Electronic Structure and Thermoelectric Properties of Half-Heusler Alloys NiTZ
Dhurba R. Jaishi, Nileema Sharma, Bishnu Karki, Bishnu P. Belbase, Rajendra P. Adhikari, Madhav Prasad Ghimire
EElectronic Structure and Thermoelectric Properties of Half-Heusler AlloysNiTZ
Dhurba R. Jaishi,
1, 2
Nileema Sharma,
1, 2
Bishnu Karki,
1, 2
Bishnu P. Belbase,
1, 2
Rajendra P. Adhikari, andMadhav P. Ghimire
1, 2, a) Central Department of Physics, Tribhuvan University, Kirtipur 44613, Kathmandu, Nepal Condensed Matter Physics Research Center (CMPRC), Butwal, Rupandehi, Nepal Department of Physics, Kathmandu University, Dhulikhel 45200, Nepal (Dated: 5 October 2020)
We have investigated the electronic and thermoelectric properties of half-Heusler alloys NiTZ (T = Sc, and Ti; Z =P, As, Sn, and Sb) having 18 valence electron. Calculations are performed by means of density functional theoryand Boltzmann transport equation with constant relaxation time approximation, validated by NiTiSn. The chosen half-Heuslers are found to be an indirect band gap semiconductor, and the lattice thermal conductivity is comparable with thestate-of-the-art thermoelectric materials. The estimated power factor for NiScP, NiScAs, and NiScSb reveals that theirthermoelectric performance can be enhanced by appropriate doping rate. The value of ZT found for NiScP, NiScAs,and NiScSb are 0.46, 0.35, and 0.29, respectively at 1200 K. I. INTRODUCTION
In the past few decades, researchers have been focusedon the investigation of the multi-functional materials, whichcan be used as various applications such as in spintronics,optoelectronics, thermoelectrics (TE), etc. With the surgein demand for green energy sources, TE materials are ex-tensively taken into considerations for their ability to con-vert relatively small and waste heat into useful energy at thetime of energy consumption. Wide range of materials hasbeen explored for the potential TE devices such as organic ,chalcogenides , skutterudites , oxide perovskites , hy-brid perovskites , triple-point metals , and half-Heusler(hH) alloys . Among them, Heusler compounds havegained much more attention since their discovery in 1903 dueto their simple crystalline structure with fascinating propertiesthat includes magnetism, half metallicity, superconductivity,optoelecronic, piezoelectric semiconductors, thermoelectric-ity, topological insulators and semimetals .Thermoelectric materials are found applicable in day-to-day lives to fulfill the increasing demand of energy of theglobalized society. The highly efficient TE devices (cooler,power generator, temperature sensors, etc) can utilize a largeamount of wasted thermal energy to generate electricity andvice-versa . For this, the device needs a larger figure ofmerit ( ZT ), which depends on the transport properties de-fined by ZT = α σ T κ (1)where α (V K − ) is the Seebeck coefficient, σ (S m − ) isthe electrical conductivity, κ = κ e + κ l (W m − K − ) is thermalconductivity, and T(K) is the absolute temperature. α σ isdefined as the power factor (PF). The symbol κ e and κ l rep-resents the electronic and lattice thermal conductivity, respec-tively. The materials having a high value of PF along with thelow value of κ are suitable for the efficient TE devices . a) Electronic mail: [email protected]
Among others, most of the cubic hH alloys with 18 valenceelectron count (VEC) exhibits high Seebeck coefficients andare reported as promising materials for TE application due tohigh electrical conductivity and narrow band gap semiconduc-tors with novel electrical and mechanical properties even athigh-temperatures . In addition to it, hH alloys containnon-toxic and readily available elements, making them envi-ronmentally friendly and more cost effective.Recent experimental and theoretical investigations on hHalloys are mainly focused on improving their thermoelectricefficiency ZT by tuning the power factor and thermal conduc-tivity. Band gap