Transport properties of composition tunedα- andβ−Eu8Ga16−xGe30+x

This paper presents the transport properties of several composition tuned $\alpha$- and $\beta \text{−}{\mathrm{Eu}}_8{\mathrm{Ga}}_{16-x}{\mathrm{Ge}}_{30+x}$ samples where $0.28⩽x⩽0.48$ for the $\alpha$ samples and $0.49⩽x⩽1.01$ for the $\beta$ samples. Among samples with the same structure ($\alpha$ or $\beta$), the varying physical properties can be understood in terms of a rigid conduction band where only the charge carrier concentration is varied. The differences in the physical properties between $\alpha$ and $\beta$ samples can be explained by a charge-carrier effective mass $\left(m^{*}\right)$ that is more than three times larger in the $\beta$ phase than in the $\alpha$ phase. As a result of the low charge-carrier mobility we argue that the thermoelectric figure of merit of $n$-type $\alpha$- and $\beta \text{−}{\mathrm{Eu}}_8{\mathrm{Ga}}_{16-x}{\mathrm{Ge}}_{30+x}$, without modifications to enhance the thermoelectric properties, will not exceed that of the best materials at room temperature. From modeling the lattice thermal conductivity $\left({\kappa }_L\right)$ of $\alpha$- and $\beta \text{−}{\mathrm{Eu}}_8{\mathrm{Ga}}_{16-x}{\mathrm{Ge}}_{30+x}$, it is proposed that ${\kappa }_L$ of all clathrates with divalent cations can be described by phonon-charge-carrier scattering at low temperatures and resonant scattering at higher temperatures. This contradicts earlier models where the low-temperature ${\kappa }_L$ of $\beta \text{−}{\mathrm{Eu}}_8{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ and ${\mathrm{Sr}}_8{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ is modeled by scattering of phonons from tunneling states. However, since the phonon-charge-carrier scattering rate increases with ${\left(m^{*}\right)}^2$ the advantage of the phonon-charge-carrier scattering model is the ability to explain the lower low-temperature ${\kappa }_L$ of $\beta \text{−}{\mathrm{Eu}}_8{\mathrm{Ga}}_{16-x}{\mathrm{Ge}}_{30+x}$, compared to $\alpha \text{−}{\mathrm{Eu}}_8{\mathrm{Ga}}_{16-x}{\mathrm{Ge}}_{30+x}$.