Transport and thermoelectric properties of Hf-doped FeVSb half-Heusler alloys

Journal Pre-proof Transport and thermoelectric properties of Hf-doped FeVSb half-Heusler alloys A. El-Khouly, A. Novitskii, A.M. Adam, A. Sedegov, A. Kalugina, D. Pankratova, D. Karpenkov, V. Khovaylo PII:

S0925-8388(19)34659-6

DOI:

https://doi.org/10.1016/j.jallcom.2019.153413

Reference:

JALCOM 153413

To appear in:

Journal of Alloys and Compounds

Received Date: 18 September 2019 Revised Date:

11 December 2019

Accepted Date: 16 December 2019

Please cite this article as: A. El-Khouly, A. Novitskii, A.M. Adam, A. Sedegov, A. Kalugina, D. Pankratova, D. Karpenkov, V. Khovaylo, Transport and thermoelectric properties of Hf-doped FeVSb half-Heusler alloys, Journal of Alloys and Compounds (2020), doi: https://doi.org/10.1016/ j.jallcom.2019.153413. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Transport and thermoelectric properties of Hf-doped FeVSb half-Heusler alloys A. El-Khouly1,3, A. Novitskii1, A. M. Adam2,*, A. Sedegov1, A. Kalugina1, D. Pankratova1, D. Karpenkov1, V. Khovaylo1,4. 1 National University of Science and Technology MISIS, Moscow 119049, Russian Federation 2 Physics Department, Sohag University, Sohag 82524, Egypt 3 Physics Department, Damanhour University, Damanhour 22516, Egypt 4 National Research South Ural State University, Chelyabinsk 454080, Russian Federation ABSTRACT Nearly single-phase FeVSb half-Heusler alloys with fine grains were obtained by induction melting followed by mechanical alloying (MA), spark plasma sintering (SPS) and annealing process. Hf as a heavy element was used as dopant to present point defects aiming at decreasing the material’s thermal conductivity during phonon scattering. Thermoelectric properties of the FeV1−xHfxSb samples (0.0 ≤ x ≤ 0.3) were investigated as a function of temperature in a range from 300 to 600 K. Microstructure investigations showed that grain size decreases with increasing the level of Hf doping (x). Seebeck coefficient of the parent FeVSb compound showed negative sign which refers to n-type conduction. Interestingly, the sign has changed to positive with introducing Hf in the FeVSb lattice at different concentrations (x ≥ 0.1), which is due to one less valence electron in Hf as compared to V. The difference between the host atom (V) and the impurity atom (Hf) in terms of mass and size has resulted in a mass fluctuation and consequently a disorder scattering. The absolute value of the Seebeck coefficient |S| of the FeVSb system was measured at 110 µV/K, while the thermal conductivity value was obtained at 10.46 Wm-1K-1 near room temperature. A maximum power factor of 1.07 mWm−1 K−2 at 420 K was recorded. The thermal conductivity decreased rapidly upon Hf doping due to increased point defect scattering caused by Hf introducing to the FeVSb system. A maximum ZT value of 0.08 at 573 K for FeV0.9Hf0.1Sb was recorded in this study. Keywords: Half-Heusler alloys; Hf doping; Mass fluctuation; Seebeck coefficient; Thermal conductivity. Corresponding author: A. M. Adam E-mail: [email protected] Corresponding author: A. El-Khouly E-mail: [email protected], [email protected] 1 Introduction The need of clean and renewable energy become more and more urgent due to the ever-increasing environmental issues in addition to the shortage of the conventional energy sources. In this regard,