engineering and fluctuation of carrier concen-tration around the Fermi level ( E F ) in Z position is a widelyused method to enhance the power factor, whereas, thermalconductivity can be decreased by alloying or by doping on X or Y site to fluctuate the mass of the carriers introducing im-purities and nanostructuring .From the literature survey, we noticed that Ni-based hH al-loys with 18-VEC are less investigated. This motivates us toexplore the electronic, TE, and other related properties to con-firm if these groups of materials could be suitable for TE de-vices. II. COMPUTATIONAL DETAILS
The cubic hH alloys NiTZ (T= Sc, and Ti; Z= P, As, Sn,and Sb) belongs to Cl b structure with space group F ¯43 m . Itcontains three in-equivalent atoms forming inter-penetratingfcc sublattices with the Wyckoff positions Ni (1/4, 1/4, 1/4), T(1/2, 1/2, 1/2) and Z (0, 0, 0), respectively as shown in Figure1. The iso-structural NiTiSn is used here to validate our cal-culations based on the earlier reported results (both theoreticaland experimental).The density functional (DF) calculations has been per-formed using the full-potential linear augmented plane wave(FP-LAPW) method as implemented in the WIEN2k code .We double checked some parts of our calculations using theplane-wave based pseudopotentials Quantum Espresso (QE)package . The standard generalized-gradient approximation a r X i v : . [ c ond - m a t . m t r l - s c i ] O c t FIG. 1. The crystal structure of cubic hH NiTZ (T= Sc, and Ti; Z=P, As, Sn, and Sb). The balls in blue, black, and red color representsNi, T, and Z atoms, respectively. (GGA) in the parameterization of Perdew, Burke, and Ernzer-hof (PBE) was used in scalar-relativistic mode. The mod-ified Becke-Johnson (mBJ) potential was further includedto check the accuracy of the band gaps. The self-consistencyconvergence criteria for charge was set to 10 − e , and energyto 10 − Ry.In the plane-wave pseudopotential approach, we used thenorm-conserving pseudopotentials with plane wave cut-offenergy for wave function set to 90 Ry. The full BrillouinZone (BZ) was sampled with an optimized 10 × ×
10 meshof Monkhorst-Pack k − points. To check the dynamical sta-bility, phonon spectrum calculations have been performedwith 4 × × q − mesh in the phonon BZ, which is based onthe DF perturbation theory (DFPT) implemented in the QEpackage .The TE properties were calculated using the Boltzmannsemi-classical transport equation and constant relaxation timeapproximation based on a smoothed Fourier interpolation ofthe bands implemented on BoltzTraP code . The full BZwas sampled with 50 × × k − mesh for the calculationof the transport properties. The electrical conductivity and PFwere calculated under constant relaxation time approximation( τ ) using the BoltzTraP code based on Boltzmann theory. τ is approximated by fitting the experimental data from Kim etal . . The lattice thermal conductivity was obtained by solv-ing linearized Boltzmann transport equation (BTE) within thesingle-mode relaxation time approximation (SMA) using ther-mal2 code implemented in QE package . III. RESULTS AND DISCUSSIONA. Structure Optimization and Phonon Stability
We started our calculations by optimizing the cubic hH al-loys with F ¯43 m symmetry. Our calculated values of latticeparameters and the band gap within GGA and GGA + mBJare listed in Table I. These values are found to be in fair agree-ment with the earlier reports of Ma et al . for the GGA case. TABLE I. The optimized lattice constant a and the band gap E g within GGA and GGA + mBJ for the cubic hH alloys NiTZ.GGA GGA+mBJSystem a (Å) E g (eV) E g (eV)NiScP 5.69 0.54 0.62NiScAs 5.84 0.48 0.52NiScSb 6.12 0.28 0.32NiTiSn 5.95 0.46 0.45 Γ X L WK Γ L Ka) F r equen cy ( c m - ) Γ X L WK Γ L Kb) 0 100 200 300 Γ X L WK Γ L Kc) F r equen cy ( c m - ) Γ X L WK Γ L Kd)
FIG. 2. Phonon band structures for finding the dynamic stability ofa) NiScP, b) NiScAs, c) NiScSb, and d) NiTiSn.
