Conduction lattice thermal

Returning now to thermal conductivity, Eq. (4.40) tells us that any functional dependence of heat capacity on temperature should be implicit in the thermal conductivity, since thermal conductivity is proportional to heat capacity. For example, at low temperatures, we would expect thermal conductivity to follow Eq. (4.43). This is indeed the case, as illustrated in Figure 4.25. In copper, a pure metal, electrons are the primary heat carriers, and we would expect the electronic contribution to heat capacity to dominate the thermal conductivity. This is the case, with the thermal conductivity varying proportionally with temperature, as given by Eq. (4.42). For a semiconductor such as germanium, there are less free electrons to conduct heat, and lattice conduction dominates—hence the dependence on thermal conductivity as suggested by Eq. (4.41). 

ZT Y r A A A A A AC dimensionless thermoelectric figure of merit electronic coefficient of heat capacity (1+ZT)F2 crystal field singlet non-Kramers doublet (crystal field state) crystal field triplet crystal field triplet hybridization gap jump in heat capacity at Tc K KL -min P 6>d X JCO total thermal conductivity of solid thermal conductivity of electrons or holes thermal conductivity of lattice minimum lattice thermal conductivity electrical resistivity Debye temperature magnetic susceptibility magnetic susceptibility at T = 0... 

Table 1.1. Abundance of the metal in the earths s crust, optical band gap Es (d direct i indirect) [23,24], crystal structure and lattice parameters a and c [23,24], density, thermal conductivity k, thermal expansion coefficient at room temperature a [25-27], piezoelectric stress ea, e3i, eis and strain d33, dn, dig coefficients [28], electromechanical coupling factors IC33, ksi, fcis [29], static e(0) and optical e(oo) dielectric constants [23,30,31] (see also Sect. 3.3, Table 3.3), melting temperature of the compound Tm and of the metal Tm(metal), temperature Tvp at which the metal has a vapor pressure of 10 3 Pa, heat of formation AH per formula unit [32] of zinc oxide in comparison to other TCOs and to silicon...

Calculations of the generalized conductivity (electroconductivity, thermal conductivity, dielectric and magnetic permeability) of heterogeneous systems have been carried out by Kemer and Odelevsky For a matrix heterogeneous system with cubical inchtaons whose centers form a cubic lattice and whose faces are parallel, Odelevsky s relationship may be applied ... 

Balandin, A., and Wang, K.L., Significant Decrease of the Lattice Thermal Conductivity due to Phonon Confinement in a Free-standing Semiconductor Quantum Well. Physical Review B, 1998. 58(3) p. 1544-1549. 

Ladd, A., B. Moran, and W.G. Hoover, Lattice Thermal Conductivity A Comparison of Molecular Dynamics andAnharmonic Lattice Dynamics. Physical Review B, 1986. 34 p. 5058-5064. McGaughey, A.J. and M. Kaviany, Quantitative Validation of the Boltzmann Transport Equation Phonon Thermal Conductivity Model Under the Single-Mode Relaxation Time Approximation. Physical Review B, 2004. 69(9) p. 094303(1)-094303(11). 

Now as regards the statements made by theory, Peierls requires that [L] should decrease towards the absolute zero, as we explained above (section 9, p. 57). But Peierls also holds that the constancy of Z at low temperature is intelligible, if the additivity of the ideal resistance and the residual resistance . .. is strictly valid, both for electrical conductivity and thermal conductivity For the classical theorem on the number of collisions is justified even at low temperatures for the statical lattice disturbances regarded as causing the resistance, whereas it is not so for the thermal agitation here. 

For the lattice thermal conductivity, the model due to Steigmeier and Abels is adopted, here [3]. The lattice thermal conductivity is given by... 

Here o is electrical conductivity, u is thermopower, k is thermal conductivity, t is energy of carrier, p is chemical potential, e is bare charge of electron, and f (e) is Fermi-Dirac distribution function. In deriving eq.(2) we treat the lattice thermal conductivity as a constant. Following we consider the n-type semiconductors, then the change of differential conductivity can be given by ... 

Origin of the notable difference can be easily understood, if one examine grain size dependence of electric conductivity and lattice thermal conductivity show in fig. 4. Lattice... 

Figure 4. Grain size dependence of electric conductivity a and lattice thermal conductivity Kl for (a) SiGe and (b) PbTe.

The best material system available at this time to meet the above criteria is the bismuth-antimony crystal system [ ]. In pure bismuth, the conduction and valence bands are slightly overlapped and, in the proper orientation, both holes and electrons have high and reasonably equal mobilities. The addition of a small amount of antimony has the effect of greatly reducing the lattice thermal conductivity. However, the addition of antimony also has the effect of decreasing the overlap of the principal conduction and valence bands in fact, for antimony concentrations greater than 5 atomic %, a gap exists and the system becomes a semiconductor, which is undesirable for these purposes [ ]. At present it appears that the optimum antimony content is about 3 atomic %. 

Wei = lattice thermal resistivity due to interaction with conduction electrons Wg = lattice thermal resistivity Wh = thermal resistivity under magnetic field H... 

Wi = electronic thermal resistivity due to phonon interaction with conduction electrons Wo = electronic thermal resistivity due to static defects Wp = lattice thermal resistivity due to point defects... 

Two-electron covalent bonds are formed between the metal (Me) and silicon atoms in monosilicides. The overall electron-valence nature of these bonds determines the uniformity of the crystal structure of silieides. The high value of their lattice thermal conductivity (Table 2) is an indirect confirmation that stable covalent bonds are present in monosllicide crystals. The uniformity of the structures amounts not only... 

Therefore, the anisotropy of the carrier mobility (Up) and the lattice thermal conductivity ( Kiatt) Is due to the characteristic features of the distribution of chemical bonds in the crystal according to the scheme in [8],... 

By analyzing the temperature dependence of the electrical properties, using our results (Fig. 5) and published data [9,10], another characteristic feature of the structure of CrSi2 crystals becomes apparent, which makes the energy spectrum of valence electrons in this compound more precise. A calculation of the lattice thermal conductivity of single crystals, taken as the difference between the total and electronic thermal conductivities (Fig. 5), as a function of temperature, shows that it decreases continuously up to the maximum measurement temperature. This Indicates the absence of an additional heat transfer component due to ambipolar diffusion of carriers [18] in the intrinsic conduction range. 

Fig. 5. Temperature dependence of some electrical properties of CrSi2 a) thermoelectric power b) electrical conductivity c) total thermal conductivity d) lattice thermal conductivity H) parallel to the c axis i.) perpendicular to the c axis.

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