably, the combined electronic-lattice mode vibronic level f8 x l obviously also needs a promotion of the complex by odd molecular vibrations in order to be detected in the d-d absorption spectrum. 

---