The calculated phonon dispersion curves along the high-symmetry points shown in Figure 2 depicts that the proposedhH alloys are thermally stable. This is evidenced by the ab-sence of imaginary phonon frequencies throughout the wholeBZ, as expected for dynamic stability . We observed threeacoustic (low-frequency region) and six optical phonon (high-frequency region) branches due to three atoms per unit cell.The majority of the lattice contribution to the thermal conduc-tivity arises from the acoustic part as it has high group veloc-ity compared to the optical part. We found that the acousticalphonon branches of NiScP and NiScAs extends nearly to 200cm − while NiScSb and NiTiSn lies within 150 cm − in fre-quency. The observation of dynamical stability and preferableenergy gap in our proposed hH alloys motivate us to explorethe electronic and transport properties for their potential ap-plication as TE materials. B. Electronic Properties
To understand the ground state electronic properties of thematerial, the total and partial density of states (DOS) areshown in Figure 3. The proposed systems are found to besemiconducting with an energy gap lying within ∼ . − . . As seen in thePDOS the main contribution to the total DOS at and around E F are from the 3 d -orbitals of Ni and Sc atoms while the contri-butions from atom on the Z site is negligible (see in Figure 3).This is an indication that doping onto the Z site may improvethe carrier concentration. D en s i t y o f s t a t e s ( s t a t e s / e V ) TotalNi-3dSc-3dP-3p b) TotalNi-3dSc-3dAs-4p 0 2 4 6 8 -3 -2 -1 0 1 2 3c) D en s i t y o f s t a t e s ( s t a t e s / e V ) Energy (eV)TotalNi-3dSc-3dSb-5p -3 -2 -1 0 1 2 3d) Energy (eV)TotalNi-3dTi-3dSn-5p
FIG. 3. Total and Partial density of states of a) NiScP, b) NiScAs,c) NiScSb, and d) NiTiSn within GGA + mBJ. Vertical dotted linerepresent E F . It is interesting to note that with increase in the atomic ra-dius of atoms at Z site, say, from P to Sb, the band gap re-duces gradually which further leads to the decrease in the hy-bridization of Ni-3 d and Sc-3 d states. An indirect band gapis observed in the band structures for hH alloys (see Figure4) with their valence band maximum (VBM) lying at Γ andconduction band minimum (CBM) at X in the BZ. The VBMfor the hH alloys are 3-fold degenerate comprising of heavyand light bands. From the observed band structure in Figure4, the scenario of heavy bands can enhance the Seebeck co-efficient, whereas, the light band can facilitate the mobility ofcharge carriers . Thus, the combination of heavy and lightbands are preferable for increasing the TE performance. Theband structure shown in Figure 4 (a), (b), and (c) dictates theeffective mass to be more at X − Γ in CBM than that of VBMat Γ (i.e., the effective mass of electron at CBM is greater thanthat of the hole at VBM), which play an significant role in TEproperties. As seen in NiTiSn (Figure 4 (d)), the VBM (at Γ X L W K Γ L K -4-3-2-101234 E n e r gy ( e V ) a) E g =0.62 Γ X L W K Γ L K -4-3-2-101234 b) E g =0.52 E F Γ X L W K Γ L K -4-3-2-101234 E n e r gy ( e V ) c) E g =0.32 Γ X L W K Γ L K -4-3-2-101234 d) E g =0.45 E F FIG. 4. Electronic band structure of a) NiScP, b) NiScAs, c) NiScSb,and d) NiTiSn within GGA + mBJ. Γ ) is flatter than the CBM (at X ) indicating that the effectivemass of holes at VBM is more than that of electrons on CBM. C. Transport Properties
