Electrical transport properties of Co-based skutterudites filled with Ag and Au

This work presents theoretical calculations of the electrical transport properties of the Ag, Au, and La fractionally filled bulk skutterudites: CoSb${}_3$, CoAs${}_3$, and CoP${}_3$. Density functional theory, along with projector augmented wave potentials, was used to calculate bulk band structures and partial density of states. The Seebeck coefficient ($S$), electrical conductivity ($\sigma$), and power factor ($S^2\sigma$) were calculated as a function of temperature and filling fraction using the momentum matrix method along the entire first Brillouin zone. Calculated trends in the electrical transport properties agree with previously published experimental measurements for $p$-type unfilled and La-filled CoSb${}_3$. The calculated $S$ and $\sigma$ values for the Ag- and Au-filled compounds indicate that the most promising electronic properties are exhibited by $p$-type Au${}_{0.125}$(CoSb${}_3$)${}_4$, Au${}_{0.25}$(CoSb${}_3$)${}_4$, and Au(CoSb${}_3$)${}_4$. Au is therefore recommended as a promising filler for improved thermoelectric properties in cobalt antimonides. Ag is also a good filler for cobalt phosphides; the creation of a negative indirect band gap is observed in Ag(CoP${}_3$)${}_4$, which indicates semimetallic behavior, so this compound may possibly exhibit lower thermal conductivity than metallic CoP${}_3$. Finally, we recommend future directions for improving the thermoelectric figure of merit of these materials.

Figure 1

Skutterudite (Co$M$${}_3$) unit-cell structure. The top unit cell shows the sixfold-coordinated Co atoms (blue). The bottom unit cell shows a filler atom (gold) inserted in the center void. The second void in the unit cell is located at the corners.

Figure 2

Band structure and partial density of states for unfilled skutterudites.

Figure 3

Comparison of theoretically computed and experimental (Ref. 36) electrical transport properties $S$ and $\rho$ for unfilled $p$-type CoSb${}_3$, at different hole carrier concentrations $n$.

Figure 4

Comparison of theoretically computed and experimental (Ref. 36) electrical transport property $S$ for unfilled $n$-type CoSb${}_3$, at different hole carrier concentrations $n$.

Figure 5

Comparison of theoretically computed and experimental (Ref. 6) electrical transport properties $S$ and $\rho$ for La(Co${}_{0.25}$Fe${}_{0.75}$Sb${}_3$)${}_4$ and La${}_{0.9}$(Co${}_{0.25}$Fe${}_{0.75}$Sb${}_3$)${}_4$, respectively.

Figure 6

Comparison of Ag, Au, and La fillers for Co$M$${}_3$ ($M$ $=$ P, As, Sb) skutterudites at filling fractions corresponding to $Im$$\overline{3}$ symmetry in the unit cell.

Figure 7

Band structures and partial density of states for best-performing Ag- and Au-filled Co-based skutterudites: 12.5$\%$ and 100$\%$ Au-filled CoSb${}_3$, 100$\%$ Au-filled CoAs${}_3$, and 100$\%$ Ag-filled CoP${}_3$.

Figure 8

Electrical transport properties $S$, $\sigma$, and $S^2\sigma$ as a function of temperature for 12.5$\%$ and 100$\%$ Au-filled CoSb${}_3$ and 100$\%$ Au-filled CoAs${}_3$.

Figure 9

Electrical transport properties $S$, $\sigma$, and $S^2\sigma$ as a function of temperature for 100$\%$ Ag-filled CoP${}_3$.

Figure 10

Thermodynamic cycle indicating the thermodynamically downhill energy of formation for Au-filled CoSb${}_3$.

Figure 11

Symmetries of filled skutterudite systems. Cubic systems have the highest symmetry, followed by rhombohedral and then orthorhombic systems.

Figure 12

Electrical transport properties $S$, $\sigma$, $S^2\sigma$ as a function of Au-filling fraction $x$ for all symmetries computed for Au${}_x$(CoSb${}_3$)${}_4$.

Figure 13

Thermoelectric power factor $S^2\sigma$ as a function of temperature for 25$\%$ Au-filled CoSb${}_3$.

Figure 14

Directional (i.e., $xx$, $yy$, and $zz$) electrical transport properties $S$, $\sigma$, and $S^2\sigma$ as a function of energy for 12.5$\%$ ($Im$$\overline{3}$), 25$\%$ ($R$$\overline{3}$), and 100$\%$ ($Im$$\overline{3}$) Au-filled CoSb${}_3$.