Phase Stability and Ordering in Rock Salt-Based Thermoelectrics: NaSbX₂, AgSbX₂, and Their Alloys with PbX and SnX (X = S, Se, Te)

Using first-principles density functional calculations, we study the phase stability and cation ordering behavior in ABX₂, PbX-ABX₂, and SnTe-ABTe₂ (A = Na, Ag; B = Sb; X = S, Se, Te) thermoelectrics that crystallize in rock salt-based lattices. We construct, separately for each ABX₂ system, cluster expansions fitted to T = 0 K energies of cation-ordered arrangements in order to identify the respective ground-state structures. We calculate the mixing energetics of A/B and {Pb, Sn}/AB cation-disordered solid solutions in ABX₂ and {Pb, Sn}X-ABX₂ systems, respectively, using special quasirandom structures. We find that (i) L1₁, a rock salt-based superlattice with A₁B₁ stacking of cations along [111], is often the most favored cation ordering type across ABX₂ systems due to the ability of this superlattice structure to accommodate large size mismatches between A and B; (ii) A/B cation ordering is only weakly preferred over disorder in all ABX₂ systems, by <34 meV/cation, consistent with experimental observations of disordered rock salt phases at high temperatures; (iii) Na-containing ABX₂ systems strongly favor the formation of the ternary compound over the corresponding ground-state mixture of A₂X + B₂X₃ binary compounds, while Ag-containing ABX₂ systems do not; (iv) the experimentally reported noncubic phases of NaSbS₂ and AgSbS₂ are in fact distorted cation-ordered rock salt structures; and (v) all {Pb, Sn}X-ABX₂ systems show miscibility gaps in their phase diagrams, and this is partly due to the unfavorable electrostatics of ternary cation mixing relative to Pb or Sn + AB cation phase separation; however, estimation of the miscibility gap temperature using mean-field configurational entropy indicates that all systems except PbTe-AgSbTe₂ will readily mix at relatively low temperatures. Our study of the structural properties, alloying behavior, and solubility limits in these promising materials is a crucial step forward in improving their thermoelectric performance.