THERMOELECTRIC PROPERTIES INVESTIGATION OF Ni/Co DOPED ZrCoBi HALF-HEUSLER ALLOY †

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INTRODUCTION
Since humans have started depending on fossil fuel energy, many environmental issues appeared.Climate change and global warming are of the most serious problems humans have to face.Recently, a decline rate of environmental issues was noticed due to COVID-19 breakout.However, these issues began to increase gradually after recovering from this pandemic [1].Developing new renewable and sustainable energy technologies has become a vital choice for mankind in 21 st century to confront such threats.Finding new and reliable metamaterials with desired thermoelectric (TE) characteristics has attracted more ambitious researchers and manufacturers as well.The new metamaterials with enhanced properties are utilized in many practical applications.Generally, the performance of TE metamaterials is estimated by the thermoelectric figure-of-merit (ZT) that is described by the following formula: here S, σ, σS , κ, T are Seebeck coefficient, electrical conductivity, thermoelectric power factor, thermal conductivity and absolute temperature, respectively [2][3][4].
The thermal conductivity (κ) has electronic and lattice contributions: Where κ is the electronic thermal conductivity and κ is the lattice thermal conductivity.The ZT of a TE metamaterial can be enhanced by increasing the σS and/or by decreasing κ.But the close interdependent relations among S, σ, and κ via the carrier concentration leads to a real challenge in optimizing the TE transport properties while κ is considered relatively independent [5].Generally, in order to produce promising TE metamaterials, a high ZT must be achieved [6][7][8], which can be fulfilled by optimizing σS through tuning the carrier concentration.Usually, tuning carrier concentration can be obtained either by doping or by band engineering [9,10], and reducing the thermal conductivity κ [11][12][13].
However, the main issue with HH compounds is their relatively high thermal conductivity that reduces ZT value and, accordingly, limits their TE performance.For that reason, many researchers have recently spent many efforts in searching for enhanced HH thermoelectric materials.That enhancement can be attained through reducing the lattice thermal conductivity via optimizing nanoparticle phonon scattering centers [28], point defects [29], and grain size reduction [30].
Since experimental improving the TE materials is sometimes time consuming and/or costs a lot, many researchers prefer ab initio calculations.This procedure allows screening bigger sets of compounds along with shorter time using efficient codes and modern computers [31].Hence, new high performance TE compounds might be identified.For example, Qureshi, M.T. et al. studied the Cu O based semiconductor materials and observed an elevation in the Seebeck coefficient consequent of Ag doping.They stated that these materials are promising candidates for modern electric devices.[32].Huang et al. found interstitial Sn atoms in substitution leads to increase S and decrease the κ of n-type NbCoSb; thus, an enhanced figure-of-merit of ~ 0.56 is acquired [33].Nenuwe et al. announced figure-of-merit values of (ZT = 3.27 and 1.43), suggesting that FeCrSb, and RuCrSb are potential materials for TE applications [34].Dhakshayani et al. found that XCaB (X = Na, K and Rb) compounds have desired ferromagnetic and half-metallic behaviors with ZT of 1.00, and can be used for TE and spintronics applications [35].
One of the recently studied HH compounds with interesting TE properties is ZrCoBi.Nura Ibrahim et al. studied the TE properties of the heavily doped ZrCoBi.The results revealed desired TE properties, such as a high σS at hightemperature region, and a high ZT of ~ 0.35 for ZrCo .Ni .Bi at 900 K [36].Zhu et al. announced the discovery the Half-Heusler of ZrCoBi with a huge TE conversion efficiency of ∼ 9%, which is computed at a wide temperature variation of about 500 K, and reached a good ZT amount of about 1.42 at 973 K [37].Yazdani-Kachoei, M. et al. studied the electronic and structural characteristics of ZrRhBi and ZrCoBi.They showed that those compounds have high Seebeck value and low electrical conductivity [38].Hangtian Zhu et al. have studied the TE characteristics of ZrCoBi-based Half-Heuslers.They showed that those compounds can be used as mid-and high-temperature TE power generators [39].
In this research, the ab-initio calculations are used to investigate the TE properties of Ni-doped Half-Heusler ZrCoBi compounds.In the following section, the computational details are briefly summarized.The effects of Ni doping into Co site on the thermoelectric behavior of ZrCoBi were demonstrated and discussed in section 3. The conclusion is given in section 4.

