Framework vibrations modes

Raman spectra of hydrazine (a) and of the kaolinite-hydrazine (KH) intercalate (b) suspended in liquid hydrazine are shown in Fig. 1. In contrast to the strong IR-active absorption bands characteristic of clay minerals below 1200 cm-1, the corresponding Raman bands of kaolinite are relatively weak. Nonetheless, both the kaolinite and the hydrazine bands can clearly be resolved (Fig. lb). Hydrazine bands occur at 903,1111,1680, 3200,3280, and 3340 cm-1, whereas the kaolinite bands are found at 140 (not shown), 336, 400, 436, 467, 514, 636, 739, 794, and 3620 cm-1. Observation of lower-frequency adsorbate modes below 1200 cm-1 are often obfuscated in IR absorption spectra because of the strong lattice- framework vibrational modes. As the Raman spectrum of the KH complex shown in Fig. la indicate, the lower-frequency modes of hydrazine below 1200 cm-1 can readily be resolved. The positions of die hydrazine bands in the KH spectrum (Fig. lb) are similar to those of liquid hydrazine (Fig. la) and agree well with published vibrational data for hydrazine (22.23.29-31). The observed band positions for the KH complex, for hydrazine, and for kaolinite are listed in Table 1. 

Further support for the direct relationship of the 960 cm-1 band to the presence of 4-coordinated Ti atoms in the framework of TS-1 came from the photoluminescence investigations of Soult et al. (94). At 12 K, an emission band was observed at 490 nm, which was unequivocally attributed to titanium (Section II.A.4). This band showed a resolved vibrational structure of 966 24 cm-1, which clearly demonstrates that Ti is involved in the corresponding vibrational mode. 

They concluded that the infrared spectrum contained vibrational modes from both structure insensitive internal tetrahedra and structure sensitive external linkages. The exact frequency of these bands depends on the structure of the zeolite as well as its silicon to aluminum raho (Si/Al). A typical framework IR spectrum for a Y zeolite sample is shown in Figure 4.17. The accepted band assignments and frequency ranges are shown on the figure. 

Some vibrational modes of zeolites are sensitive to the amount of aluminum in the framework [93]. The substitution of aluminum for silicon atoms in the zeolite framework changes the T-O-T bond angles (where T is a tetrahedral atom that can be either Si or Al). This is primarily due to the smaller size and different charge density of the aluminum atoms compared to silicon. This results in a shift in frequency for vibrational modes in the zeolite due to external linkages. The T-O-T asymmetric (1100-980 cm ) and symmetric (800-600 cm ) stretching modes as well as structural unit vibrations Mke double four- and double six-rings exhibit a shift to lower frequencies as the aluminum content of the framework is increased. Figure 4.19 shows this relationship for a faujasite-type framework. 

In a study on acid-leached mordenites, Vansant and coworkers found a linear correlation between the frequency of a skeletal vibration mode and the framework... 

Figure 4.19 Frequency dependence on mole fraction of framework aluminum for various vibrational modes ofX and Y zeolites. D6R means double six-ring, and Uj are the...

The quantum alternative for the description of the vibrational degrees of freedom has been commented by Westlund et al. (85). The comments indicate that, to get a reasonable description of the field-dependent electron spin relaxation caused by the quantum vibrations, one needs to consider the first as well as the second order coupling between the spin and the vibrational modes in the ZFS interaction, and to take into account the lifetime of a vibrational state, Tw, as well as the time constant,T2V, associated with a width of vibrational transitions. A model of nuclear spin relaxation, including the electron spin subsystem coupled to a quantum vibrational bath, has been proposed (7d5). The contributions of the T2V and Tw vibrational relaxation (associated with the linear and the quadratic term in the Taylor expansion of the ZFS tensor, respectively) to the electron spin relaxation was considered. The description of the electron spin dynamics was included in the calculations of the PRE by the SBM approach, as well as in the framework of the general slow-motion theory, with appropriate modifications. The theoretical predictions were compared once again with the experimental PRE values for the Ni(H20)g complex in aqueous solution. This work can be treated as a quantum-mechanical counterpart of the classical approach presented in the paper by Kruk and Kowalewski (161). 

