Thermoelectric transport properties of CaMg${}_{2}$Bi${}_{2}$, EuMg${}_{2}$Bi${}_{2}$, and YbMg${}_{2}$Bi${}_{2}$

Thermoelectric transport properties of CaMg $_{2}$ Bi $_{2}$ , EuMg $_{2}$ Bi $_{2}$ , and YbMg $_{2}$ Bi $_{2}$

Andrew F. May, Michael A. McGuire, David J. Singh, Jie Ma, Olivier Delaire, Ashfia Huq, Wei Cai, and Hsin Wang

Phys. Rev. B 85, 035202 – Published 11 January 2012

Abstract

The thermoelectric transport properties of CaMg $_{2}$ Bi $_{2}$ , EuMg $_{2}$ Bi $_{2}$ , and YbMg $_{2}$ Bi $_{2}$ were characterized between 2 and 650 K. As synthesized, the polycrystalline samples are found to have lower $p$ -type carrier concentrations than single-crystalline samples of the same empirical formula. These low carrier concentration samples possess the highest mobilities yet reported for materials with the CaAl $_{2}$ Si $_{2}$ structure type, with a mobility of $\sim$ 740 cm $^{2}$ /V/s observed in EuMg $_{2}$ Bi $_{2}$ at 50 K. Despite decreases in the Seebeck coefficient ( $α$ ) and electrical resistivity ( $ρ$ ) with increasing temperature, the power factor ( $α^{2} ρ$ ) increases for all temperatures examined. This behavior suggests a strong asymmetry in the conduction of electrons and holes. The highest figure of merit ( $z T$ ) is observed in YbMg $_{2}$ Bi $_{2}$ , with $z T$ approaching 0.4 at 600 K for two samples with carrier densities of approximately $2 \times 10^{18}$ cm $^{- 3}$ and $8 \times 10^{18}$ cm $^{- 3}$ at room temperature. Refinements of neutron powder diffraction data yield similar behavior for the structures of CaMg $_{2}$ Bi $_{2}$ and YbMg $_{2}$ Bi $_{2}$ , with smooth lattice expansion and relative expansion in $c$ being $\sim$ 35 $%$ larger than relative expansion in $a$ at 973 K. First-principles calculations reveal an increasing band gap as Bi is replaced by Sb and then As, and subsequent Boltzmann transport calculations predict an increase in $α$ for a given $n$ associated with an increased effective mass as the gap opens. The magnitude and temperature dependence of $α$ suggests higher $z T$ is likely to be achieved at larger carrier concentrations, roughly an order of magnitude higher than those in the current polycrystalline samples, which is also expected from the detailed calculations.