Presence of $\alpha $ phase domains in the phonon-glass thermoelectric $\beta $-Zn$_{4}$Sb$_{3}$ from atomic pair distribution function (PDF) analysis

The promisingly high \textit{ZT} of $\beta $-Zn$_{4}$Sb$_{3}$ between 450 K and 670 K is known to be due to its exceptionally low thermal conductivity. The discovery of significant Zn interstitial disorder in $\beta $-Zn$_{4}$Sb$_{3}$ provides foundation for better understanding of the origin of the glass-like thermal conductivity[1]. Furthermore, it has been reported that Zn interstitial atoms become ordered in $\alpha $-phase[2]. We report on the \textit{local} structural study of $\beta $-Zn$_{4}$Sb$_{3}$ using PDF technique, which has been successfully applied to solve the structures of crystallographically challenged materials[3,4]. Prominent diffuse scattering is found both in neutron and x-ray data. The PDF analysis suggests that the average $\beta $-structure consists of locally $\alpha $-structure like domains where Zn interstitial atoms are ordered. This provides an important local structural insight into not well understood $\alpha $ to $\beta $ order-disorder phase transition in Zn$_{4}$Sb$_{3}$ at 260 K. [1] G. J. Snyder \textit{et al}. Nat. Mater. \textbf{3}, 458 (2004) [2] J. Nyl\'{e}n \textit{et al}. J. Am. Chem. Soc. \textbf{126}, 16306 (2004) [3] T. Egami and S. J. L. Billinge, \textit{Underneath the Bragg peaks}, Pergamon Press, Elsevier, Oxford, England, 2003 [4] S. J. L. Billinge and M. G. Kanatzidis, Chem. Commun., 749 (2004)