Systematic over-estimation of lattice thermal conductivity in materials with electrically-resistive grain boundaries†
Reducing the thermal conductivity κ of a material via nano-structuring to create small grain sizes is one of the most common strategies to improve thermoelectric materials. In such polycrystalline materials heat carrying phonons are scattered at the grain boundaries, which directly improves the thermoelectric quality factor and ultimately the figure-of-merit zT. In some cases, however, such as in Mg3Sb2, SnSe, and Mg2Si an opposite trend is found where higher lattice thermal conductivity reported in small grain polycrystalline material than in large grain or single crystal materials. This unphysical result indicates a problem with the conventional use of the Wiedemann–Franz law. Here, we trace this problematic finding to the electrical resistance at the grain boundaries, which leads to an overestimation of the phonon or lattice contribution of the thermal conductivity κL. In materials with significant grain boundary electrical resistance, the estimated electronic contribution to the thermal conductivity LσT is low because the measured electrical conductivity σ is low. However within the grain electrons may still be transporting more heat than the total conductivity suggests, leading to an overestimation of κL if the conventional κL = κ − LσT is used with the measured values of κ and σ. The overestimation of κL in small-grain samples is shown to be pervasive across a broad range of thermoelectric materials, including Mg3Sb2, Mg2Si, PbTe, PbSe, SnSe, (Hf,Zr)CoSb, CoSb3, and Bi2Te3 alloys, and a correction is necessary to properly understand and predict their charge and heat transport.