Crystal, vibrational spectra

F. Fillaux, M.H. Limage F. Remain (2002). Chem. Phys., 276, 181-210. Quantum proton transfer and interconversion in the benzoic acid crystal vibrational spectra, mechanism and theory. 

Keywords Cubic crystal Vibrational Spectra Luminescence Absorption Crystal Field ... 

Since then, the vibrational spectrum of Ss has been the subject of several studies (Raman [79, 95-100], infrared [101, 102]). However, because of the large number of vibrations in the crystal it is obvious that a full assignment would only be successful if an oriented single-crystal is studied at different polarizations in order to deconvolute the crystal components with respect to their symmetry. Polarized Raman spectra of samples at about 300 K have been reported by Ozin [103] and by Arthur and Mackenzie [104]. In Figs. 2 and 3 examples of polarized Raman and FTIR spectra of a-Ss at room temperature are shown. If the sample is exposed to low temperatures the band-widths can enormously be reduced (from several wavenumbers down to less than 0.1-1 cm ) permitting further improvements in the assignment. 

Weishaupt, M. and Strahle, J. (1976) Crystal structure and vibrational spectrum of tetraamminegold(III) nitrate. Zeitschrijifur Naturforschung, B31, 554-557. 

The damping of such vibrations may also heat the detectors. For this reason, the vibration spectrum of the cryostat has been measured with piezoelectric accelerometers placed on the 1 K pot, the Still, the mixing chamber and the crystal copper frame [98],... 

Molecules, in general, have some nontrivial symmetry which simplifies mathematical analysis of the vibrational spectrum. Even when this is not the case, the number of atoms is often sufficiently small that brute force numerical solution using a digital computer provides the information wanted. Of course, crystals have translational symmetry between unit cells, and other elements of symmetry within a unit cell. For such a periodic structure the Hamiltonian matrix has a recurrent pattern, so the problem of calculating its eigenvectors and eigenvalues can be reduced to one associated with a much smaller matrix (i.e. much smaller than 3N X 3N where N is the number of atoms in the crystal). 

I think the very simplicity of the system, and the simplicity in the study of the crystal structure, suggests that people would do well to look very closely at the vibrational spectrum of the crystal and at the details of the electron transfer in that system. 

Crystals lack some of the dynamic complexity of solutions, but are still a challenging subject for theoretical modeling. Long-range order and forces in crystals cause their spectrum of vibrational frequencies to appear more like a continuum than a series of discrete modes. Reduced partition function ratios for a continuous vibrational spectrum can be calculated using an integral, rather than the hnite product used in Equation (3) (Kieffer 1982),... 

With further increase of the concentration (in p, phase range for H cLii cNb03) many new bands were observed. The fact that the low concentration boundary of the P phases is approximately x = 0.5 leads to the assumption for some kind of ordering of Li and as reported. On one hand, it can be assumed that the protons form a (nearly) ordered sub-lattice. Such a structure would have a phonon spectrum different from that of a pure LiNbOs, see . On the other hand, the PE probably leads to a reduction of the crystal symmetry, i.e. due to the incorporation of H, the two Li sites in the unit cell may become non-equivalent. In such case, the symmetry would be reduced from Csv to C3. As a result, the number of molecules per unit cell would remain the same, but new bands would appear in the vibration spectrum. 

The vibrational entropy (AAAB,vibr) contributing to the bulk entropy of defect process arises from the variation of the vibrational spectrum of the crystal in the neighborhood of the associate ... 

As the interpretation of the vibrational spectrum of sohd state samples can provide information concerning the cation-anion interactions, it is of special interest to the chemist. In some cases information about the crystal structure can be obtained from the interpretation of spectra of the solid state when the substance possesses an anion of high symmetry. 

Diamond is crystallized in cubic form (O ) with tetrahedral coordination of C-C bonds around each carbon atom. The mononuclear nature of the diamond crystal lattice combined with its high symmetry determines the simplicity of the vibrational spectrum. Diamond does not have IR active vibrations, while its Raman spectrum is characterized by one fundamental vibration at 1,332 cm . It was found that in kimberlite diamonds of gem quality this Raman band is very strong and narrow, hi defect varieties the spectral position does not change, but the band is slightly broader (Reshetnyak and Ezerskii 1990). 

Several other heteropolytungstates are known or presumed to have the Keggin structure (Table 6). Two 12-tungstoborates have been known for over a century, but these prove not to be simple a or (S isomers. The anion a -[BWi2O40]5 " seems to be an undoubted Keggin species based on isomorphism, vibrational spectrum and its behavior upon reduction. Tlie second isomer ( h ), crystallizing as the acid in hexagonal crystals, clearly is not a /3 isomer for its... 

We commence our discussion with a consideration of the vibrational spectrum of the much-studied cyclohexane molecule when adsorbed on various metal surfaces. The majority of published papers have been concerned with adsorption on metal single-crystal faces. 

It should be noted that the degree to which the vibrational spectrum of a molecule in a site of low symmetry will deviate observably from the behavior of the free molecule depends on just how strongly the molecule interacts with it surroundings in the crystal. Symmetry considerations alone can of course tell us nothing about this, and the degree of deviation varies from one case to another. A few examples now to be considered will give some indication of the magnitude of such effects in these typical cases. 

Protonation of 21 yields H2Os,0C(CO)24 (5 7). The crystal structure of the dihydride has not been determined, but analysis of the vibrational spectrum of the cluster in the region associated with motion of the interstitial carbon atom has led to the conclusion that the symmetry of 21 is reduced on protonation, probably by protonation of the central Os6 octahedron (see Section VI,A) (57). Cluster 21 also reacts with iodine to yield sequentially [Osl0C(CO)24I]", 22, and Os.oCfCO), 23, the result of electrophilic attack by 1+ on the dianion [Eq. (16)] (55). 

If the symmetry analysis for the unit cell is compared with that for the single chain (section III. A. 1.), several interesting features of the vibrational spectrum are seen to emerge. First, infrared active modes of the single chain having a polarization should be split in the crystal, with... 

In order to discuss the selection rules for crystalline lattices it is necessary to consider elementary theory of solid vibrations. The treatment essentially follows that of Mitra (47). A crystal can be regarded as a mechanical system of nN particles, where n is the number of particles (atoms) per unit cell and N is the number of primitive cells contained in the crystal. Since N is very large, a crystal has a huge number of vibrations. However, the observed spectrum is relatively simple because, as shown later, only where equivalent atoms in primitive unit cells are moving in phase as they are observed in the IR or Raman spectrum. In order to describe the vibrational spectrum of such a solid, a frequency distribution or a distribution relationship is necessary. The development that follows is for a simple one-dimensional crystalline diatomic linear lattice. See also Turrell (48). 

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