Transport and thermodynamic properties under anharmonic motion in type-I Ba${}_8$Ga${}_{16}$Sn${}_{30}$ clathrate

Anharmonic guest atom oscillation has direct connection to the thermal transport and thermoelectric behavior of type-I Ba${}_8$Ga${}_{16}$Sn${}_{30}$ clathrates. This behavior can be observed through several physical properties, with for example the heat capacity providing a measure of the overall excitation level structure. Localized anharmonic excitations also influence the low-temperature resistivity, as we show in this paper. By combining heat capacity, transport measurements, and our previous NMR relaxation results, we address the distribution of local oscillators in this material, as well as the shape of the confining potential and the excitation energies for Ba(2) ions in the cages. We also compare to the soft-potential model and other models used for similar systems. The results show good agreement between the previously deduced anharmonic rattler potential and experimental data.

Figure 1

${}^{71}$Ga NMR quadrupole contribution to inverse $T_{1}T$ product (circles) from Ref. 9 for type-I Ba${}_8$Ga${}_{16}$Sn${}_{30}$, and a fit to anharmonic oscillator behavior (solid curve). Inset: Corresponding 1D double-well potential and its first few energy levels (Ref. 11).

Figure 2

Resistivity measurements (open circles) and fitting (solid curve) from Bloch-Grüneisen function and Einstein model with ${\Theta }_D=230$ K and ${\Theta }_{E1}=56$ K, ${\Theta }_{E2}=49$ K. Inset: Expanded view at the low-temperature end of the data and fitting, where there is a clear mismatch between the model and data.

Figure 3

Resistivity data (open circles) and fitting (solid curve) with rattler contribution added to the previous model, ${\Theta }_D=230$ K, ${\Theta }_{E1}=66$ K, and ${\Theta }_{E2}=54$ K. Inset: Expanded view of the low-temperature region. The mismatch between the data and the model has been reduced significantly compared to that of Fig. 2.

Figure 4

Heat capacity measurement (open circles) and fitting (solid curve) to the model described in text. Inset: Temperature-dependent ${\Theta }_D\left(T\right)$ (solid curve). For comparison, the Debye temperature from the resistivity fit is also shown here (dashed line).

Figure 5

Measured $C/T^3$ vs $T$ and the fit to model described in text (solid curve). Individual contributions as labeled: Debye (dash-dotted), Einstein (dotted), and anharmonic oscillator (dashed). The Einstein part is a superposition of several oscillators.

Figure 6

Comparison of the anharmonic contribution and total calculated heat capacity with different anharmonic potentials. Compared to the model based on previous NMR results (solid curves), the dotted curves represent a narrower anharmonic potential and the dashed curves represent a broader anharmonic potential, as described in the text.