thermoelectric (TE) materials which can directly convert heat into electric energy have received enormous interest [1]. Moreover, medium and even high temperature TE materials are quite needed for waste heat recovery applications due to the high temperature of most industrial waste heat sources as well as the exhaust gas. Half-Heusler (HH) materials have been investigated for mid-high temperature in the Ti-doped Hf0.5Zr0.5 NiSn0.998Sb0.002 system, and a figure of merit ZT~0.92 at 837 K was obtained for (Hf0.5Zr0.5)1-xTixNiSn0.998Sb0.002 at x =0.3 [2]. The needed basis for understanding defect engineering towards highly efcient and cost efective HH compositions was presented in [3], a ZT of ∼0.7 at 873K was obtained for optimized p-type ZrCo1.03Sb0.8Sn0.2 HH nanocomposites, which is among the highest obtained in p-type HH samples. In previous attempts, chalcogenides have long been investigated as thermoelectric materials [4-7], meanwhile many thermoelectric materials are being explored for power generation applications, such as silicides [8], PbTe [9-11] and now HH alloys [12]. The HH alloys are attracting highly increased attention due to their interesting electrical transport features beside their variant elemental combinations [13]. They are usually based on environmentally friendly elements showing stable transport, thermal and mechanical properties. Such features of HH compounds besides the 18-valence electron count (VEC) per unit cell make them amongst the most promising TE materials for the medium temperature range. Regarding the current state-of-knowledge on half-Heusler and based alloys, they have been verified as a class of promising thermoelectric materials because of their mechanical strength, thermal stability at high temperatures and interesting physical properties [14]. Geometric, electronic, and magnetic properties of Pt-, Ni-, and Co-based HH alloys were studied, using first-principles calculations based on density functional theory, by Madhusmita Baral and Aparna Chakrabarti (2019) [15]. The formation energies of these alloys in various crystal symmetries were calculated. From their theoretical calculation it was found that many of the half-Heusler alloys are reported to be half-metals in the cubic phase. In comparison to the reported efficiencies of other state-of-the-art thermoelectric materials, the thermoelectric efficiency of Zr1-xHfxCoSb0.9Sn0.1 HH alloys was investigated exhibiting a leg efficiency of ~10% [16]. The materials showed very low thermal conductivity of ~2.2 W m-1 K-1 at 873 K, which is amongst the lowest reported values in HH alloys. In terms of figure of merit (ZT) comparison, Ti2NiCoSnSb with the HH structure was synthesized for the first time by vacuum arc melting followed by ball-milling [17]. Nanocrystalline alloy of the Ti2NiCoSnSb system exhibited a ZT of 0.047 at 860K, while microcrystalline alloy of the same system showed a ZT of 0.144 at 860K. Furthermore, Lihong et al., have achieved ZT value of 0.6, and a power factor of 29 µW cm−1 K−2 at 873 K, for nonstoichiometric V0.9CoSb samples [18]. The

authors attributed the notable improvement in the ZT value to the increment in Seebeck coefficient, which resulted from the optimized carrier concentration. It was previously reported that the un-doped FeVSb HH phases show an intrinsic n-type of conduction [19], whereas, other reviews showed that the FeVSb alloy, with valence electron count of 18, is estimated to have good p-type TE properties [20–23]. On the other hand, it was demonstrated that FeVSb possesses high electrical conductivity and high negative Seebeck coefficient [24, 25], however, it exhibits low TE performance due to its high thermal conductivity [26]. Considering that the performance of a TE material is given by the dimensionless figure of merit ZT = S2σT/(ke+kl), where S, σ, T, ke and kl are the Seebeck coefficient, electrical conductivity, absolute temperature, electronic and lattice contributions to the thermal conductivity k, respectively, a good TE material should exhibit high electrical transport properties and low thermal conductivity [27]. But, the thermal conductivity of FeVSb HH alloy is around 10–13 Wm−1K−1 at room temperature [21], which is very high to be acceptable for industrial application for a TE device. Consequently, the vast majority of HH alloys studies were focused on the thermal conductivity reduction, which may lead to great improvement in ZT. The fine-grained materials besides the formation of nanocomposite through a high energy ball milling followed by hot pressing method increases grain surface densities and therefore phonon scattering resulting at last in enhanced TE performance [28, 29]. As previously reported, due to the formation of nanocomposite, lattice thermal conductivity at room temperature was decreased for ~30% (from 4.1 W m-1 K-1 to 2.8 W m-1 K-1) for p-type Hf0.5Zr0.5CoSb0.8Sn0.2 [30] and for ~23% (from 4.0 W m-1 K-1 to 3.1 W m-1 K-1) for ntype Hf0.75Zr0.25NiSn0.99Sb0.01 [31]. Enhanced alloy scattering through the phonon, mass fluctuation and the point defect scattering which adapted by heavy elements substitution as in Ti(Zr, Hf)-Ni(Pd, Pt)-Sn alloy [31, 32] can play an effective role for further depression in the lattice thermal conductivity. As a result, lower thermal conductivity was achieved at ~2.7 W m-1 K-1 for Hf0.8Ti0.2CoSb0.8Sn0.2 [33] and decreased by 55% (from 12.8 Wm-1K-1 to 5.8 W m-1 K-1) for Nbdoped FeVSb n-type HH alloys due to the mass and stress fluctuations between host vanadium atoms and impurity niobium atoms [34]. Using the conventional melting method, it would be difficult to have homogeneous FeVSb ingots because of the large difference in melting point of the constituting elements. Mechanical ball milling and repeated arc melting are widely used to fabricate the FeVSb based alloys [22, 23]. The SPS can rapidly produce regular-shaped compact samples [35]. In this study, ultrafine grained Hf-doped FeVSb HH alloys were successfully synthesized by arc melting accompanied with induction melting followed by MA, SPS and annealing process. Such synthesis method has many advantages as

