Acoustic phonons thermal

Brillouin scattering measures the velocity and attenuation of hypersonic thermal acoustic phonons. A theory of Brillouin scattering from polymer blends is presented and illustrated qualitatively by several examples. The study of blend compatibility is illustrated for the system PMMA-PVFS. The detection of inhomogeneous additives is shown for commercial PVC film and cellulose acetate, and simultaneous measurements on separated phases are presented for Mylar film. The main purpose of the paper is to stimulate further work in a potentially promising field. 

T> rillouin scattering measures the spectrum attributable to the inter-action of light with thermal acoustic phonons (I). The scattered light is shifted in frequency with a splitting given by... 

Brillouin scattering is the inelastic scattering of light by thermal acoustical phonons in a material. Energy and wavevector conservation in the process are given, respectively, by... 

T ight scattering in dense media is caused by fluctuations in the local " dielectric tensor c (i). In 1922 Brillouin (2) predicted that thermal acoustic phonons would lead to such fluctuations and hence to light scattering. In addition, the scattered light should be shifted in frequency because the phonons are moving. The frequency shift is given by ... 

Molecules vibrate at fundamental frequencies that are usually in the mid-infrared. Some overtone and combination transitions occur at shorter wavelengths. Because infrared photons have enough energy to excite rotational motions also, the ir spectmm of a gas consists of rovibrational bands in which each vibrational transition is accompanied by numerous simultaneous rotational transitions. In condensed phases the rotational stmcture is suppressed, but the vibrational frequencies remain highly specific, and information on the molecular environment can often be deduced from hnewidths, frequency shifts, and additional spectral stmcture owing to phonon (thermal acoustic mode) and lattice effects. 

The application of an electric field E to a conducting material results in an average velocity v of free charge carriers parallel to the field superimposed on their random thermal motion. The motion of charge carriers is retarded by scattering events, for example with acoustic phonons or ionized impurities. From the mean time t between such events, the effective mass m of the relevant charge carrier and the elementary charge e, the velocity v can be calculated ... 

Acoustical phonons are important in the thermal broadening of the h-polarized exciton of anthracene. 

Figure 2.20. Right part The polariton dispersion at a few tens of reciprocal centimeters below the bottom of the excitonic band, vs the wave vector, or the refractive index n = ck/w (notice the logarithmic scale). The arrows indicate transitions with creation of one acoustical phonon, with linear dispersion in k (with a sound velocity of 2000 m/s). For the transitions T, Tt, T3 the final momentum is negligible compared to the initial momentum, and the unidimensional picture suffices. For the transitions between T3 and the point A, the direction of the final wave vectors should be taken into account. Left part The density of states m( ) (2.141) of the polaritons in the same energy region. This diagram explains why the transitions T, will be much slower than the transitions around T3 and the point A. The very rapid increase of m( ) at a few reciprocal centimeters below E0 shows the effect of the thermal barrier.

In Brillouin scattering, the light interacts with thermal excitations in a material, in particular acoustical phonons in a crystal. The energy of the scattered light is therefore modified, increased in the case of the annihilation of the excitation, or decreased in the case of creation of the excitation. The measurement of this energy difference gives information on the energy of the phonons and therefore on the interatomic potentials of the material. 

Another significant source of variations in the local site energies of molecular ions and excitons in condensed media is the modulation of these energies by the thermal vibrations either of the medium (e.g., acoustical phonons and librons) or of the molecular ion (exciton) itself (intramolecular vibrations). A model Hamiltonian which incorporates electronic interactions with... 

The thermal conductivity is described as a sum of two contributions k(7) = Ki(7) + Kii(7) arising from propagating acoustic phonons and from localized short-wavelength vibrational modes, or phonons with the mean free path equal to the phonon half-wavelength, respectively. The temperature dependence of Ki(7) for all glasses was first analyzed on phenomenological... 

Under conditions where large amplitude mechanical perturbations create a dense sea of phonons, especially phonons near the zone edge, the mean-free path in Eq. (15) may be decreased due to phonon-phonon anharmonic coupling. In other words there is a second-order correction to Eq. (15) that reduces the thermal conductivity at higher phonon concentrations. For instance terms where two phonons efficiently combine to pump a doorway vibration drastically reduce the thermal conductivity by converting a mobile pair of phonons into an essentially immobile vibration. Similarly, interactions that convert faster acoustic phonons into slower optic phonons also reduce the mean-free path. 

Phonon velocity is constant and is the speed of sound for acoustic phonons. The only temperature dependence comes from the heat capacity. Since at low temperature, photons and phonons behave very similarly, the energy density of phonons follows the Stefan-Boltzmann relation oT lvs, where o is the Stefan-Boltzmann constant for phonons. Hence, the heat capacity follows as C T3 since it is the temperature derivative of the energy density. However, this T3 behavior prevails only below the Debye temperature which is defined as 0B = h( DlkB. The Debye temperature is a fictitious temperature which is characteristic of the material since it involves the upper cutoff frequency ooD which is related to the chemical bond strength and the mass of the atoms. The temperature range below the Debye temperature can be thought as the quantum requirement for phonons, whereas above the Debye temperature the heat capacity follows the classical Dulong-Petit law, C = 3t)/cb [2,4] where T is the number density of atoms. The thermal conductivity well below the Debye temperature shows the T3 behavior and is often called the Casimir limit. 

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