External modes vibration

This report provides an aging assessment of electric motors and was conducted under the auspices of the USNRC NPAR. Pertinent failure-related information was derived from LERs, IPRDS, NPRDS, and NPE including failure modes, mechanisms, and causes for motor problems. In addition, motor design and materials of construction were reviewed to identify age-sensitive components. The study included consideration of the seismic susceptibility of age-degraded motor components to externally-induced vibrational effects. 

The classification of external modes into librations and translations was ensured by group theoretical considerations and by comparison of expected with observed intensities in the vibrational spectra [107]. In addition, it was... 

Up to now, the intermolecular potential models are only fair in reproducing the wavenumbers of the external modes. Although various refinements have been made, none of the models seems to be superior to the others. More recently developed intermolecular potentials have been applied to structural and thermodynamical studies but not to the analysis of the vibrational spectra [122-125]. 

The presence of isotopic impurities causes clear effects in the vibrational spectra. Almost all modes studied so far show frequency shifts on S/ S substitution [81, 107]. The average shift of the internal modes is ca. 0.6 cm , and of the external modes it is 0.1-0.3 cm (Tables 3, 4 and 5). Furthermore, the isotopomers which are statistically distributed in crystals of natural composition can act as additional scattering centers for the phonon propagation. Therefore, in such crystals the lifetime of the phonons is shortened in comparison with isotopically pure crystals and, as a conse-... 

Diphenyl-l,3,4-oxadiazole crystallization revealed two polymorphic forms (centrosymmetric and non-centrosymmetric) of the substance. Raman spectra of both phases recorded between 15 and 1700 cm-1 showed well-resolved internal modes and the external lattice vibrations below 200 cm-1, offering a fast tool for discrimination between different polymorphs. The internal modes were dominated by two groups, one around 1000 cm-1 and the second one between ca. 1500 and 1600 cm-1 <2003JST219>. 

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. 

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. 

The unit cell is 2(7 ). The two La atoms sit on a C3h site, and the six chlorine atoms are on a Cs site (see Appendix 4). Since the Hermann-Mauguin nomenclature cites that the unit cell is primitive (Pb6 /m) we need not reduce it. For the two La atoms there are six degrees of freedom (3n,Z ) = 3 x 1 x 2 = 6. The six Cl atoms possess 18 degrees of freedom (3 , Z ) = 3x3x2=18. Since all vibrational modes can be considered external modes, we need only correlate the site group to factor group. For the... 

If the solid is molecular, the molecules (considered to be formed by M atoms, where M = N/r and r is the number of molecules in the smallest Bravais cell) can be treated as for the gas phase, so giving rise to 3M- 6 (or 3M- 5 if linear) vibrations for each molecule. The degrees of freedom associated with the external modes of every molecular unit (6r for non-linear molecules and 5r for linear molecules) give rise to lattice vibrations ( frustrated translations and rotations ) and to three acoustic modes. On the other hand, the internal vibrations of each molecules should in principle give rise to r-fold splitting, owing to the coupling of the vibrations within its primitive unit cell as a whole. 

Finally the symmetries of the internal or vibrational degrees of freedom are obtained by subtracting the external modes from the space of nuclear motions ... 

Upon melting, the long-range order and space symmetry of the solids are destroyed. In principle, the vibration modes of the liquids can be considered as a long-wavelength limit of the solid vibrations and thus certain internal and/or external modes may be present in the vibration spectrum of the melt. The internal modes in melts have been investigated mainly by Raman spectroscopy in a variety of melt mixtures. The objective of these studies is the determination and characterization of possible discrete species (i.e. complexes ) in the melt. 

The g((o) can be used to provide a simple approximation to the lattice vibrations, the Einstein approximation. Let us begin by agreeing that single characteristic frequencies, could be chosen to individually represent each of the six types (three translational and three rotational) of external mode. The ( 6)y value is the density of states weighted mean value of all of the frequeneies over which that external mode, j, was dispersed. Normalising as discussed above ... 

Fig. 2.6 A diagrammatic representation of the relationship between, below, the acoustic (left) and the optic (right) types of dispersion and, above, their respective density of vibrational states, g(0), for the external modes of a solid. The symbols are defined in the text. Notice, that we have inverted the conventional representation of dispersion to maintain a conventional display of the spectrum.

The external vibrations can be expanded along similar lines to our treatment of the internal dynamics, except that the vibrating mass is now the effective molecular mass. The resulting spectrum of the external modes is somewhat similar to that arising from the internal modes. 

Phonon wings were introduced in the context of their impact on the internal vibrational spectrum of molecules but the librational mode is an external mode, it is itself a phonon. However, this is only a question of classification and semantics. The phonon wing treatment is simply one approach to calculating the intensities of combination bands. It is the method of choice when detailed information on the external mode atomic displacements is absent. We now proceed to apply the phonon wing treatment of 2.6.3, from which we shall obtain the value of the mean square displacement of the ammonium ion due to the translational vibrations of the lattice, own (which is but one of the contributions to the full ext.)... 

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