For an efficient TE material, a high value of α and σ with alow κ is expected, as depicted in equation (1). The dimension-less figure of merit ZT can be optimized when these parame-ters are optimum. But these parameters are inter-related withthemselves. Thus, to obtain high value of ZT is in-sufficientjust by tuning one or two parameters. To get insight intothe TE properties of hH alloys, we calculate the Seebeck co-efficient α , electrical conductivity σ / τ , thermal conductivity( κ = κ e + κ l ), power factor (PF), and the figure of merit ZT byusing constant relaxation time approximation and rigid bandapproximation.We first initiate our calculations for NiTiSn by validatingthe theoretical results, such as PF and thermal conductiv-ity with the reported experimental measurements . Fromthe comparison of the calculated and experimental electri-cal conductivity, we approximated the relaxation time τ = ∼ × − s . In the whole process, we use the constantrelaxation time, even though it depends on doping level andtemperature, obtained for NiTiSn to implement for all the iso-electronic systems.The PF of NiTiSn was reported to be ∼ µ Wcm − K − at700 K, which upon electron doping (by 1% of Sb atom to Sn a) α σ ( µ W c m - K - ) n (e/uc)
300 K500 K800 K1000 K1200 K 10 12 14 16 18 20 22 400 600 800 1000 1200 b) κ ( W m - K - ) Temperature (K)
FIG. 5. Power factor as a function of doping level (e/uc) for NiTiSn.The negative (positive) value represents the electron (hole) doping,and b) Total thermal conductivity as a function of temperature. site), PF rises to ∼ µ W cm − K − . When temperature risesabove 700 K, PF is found to decrease in both cases. Com-paring these values we estimate that PF may range between10 − µ Wcm − K at 0 . − .
06 doping level of electronper unit cell in the same temperature range. In case of holedoping, PF lies within 17 − µ W cm − K − at the sametemperature range when dopants is 0 . − . −
10 Wm − K − (see Figure 5 (b)) was slightly higher thanthe earlier report (i.e., 7 −
10 Wm − K − ), which is mainlydue to the electronic contribution found prominent at highertemperature. Our calculated results are comparable with theexperimental measurements .The Seebeck coefficient (a, c, e) and the PF (b, d, f) for dif-ferent level of doping are shown in Figure 6 for NiScP, NiS-cAs, and NiScSb, respectively. Around E F (i.e., at µ = > ± µ V / K ), which on dop-ing to either side, falls-off significantly. This is evident fromits inverse relation with the carrier concentration.The optimum values of the doping levels and correspondingTE parameters for 1200 K are listed in Table II.PF is another parameter to check the reliability of TE ma-terials. As observed in Figure 6, the PF value for p or n − type is significant within the doping range of ± .
3. To bespecific, at 1000 K the calculated values are approximately15, 12 and 13 µ Wcm − K − for NiScP, NiScAs, and NiScSbwithin 0 . − .
04 hole per unit cell reaching its maximumvalue at 1200 K. Similarly, for doping range 0 . − .
07 elec-tron per unit cell, PF rises to ∼
27, 25, and 20 µ Wcm − K − at 1000 K. The sizable value of PF within the doping range0 . − .
