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The lattice thermal conductivity of the candidate thermoelectric materialMg$_3$Sb$_2$ is studied from first principles, with the inclusion ofanharmonic, isotope, and boundary scattering processes, and via an accuratesolution of the Boltzmann equation. We find that the anomalously low observedconductivity is due to grain-boundary scattering of phonons, whereas the purelyanharmonic conductivity is an order of magnitude larger. Mass disorder due toalloying and off-stoichiometry is also found to contribute significantly to itsdecrease. Combining ab initio values vs sample size with measured grain-sizedistributions, we obtain an estimate of $\kappa$ vs T in nano-polycrystallinematerial in good agreement with typical experiments, and compute the ZT figureof merit in the various cases.

Ab initio thermal conductivity of thermoelectric Mg$_3$Sb$_2$: evidence for dominant extrinsic effects