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

TL;DR

This study uses first-principles calculations to analyze the thermal conductivity of Mg$_3$Sb$_2$, revealing that extrinsic effects like grain boundaries and alloying significantly reduce conductivity compared to intrinsic anharmonic phonon scattering.

Contribution

It provides a detailed ab initio analysis of extrinsic and intrinsic factors affecting Mg$_3$Sb$_2$'s thermal conductivity, highlighting the dominant role of grain-boundary scattering.

Findings

Grain-boundary scattering explains low experimental thermal conductivity.

Intrinsic anharmonic conductivity is much higher than observed.

Alloying and off-stoichiometry significantly decrease thermal conductivity.

Abstract

The lattice thermal conductivity of the candidate thermoelectric material Mg$_3$Sb$_2$ is studied from first principles, with the inclusion of anharmonic, isotope, and boundary scattering processes, and via an accurate solution of the Boltzmann equation. We find that the anomalously low observed conductivity is due to grain-boundary scattering of phonons, whereas the purely anharmonic conductivity is an order of magnitude larger. Mass disorder due to alloying and off-stoichiometry is also found to contribute significantly to its decrease. Combining ab initio values vs sample size with measured grain-size distributions, we obtain an estimate of $\kappa$ vs T in nano-polycrystalline material in good agreement with typical experiments, and compute the ZT figure of merit in the various cases.