08 electron per unit cell suggests that these materialcould be a good TE materials.Figure 7 shows the calculated thermal conductivity as afunction of temperature for NiScP, NiScAs, NiScSb, and Ni-TiSn, respectively. The total thermal conductivity consists oftwo components viz. electronic ( κ e ) and lattice ( κ l ) parts. Atlow temperature (say 300 K), the lattice part was found domi-nant over the electronic part, and with rise in temperature (sayupto ∼
900 K, except NiScP), the lattice thermal conductivity -200-100 0 100 200 a) α ( µ V K - )
300 K500 K800 K1000 K1200 K-200-100 0 100 200 c) α ( µ V K - ) -200-100 0 100 200 -0.6 -0.3 0 0.3 0.6e) α ( µ V K - ) n (e/uc) α σ ( µ W c m - K - ) α σ ( µ W c m - K - ) α σ ( µ W c m - K - ) n (e/uc) FIG. 6. The Seebeck coefficient (a, c, e) and the Power factor (b,d, f) vs the doping level (in e/uc) at various temperature for NiScP,NiScAs, and NiScSb, respectively. The values in negative (positive)values on the horizontal axes represents the electron (hole) doping,respectively. κ t o t a l ( W m - K - ) Temperature (k) κ l a tti ce ( W m - K - ) Temperature (k)
NiTiSnNiScPNiScAsNiScSb
FIG. 7. Total thermal conductivity ( κ ) as a function of tempera-ture, inset dictates lattice contribution to thermal conductivity ( κ l )of NiScP, NiScAs, NiScSb, and NiTiSn. and the overall conductivity decreases uniformly. To note is,with an increase in temperature starting from 300 K, the car- TABLE II. Calculated optimal doping levels and the correspondingSeebeck coefficient, electrical conductivity, power factor, and figureof merit of NiTZ (T= Sc, and Ti; Z= P, As, Sn, and Sb) in cubicsymmetry F ¯43 m at 1200 K. Negative ( − ) sign indicates the n − typecharacteristics.System n α σ α σ ZTe/uc µ VK − ( × S cm − ) µ Wcm − K − NiTiSn 0.20 154 1.15 27.61 0.30NiScP -0.08 -177 1.05 33.16 0.46NiScAs -0.08 -168 1.12 31.50 0.35NiScSb -0.07 -163 0.90 24.20 0.29 ZT Temperature (k)
NiTiSnNiScPNiScAsNiScSb
FIG. 8. The figure of merit ( ZT ) as a function of temperature. rier concentration increases resulting in higher electrical con-ductivity, and hence the overall thermal conductivity. Simi-lar features was observed in the recent report of CoMnSb .The calculated lattice conductivity was 10.6, 19, and 18.5Wm − K − at 300 K which reduces abruptly to 2.5, 4.7, and4.5 Wm − K − at 1200 K for NiScP, NiScAs, and NiScSb,respectively.The figure of merit ( ZT ) for hH alloys is as shown in Figure8. With low value (say, 0.05) of ZT at 300 K, it is found torise linearly with the increase in temperature. At 1200 K, thecalculated values are 0.30, 0.45, 0.35 and 0.29, respectivelyfor NiTiSn, NiScP, NiScAs, and NiScSb alloys. Though thevalues we reported are lower than the commercialized TE ma-terials such as Bi Te and PbTe, ZT can be enhanced furtherby means of doping to any of the three sites. The observed ZT is low mainly due to a higher value of κ .As observed from the calculations above, ZT value can in-crease when PF is enhanced while minimizing the thermalconductivity. The possible route to tune this from DF is by proper tuning of the band gap with appropriate electron/holedoping as discussed. IV. CONCLUSIONS
On the basis on density functional calculations, we inves-tigate the half-Heuslers NiTiSn, NiScP, NiScAs, and NiScSb,respectively. Electronic properties reveal that these materialsare semiconductor with an indirect band gap. The narrow-band gap marks them as suitable candidate for TE perfor-mance. The calculated power factor shows large value in boththe electron and hole doping case. Electron doping is foundmore preferable than hole for NiScP, NiScAs, and NiScSb,while hole doping is preferable for NiTiSn. Based on the con-stant relaxation time approximation and rigid band approxi-mation with sizable ZT , these compounds are predicted as apossible TE materials. ACKNOWLEDGMENTS
MPG acknowledges the Alexander von Humboldt Foun-dation for the equipment subsidy grants. Part of this workwas performed with the computational resources provided bythe Kathmandu University Supercomputer Center establishedwith the equipment donated by CERN, and the Arkansas HighPerformance Computing Center which is funded through mul-tiple National Science Foundation grants and the ArkansasEconomic Development Commission.
DATA AVAILABILITY
The data that supports the findings in this study can be ob-tained from the corresponding author upon request.
