Phase separation and nanostructuring in the thermoelectric material ${\text{PbTe}}_{1-x}{\text{S}}_x$ studied using the atomic pair distribution function technique

The average and local structures of the ${\left(\text{PbTe}\right)}_{1-x}{\left(\text{PbS}\right)}_x$ system of thermoelectric materials has been studied using the Rietveld and atomic pair distribution function methods. Samples with $0.25\le x$ are macroscopically phase separated. Phase separation was suppressed in a quenched $x=0.5$ sample which, nonetheless, exhibited a partial spinodal decomposition. The promising thermoelectric material with $x=0.16$ showed intermediate behavior. Combining TEM and bulk scattering data suggests that the sample is a mixture of PbTe-rich material and a partially spinodally decomposed phase similar to the quenched 50% sample. This confirms that, in the bulk, this sample is inhomogeneous on a nanometer length scale, which may account for its enhanced thermoelectric figure of merit.

Figure 1

(Color online) Comparison of temperature dependencies of measured thermoelectric figure of merit, $ZT$, for PbTe (solid blue squares) and ${\text{PbTe}}_{0.84}{\text{S}}_{0.16}$ (solid red circles).

Figure 2

Raw x-ray powder-diffraction data from the 2D detector for the $x=0.50$ ${\left(\text{PbTe}\right)}_{1-x}{\left(\text{PbS}\right)}_x$ sample. Data from the (a) unquenched and (b) quenched samples are shown for comparison. The one-dimensional integrated powder-diffraction patterns obtained from these data are shown in Fig. 3a and on an expanded scale in Fig. 5. The white circle in the center of each 2D diffractogram represents a shadow from the beam stop.

Figure 3

(Color online) Experimental (a) $F\left(Q\right)$ and (b) $G\left(r\right)$ for all unquenched samples. In the Fourier transform, $Q_{\text{max}}$ was set to $26.0{\text{Å}}^{-1}$. The data are offset for clarity. The compositions of the ${\left(\text{PbTe}\right)}_{1-x}{\left(\text{PbS}\right)}_x$ samples are indicated in panel (a). From top to bottom: $x=1.00$ (green), $x=0.75$ (yellow), $x=0.50$ (magenta), $x=0.25$ (blue), $x=0.16$ (cyan), and $x=0.00$ (black).

Figure 4

(Color online) Representative refinements of the PbTe data using (a) Rietveld and (b) PDF approaches. Symbols represent data and solid lines are the model fits. The difference curves are offset for clarity.

Figure 5

(Color online) Powder diffraction patterns from laboratory x-ray source of all the ${\left(\text{PbTe}\right)}_{1-x}{\left(\text{PbS}\right)}_x$ samples studied. From top to bottom: $x=1.00$ (green), $x=0.75$ (yellow), $x=0.50$ (light and dark magenta), $x=0.25$ (blue), $x=0.16$ (cyan), and $x=0.00$ (black). The data corresponding to the quenched $x=0.50$ sample (light magenta) is superimposed on top of those of the unquenched sample (dark magenta) without being offset. The other data are offset for clarity. Vertical dashed lines indicate positions of several characteristic Bragg peaks in the end-member data to allow for easier comparison.

Figure 6

(Color online) Experimental PDFs for various ${\left(\text{PbTe}\right)}_{1-x}{\left(\text{PbS}\right)}_x$ samples on expanded scale. The PDFs, from top to bottom, correspond to $x=1.00$ (green), $x=0.75$ (yellow), $x=0.50$ (magenta), quenched $x=0.50$ (bright magenta), $x=0.25$ (blue), $x=0.16$ (cyan), and $x=0.00$ (black). The data corresponding to the quenched $x=0.50$ sample (light magenta) is superimposed on top of those of the unquenched sample (dark magenta) without being offset. The other data are offset for clarity. Vertical dashed lines indicate positions of a few selected characteristic PDF features of the end members for easier comparison.

Figure 7

(Color online) Representative refinements of the $x=0.50$ sample data using (a) Rietveld and (b) PDF approach. Symbols represent data and solid lines are the model fits. The difference curves are offset for clarity.

Figure 8

(Color online) PDFs of converged models for (a) $x=0.00$ and (b) $x=1.00$ ${\left(\text{PbTe}\right)}_{1-x}{\left(\text{PbS}\right)}_x$ samples. Comparison of the data for (c) quenched and (d) unquenched $x=0.50$ samples (open symbols) with the solid solution (c) and mixture (d) models (solid lines), respectively. See text for details. Vertical dashed lines indicate positions of selected PDF features characteristic for the end-member compositions, for easier comparison.

Figure 9

HRTEM images of (a) $x=0.16$ and (b) quenched $x=0.50$ ${\left(\text{PbTe}\right)}_{1-x}{\left(\text{PbS}\right)}_x$ samples.

Figure 10

(Color online) Representative refinements of the $x=0.16$ sample data using (a) Rietveld and (b) PDF approach. Symbols represent data and solid lines are the model fits. The difference curves are offset for clarity.