reducing impurity phase amount, improving the uniformity of microstructure and distribution of the elements homogeneously. The TE properties of FeVSb based HH alloys were measured in the temperature range from 300 K to 600 K. The thermal conductivity of the FeV0.8Hf0.2Sb is decreased by ~54% compared with that of pure FeVSb compound near room temperature. 2 Experimental procedures FeV1−xHfxSb samples (0.0 ≤ x ≤ 0.3) were synthesized from pure elements: Fe (99.99%), V (99.99%), Hf (99.99%), and Sb (99.999%). The Fe(V, Hf) pre-alloy was prepared by arc melting under an argon atmosphere according to the relative high melting temperature ˃ 1500 °C of vanadium and hafnium. During the melting process the mixture was re-melted several times to provide homogeneity of the pre-alloys. The target Fe(V, Hf)Sb alloys were synthesized in an induction furnace under Ar protective atmosphere by melting of the pre-alloy and antimony together with 3 wt.% excess of the latter. The prepared ingots were annealed at 923 K for 48 h in an evacuated quartz tube, followed by quenching in cold water. Then, the resultant ingots were crushed into powder and ball milled using a planetary micro mill (Pulverisette 7 premium line, Fritsch, Germany) using stainless steel vials and balls of 45 ml volume and 10 mm diameter, respectively. In order to avoid any contamination during handling and processing of samples all process was carried out under argon atmosphere in a glove box. Ball milling was performed at 450 rpm for 1 hour under the protection of argon atmosphere. The pulverized powders were consolidated into bulk under vacuum atmosphere using SPS system (Labox 650, Sinter-Land, Japan) at 1023 K under pressure of 65 MPa for 15 minutes. Densification process was carried out using a graphite die of 12.7 mm diameter. The obtained disk-shaped specimens were sealed in evacuated quartz tube and annealed at 923 K for 3 days to reduce any impurity phase and improve microstructure. Phase Structure identification of bulk samples was performed by X-ray diffraction (XRD) analysis (Difray 401 diffractometer, Scientific Instruments, Russia) with Cr Kα (λ = 2.2911 Å) radiation at room temperature. Scanning electron microscopy in conjunction with energy-dispersive X-ray spectroscopy (Vega 3 SB, Tescan, Czech Republic) was employed to observe the morphology, microstructure and chemical composition of the samples. Thermal diffusivity was measured by a laser flash diffusivity method (LFA 457 MicroFlash, Netzsch, Germany) from room temperature to 600 K and the thermal conductivity k was determined as k = D·Cp·d, where D, Cp and d are the thermal diffusivity, specific heat and the density, respectively. The relative bulk density d was measured by the Archimedes method. For the Seebeck and electrical conductivity measurement, the pellets were cut into rectangular bars with dimensions of about 10 mm × 2.5 mm × 1.5 mm, which were used for measurements of the electrical transport properties. The electrical conductivity σ and

