Lattice vibrations large-amplitude

GPa indicate the presence of a bcc lattice undergoing large amplitude vibrations, even though each RDF in Figure 10 has width similar to that of a liquid or a glass. The RDFs for the amorphous phase (not shown) are similar to those of the solid phase obtained in the S simulations. 

The vibrations of a simple dipole AB of unit length will result in an increase in the mean interval i for large amplitudes, just as when crystal lattices expand as the result of heat Ay - > o. 

When the molecules get larger and more flexible, the separation between the intramolecular vibrations and the lattice vibrations becomes less strict. Some of the intramolecular modes have relatively low frequencies and large amplitudes and they will mix with the lattice modes. A clear example of such mixing occurs in solid TCNE. 

The amount of high precision experimental structural data on conjugated polyenes is limited. Some structure results are presented in Table 5. In gas electron diffraction studies it is difficult to determine closely spaced bond distances accurately, because these parameters are highly correlated with the corresponding vibrational amplitudes. Today it is possible to calculate the vibrational amplitudes accurately, if the vibrational frequencies are known. This was, however, not the case when the GED studies presented in Table 5 were carried out. The observed differences between the terminal and central C=C bonds in the GED studies of trtMs-i,3,5-hexatriene and c/s-l,3,5-hexatriene are probably too large. A very accurate X-ray study of trows-1,3,5-hexatriene has, however, been carried out also in connection with the preparation of this chapter. Figure 4 shows the molecular structures of trows-1,3-butadiene and trows-1,3,5-hexatriene as found in the crystal lattice. 

The aforementioned frequencies have been used for a force-constant calculation (13). The bond orders deduced with the simple method of Siebert (167) are 0.63 for the Se—F bond and 1.5 for the Se—O bond. These values also prove a general similarity to BrO F and CIO F. The low value of the Se—F force constant and high value of the corresponding mean vibrational amplitude, as well as its large temperature dependence, are attributed to a large ionic character and also point to the possibility of some fluorine bridging in the crystal lattice, as suggested earlier 130, 167). 

Measurements of the diffraction peak intensities at various temperatures indicated that the vibrations of the ions in the AIN lattice were anisotropic. The Intensities of different diffraction lines depended differently on the temperature (Fig. 3). Variation of the temperature affected most the lines with large values of the Miller index I and least the lines characterized by I — 0. This indicated that the vibrations of the ions had a larger amplitude along the c axis than in the basal plane. Under these conditions, the atomic scattering factors of the Al and the N ions should also be anisotropic, I.e.,... 

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