ICT2014 Abstracts

Despite the extensive experimental results related to the electrical and thermal transport in disordered thermoelectric materials with nanograins, there is little theoretical or modeling work in the literature regarding the lattice thermal conductivity of such kind materials. A fundamental theory of boundary scattering of phonons in solid solutions was given by Parrott, who introduced a “virtual crystal” into his model. However, the estimation of the lattice thermal conductivity of such “virtual crystal” remained a problem in Parrott’s model.
Here we report a phenomenological model to calculate the high temperature lattice thermal conductivity of n-type MNiSn and p-type MCoSb (M is the combination of Hf, Zr, and Ti) alloys. This model expresses the lattice thermal conductivity of half-Heusler alloys in terms of their atomic weights, their lattice constants, the temperature, and the grain size. The model indicates the reduction of lattice thermal conductivity depends on the grain size as L-1/2 and is independent of the scattering parameter , which characterizes the phonon scattering cross section of point defects. In addition, the model indicates the reduction of lattice thermal conductivity due to grain boundary scattering falls off with temperature as T-1/2 around the Debye temperature.