Molecular crystals vibrations

DIott D D 1988 Dynamics of molecular crystal vibrations Laser Spectroscopy of Solids 7/ed W Yen (Berlin Springer) pp 167-200... 

Dlott DD. Dynamics of molecular crystal vibrations. In Yen W, ed. Laser Spectroscopy of Solids II. Berlin Springer-Verlag, 1988 167-200. 

Hill J R, Chronister E L, Chang T-C, Kim H, Postlewaite J C and DIott D D 1988 Vibrational relaxation and vibrational cooling in low temperature molecular crystals J. Chem. Phys. 88 949-67... 

Chang T-C and DIott D D 1988 Picosecond vibrational cooling in mixed molecular crystals studied with a new coherent Raman scattering technique Chem. Phys. Lett. 147 18-24... 

Kiefte H. Clouter M. J., Rich N. H., Ahmad S. F. Pure vibrational Raman spectra of some simple molecular crystals y-02, 02 in hep Ar, /J-N2, Chem. Phys. Lett. 70, 425-9 (1980). 

Tables Assignment and wavenumbers (cm ) of the external and torsional vibrations of a-Ss based on polarization dependent studies [106, 107]. In the first two columns the type and symmetry classes of the molecular and crystal vibrations, respectively, are given. The wavenumbers of the vibrations are listed in the columns infrared and Raman corresponding to the order of symmetry species given in the second column (crystal). " S means orthorhombic Sg with natural isotopic composition, while stands for isotopically pure Sg crystals (purity >99.95%)... 

The composition factor for the acoustic branch of the NIS spectrum is derived from (9.10) by assuming (in the approximation of total decoupling of inter- and intramolecular vibrations) that the msd in acoustic modes are identical for all the atoms in the molecular crystal ... 

As a rule, the density of states for molecular lattice vibrations is negligible as compared to that for crystal phonons. Therefore, the K-mode of a molecular lattice is coupled with the crystal phonons specified by the same wave vector K. Besides, the low-frequency collective mode m of adsorbed molecules can be considered as a... 

Matter (anything that has mass and occupies space) can exist in one of three states solid, liquid, or gas. At the macroscopic level, a solid has both a definite shape and a definite volume. At the microscopic level, the particles that make up a solid are very close together and many times are restricted to a very regular framework called a crystal lattice. Molecular motion (vibrations) exists, but it is slight. 

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. 

As the oscillators of the OPP model vibrate independently of each other, the frequencies are dispersionless, that is, independent of a wavevector q. For the internal modes of a molecular crystal, this tends to be a very good approximation. For the external modes, the dispersion can be pronounced, as shown in Figs. 2.1 and 2.2. In order to obtain the mean-square vibrational amplitudes for the latter, a summation over all phonon branches in the Brillouin zone must be performed. 

As has become clear in previous sections, atomic thermal parameters refined from X-ray or neutron diffraction data contain information on the thermodynamics of a crystal, because they depend on the atom dynamics. However, as diffracted intensities (in kinematic approximation) provide magnitudes of structure factors, but not their phases, so atomic displacement parameters provide the mean amplitudes of atomic motion but not the phase of atomic displacement (i.e., the relative motion of atoms). This means that vibrational frequencies are not directly available from a model where Uij parameters are refined. However, Biirgi demonstrated [111] that such information is in fact available from sets of (7,yS refined on the same molecular crystals at different temperatures. 

An interesting aspect of many structural phase transitions is the coupling of the primary order parameter to a secondary order parameter. In transitions of molecular crystals, the order parameter is coupled with reorientational or libration modes. In Jahn-Teller as well as ferroelastic transitions, an optical phonon or an electronic excitation is coupled with strain (acoustic phonon). In antiferrodistortive transitions, a zone-boundary phonon (primary order parameter) can induce spontaneous polarization (secondary order parameter). Magnetic resonance and vibrational spectroscopic methods provide valuable information on static as well as dynamic processes occurring during a transition (Owens et ai, 1979 Iqbal Owens, 1984 Rao, 1993). Complementary information is provided by diffraction methods. 

Bashkin IO, Kolesnikov AI, Antonov VE, Ponyatovsky EG, Kobzev AP, Muzychka AY, Moravsky AP, Wagner FE, Grosse G (1998) Vibrational spectra of C-60 hydrofullerite prepared under high hydrogen pressure. Molecular crystals and liquid crystals science and technology section c. Mol Mater 10 265-270... 

But if we examine the localized near the donor or the acceptor crystal vibrations or intra-molecular vibrations, the electron transition may induce much larger changes in such modes. It may be the substantial shifts of the equilibrium positions, the frequencies, or at last, the change of the set of normal modes due to violation of the space structure of the centers. The local vibrations at electron transitions between the atomic centers in the polar medium are the oscillations of the rigid solvation spheres near the centers. Such vibrations are denoted by the inner-sphere vibrations in contrast to the outer-sphere vibrations of the medium. The expressions for the rate constant cited above are based on the smallness of the shift of the equilibrium position or the frequency in each mode (see Eqs. (11) and (13)). They may be useless for the case of local vibrations that are, as a rule, high-frequency ones. The general formal approach to the description of the electron transitions in such systems based on the method of density function was developed by Kubo and Toyozawa [7] within the bounds of the conception of the harmonic vibrations in the initial and final states. 

The vibrations within a molecular crystal cell are not only a result of molecular motions, but also the relative motions between neighboring molecules. Dominant features of the THz spectra are the sharp absorption peaks caused by phonon modes directly related to the crystalline structure [14], This result originates from the molecular vibrational modes and intramolecular vibrations associated, for example, with RDX [39], Consequently, vibrational modes are unique and distinctive feature of the crystalline explosive materials. The presence of broad features might also be caused by scattering from a structure with dimensions comparable to the THz wavelength. This can occur in materials that contain fibers or grains [37],... 

The optical spectral region consists of internal vibrations (discussed in Section 1.13) and lattice vibrations (external). The fundamental modes of vibration that show infrared and/or Raman activities are located in the center Brillouin zone where k = 0, and for a diatomic linear lattice, are the longwave limit. The lattice (external) modes are weak in energy and are found at lower frequencies (far infrared region). These modes are further classified as translations and rotations (or librations), and occur in ionic or molecular crystals. Acoustical and optical modes are often termed phonon modes because they involve wave motions in a crystal lattice chain (as demonstrated in Fig. l-38b) that are quantized in energy. 

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