Microstructure and a Nucleation Mechanism for Nanoprecipitates in $\mathrm{PbTe}\mathrm{\text{−}}{\mathrm{AgSbTe}}_2$

Many recent advances in thermoelectric (TE) materials are attributed to their nanoscale constituents. Determination of the nanocomposite structures has represented a major experimental and computational challenge and eluded previous attempts. Here we present the first atomically resolved structures of high performance TE material $\mathrm{PbTe}\mathrm{\text{−}}{\mathrm{AgSbTe}}_2$ by transmission electron microscopy imaging and density functional theory calculations. The results establish an accurate structural characterization for $\mathrm{PbTe}\mathrm{\text{−}}{\mathrm{AgSbTe}}_2$ and identify the interplay of electric dipolar interactions and strain fields as the driving mechanism for nanoprecipitate nucleation and aggregation.

Figure 1

(a) HRTEM image of a single crystal $({\mathrm{AgSbTe}}_2)\mathrm{\text{−}}(\mathrm{PbTe}{)}_{18}$ sample. The red squares I and II highlight two typical nanoprecipitates in the sample. (b) and (c) are the magnified images of I and II, respectively, and the corresponding simulated images in (d) and (e) are based on the atomic positions predicted by our DFT calculations shown in (f) and (g), respectively. The diffusive nature of the nanoprecipitates is caused by Ag atoms taking interstitial positions. Panel (a) also demonstrates the $⟨100⟩$ preferential growth direction in full agreement with the DFT calculations.

Figure 2

Top panel: Two structures (a) and (b) of nanocluster ${\mathrm{Ag}}_{20}{\mathrm{Sb}}_{20}$ in the ${\mathrm{Ag}}_{20}{\mathrm{Pb}}_{824}{\mathrm{Sb}}_{20}{\mathrm{Te}}_{864}$ supercell. Bottom panel: Their formation energy difference obtained using constrained or full structural relaxation.

Figure 3

Arrangements of a Ag-Sb pair in PbTe matrix in the (001) plane of the 1728-atom ($12\times 12\times 12$ atoms) supercell (left) and their formation energies versus Ag-Sb distance $d$ indicated by the same symbols (right).

Figure 4

Calculated formation energy for various arrangements of two Ag-Sb pairs in ${\mathrm{Ag}}_2{\mathrm{Sb}}_2{\mathrm{Pb}}_{860}{\mathrm{Te}}_{864}$ (the supercell is partially shown). Each Ag-Sb pair is marked by a red rectangle as a guide for the eye.

Figure 5

Top panel: The atomic orderings for the most stable nanoclusters ${\mathrm{Ag}}_n{\mathrm{Sb}}_n$ in ${\mathrm{Ag}}_n{\mathrm{Pb}}_{864-2n}{\mathrm{Sb}}_n{\mathrm{Te}}_{864}$ with $n=1$, 2, 4, 8, 12, 16, 20, 24, 28, 32, 36, and 40 [(a) to (l)]. The thick lines and $+/-$ signs indicate the arrangements of dipoles formed by $\mathrm{Ag}(-)$ and $\mathrm{Sb}(+)$ atoms. Other notations are the same as in Fig. 4. Bottom panel: The calculated formation energies (in $\mathrm{eV}/\mathrm{Ag}\mathrm{\text{−}}\mathrm{Sb}$ pair).