Lead chalcogenides are dominant thermoelectric materials in the medium-temperature range,owing to their highly favorable electronic band structures and low thermal conductivities achievable.An important system is the PbTe-PbS pseudo-binary and its low thermal conductivity originates largely from the coexistence of both alloying and nanostructuring through phase-separation.To better understand the competition between alloying and phase separation,and its pronounced effects on the thermoelectric performance in PbTe-PbS,we systematically studied,via transmission electron microscopy(TEM)observations and theoretical calculations,K-and Na-doped(PbTe)1-x(PbS)x pseudo-binaries.In both systems,we have achieved broad plateau of figure of merit ZT,with the highest values of 2.2[1] and 2.3 [2]at 923 K,individually.In K-doped system,the high-density nano-precipiates in both PbTe and PbS grains,together with the PbTe-PbS phase boundaries,provide very strong scattering effect on phonons,leading to a record low thermal conductivity ever reported in lead chalcogenides.In Na-doped system,the lowest lattice thermal conductivity of the series was achieved when the PbS phase-fraction,x,was 20%,originating from the all-scale hierarchical structures and SPS processes;we also studied the onset of carrier concentration modulation~600 K,which leads to the observed saturation of electrical transport properties due to the diffusion and re-dissolution of excessive Na into the PbTe-PbS matrix.This carrier concentration modulation,is equally crucial to achieve the very high power factors(up to 26.5 μW/cmK2 at 623 K)and the outstanding thermoelectric performances in SPSed PbTe-PbS binaries.