Characteristic phonons

The first term on the right-hand side of Equation (1.24) accounts for the generated intensity due to Rayleigh scattered light, while the second term is related to the intensity of the Raman scattered light. For visible light coo 10 Hz, while the characteristic phonon frequencies are much shorter, typically 12 10 Hz. Then coq and the intensity of Raman scattering varies as coq, as stated in point (iv) above. 

The silicon raw material can be analyzed by FT-IR spectroscopy. The oxygen and carbon content is determined by comparing the ratios of the oxygen and carbon bands with those of the characteristic phonon absorptions of the silicon lattice (see Fig. 5.1-9 Zachmann, 1987). The measurements are calibrated by a reference wafer of similar thickness and surface condition in order to avoid complicated correction calculations. In a special manufacturing process for integrated circuits. Si wafers are coated with very thin films... 

Perylene, in contrast, has only two molecules per unit cell and thus again nine optical and three acoustic phonons [18]. Fig. 5.15 shows the molecular displacements of characteristic phonons in both phases of the perylene crystals. There, one can readily see that the doubling of the modes in a perylene in comparison to perylene has its origin in the differences between the cophase and the corresponding counterphase displacements of the two molecules in the dimers. The counterphase modes have higher frequencies and can therefore be considered to be excitation states of the dimers within the crystal. 

Fig. 5.15 The characteristic phonons in perylene crystals (see also Fig. 2.12). K = 0. From [18].

In case, Er is smaller than the characteristic phonon energy ( 10-2 gv for solids), E vib causes a change in the vibrational energy of the oscillators by integral multiples of phonon energy i.e. 0, 1 fta E, 2 fttus etc. (where h = h./2 K and cue is the Einstein frequency i.e. frequency with which each atom vibrates). 

Recently, the characteristic phonon transport in nanostructures was analyzed by molecular dynamics simulations (Fang and Pilon 2011) in relation to the scaling laws for the thermal conductivity in nanodot array (Fang et al. 2012) and by hydrodynamic approach (Alvarez et al. 2010) for investigating the influence of PS porosity and pore size on the reduction in the thermal conductivity. 

In solids, Raman scattering results from inelastic interactions between photons and phonons in the optical mode. (Similar inelastic scattering from phonons in the acoustic mode is called Brillouin scattering.) Solids have characteristic phonon modes, which can be... 

SS Mitra, R Marshall. Trends in characteristic phonon frequencies of NaCl-, diamond-, zinc-blende, and Wurtz-type crystals. J Chem Phys 41 3158, 1964. 

The films used in electrochemistry are polycrystalline and the phonon confinement within one crystallite allows phonons with wavevectors slightly different but close to the Brillouin zone center to eventually participate in the observed Raman scattering process. Finally, the finite size of the crystallites can induce a partial breaking of the selection rules and allows the scattering of incident photons by phonons situated near the Brillouin zone center. Some species present in the films, such as monocrystalline graphite, are characterized by two peaks at 1350 and 1580 cm fi At a greater level of disorder, all of the selection rules can be broken and the total density of phonons can be observed. Characteristic phonons that can be observed are the following ... 

---