Thermal phonons

Brillouin scattering of laser light in liquids has been studied by several authors. Shapiro etal. 233) measured hypersonic velocities in various liquids and obtained a Brillouin linewidth of 0.011 cm" in methylene chloride but of less than 0.002 cm in benzene, carbon disulfide and chloroform. The broadening of the Brillouin components arises from damping of thermal phonons and is closely connected with the viscosity coefficient of the medium. From the measured linewidths, the lifetimes of the phonons responsible for Brillouin scattering at 89 45 were calculated to be 4.8 x 10 sec for methylene chloride and 7.6 x 10 sec for toluene. 

In order to image the interaction of phonons with internal structure in a specimen, scattering by thermal phonons can be used to attenuate the acoustic beam in a cryogenic microscope (Foster 1984). Experiments to test this confirmed that the cryogenic microscope was indeed able to detect on one surface of a sapphire disc the arrival of thermal phonons generated by a... 

Fig. 3.5. Thermal phonon imaging, 4.2 GHz. (a) Direct acoustic micrograph (b) heater pulsed synchronously with acoustic microscope (c) the second picture divided by the first (Foster and Rugar 1985).

Frequency-domain BSS. In this mode, the spectrum of the diffracted probe light is obtained by using a Fabry-Perot interferometer. Light is diffracted by incoherent thermal phonons and the scattering wavevector is determined by the detection angle, which can be accurately fixed by limiting the collection aperture. 

Heat is transferred through slags by a variety of mechanisms which include convection, radiation and various thermal conduction processes, viz. thermal ("phonon") conductivity, (k ), electronic conductivity (kg ) and radiation conductivity (k ). Methods for estimating the various physical properties involved in these processes are considered below. 

In pure metals the electron-phonon interaction is inversely proportional to the number of thermal phonons Te-ph 7 [1]. This result is valid for pure limit 97- / 1 qr is thermal phonon wave vector, / is the electron mean free path) [2,3]. In dirty limit qt / 1) electrons mostly scatter from defects and impurities and the electron-phonon interaction demonstrates more complicated behavior. According to the theoretical analysis made by Thouless [4] and Reizer [3] the relaxation time is proportional to T Te.pf x T ) in the case of full phonon drag of scattering centers. 

Brillouin Spectroscopy on Thermal Phonons and Other Elementary Excitations... 

The intrinsic back-scattering rate resulting from thermal phonons has been calculated ... 

The intrinsic origin of damping constant y in Eq. 3 is the inharmonic terms in the crystal s potential energy by which the phonons of infrared active modes decay into the thermal phonons. As the phonon energy follows the Planck distribution, y, and tan, increase proportionately to temperature when the abnormality such as phase transition does not occur in the observed temperature range. Figure 5.1.16 shows the temperature dependence of tan 5 from 30 to 300 K. 

At temperatures T < 0 thermal phonons in metals are mainly scattered by conduction electrons. According to a theory of Klemens (1969), the predominant phonon-electron scattering is given by... 

Only phonons with q less than 2k k is the absolute value of the electron wave vector) can interact with electrons. In nondegenerate semiconductors the wave vector of most electrons is much smaller than the wave vector of the thermal phonons at not very low temperatures. Therefore, only the longest-wavelength phonons can interact with electrons giving rise to a small contribution to the thermal conductivity. 

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