DECLARATION OF COMPETING INTEREST
There is no conflict of interest. B. Russ, A. Glaudell, J. J. Urban, M. L. Chabinyc, and R. A. Segalman,“Organic thermoelectric materials for energy harvesting and temperaturecontrol,” Nature Reviews Materials , 1–14 (2016). M. G. Kanatzidis, “Nanostructured thermoelectrics: the new paradigm?”Chemistry of materials , 648–659 (2010). G. J. Snyder and E. S. Toberer, “Complex thermoelectric materials,” in ma-terials for sustainable energy: a collection of peer-reviewed research andreview articles from Nature Publishing Group (World Scientific, 2011) pp.101–110. Y. Lan, A. J. Minnich, G. Chen, and Z. Ren, “Enhancement of thermoelec-tric figure-of-merit by a bulk nanostructuring approach,” Advanced Func-tional Materials , 357–376 (2010). J. R. Szczech, J. M. Higgins, and S. Jin, “Enhancement of the thermo-electric properties in nanoscale and nanostructured materials,” Journal ofMaterials Chemistry , 4037–4055 (2011). P. Roy, V. Waghmare, and T. Maiti, “Environmentally friendly ba x sr 2- xtifeo 6 double perovskite with enhanced thermopower for high temperaturethermoelectric power generation,” RSC Advances , 54636–54643 (2016). W. S. Choi, H. K. Yoo, and H. Ohta, “Polaron transport and thermoelectricbehavior in la-doped srtio3 thin films with elemental vacancies,” AdvancedFunctional Materials , 799–804 (2015). A. Filippetti, C. Caddeo, P. Delugas, and A. Mattoni, “Appealing perspec-tives of hybrid lead–iodide perovskites as thermoelectric materials,” TheJournal of Physical Chemistry C , 28472–28479 (2016). C. Lee, J. Hong, A. Stroppa, M.-H. Whangbo, and J. H. Shim, “Organic–inorganic hybrid perovskites abi 3 (a= ch 3 nh 3, nh 2 chnh 2; b= sn, pb)as potential thermoelectric materials: a density functional evaluation,” RscAdvances , 78701–78707 (2015). Y. Liu, X. Li, J. Wang, L. Xu, and B. Hu, “An extremely high power factorin seebeck effects based on a new n-type copper-based organic/inorganichybrid c 6 h 4 nh 2 cubr 2 i film with metal-like conductivity,” Journal ofMaterials Chemistry A , 13834–13841 (2017). S. Singh, Q. Wu, C. Yue, A. H. Romero, and A. A. Soluyanov, “Topologicalphonons and thermoelectricity in triple-point metals,” Phys. Rev. Materials , 114204 (2018). S.-W. Kim, Y. Kimura, and Y. Mishima, “High temperature thermoelectricproperties of tinisn-based half-heusler compounds,” Intermetallics , 349–356 (2007). C. Fu, S. Bai, Y. Liu, Y. Tang, L. Chen, X. Zhao, and T. Zhu, “Realiz-ing high figure of merit in heavy-band p-type half-heusler thermoelectricmaterials,” Nature communications , 1–7 (2015). H. Zhu, R. He, J. Mao, Q. Zhu, C. Li, J. Sun, W. Ren, Y. Wang, Z. Liu,Z. Tang, et al. , “Discovery of zrcobi based half heuslers with high thermo-electric conversion efficiency,” Nature communications , 1–9 (2018). H. Zhu, J. Mao, Y. Li, J. Sun, Y. Wang, Q. Zhu, G. Li, Q. Song, J. Zhou,Y. Fu, et al. , “Discovery of tafesb-based half-heuslers with high thermo-electric performance,” Nature communications , 1–8 (2019). T. Graf, P. Klaer, J. Barth, B. Balke, H.-J. Elmers, and C. Felser, “Phaseseparation in the quaternary heusler compound coti (1- x) mnxsb a reduc-tion in the thermal conductivity for thermoelectric applications,” ScriptaMaterialia , 1216–1219 (2010). M.