Vibrational Spectra of Crystals

The symmclry of a molecule may be the lowest in solution (or liquid) because it interacts with randomly oriented molecules. 

To analyze the spectra of crystals, it is necessary to carry out the site group or factor group analysis described in the following subsection. 

The vibrational spectra of calcite and aragonite crystals are markedly different, although both have the same composition (Sec. 11-4). This result can be explained if we consider the difference in site symmetry of the CO, ion between these crystals. According to X-ray analysis, the space group of calcite is Djd and Z is tv o. Halford s table gives 

Since C is not a subgroup of D,, the site symmetry of the CO, ion in aragonite must be C,. Thus the D,fc symmetry of the CO ion in an isolated state is lowered to D3 in calcite and to C, in aragonite. Then the selection rules are changed as shown in Table 1-12. 

There is no change in the selection rule in going from the free COs ion to calcite. In aragonite, however, r, becomes infrared active, and and each 

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The effect of intermolecular interactions on molecules in the crystalline state (where such interactions are most specific) is best approached by a consideration of the vibrational spectra of crystals. The solution to this problem proceeds in a manner similar to that for a molecule. The potential energy, which is of salient interest here, is given by [Hornig (50)]... 

Vibrational spectra of crystals from a chemical point of view... 

BIPHONONS AND FERMI RESONANCE IN VIBRATIONAL SPECTRA OF CRYSTALS... 

Effects of strong anharmonicity in vibrational spectra of crystals... 

The study of bound states of optical phonons or, stated more generally, the study of the effects of strong anharmonicity in the vibrational spectra of crystals, has grown out of the development of modern solid-state physics and to no less extent, it was motivated by the requirements of experiment. 

Agranovich, V. M. (1983). Biphonons and Fermi resonance in vibrational spectra of crystals. In Spectroscopy and Excitation Dynamics of Condensed Molecular Systems. Edited by V. M. Agranovich and R. M. Hochstrasser. North-Holland, Amsterdam, pp. 83-138. 

Let us consider in more detail the peculiarities of the vibration spectra of crystals, limiting the investigation to ion oscillations, mainly in cubic crystals. 

The fundamental vibrational spectra of crystals are properly interpreted on the basis of normal vibrations of the crystal as a whole. They are usually described as one- or multi-phonon transitions. These are governed by the laws of conservation of energy and wavevector in the photon-phonon system, e.g., for one phonon transition this latter rule allows only transitions creating phonons with the wavevector q = 0. In addition to these fundamental rules, there are selection rules based on symmetry considerations. For example, in elemental crystals which contain only 2 atoms per unit cell (such as Ge) the one optical phonon transition is forbidden (see Zallen (1968)). 

It is not possible to transfer these considerations to noncrystalline solids because here the concepts used in the crystal are not meaningful. A rigorous general theory applicable to highly disordered structures, such as amorphous semiconductors, is not available. Taylor s (1967) work on the vibrational spectra of crystals with large defect concentration may be a step towards such a theory. Under these circumstances two approximate methods may be useful distorted lattice model and localized model. 

Raman spectroscopy is particularly useful for investigating the structure of noncrystalline solids. The vibrational spectra of noncrystalline solids exhibit broad bands centered at wavenumbers corresponding to the vibrational modes of the corresponding crystals (Figure 5). In silicate glasses shifts in the high-wavenumber bands... 

Crystal field aspects of the vibrational spectra of metal complexes. D. A. Thornton, Coord. Chem. Rev., 1984,55,113-149 (66). 

The first Raman and infrared studies on orthorhombic sulfur date back to the 1930s. The older literature has been reviewed before [78, 92-94]. Only after the normal coordinate treatment of the Sg molecule by Scott et al. [78] was it possible to improve the earlier assignments, especially of the lattice vibrations and crystal components of the intramolecular vibrations. In addition, two technical achievements stimulated the efforts in vibrational spectroscopy since late 1960s the invention of the laser as an intense monochromatic light source for Raman spectroscopy and the development of Fourier transform interferometry in infrared spectroscopy. Both techniques allowed to record vibrational spectra of higher resolution and to detect bands of lower intensity. 

Cyc/o-Undecasulfur Su was first prepared in 1982 and vibrational spectra served to identify this orthorhombic allotrope as a new phase of elemental sulfur [160]. Later, the molecular and crystal structures were determined by X-ray diffraction [161, 162]. The Sn molecules are of C2 symmetry but occupy sites of Cl symmetry. The vibrational spectra show signals for the SS stretching modes between 410 and 480 cm and the bending, torsion and lattice vibrations below 290 cm [160, 162]. For a detailed list of wavenumbers, see [160]. The vibrational spectra of solid Sn are shown in Fig. 23. 

The other technique is HREELS (high resolution EELS) which utilises the inelastic scattering of low energy electrons in order to measure vibrational spectra of surface species. The use of low energy electrons ensures that it is a surface specific technique, and is often chosen for the study of most adsorbates on single crystal substrates. 

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. 

In this review, the vibrational spectra of solid chalcogenometallates are presented and a critical discussion of the results given. Initially, measurements of powdered, crystalline samples with isolated ions or molecules are presented followed by single crystal Raman studies which are rarer. Additionally, a group of topics including the interpretation of Raman band intensities and widths. Resonance Raman spectra, the influence of pressure, temperature and sample preparation will be discussed. 

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. 

Donovan, B., Angress, F. Lattice vibrations. London Chapman and Hall 1971. Turrell, G. lniia.red and Raman spectra of crystals. New York Academic Press 1972. Fateley, W. G., Dollish, F. R., McDevitt, N. T., Bentley, F. F. Infrared and raman selection rules for molecular and lattice vibrations The correlation method. New York J. Wiley 1972. 

Vibrational spectra of solid samples are also influenced by the packing of the molecules in the crystal lattice. For instance, the spectra of orthorhombic a-Sg and monoclinic P-Sg are somewhat different. Thus it was found by Raman spectroscopy that Sy crystallizes as four and S, as two allotropes which consist of identical molecules but must have different crystal structures. 

Spectroscopic (MS, NMR, IR) studies of quinoxalines were conducted . The structure and vibrational spectra of 2,3-bis(2-pyridyl)quinoxaline (bpq) and 2(A -methylpyridyl)-3-pyridylquinoxaline (meppq) useful for building blocks for dendrimers were measured by crystal X-ray diffraction and IR spectral experiments, respectively <2002JMT(589/90)301>. Those results were compared with ones calculated from the ab initio Hartee-Fock and the hybrid density functional methods. 

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