the Seebeck coefficient S were measured from room temperature to 600 K by the standard fourprobe and differential methods, respectively, using laboratory made system (Cryotel, Russia) in He2 flow. Hall coefficient (RH), was measured at room temperature by the Van der Pauw technique using a galvanomagnetic properties measurement system in a magnetic field varied from -1 to 1 T and a constant electric current of 30 mA. Carrier concentration (n) and Carrier mobility (µ) were calculated using the equations n=1/eRH and µ= RH.σ, respectively, where e is the electronic charge and σ is the electrical conductivity. 3 Results and discussion 3.1 Characterization Identifications of the microstructure and the surface morphology of the powder samples after MA were carried out by the scanning electron microscope. The micrographs are shown in Fig. 1. It is clearly seen that the samples are polycrystalline of high crystallinity, homogeneity and density. Although the drains are randomly distributed, the connectivity between grains is quite strong. The average particle size was estimated under the scanning electron microscope and shown to be approximately 0.70 µm, 0.64 µm, 0.51 µm and 0.34 µm for x = 0.0-0.3, respectively.

Fig. 1 SEM images of FeV1−xHfxSb powder samples after MA at 450 rpm for 1 h; a) x = 0.0, b) x = 0.1, c) x = 0.2 and d) x = 0.3 Quantitative analysis of each composition, in terms of the percentage of elements in each sample, was carried out by energy dispersive x-ray spectroscopy (EDX). EDX confirms that the actual elemental percentage is in good agreement with the nominal composition of respective elements (Fe, V, Sb and Hf). The elemental distribution in each FeV1−xHfxSb sample is tabulated in Table 1. Table 1: Elemental distribution in FeV1−xHfxSb system given by EDX analysis. Sample FeVSb FeV0.9SbHf0.1 FeV0.8SbHf0.2 FeV0.7SbHf0.3

Sb (At. %) 33.6 33.7 34.5 34.7

Fe (At. %) 33.1 32.7 32.3 32.6

V (At. %) 33.3 30.3 26.7 23.1

Hf (At. %) 0.0 3.3 6.5 9.6

Microstructure and surface morphology after treating the samples by SPS and annealing processes are shown in Fig. 2. Fine grains of high-density can be observed. Although it was difficult to precisely calculate the grain size for the samples because the samples are ultrafine, due to MA+SPS processes [36], we can say that the grain size decreases with increasing the Hf doping concentrations. This reduction is due to the substitution of V with a larger size atom (Hf), a matter inducing a lattice strain and resulting in reduction of the grain size [37].

Fig. 2: SEM micrographs of FeV1−xHfxSb samples after SPS at 65 MPa for 15 minutes and annealing at 923 K for 3 days; a) x = 0.0, b) x = 0.1, c) x = 0.2 and d) x = 0.3. The density was measured at 7.39 g cm−3 for the FeVSb compound, corresponding to 96.85% of the theoretical value which decreased with increasing x value and reached its minimum for the composition with x = 0.2, as illustrated in Fig. 3.

Fig. 3: Relative density as a function of the Hf doping amounts in the FeV1−xHfxSb samples.

