Phonon transport

Phonon transport is the main conduction mechanism below 300°C. Compositional effects are significant because the mean free phonon path is limited by the random glass stmcture. Estimates of the mean free phonon path in vitreous siUca, made using elastic wave velocity, heat capacity, and thermal conductivity data, generate a value of 520 pm, which is on the order of the dimensions of the SiO tetrahedron (151). Radiative conduction mechanisms can be significant at higher temperatures. 

Metals, on the other hand being predominantly conduction electron dominated phonon transport, would not show the same relationship, but would mainly reflect the electrical conductivity. 

The uTadiation-induced thermal conductivity degradation of graphites and CFCs will cause serious problems in fusion system PFCs. As with ceramics, the thermal conductivity of graphite is dominated by phonon transport and is therefore greatly... 

The transport of heat in metallic materials depends on both electronic transport and lattice vibrations, phonon transport. A decrease in thermal conductivity at the transition temperature is identified with the reduced number of charge carriers as the superconducting electrons do not carry thermal energy. The specific heat and thermal conductivity data are important to determine the contribution of charge carriers to the superconductivity. The interpretation of the linear dependence of the specific heat data on temperature in terms of defects of the material suggests care in interpreting the thermal conductivity results to be described. 

Rama Venkatasubramanian, Phonon Blocking Electron Transmitting Superlattice Structures as Advanced Thin Film Thermoelectric Materials G. Chen, Phonon Transport in Low-Dimensional Structures... 

Seol JH, Jo I, Moore AL, Lindsay L, Aitken ZH, Pettes MT, Li X, Yao Z, Huang R, Broido D, Mingo N, Ruoff RS, Shi L (2010) Two-dimensional phonon transport in supported graphene. Science 328 213-216... 

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.

In Fig. 9, we show the temperature contours in the domain represented by Fig. 8, obtained by using the full phonon dispersion BTE model discussed in section 2.3. The maximum temperature occurs in the hotspot. The silicon layer is isothermal in the y-direction as a consequence of the ballistic phonon transport in the silicon thin film layer. Qualitatively, the results look similar when Fourier diffusion or other BTE models are applied in the silicon layer. However, quantitatively there are significant differences in the hotspot temperature obtained from the different models. Table 1 shows the maximum temperature in the hotspot, obtained by applying different BTE models in the silicon layer. There is a large difference between the results from Fourier diffusion and the BTE-based models [46]. Fourier diffusion underpredicts the temperature rise in the hotspot since it cannot capture the non-equilibrium effects at these small scales. This is the reason why subcontinuum modeling approaches are essential. 

Joshi, A.A. and A. Majumdar, Transient Ballistic and Diffusive Phonon Transport in Thin Films. Journal of Applied Physics, 1993. 74(1) p. 31-39. 

Chen, G., Thermal Conductivity and Ballistic-phonon Transport in the Cross-plane Direction of Superlattices. Physical Review B, 1998. 57(23) p. 14958-14973. 

Mazumder, S., and Majumdar, A., Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization. ASME Journal of Heat Transfer, 2001.123 p. 749-759. 

The differences in the heat transfer processes for the glass, supercooled liquid and normal liquid phases of the three materials are attributed to the competition between the phonon transport and diffusive heat-transfer effects that are governed by dynamical processes taking place within the GHz-range. 

A computational design procedure of a thermoelectric power device using Functionally Graded Materials (FGM) is presented. A model of thermoelectric materials is presented for transport properties of heavily doped semiconductors, electron and phonon transport coefficients are calculated using band theory. And, a procedure of an elastic thermal stress analysis is presented on a functionally graded thermoelectric device by two-dimensional finite element technique. First, temperature distributions are calculated by two-dimensional non-linear finite element method based on expressions of thermoelectric phenomenon. Next, using temperature distributions, thermal stress distributions are computed by two-dimensional elastic finite element analysis. 

Governing Equations. If the problem is to be solved rigorously, the BTE must be solved for electrons in each valley, optical phonons, and acoustic phonons. The distribution function of each of these depends on six variables—three space and three momentum (or energy). The solution to BTE for this complexity becomes very computer intensive, especially due to the fact that the timescales of electron-phonon and phonon-phonon interactions vary by two orders of magnitude. Monte Carlo simulations are sometimes used although this, too, is very time-consuming. Therefore, researchers have resorted mainly to hydrodynamic equations for modeling electron and phonon transport for practical device simulation. 

MODELING OF NON-STATIONARY ELECTRON-PHONON TRANSPORT IN ARMCHAIR SINGLE-WALL CARBON NANOTUBES... 

The kinetic Boltzmann equation was solved to describe the non-stationary electron-phonon transport in armchair single-wall carbon nanotubes. The equation was solved numerically by using the finite difference approach. The current in the armchair singlewall carbon nanotubes was calculated. 

To avoid the account of the edge effects let us consider rather long structures (L > 50 nm), i.e. we will consider the armchair single-wall carbon nanotubes with the length greater than electron mean free path [2-6]. To describe the electron-phonon transport in nanotubes like that the semiclassical approach and the kinetic Boltzmann equation for one-dimensional electron-phonon gas can be used [4,6]. In this connection the purpose of the present study is to develop a model of electron transport based on a numerical solution of the Boltzmann transport equation. 

Thus, in the present study the peculiarities of non-stationary electron-phonon transport in the armchair single-wall carbon nanotubes of an infinite length are investigated. It is shown that exactly non-equilibrium phonons [4,6] (t —> +oo) determine the kinetics of transient electron processes in the armchair single-wall carbon nanotubes in an external electric field. 

The second practical challenge in phononic transport rises from heat-to-electricity conversion technology. Here, in order to develop efficient thermoelectric materials, one seeks structures with ultralow heat conductivity in conjunction with high electrical conductivity and a high Seebeck coefficient. Ultralow conductivity was manifested in disordered-layered WSe2 crystals [13], probably due to the localization of lattice vibrations. Si nanowires show enhanced thermoelectric efficiency compared... 

Eventually / decreases to a value close to the interplanar spacing and k due to phonon transport becomes temperature independent. The temperature variation of / for several ceramics is shown in Figure 34.4. 

As previously indicated, the thermal conductivities of borides are typically high, in comparison to many other ceramics and are a result of both a lattice and an electronic contribution to phonon transport. Figure 8 illustrates the large difference in conductivities of... 

Thermal conductivity by phonon transportation in the temperature range equal to or higher than Debye temperature is given by ... 

The formation of the MWCNTs bundles restrict the phonon transport in composites, which may be attributed to two reasons (i) the MWCNTs aggregation reduces the aspect ratio, consequently, decreasing the contact area between the MWCNTs and the TPNR matrix (ii) the MWCNTs bundles cause the phenomenon of reciprocal phonon vector, which acts like a heat reservoir and restricts heat flow diffusion. ... 

For an ideal crystalline material, the thermal conduction contributed by phonon transport in a temperature gradient can be described by the Debye theory ... 

Compositional modification. As suggested by Eq.(2), the thermal conduction by phonon transport can be reduced by increasing the mean atom weight (M/m) of the material. The major trends in compositions for reducing and/or stabilising thermal conductivity are based on zirconia modified by rare-earth (lanthanide) oxide (REO), since they have a higher atom mass. These dopants, not only reduce the phonon transport, but also reduce the photon transport (radiative) by introducing vacancies [44],... 

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