Thermal conductivity of bulk and nanowire Mg₂Si _xSn_1-x alloys from first principles

The lattice thermal conductivity (κ) of the thermoelectric materials, Mg₂Si, Mg₂Sn, and their alloys, are calculated for bulk and nanowires, without adjustable parameters. We find good agreement with bulk experimental results. For large nanowire diameters, size effects are stronger for the alloy than for the pure compounds. For example, in 200 nm diameter nanowires κ is lower than its bulk value by 30%, 20%, and 20% for Mg ₂Si_0.6Sn_0.4, Mg₂Si, and Mg ₂Sn, respectively. For nanowires less than 20 nm thick, the relative decrease surpasses 50%, and it becomes larger in the pure compounds than in the alloy. At room temperature, κ of Mg₂Si_xSn _1-x is less sensitive to nanostructuring size effects than Si _xGe_1-x, but more sensitive than PbTe_xSe _1-x. This suggests that further improvement of Mg₂Si _xSn_1-x as a nontoxic thermoelectric may be possible.