COMPUTATIONAL DETAILS
Half-Heusler ZrCo Ni Bi compounds have a cubic lattice structure with space group of F4 3m.The Ni concentrations (x) are chosen to be (0, 0.25, 0.75 and 1) such that an optimal structural stability is achieved.Their structural, thermal, and electronic properties were discussed in details in a previous study [40].Where the Full-Potential Wien2k package [41], the Linearized Augmented Plane Wave (FP-LAPW) method [42], the generalized gradient approximation (PBE-GGA) [43] were used.The convergence test limits of the self-consistent calculations were chosen to be 0.1 × 10 Ry for the determined total energy and 0.1 × 10 e for crystal charge.In this work, the thermoelectric transport coefficients were calculated using BoltzTraP code, which is interfaced within Wien2k.The calculations are based on DFT and Boltzmann theory [44].

RESULTS AND DISCUSSION
In this section, the thermoelectric behavior of Ni-doped ZrCoBi alloys are presented and discussed.Seebeck coefficient (S), electrical conductivity to relaxation time ratio (σ/τ), electronic thermal conductivity to relaxation time ratio (κ /τ) were calculated in the temperature range 0 -500 K. Then the thermoelectric power factor to relaxation time ratio (S σ/τ), and the dimensionless figure-of-merit (ZT) were worked out.The temperature (T) dependence of the Seebeck coefficient (S) is plotted in Fig. 1, where S behavior for both charge carriers is illustrated.It is noticed that Seebeck coefficient reaches its optimal value in the low-temperature region then decreases exponentially with increase in temperature.
The dependence of Seebeck coefficient on charge carrier concentration (n) of ZrCo Ni Bi alloys are plotted in Fig. 2. The S values relative to n are located at 0, 1, 1, and 3 for ZrCoBi, ZrNiBi, ZrCo .Ni .Bi, and ZrCo .Ni .Bi, respectively.It is obviously noticed that the change of temperature does not influence S values for both charge carriers.However, Ni-doping shifts the curves to the higher positive (hole) concentration region, especially the ZrCo .Ni .Bi.According to the obtained S and n values, it is found that ZrCo Ni Bi can alter between both charge carriers (holes and electrons) with the same thermoelectric efficiency and work as p-type alloys.The potential applicability of ZrCo Ni Bi as a thermoelectric material not only depends on the thermoelectric power, but also on the most important charge transport properties, namely the electrical and thermal conductivities.The temperature dependence of electrical conductivity to relaxation time ratio (σ/τ) is calculated.σ/τ is found directly (inversely) proportional to T (S) satisfying the Mott formula [45].A remarkable preference of ZrCo .Ni .Bi is noticed, as shown in Fig. 3.
The desired response of σ/τ implies a growing of n that elevates holes to the conduction band.The highest σ/τ value is found to be for ZrCo .Ni .Bi for all chosen temperatures.By comparison to the other studied compounds, the elevated σ/τ amount of ZrCo .Ni .Bi for both charge carrier concentrations exhibits significantly large band dispersion at the band edges, and hence a small effective mass.Moreover, the computed σ/τ values are found nearly the same for both charge carriers, which is in agreement with the previous conclusion about the ability of all Ni-doped compounds to exchange between charge carriers (holes and electrons).The variation of the electronic thermal conductivity to relaxation time ratio (κ /τ) with temperature is demonstrated in Fig. 5.It is found that κ /τ vs T and σ/τ vs T curves have a comparable behavior.They are directly (inversely) proportional to T (S) that satisfies the Mott formula.Below room temperature, there is a monotonic variation in κ /τ.While, beyond room temperature, the κ /τ shows strong temperature dependence.This implies a stoichiometric composition of the alloys, and an increasing charge carrier flow with the raising temperature.In addition, Wiedemann-Franz law, which describes the κ and σ relationship, is also verified as κ /σ is found to be constant.The high electronic thermal conductivity values, especially for ZrCo .Ni .Bi, suggests a use in heat sink applications for studied compounds.
Besides S, the thermoelectric power factor to relaxation time ratio (S σ/τ) is an excellent measure that grants credibility to ZrCo Ni Bi to be used in thermoelectric applications.Fig. 6 presents the temperature dependence of the thermoelectric power factor to relaxation time ratio for both charge carriers.It is found that S σ/τ raises as the temperature elevates for both doping systems.A clear preference of ZrCo .Ni .Bi is noticed, which exhibits a sharp elevation above ambient temperature region.This behavior indicates that ZrCo .Ni .Bi has promising thermoelectric properties, like waste heat usage in power generators.

