Two functionals approach in DFT for the prediction of thermoelectric properties of Fe$_{2}$ScX (X = P, As, Sb) full Heusler compounds

Abstract: In the quest of new thermoelectric (TE) materials with high power factors, full-Heusler compounds having flat band are found to be promising candidates. In this direction, Fe${2}$ScX (X=P,As,Sb) compounds are investigated using mBJ for the band gap and SCAN to describe the electronic bands and phonon properties for TE applications. The band gaps obtained from mBJ are 0.81 eV, 0.69 eV and 0.60 eV for Fe${2}$ScX compounds, respectively. The phonon dispersion, phonon density of states (DOS) and partial DOS are calculated. The phonon contributions to specific heat are obtained as a function of temperature under harmonic approximation. The electronic band structutre calculated from mBJ and SCAN functionals are qualitatively compared. The TE parameters are calculated for both hole and electron dopings under semiclassical theory. We use simple, but reasonable method to estimate phonon relaxation time ($\tau_{ph}$). Using the specific heat, estimated $\tau_{ph}$ and slopes (phase velocity) of acoustic branches in the linear region, lattice thermal conductivity ($\kappa_{ph}$) at 300 K is calculated for three compounds. The obtained values of $\kappa_{ph}$ with constant $\tau_{ph}$ are 18.2, 13.6 and 10.3 $Wm^{-1}K^{-1}$, respectively. Finally, the temperature dependent figure of merit $ZT$ values are calculated for optimal carrier concentrations in the doping range considered, to evaluate the materials for TE application. The $ZT$ values for n-type Fe${2}$ScX, in 900-1200 K, are 0.34-0.43, 0.40-0.48 and 0.45-0.52, respectively. While, the p-type Fe${2}$ScX have $ZT$ of 0.25-0.34, 0.20-0.28 and 0.18-0.26, respectively in the same temperature range. The $ZT$ values suggest that, Fe${2}$ScX compounds can be promising materials in high temperature power generation application on successful synthesis and further $\kappa{ph}$ reduction by methods like nanostructuring.