Density-functional band-structure calculations for La-, Y-, and Sc-filled ${\mathrm{CoP}}_3$-based skutterudite structures

The crystal structure, thermodynamic stability, and electronic structure of La-, Y-, and Sc-filled ${\mathrm{CoP}}_3$ are predicted from density-functional band-structure calculations. The size of the cubic voids in the skutterudite structure is changed much less than the difference in size between the different filling atoms, and we expect that the larger rattling amplitude of the smaller Sc and Y atoms may decrease the lattice thermal conductivity of Sc- and Y-filled structures significantly compared to La-filled structures. The solubility of La, Y, and Sc in ${\mathrm{CoP}}_3$ is calculated to be around 5, 3-6 %, and below 1% at 0 K, respectively. Based on similar systems, this is expected to increase considerably if Fe is substituted for Co. Fe substitution is also expected to compensate the increased charge carrier concentration of the filled structures that is seen in the calculated electron density of states. In conclusion, Sc- or Y-filled $\left(\mathrm{FeCo}\right){\mathrm{P}}_3$ skutterudite structures are promising materials for thermoelectric applications.

Figure 1

The filled skutterudite crystal structure. The composition is $M{T}_4{X}_{12}$, where $M$ is the rare-earth filling atom (large grey balls), $T$ is the transition metal (black balls), and $X$ is the pnictogen (white balls). The conventional cubic unit cell containing two formula units is shown, only with the origin translated by (0.25,0.25,0.25).

Figure 2

The relaxed volume in ${\mathrm{nm}}^3$ of the models $M_x{\mathrm{Co}}_4{\mathrm{P}}_{12}$ as a function of the filling fraction $x$, with $M=\mathrm{La}$, Y, and Sc. The experimental volume of ${\mathrm{CoP}}_3$ is $0.4585{\mathrm{nm}}^3$ (Ref. 27).

Figure 3

The decomposition enthalpy of filled ${\mathrm{CoP}}_3$ as a function of filling fraction $x$. The enthalpy has been normalized to the conventional cell, that is, ${\mathrm{Co}}_8{\mathrm{P}}_{24}$. The dotted lines are linear extrapolations of the data points at 25 and 12.5 %.

Figure 4

The total DOS of ${\mathrm{CoP}}_3$ calculated by ADF-BAND (a) and VASP (b). The energy is in eV relative to the Fermi level.

Figure 5

The band structure of ${\mathrm{CoP}}_3$. The energy is in eV relative to the Fermi level.

Figure 6

The total DOS of 12.5, 25, 50, and 100 % La-filled ${\mathrm{CoP}}_3$. The energy is in eV relative to the Fermi level.

Figure 7

The band structure of ${\mathrm{LaCo}}_8{\mathrm{P}}_{24}$. The energy is in eV relative to the Fermi level.