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Using a first-principles cluster expansion, we shed light on the solid-statephase diagram and structure of the recently discovered high-performancethermoelectrics, Pb-Ag-Sb-Te alloys. The observed nanoscale inhomogeneities areshown to be coherent precipitates of ordered (Ag)m(Sb)n(Te)m+n phases, such asAgSbTe2, all immiscible with rocksalt PbTe. The solubility is high for PbTe inAgSbTe2 and low for (Ag,Sb)Te in PbTe (8% vs. 0.6% at 850 K). The differencesin the phonon spectra of PbTe and AgSbTe2 confirm that the inhomogeneitiesenhance the thermoelectric performance.

First-Principles Theory of Competing Order Types, Phase Separation, and Phonon Scattering in Thermoelectric Pb-Sb-Ag-Te Alloys