Google Search
A4: Theory - bulk materials
The classical expression for phonon thermal conductivity κph is κph=(1/3)Cvvslph, where Cv is heat capacity, vs is sound velocity and lph is phonon mean free path. Among these parameters, vs is largely dependent on the parent compound, while Cv is usually a constant according to Dulong-Petit law, and lph can be controlled by introduction of phonon scattering centers. In this study, we investigated the material dependence of vs, from a simple analysis using first-principles calculations by WIEN2k [1]. Bulk moduli B of various thermoelectric materials were calculated from the volume dependence of total energy, using Murnaghan’s formula [2]. Then we obtained acoustic sound velocity vs=(B/D)1/2, where D is the density of the compound. We also calculated the minimum phonon thermal conductivity κph=1.2kBV-2/3vs [3], where Vatom is the average atomic volume. We found that transition metal compounds tended to exhibit high B, vs and κmin, compared to p-group compounds. Among the selected materials, Bi2Te3 and PbTe were found to exhibit the lowest B. This indicated that the low κph in these compounds are not only because of the large atomic mass, but also because of the weak chemical bonding. We will introduce designing principles for low-κmin compounds, by investigating the trends in B, D and Vatom on the periodic table.
[1] P. Blaha et al., WIEN2k Users’ guide, Vienna Univ. of Technology (2001).
[2] F. D. Murnaghan, Proc. Nat. Acad. Sci. USA 30, 244 (1944).
[3] D. G. Cahill et al., Phys. Rev. B, 46, 6131 (1992).