Ca4Sb2O and Ca4Bi2O: two promising mixed-anion thermoelectrics

The environmental burden of fossil fuels and the rising impact of global warming have created an urgent need for sustainable clean energy sources. This has led to widespread interest in thermoelectric (TE) materials to recover part of the ∼60% of global energy currently wasted as heat as usable electricity. Oxides are particularly attractive as they are thermally stable, chemically inert, and formed of earth-abundant elements, but despite intensive efforts there have been no reports of oxide TEs matching the performance of flagship chalcogenide materials such as PbTe, Bi2Te3 and SnSe. A number of ternary X4Y2Z mixed-anion systems, including oxides, have predicted band gaps in the useful range for several renewable-energy applications, including as TEs, and some also show the complex crystal structures indicative of low lattice thermal conductivity. In this study, we use ab initio calculations to investigate the TE performance of two structurally-similar mixed-anion oxypnictides, Ca4Sb2O and Ca4Bi2O. Electronic-structure and band-alignment calculations using hybrid density-functional theory (DFT), including spin–orbit coupling, suggest that both materials are likely to be p-type dopable with large charge-carrier mobilities. Lattice-dynamics calculations using third-order perturbation theory predict ultra-low lattice thermal conductivities of ∼0.8 and ∼0.5 W m−1 K−1 above 750 K. Nanostructuring to a crystal grain size of 20 nm is predicted to further reduce the room temperature thermal conductivity by around 40%. Finally, we use the electronic- and thermal-transport calculations to estimate the thermoelectric figure of merit ZT, and show that with p-type doping both oxides could potentially serve as promising earth-abundant oxide TEs for high-temperature applications.


Respect to the Interpolation Factor
The interpolation factor in the AMSET package 1 controls the density of k-points in the interpolated band structures, with the number of interpolated k-points being approximately equal to the interpolation factor times the number of k-points in the DFT calculation. The transport properties can be highly sensitive to the k-point density, so it is important to explicitly converge the calculated results with respect to this parameter. Figure S2

Convergence of the Phonon Frequencies with Respect to Supercell Expansion
The harmonic phonon dispersions of Ca 4 Sb 2 O and Ca 4 Bi 2 O were explicitly converged with respect to the supercell expansion used to evaluate the force constants. The tests in Figure S4 show that the phonon dispersion curves are almost converged with a 4×4×1 expansion of the conventional unit cell (224 atoms), but for greater accuracy we opted to use a larger 4×4×4 expansion of the primitive cell (448 atoms).
The third-order interatomic force constants are typically short-ranged compared to the second-order force constants, and we therefore used an 84-atom cubic supercell expansion of the primitive cell to evaluate them. The non-diagonal supercell matrix used to generate this supercell, which is done according to Eq. (1), is shown in Eq. (2): where M s is the supercell matrix, the lattice vectors of unit cell are given by a column vector with components a u , b u , c u , and the vectors of the supercell are given by a vector with

Mesh
The changes in the principal xx, yy and zz components of κ l tensors and the isotropic average κ iso = 1 3 (κ xx + κ yy + κ zz ) at T = 300 K, obtained using different q-point sampling meshes, are shown in Figure S5. The κ l of Ca 4 Sb 2 O converges with a 15×15×15 mesh, which produces a κ iso within ≈ 1 % of that obtained using a smaller 13×13×13 mesh. The convergence of

Effect of Phonon-Isotope Scattering on κ l
The presence of isotopes with different masses introduces natural variation at atomic sites that can act as an additional source of phonon scattering. Phono3py 2 implements the model described in ref. 3 to estimate this contribution. As shown in Figure S6, we find that natural isotope scattering has a negligible effect on the κ l of both materials.  Figure S7 shows the cumulative % lattice thermal conductivity as a function of frequency for Ca 4 Sb 2 O and Ca 4 Bi 2 O separately along the a/b and c directions. In both materials, the cumulative contributions to κ l along both directions shows a sharp increase over the acoustic-mode frequencies and a slower rise over the optic-mode frequencies. Therefore, the acoustic modes make the largest contribution to the heat transport along both directions, with a significant further contribution from the optic modes.

Anisotropic Modal Contributions to the κ l
As described in the text, due to the tetragonal symmetry of the crystals the lattice thermal conductivities of Ca 4 Sb 2 O and Ca 4 Bi 2 O are anisotropic and differ along the a/b and c directions. Figure S8 compares the directional group velocity norms |ν λ | and mean free path norms |Λ λ | of each material along the in-plane and out-of-plane directions.
(We note that for this comparison we compute ν λ from √ Tr[ν λ ⊗ ν λ ]. Phono3py outputs ν λ at irreducible q-points which, depending on symmetry, may not be representative of the group velocities along directions. However, the outer products ν λ ⊗ ν λ output by Phono3py are summed over symmetry-related q-points and therefore are representative.) Figure S8 shows that for both structures the maximum ν λ along the c direction are higher than along the a/b direction. However, the density of modes with low ν λ in the c direction is much larger, and thus the average velocity along this direction is smaller. Similarly, there is a much higher density of modes with short mean free paths along the c direction compared to the a and b directions. The lower average ν λ and Λ λ along the c direction compared to the a/b direction leads to lower out-of-plane κ l in both materials. The left-hand columns show data for transport in the a/b directions and the righthand column shows data for transport along the c axis. The data points are colour coded by the modal contributions to κ l , κ λ , from purple to green (low to high κ λ ) for Ca 4 Sb 2 O and pink to blue (low to high κ λ ) for Ca 4 Bi 2 O.