In this work, we have studied the electronic structure of a promising thermoelectric half-Heusler FeVSb using FP-LAPW method and SCAN meta-GGA including spin–orbit coupling. Using the obtained electronic structure and transport calculations we try to address the experimental Seebeck coefficient S of FeVSb samples. The good agreement between the experimental and calculated S suggests the band gap could be ∼0.7 eV. This is supported by the obtained mBJ band gap of ∼0.7 eV. Further, we study and report the phonon dispersion, density of states and thermodynamic properties. The effect of long range Coulomb interactions on phonon frequencies are also included by nonanalytical term correction. Under quasi-harmonic approximation, the thermal expansion behaviour up to 1200 K is calculated. Using the first-principles anharmonic phonon calculations, the lattice thermal conductivity κ ph of FeVSb is obtained under single-mode relaxation time approximation considering the phonon-phonon interaction. At 300 K, the calculated κ ph is ∼18.6 W m−1 K−1 which is higher compared to experimental value. But, above 500 K the calculated κ ph is in good agreement with experiment. A prediction of figure of merit ZT and efficiency for p-type and n-type FeVSb is made by finding out optimal carrier concentration. At 1200 K, a maximum ZT of ∼0.66 and ∼0.44 is expected for p-type and n-type FeVSb, respectively. For p-type and n-type materials, maximum efficiency of ∼12.2% and ∼6.0% are estimated for hot and cold temperature of 1200 K and 300 K, respectively. A possibility of achieving n-type and p-type FeVSb by elemental doping/vacancy is also discussed. Our study is expected to help in further exploring the thermoelectric material FeVSb.

Fe2VAl and Fe2TiSn are full Heusler compounds with non-magnetic ground state. The two compouds are good thermoelectric materials. PBE and LDA(PW92) are the two most commonly used density functionals to study the Heusler compounds. Along with these two well studied exchange-correlation functionals, recently developed PBEsol, mBJ and SCAN functionals are employed to study the two compounds. Using the five functionals equilibrium lattice parameter and bulk modulus are calculated. Obtained values are compared with experimental reports wherever available. Electronic structure properties are studied by calculating dispersion curves, total and partial density of states. For Fe2VAl, band gap of 0.22 eV is obtained from the mBJ potential which is in reasonable agreement with experimental value while, for Fe2TiSn band gap of 0.68 eV is obtained. Fe2VAl is predicted to be semimetallic with different values of negative gaps from LDA,PBEsol,PBE and SCAN functionals. Whereas, Fe2TiSn is found to be semimetallic(semiconducting) from LDA,PBEsol(PBE,SCAN) functionals employed calculations. From the dispersion curve effective mass values are also computed to see the contribution to the Seebeck coefficient. In Fe2TiSn, a flat band is present along the Γ-X direction with calculated value of effective mass ∼36 more than the mass of electron. The improvements or inadequacies among the functionals in explaining the properties of full Heusler alloys for thermoelectric application are thus observed through this study.

In the quest of new thermoelectric materials with high power factors, full-Heusler compounds having flat band are found to be promising candidates. In this direction, Fe2ScX (X=P,As,Sb) compounds are investigated using mBJ for the band gap and SCAN to describe the electronic bands and phonon properties for thermoelectric applications. The band gaps obtained from mBJ are 0.81 eV, 0.69 eV and 0.60 eV for Fe2ScX 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 effective mass values are calculated at the band extrema from SCAN functional. The thermoelectric parameters are calculated for both hole and electron dopings under semiclassical theory. We use simple, but reasonable method to estimate the phonon relaxation time (τ ph ). Using the specific heat, estimated τ ph and slopes (phase velocity) of acoustic branches in the linear region, lattice thermal conductivity (κ ph ) at 300 K is calculated for three compounds. The obtained values of κ ph with constant τ ph are 18.2, 13.6 and 10.3 W m −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 thermoelectric application. The ZT values for n-type Fe2ScX, in 900-1200 K, are 0.34-0.43, 0.40-0.48 and 0.45-0.52, respectively. While, the p-type Fe2ScX 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, Fe2ScX compounds can be promising materials in high temperature power generation application on successful synthesis and further κ ph reduction by methods like nanostructuring.

In this work, we try to understand the experimental thermoelectric (TE) properties of a ZrNiSn sample with DFT and semiclassical transport calculations using SCAN functional. SCAN and mBJ provide the same band gap Eg of ∼0.54 eV. This Eg is found to be inadequate to explain the experimental data. The better explanation of experimental Seebeck coefficient S is done by considering Eg of 0.18 eV which suggests the non-stoichiometry and/or disorder in the sample. Further improvement in the S is done by the inclusion of temperature dependence on chemical potential. In order to look for the possible enhanced TE properties obtainable in ZrNiSn with Eg of ∼0.54 eV, power factor and optimal carrier concentrations are calculated. The optimal electron and hole concentrations required to attain highest power factors are ∼7.6x10 19 cm −3 and ∼1.5x10 21 cm −3 , respectively. The maximum figure of merit ZT calculated at 1200 K for n-type and p-type ZrNiSn are ∼0.6 and ∼0.7, respectively. The % efficiency obtained for n-type ZrNiSn is ∼5.1 % while for p-type ZrNiSn is ∼6.1 %. The ZT are expected to be further enhanced to ∼1.2 (n-type) and ∼1.4 (p-type) at 1200 K by doping with heavy elements for thermal conductivity reduction. The phonon properties are also studied by calculating dispersion, total and partial density of states. The calculated Debye temperature of 382 K is in good agreement with experimental value of 398 K. The thermal expansion behaviour in ZrNiSn is studied under quasi-harmonic approximation. The average linear thermal expansion coefficient αave(T ) of ∼7.8x10 −6 K −1 calculated in our work is quite close to the experimental values. The calculated linear thermal expansion coefficient will be useful in designing the thermoelectric generators for high temperature applications.

First-principles phonon calculations along with Kohn-Sham density functional theory (DFT) is an essential tool to study the lattice dynamics, thermodynamical properties and phase-transitions of materials. The two full-Heusler compounds Fe2VAl and Fe2TiSn are studied for lattice vibration dependent properties using finite displacement method and supercell approach. For the investigation, four density functionals viz., LDA, PBE, PBEsol and meta-GGA SCAN are employed. Using these functionals, phonon dispersion, phonon density of states (DOS), partial density of states (PDOS) thermal propertis and zero-point energy are calculated at equilibrum lattice parameters under harmonic approximation. For the two compounds the Debye temperatures are calculated from the obtained phonon DOS which are ∼660 K and ∼540 K, respectively. The obtained results from different functionals are compared among each other. The overall phonon energy in the dispersion is found to be ∼15 meV higher in Fe2VAl than the Fe2TiSn compounds. For the two compounds PBE is yielding the lowest phonon frequencies while LDA or SCAN functional is giving the highest. The same pattern is observed in phonon DOS plots of two compounds. The zero-point energy calculated is the highest from SCAN (21.04 and 16.95 J) and the lowest from PBE functionals (20.09 and 16.02 J) obeying the same trend as frequency for both compounds. A general prediction of nature of lattice thermal conductivity is made based on the velocities of acoustic phonons which is in agreement with the qualitative behavior of reported experimental thermal conductivity of two compounds. Phonon spectra obtained from PBE and SCAN have similar general features while those from LDA and PBEsol have resembling features for Fe2VAl, while this trend is not observed for the compound Fe2TiSn.