Theoretical models of lattice thermal conductivity of single-crystal bismuth telluride
Keywords:
cyclic stability of thermoelements, reliability of thermoelectric legs, thermomechanical stresses, real and Debye densities of phonon states, normal processes, Umklapp processesAbstract
In the isotropic approximation, the effect of the real density of phonon states on the lattice thermal conductivity of single-crystal bismuth telluride is taken into account within the framework of two model approaches. First, the problem is considered in the isotropic approximation, and then the layered structure and anisotropy are roughly taken into account. It is shown that the real density of phonon states almost does not change the temperature dependence of the lattice thermal conductivity of bismuth telluride both in the plane of the layers (cleavage) and perpendicular to it compared to the Debye density of phonon states. This weakness is explained by the fact that the change in the differential heat capacity contribution to thermal conductivity caused directly by the density of phonon states is compensated by the effect of this density on scattering, which is caused by the nonlinear dependence of the wave vector on the frequency, the difference between the group velocity of sound and the phase velocity, and a significant increase in the Umklapp coefficient. The obtained results are not only in qualitative, but also in satisfactory quantitative agreement with the theoretical studies of previous authors and the experiment. This allows us to hope that the real density of phonon states will not have a significant effect on the thermomechanical deformations of thermoelectric legs in comparison with the Debye density of phonon states. Bibl. 7, Fig. 2.
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