First-Principles Theory of Ordering, Phase Separation, and Phonon Scattering in Thermoelectric LAST (Lead-Antimony-Silver-Telluride) alloys

Bulk LAST (Pb$_{2-x-y}$Ag$_{y}$Sb$_{x}$Te$_{2})$ alloys exhibit$^{\ast }$ high thermoelectric figure of merit (ZT$\sim $2 at 800K, considerably exceeding ZT of pure PbTe or AgSbTe$_{2})$, and nano-scale inhomogeneities, origin of which is poorly understood. The atomic structure of the nano-regions, as well as that of the pure AgSbTe$_{2}$, remains the subject of an experimental debate. Using density-functional theory (DFT), we calculate the composition-temperature phase diagram and vibrational spectra of Pb$_{2-x-y}$Ag$_{y}$Sb$_{x}$Te$_{2}$ alloys. We predict that the experimentally observed nanoscale inhomogeneities are due to the precipitation of ordered AgSbTe$_{2}$ phases. Two types of cation order type closely compete in AgSbTe$_{2}$, the dominant order type being D4; the predicted hypothetical order-disorder transition temperature exceeds the melting temperature of pure AgSbTe$_{2}$. The miscibility gap between solid PbTe and AgSbTe$_{2}$ phases is highly asymmetric, with a high solubility of PbTe in ordered AgSbTe$_{2}$. We also characterize the shape of coherent precipitates. Finally, the phonon spectra of AgSbTe$_{2}$ and PbTe suggest that boundary scattering of acoustic phonons causes the observed suppression of thermal conductivity. $^{\ast }$K.F. Hsu \textit{et al.}, Science \textbf{303}, 818 (2004).