However, the influence of the exchangeable cation on the framework vibrations has not been systematically investigated. From x-ray diffraction studies (2) on zeolites it is known that most of the exchangeable cations are firmly bound onto the negatively charged framework. Therefore these cations might have some influence on the lattice vibrational modes. 

The exchangeable monovalent cations have a marked influence on the framework vibrations of hydrated Linde A and X. For some vibrational modes the frequency shifts appear to give a quantitative measure of the interaction between cations and lattice. A regularity is found for Li+, Na+, Ag+, K+, and T1+ exchanged forms which implies a similar distribution of cation sites for both zeolites. It is further deduced that in the Cs+ and Rb+ exchanged forms there is only a relatively weak interaction between the cations and the zeolite framework. This technique can be readily extended to study cation siting in other zeolites in both hydrated and dehydrated forms. 

In Section 1.4, we analyzed the vibration modes of solids. These vibrations are in the majority of cases active in the IR region and their study provides information about the structure of the material under investigation. However, the bands related with the solid framework of a material in the middle IR region, which is the region where normally the majority of commercial equipment works, are broad bands with not much information. Nevertheless, always some information can be obtained. In addition, occasionally included in solids are molecules that can be studied with IR spectroscopy, such as occluded molecules, adsorbed molecules, OH groups, and other molecular features. These molecular features are normally of polyatomic character and can be studied with the help of IR spectroscopy. 

The basic theoretical framework for understanding the rates of these processes is Fermi s golden rule. The solute-solvent Hamiltonian is partitioned into three terms one for selected vibrational modes of the solute, including the vibrational mode that is initially excited, one for all other degrees of freedom (the bath), and one for the interaction between these two sets of variables. One then calculates rate constants for transitions between eigenstates of the first term, taking the interaction term to lowest order in perturbation theory. The rate constants are related to Fourier transforms of quantum time-correlation functions of bath variables. The most common... 

Thus 28 IR active modes are expected to fall in the regions of the vibrations of the orthosilicate anions. Of these, we can expect five modes associated with V3 (asymmetric stretching) and two modes associated with Vi (symmetric stretching), three modes associated with the symmetric deformation (V2) and five with the asymmetric deformation V4, four hindered rotations, four hindered translations, and, finally, five modes associated with Al—O tetrahedra. We actually observe at least 10 components for framework vibrations. Additionally, the low-frequency modes of Na ions are expected to fall in the FIR region [68], where several bands are indeed observed. 

Our aim is to describe the extent and rate of vibrational energy flow in molecules with perhaps tens of vibrational modes. We do this within the framework of an... 

Another factor of which a nonclassical theory must take account is the quantisation of the internal modes of D and A, and the consequent relaxation of the Bom-Oppenheimer constraint that the electron must transfer within a fixed nuclear framework. In classical theory, the vibrational modes of D and A are treated as classical harmonic oscillators, but in reality their quantisation is usually significant (that is, one or more of the vibration frequencies v is sufficiently high that the classical limit hv IcT does not apply). Electron transfer then requires the overlap, not only of the electronic wavefunctions of R and P, but also of their vibrational wavefunctions. It is then possible that nuclear tunnelling may assist electron transfer. As shown in Fig. 4.12, the vibrational wave-functions of R and P extend beyond the classical parabolas and overlap to some extent. This permits nuclear tunnelling from the R to the P surface, particularly in the region just below the classical intersection point. Part of the reorganisation of D and A, required prior to ET in the classical picture, may then occur simultaneously withET, by the nuclei tunnelling short (typically < 0.1 A) distances from their R to their P positions. 

This chapter is devoted to recent developments in a class of approximation methods that aim at describing the energy-level structure and dynamics of energy transfer in vibrationally highly excited polyatomic systems. The meth ods that are the subject of the present study are the self-consistent-field (SCF) approximations, in which framework each vibrational mode is described as moving in an effective field obtained by averaging the full potential function... 

XRD Diffraction Technique using Rietveld refinement approach and infirared spectroscopy of hydroxyl groups and vibrational mode appear to be the key methods to determine if a foreign element has been incorporated at substitutional sites of the framework. 

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