Nanoscale $\alpha$-structural domains in the phonon-glass thermoelectric material $\beta \text{−}{\mathrm{Zn}}_4{\mathrm{Sb}}_3$

A study of the local atomic structure of the promising thermoelectric material $\beta \text{−}{\mathrm{Zn}}_4{\mathrm{Sb}}_3$, using atomic pair distribution function (PDF) analysis of x-ray- and neutron-diffraction data, suggests that the material is nanostructured. The local structure of the $\beta$ phase closely resembles that of the low-temperature $\alpha$ phase. The $\alpha$ structure contains ordered zinc interstitial atoms which are not long range ordered in the $\beta$ phase. A rough estimate of the domain size from a visual inspection of the PDF is $\lesssim 10\mathrm{nm}$. It is probable that the nanoscale domains found in this study play an important role in the exceptionally low thermal conductivity of $\beta \text{−}{\mathrm{Zn}}_4{\mathrm{Sb}}_3$.

Figure 1

(Color online) The crystal structure of ${\mathrm{Zn}}_4{\mathrm{Sb}}_3$. (a) Projection down the $c$ axis of the crystal structure of $\beta \text{−}{\mathrm{Zn}}_4{\mathrm{Sb}}_3$ in space group $R\overline{3}c$. There are three distinct atomic positions, 36Zn(1), 18Sb(1), and 12Sb(2). Possible Zn interstitial sites in the interstitial model are indicated with light small circles. (b) The interstitial atoms have full occupancy and become ordered in the $\alpha$ phase (light circles). To help with comparison, only a part of a triclinic supercell is shown.

Figure 2

(Color online) PDF refinement results and the change in PDF over $\alpha \text{−}\beta$ transition. (a) The experimental neutron PDF obtained at $15\mathrm{K}$ (blue circles) together with the calculated PDF from the refined $\alpha$ model (red line). (b) $300\mathrm{K}$ neutron data with the calculated PDF from the refined $\beta$-phase interstitial model. (c) The same data as (b) but this time the calculated PDF of the $\alpha$-structural model. The PDFs in (b) and (c) were calculated with a fixed $U_{\mathit{iso}}$ of $0.01{\mathrm{\AA }}^2$. In each case, the difference between the calculated and measured PDFs is plotted below the data. The good agreement in (c) indicates that the $\alpha$-structural model explains the local structure of $\beta \text{−}{\mathrm{Zn}}_4{\mathrm{Sb}}_3$ with a smaller value of $U_{\mathit{iso}}$ whereas the interstitial model does not (b). [(d) and (e)] Comparison of the change in PDF expected as the sample goes from the $\alpha$ to $\beta$ phase. The PDF in the $\alpha$ phase is shown in light red line and the $\beta$ phase in dark blue line. The difference is plotted below. (d) Experimental x-ray PDFs in $\beta$ ($270\mathrm{K}$, dark blue line) and $\alpha$ ($220\mathrm{K}$, light red line) phases. (e) The calculated PDFs based on the average structures. $U_{\mathit{iso}}$ used for the calculation is $0.01{\mathrm{\AA }}^2$ for both interstitial and $\alpha$-structural models. The observed changes in the local structure are much smaller than expected from the crystal structure models.

Figure 3

(Color online) Comparison of 15 and $300\mathrm{K}$ PDFs in different $r$ regions. (a) Comparison of low- ($15\mathrm{K}$, dark blue line) and high-temperature ($300\mathrm{K}$, light red line) neutron PDFs of ${\mathrm{Zn}}_4{\mathrm{Sb}}_3$ plotted over a wide range of $r$ to $300\mathrm{\AA }$. (b)–(d) are the same data but plotted on expanded $r$ scales. Note that at low $r$, the $300\mathrm{K}$ PDF has broader and lower peaks, but at high $r$ the situation is reversed. PDF peaks broaden with temperature due to increased thermal motion as evident at low $r$ (b). The PDF peaks are sharper and higher at room temperature in the high-$r$ region (d) because the $300\mathrm{K}$ data are from the high-symmetry $\beta$ phase. A rough estimate of the size of the local $\alpha$ domains can be obtained from where the behavior switches over (c).