-S. Lee, F. P. Poudeu, and S. D. Mahanti, “Electronic structure andthermoelectric properties of sb-based semiconducting half-heusler com-pounds,” Phys. Rev. B , 085204 (2011). M. Zeeshan, T. Nautiyal, J. van den Brink, and H. C. Kandpal, “Fetasb andfemntisb as promising thermoelectric materials: An ab initio approach,”Physical Review Materials , 065407 (2018). S. Singh, M. Zeeshan, U. Singh, J. van den Brink, and H. C. Kandpal,“First-principles investigations of orthorhombic-cubic phase transition andits effect on thermoelectric properties in cobalt-based ternary alloys,” Jour-nal of Physics: Condensed Matter , 055505 (2019). M. Zeeshan, H. K. Singh, J. van den Brink, and H. C. Kandpal, “Ab initiodesign of new cobalt-based half-heusler materials for thermoelectric appli-cations,” Phys. Rev. Materials , 075407 (2017). M. Zeeshan, J. van den Brink, and H. C. Kandpal, “Hole-doped cobalt-based heusler phases as prospective high-performance high-temperaturethermoelectrics,” Phys. Rev. Materials , 074401 (2017). S. Singh, M. Zeeshan, J. v. d. Brink, and H. C. Kandpal, “Ab initiostudy of bi-based half heusler alloys as potential thermoelectric prospects,”arXiv:1904.02488 (2019). D. Rai, A. Shankar, M. Ghimire, R. Khenata, R. Thapa, et al. , “Study ofthe enhanced electronic and thermoelectric (te) properties of zrxhf1- x-ytaynisn: a first principles study,” RSC Advances , 95353–95359 (2015). S. Sakurada and N. Shutoh, “Effect of ti substitution on the thermoelectricproperties of (zr, hf) nisn half-heusler compounds,” Applied Physics Letters , 082105 (2005). A. Roy, J. W. Bennett, K. M. Rabe, and D. Vanderbilt, “Half-heusler semi-conductors as piezoelectrics,” Phys. Rev. Lett. , 037602 (2012). Z. H. Liu, H. N. Hu, G. D. Liu, Y. T. Cui, M. Zhang, J. L. Chen, G. H. Wu,and G. Xiao, “Electronic structure and ferromagnetism in the martensitic-transformation material ni2fega,” Phys. Rev. B , 134415 (2004). W. Feng, D. Xiao, Y. Zhang, and Y. Yao, “Half-heusler topological insu-lators: A first-principles study with the tran-blaha modified becke-johnsondensity functional,” Phys. Rev. B , 235121 (2010). R. A. de Groot, F. M. Mueller, P. G. v. Engen, and K. H. J. Buschow,“New class of materials: Half-metallic ferromagnets,” Phys. Rev. Lett. ,2024–2027 (1983). M. Ghimire, Sandeep, T. Sinha, and R. Thapa, “First principles study ofthe electronic and magnetic properties of semi-heusler alloys nixsb (x= ti,v, cr and mn),” Journal of alloys and compounds , 9742–9752 (2011). Sandeep, M. Ghimire, D. Deka, D. Rai, A. Shankar, and R. Thapa, “Mag-netic and electronic properties of half-metallic nitbsb: a first principlesstudy,” Indian Journal of Physics , 301–305 (2012). Y. Nakajima, R. Hu, K. Kirshenbaum, A. Hughes, P. Syers, X. Wang,K. Wang, R. Wang, S. R. Saha, D. Pratt, et al. , “Topological rpdbi half-heusler semimetals: A new family of noncentrosymmetric magnetic super-conductors,” Science advances , e1500242 (2015). D. Yadav, S. Bhandari, G. Kaphle, and M. P. Ghimire, “Structural, elastic,electronic and magnetic properties of mnnbz (z= as, sb) and fenbz (z= sn,pb) semi-heusler alloys,” arXiv:2009.04123 (2020). J. Zhang, J. Chen, P. Li, C. Zhang, Z. Hou, Y. Wen, Q. Zhang, W. Wang,and X. Zhang, “Topological electronic state and anisotropic fermi surfacein half-heusler gdptbi,” Journal of Physics: Condensed Matter , 355707(2020). V. Zaitsev, M. Fedorov, I. Eremin, E. Gurieva, and D. Rowe, “Thermo-electrics handbook: macro to nano,” CRC Press, Taylor & Francis, BocaRaton (2006). S. B. Riffat and X. Ma, “Thermoelectrics: a review of present and potentialapplications,” Applied thermal engineering , 913–935 (2003). Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, and G. J. Snyder, “Con-vergence of electronic bands for high performance bulk thermoelectrics,”Nature , 66–69 (2011). A. D. LaLonde, Y. Pei, H. Wang, and G. J. Snyder, “Lead telluride alloythermoelectrics,” Materials today , 526–532 (2011). J. R. Sootsman, D. Y. Chung, and M. G. Kanatzidis, “New and old conceptsin thermoelectric materials,” Angewandte Chemie International Edition ,8616–8639 (2009). C. Felser, G. H. Fecher, and B. Balke, “Spintronics: a challenge for mate-rials science and solid-state chemistry,” Angewandte Chemie InternationalEdition , 668–699 (2007). J. P. Heremans, V. Jovovic, E. S. Toberer, A. Saramat, K. Kurosaki,A. Charoenphakdee, S. Yamanaka, and G. J. Snyder, “Enhancement ofthermoelectric efficiency in pbte by distortion of the electronic density ofstates,” Science , 554–557 (2008). L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton,V. P. Dravid, and M. G. Kanatzidis, “Ultralow thermal conductivity andhigh thermoelectric figure of merit in snse crystals,” Nature , 373–377(2014). K. Biswas, J. He, I. D. Blum, C.-I. Wu, T. P. Hogan, D. N. Seidman, V. P.Dravid, and M. G. Kanatzidis, “High-performance bulk thermoelectricswith all-scale hierarchical architectures,” Nature , 414–418 (2012). E. S. Toberer, A. Zevalkink, and G. J. Snyder, “Phonon engineeringthrough crystal chemistry,” Journal of Materials Chemistry , 15843–15852 (2011). P. Blaha, K. Schwarz, G. K. Madsen, D. Kvasnicka, J. Luitz, et al. ,“wien2k,” An augmented plane wave+ local orbitals program for calculat-ing crystal properties (2001). P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni,D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, et al. , “Quantumespresso: a modular and open-source software project for quantum sim-ulations of materials,” Journal of physics: Condensed matter , 395502(2009). J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approxi-mation made simple,” Physical review letters , 3865 (1996). F. Tran and P. Blaha, “Accurate band gaps of semiconductors and insula-tors with a semilocal exchange-correlation potential,” Phys. Rev. Lett. ,226401 (2009). G. K. Madsen and D. J. Singh, “Boltztrap. a code for calculating band-structure dependent quantities,” Computer Physics Communications ,67–71 (2006). J. Ma, V. I. Hegde, K. Munira, Y. Xie, S. Keshavarz, D. T. Mildebrath,C. Wolverton, A. W. Ghosh, and W. Butler, “Computational investigationof half-heusler compounds for spintronics applications,” Physical ReviewB , 024411 (2017). A. Togo and I. Tanaka, “First principles phonon calculations in materialsscience,” Scripta Materialia , 1–5 (2015). C. Kumarasinghe and N. Neophytou, “Band alignment and scattering con-siderations for enhancing the thermoelectric power factor of complex ma-terials: The case of co-based half-heusler alloys,” Physical Review B ,195202 (2019). L. Zhang, M.-H. Du, and D. J. Singh, “Zintl-phase compounds with snsb4 tetrahedral anions: Electronic structure and thermoelectric properties,”Physical Review B , 075117 (2010). C. Fu, H. Wu, Y. Liu, J. He, X. Zhao, and T. Zhu, “Enhancing the figure ofmerit of heavy-band thermoelectric materials through hierarchical phononscattering,” Advanced Science , 1600035 (2016). A. Hori, S. Minami, M. Saito, and F. Ishii, “First-principles calculationof lattice thermal conductivity and thermoelectric figure of merit in ferro-magnetic half-heusler alloy comnsb,” Applied Physics Letters116