Influence of point defects on the thermal conductivity in FeSi

The unique transport properties of B20 FeSi have been investigated for decades. The progress in theoretical calculations allows the explanation and prediction of more and more of such properties. In this paper we investigate the lattice thermal conductivity of FeSi. Calculation for pristine FeSi severely overestimates the lattice thermal conductivity compared to experiment. We point out that the defect concentration can be considerably larger than indicated by the Hall coefficient. The defect formation energies are calculated and it is found that a substantial amount of iron vacancies can form at thermal equilibrium. These will lead to an increased phonon scattering. To explain the thermal conductivity of FeSi, we consider phonon-phonon, isotope, and phonon-defect scattering to assess possible scattering mechanisms. The calculated thermal conductivities indicate that phonon-defect scattering is important in order to explain the reported experimental values.

Figure 1

Band structure, imaginary and real parts of the Green's function computed using the three-dimensional (3D) tetrahedron method as implemented in almabte [20] with a $22\times 22\times 22$ sampling grid. Second-order IFCs of defect-free FeSi are obtained with a supercell size of $3\times 3\times 3$.

Figure 2

Thermal conductivity of pure FeSi, where only three-phonon scattering was considered in Eq. (2), and natural FeSi, where three-phonon and isotope scattering were considered in Eq. (2), computed using the single-mode relaxation-time approximation as implemented in almabte [20].

Figure 3

Local coordination of the Fe atom in FeSi viewed along the [111] (left) and [101] directions. The arrows indicate the direction and magnitude of the local relaxations upon formation of a ${\square }_{\text{Fe}}$ defect.

Figure 4

Multiple phonon scattering rates present in FeSi. For acoustic phonons with long wavelengths $1/{\tau }^{\mathrm{iso}}\propto {\omega }^4$ for phonon-isotope scattering and $1/{\tau }^{{\square }_{\mathrm{Fe}}}\propto {\omega }^4$ for phonon-vacancy scattering.

Figure 5

Thermal conductivity of FeSi at 200 K as a function of Fe vacancy concentration.

Figure 6

Thermal conductivity of FeSi as a function of temperature at different vacancy concentrations. Experimental values taken from Refs. [8, 15].