Scattering of phonons

Fig. 10. The temperature dependence of thermal conductivity for pyrolytic graphite in three different conditions [66]. The reduction of thermal conductivity with increasing temperature is attributed to increasing Umklapp scattering of phonons.

On the other hand, for an amorphous insulator, Aph is determined by the scattering of phonons with defects and can be very small, even approaching atomic distances. 

In some cases (amorphous materials as polymers or glasses), the scattering of phonons with tunnelling states is also relevant. This process leads to an approximate [40-42,94,95] dependence as T1 2 of k (see Table 3.4) and to a plateau in the 2K < T < 20K range (see Fig. 3.18). 

In the hydrate lattice structure, the water molecules are largely restricted from translation or rotation, but they do vibrate anharmonically about a fixed position. This anharmonicity provides a mechanism for the scattering of phonons (which normally transmit energy) providing a lower thermal conductivity. Tse et al. (1983, 1984) and Tse and Klein (1987) used molecular dynamics to show that frequencies of the guest molecule translational and rotational energies are similar to those of the low-frequency lattice (acoustic) modes. Tse and White (1988) indicate that a resonant coupling explains the low thermal conductivity. 

Figure 6 shows the MD predicted in-plane and out-of-plane thermal eonduetivities at 376K (Fig. 6a) and lOOOK (Fig. 6b) as a function of film thickness. It is seen that both the in-plane and out-of-plane thermal conductivities are affeeted by the thiekness of the film. For thiekness smaller than the phonon mean free path (approximately 300 nm and 30 nm at 300K and lOOOK, respeetively), both the in-plane and out-of-plane thermal eonduetivities deerease with deereasing thiekness, an effeet attributed to the scattering of phonons with the boundaries of the thin film. This effeet is more pronounced in the out-of-plane direction, where the dimensions of the thin film make the phonon transport ballistic. At large thicknesses, the thermal conductivities approach the bulk value (shown as dashed lines in Fig. 6). The bulk value is reached at smaller thicknesses at lOOOK due to the smaller phonon mean free path at this temperature.

The temperature dependence of the spin-lattice relaxation time corresponding to the inelastic scattering of phonons by the Ge quadrupole moment in Ge single crystals is calculated in the framework of the adiabatic bond charge model. The results obtained agree with the experimental data. " ... 

Fig. 2. Thermal resistance of Ni3+ ions in AI2O3 (Salce and de Goer 1979134)). The full curve follows the experimental points (not shown) for pure corundum. The circles are measurements on nickel-containing-Al2C>3 (less than 20 ppm by weight). The deviation of the two data sets arises from the-scattering of phonons by the Ni impurities. Two dips near 0.7 K and 20 K are identifiable...

Secondly, if one uses monochromatic radiation, l.e.- a laser, one can obtain evidence of Stokes and anti-Stokes scattering of phonons, i.e.-lattice vibrations, as shown in the following ... 

SCATTERING OF PHONONS BY SPINS AT LOW TEMPERATURES. MORTON I P ROSENBERG H M PHYS REV LETTERS... 

Total thermal conductivity is a sum of the lattice and electronic parts, K = Ki + Ke- The lattice part of the thermal conductivity describes the scattering of phonons on the vibrations of atoms, whereas the electronic part describes thermal conductivity appearing due to conduction electrons and is related to the electrical conductivity Wiedemann-Franz equation, = a T Lo, where T is the absolute temperature and Lq is the ideal Lorenz number, 2.45 X 10 Wf2K [64]. The electronic part of the thermal conductivity is typically low for low-gap semiconductors. For the tin-based cationic clathrates it was calculated to contribute less than 1% to the total thermal conductivity. The lattice part of the thermal conductivity can be estimated based on the Debye equation /Cl = 1 /3(CvAvj), where C is the volumetric heat capacity, X is the mean free path of phonons and is the velocity of sound [64]. The latter is related to the Debye characteristic temperature 6 as Vs = [67t (7V/F)] . Extracting the... 

From a theoretical point of view, the scattering of phonons in mnltiphase systems is determined by the existence of an interfacial thermal barrier from acoustic mismatch. In a simplified model, the transmission of a phonon between two phases is affected by the presence of common vibration frequencies for the two phases. Thus, it... 

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