Selectivity-dispersion curve

Iditional importance is that the vibrational modes are dependent upon the reciprocal e vector k. As with calculations of the electronic structure of periodic lattices these cal-ions are usually performed by selecting a suitable set of points from within the Brillouin. For periodic solids it is necessary to take this periodicity into account the effect on the id-derivative matrix is that each element x] needs to be multiplied by the phase factor k-r y). A phonon dispersion curve indicates how the phonon frequencies vary over tlie luin zone, an example being shown in Figure 5.37. The phonon density of states is ariation in the number of frequencies as a function of frequency. A purely transverse ition is one where the displacement of the atoms is perpendicular to the direction of on of the wave in a pmely longitudinal vibration tlie atomic displacements are in the ition of the wave motion. Such motions can be observed in simple systems (e.g. those contain just one or two atoms per unit cell) but for general three-dimensional lattices of the vibrations are a mixture of transverse and longitudinal motions, the exceptions... 

Fig. 2.6.8 Time-of-flight dispersion curves versus the encoding position of gas flowing through a cylindrically symmetrical glass phantom with large pores on the order of 1-cm diameter, obtained with slice selective inversion of magnetization. The flow direction changes twice as the gas is flowing from inlet to outlet. Slices parallel (upper) and perpen-...

This scheme of frequency tripling was successfully tested with fuchsin in hexafluorisopropanol (a solvent selected for its low index of refraction and relatively flat dispersion curve) to frequency-triple the output of a neodymium laser 67,68) With an input power of 10 MW/cm2 a third-harmonic output of 0.2 mW/cm2 was measured. This low value was mainly due to the relatively high absorption of fuchsin at 355 nm. An improvement of the efficiency by a factor of 80 was found with hexamethylindocarbocyanine iodide in hexafluorisopropanol because of the much lower absorption of this dye at 355 nm. Since the absorption minimum of this dye is at 383 nm, one could expect an additional efficiency increase by a factor of 70 for a fundamental laser wavelength of 1.15 / 69>. Other cyanine dyes have been used for frequency tripling a fundamental wavelength of 1.89 /mi 70>. 

Around the selective-reflection band the plane of polarization of incident radiation is strongly rotated, the spectral dependence of this optical rotation resembles a dispersion curve as outlined below, position and shape give indication of both structure parameters. 

The dispersion behavior of a and y for a few selected frequencies can be found in Tables 5 and 6 for nitrogen and benzene, respectively. We have selected the ESHG process for benzene and the THG processes for nitrogen to study the frequency dependence of y. The conclusions are consistent between the processes When the CCSD dispersion is taken as a reference value, we observe that the DFT methods provide satisfactory dispersion for the polarizability a. However, for the hyperpolarizability y there is a significant tendency to deviate from the CCSD dispersion curve. The only exception is the LB94/LDA method, where the deviation from the CCSD dispersion is found to be almost constant for the examined... 

The dispersion curve for the k) of Equation (5.22) is more complicated than Figure 5.2, since kx, ky and kz can have different values. The convention is to show the energies at various selected points in the Brillouin zone. These are labeled as T, M, K and X, and are called symmetry points. 

Here is the momentum transferred from the neutron and x is one of the reciprocal lattice vectors of the palladium lattice. Thus, the incoherent scattering sees all the vibration modes but the coherent scattering selects one particular phonon for a particular experimental value of Q. It is now clear that both the incoherent and coherent one-phonon scattering will depend on the shape of the optical dispersion curves and hence will be influenced by hydrogen-hydrogen interactions. Indeed, one of the first observations of inelastic scattering from a hydride [10] interpreted the shape of the optical peak in terms of a frequency distribution broadened by H-H interactions. 

Because of the large amount of available data, only a selection of dispersion curves and surfaces has been given. For more detailed information, the reader is referred to [2.10,11]. 

HNCO experiment, modified to include CPMG relaxation period. The effect from couplings was minimised by using band-selective pulses in the CPMG pulse-train. The dispersion curves of CO are sensitive to the hydrogen bond dynamics. 

Many choices for carrying out an inspection with guided waves can be obtained from the dispersion curves. Many different combinations of phase velocity and frequency might work equally well for finding specific cohesive or adhesive type defects. As an example, wave structures for two specific points are illustrated in Fig. 10. In Fig. 10a, for example, the in-plane displacement component, which could be quite sensitive to certain kinds of defects along the interface or in the adhesive layer, is quite dominant along the interface and in the adhesive layer. In Fig. 10b, however, from the power distribution, it is expected to have best results for substrate inspection only if needed. This point would not be selected for adhesive bond inspection. Theoretical results are useful primarily for establishing... 

Fig. 12 The phonon dispersion curve and observed Raman frequencies of polyglycine II. The Raman selection rules state that vibrations which occur at 0=0 and 0 = 120° are Raman active. Note that is the rotational angle which generates the polyglycine II helfac...

Fig. 13. The phonon dispersion curves and observed Raman frequencies rf polyalanine. The Raman selection rules state that vibration whidi occurs at 0=0°, 100°, 200° (= 160°) are Raman active...

PTFE also provides an excellent example for the fact that FIR spectroscopy, espraially of polymers, opens the possibility of determining the complete set of dispersion curves for a substance, at least in the low-wave-number region. The basis for this procedure is the breakdown of the selection rules, not only when the crystalline order disafprars but ako when the chain length becomes so short... 

Many Raman scattering Unes are observed for SiC, reflecting zone folding effects in phonon dispersion curves. These lines can be used to identify the polytype of SiC crystals, as mentioned in Sec. III.A. From the shift of the Raman peaks and the discrepancy of the selection rules in optical transitions, information about the internal stress and crystallinity of SiC crystals, respectively, can be obtained, as mentioned in Sec. ni.B. 

Fig. 79. GaP(llO) (1x1) H. Surface phonon dispersion predicted from first principles calculation [99Fril]. The shaded area represents the projection of the bulk phonon bands on the SBZ. The solid lines are the dispersion curves for surface modes and resonances. The dashed curves indicate the dispersion of selected surface modes of the clean surface. The dots report the position of these modes for the unrelaxed bulk geometry.

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