EEJP. 2 (2023)
Mahmoud Al-Elaimi The results of electrical conductivity, electronic thermal conductivity, and Seebeck coefficient were used to calculate the figure-of-merit (ZT).The variation of the ZT with temperature corresponding to the hole and electron charge carrier of the present alloys are shown in Fig. 8.The obtained ZT values are nearly equal to 1 for all compounds up to 150K.At higher temperatures, ZT drops marginally, but remain in the high ZT region for all compounds except ZrNiBi.ZrNiBi shows a strong temperature dependence as its ZT value drops more promptly in the high temperature region.Being ZT is equal to 1 up to 150K and about 0.90 till 500K predicts beneficial thermoelectric properties of ZrCo Ni Bi alloys.Experimental values of figure-of-merit for Ni-doped ZrCoBi are not available for comparison.Based on Seebeck coefficient, electronic conductivity, electronic thermal conductivity, thermoelectric power factor, and relatively high ZT value, ZrCo Ni Bi are predicted to be good TE materials.These compounds might be used in TE applications, such as thermoelectric power generator from waste heat and sustainable energy systems.Moreover, the current findings may inspire experimentalists to explore these compounds at wider doping concentration and temperature ranges.

CONCLUSION
In this paper, the transport parameters of the cubic ternary ZrCo Ni Bi half-Heusler alloys have been computed using FP-LAPW and Boltzmann theory.The transport parameters, calculated by using BoltzTraP code, are Seebeck coefficient (S), electrical conductivity to relaxation time ratio (σ/τ), electronic thermal conductivity to relaxation time ratio (κ /τ), thermoelectric power factor to relaxation time ratio (S σ/τ), and the dimensionless figure-of-merit (ZT) in the temperature range 0 -500 K. Findings show that ZrCo Ni Bi have a p-type doping character with ability to alter between hole and electron charge carrier.The high value of S at low temperature range proposes favorable thermoelectric applications of the studied compounds.A remarkable high σ/τ value of ZrCo .Ni .Bi is noticed.The high electronic thermal conductivity value especially for ZrCo .Ni .Bi suggests that these compounds can be used in the heat sink applications.Due to the high values of thermoelectric power factor and figure-of-merit (ZT ≅ 1), potential thermoelectric device applications are predicted, such as sustainable energy systems.

Figure 3 .
Figure 3.The temperature dependence of electrical conductivity to relaxation time ratio (σ/τ) of ZrCo Ni Bi.Solid (dashed) lines denote hole (electron) charge carriers

Figure 4 .
Figure 4.The charge carrier concentration dependence of electrical conductivity to relaxation time ratio (σ/τ) of ZrCo Ni Bi at 300 K

Figure 5 .
Figure 5.The temperature dependence of the electronic thermal conductivity to relaxation time ratio (κ /τ) of ZrCo Ni Bi.Solid (dashed) lines denote hole (electron) charge carriers

Figure 6 .
Figure 6.The temperature dependence of the thermoelectric power factor to relaxation time ratio (S σ/τ) of ZrCo Ni Bi.Solid (dashed) lines denote hole (electron) charge carriers

Figure 7 .Figure 8 .
Figure 7.The charge carrier concentration dependence of thermoelectric power factor to relaxation time ratio (S σ/τ) of ZrCo Ni Bi at 300 K Figure 8. Figure-of-merit (ZT) of ZrCo Ni Bi.Solid (dashed) lines denote hole (electron) charge carriers