The phase composition of the Hf-doped FeVSb alloys has been investigated by the X-ray diffraction (XRD) analysis as presented in Fig. 4. The FeVSb ingot shows hexagonal FeVSb phase with Ni2Intype structure (space group P63/mmc phase). The cubic pure FeVSb HH single-phase crystallizes in MgAgAs-type structure (space group F4̅3m) with the indexed HH phase as the dominant phase. Impurity phases disappear after SPS at 1023 K followed by annealing process at 923 K for 3 days. This means that annealing of 3 days at 923 K is necessary to obtain a pure FeVSb HH phase and eliminate the impurity phase as shown in Fig. 4a. Fig. 4b shows XRD patterns of the FeV1−xHfxSb (0.0 ≤ x ≤ 0.3) system after MA and SPS processes followed by annealing at 923 K for 3 days. All the prepared samples contained HH phase as the dominant phase. However, fractions of secondary phases are obtained for x ≥ 0.2. For x = 0.2, secondary phases of FeSb2 (PDF#01-070-3985) and VSb2 (PDF#01-089-5149) -(PDF#01-089-1984) were detected, while for x = 0.3 another impurity phase of V3Sb (03-065-9591) were observed. Secondary and impurity phases are taken into consideration as they significantly affect the thermal conductivity of the samples. All these phases are based on Sb phases. Sb based phases are recommended due to its high thermoelectric properties and its low thermal conductivity. a)

b)

Fig. 4 XRD patterns of FeV1−xHfxSb; a) pure FeVSb after melting, MA+SPS and annealing processes, b) Hf-doped FeVSb HH alloys system after annealing process. The lattice parameter (a) increases with increasing Hf doping amount x due to the addition of Hf which possesses larger atomic radius than that of V as shown by Fig. 5, showing good agreement with Vegard’s law [38]. Moreover, the main diffraction peak shows slight shift to the left side due to the change in the lattice parameter, as can be observed in Fig. 4b.

Fig 5: Lattice parameters of the FeV1−xHfxSb system vs. Hf amount. The crystallite sizes D are represented in Table 2, which has been calculated using the well-known Scherrer’s equation from XRD patterns [39]: D =

λ β

θ

,

(1)

where λ is the wavelength of the X-ray source, β is the full width at half maximum (FWHM) expressed in radians, K is a constant = 0.9 (known as shape factor) related to crystallite shape and θ is the Bragg angle. The average particle sizes were approximately estimated as 15.89 nm, 15.88 nm, 15.86 nm and 10.57 nm for x = 0.0, 0.1, 0.2, 0.3 respectively. It is clear that the particle sizes decrease with increasing Hf doping amounts, which can result in different grain sizes and different number of grain boundaries [40]. It was found that Hf doping of x =0.3 resulted in significant decrease in the grain size which can be attributed to the fact that the orientation of Hf atoms occurs as interstitial not only as substitution incorporation in the crystal lattice of FeVSb. The crystallite sizes (D) as estimated from Scherrer’s equation, lattice parameter (a) and relative density (d) of the concerned FeV1−xHfxSb samples are listed in table 2. As can be seen in the table, the observed change in the crystallite size at Hf amount of x =0.3 can be ascribed to orientation of Hf atoms, i.e. position of Hf atoms in the crystal lattice of FeVSb, which happens in the way that the atoms become closer and of smaller unit cell and cell volume. This is because Hf atoms at x =0.3 occupied interstitial positions in the hosting lattice (FeVSb). In other words, the Hf content at x =0.3 became more effective and Hf atoms showed various orientations or locations in the FeVSb lattice such as interstitial occupancy rather than substitutional occupancy. This can be observed in the XRD patterns, Fig. 4b, as the sample containing Hf of x =0.3 shows the broadest peak (main peak) with a slight shift to the left, in comparison to other peaks.

Table 2: The crystallite sizes (D), lattice parameter (a) and relative density (d) of FeV1−xHfxSb system. Nominal composition

D (nm)

a (nm)

d (%)

X = 0.0

15.89

0.58367

96.85

X = 0.1

15.88

0.58475

94.64

X = 0.2

15.86

0.58602

92.97

X = 0.3

10.57

0.58718

94.29

3.2 Electrical and thermoelectric properties Thermoelectric properties were studied in the temperature range from 300 to 600 K. Fig. 7a shows the variation of electrical conductivity of FeV1−xHfxSb HH alloys as a function of temperature. The electrical conductivity of all samples decreases with increasing temperature, showing a metal-like conduction behaviour. At room temperature, electrical conductivity was decreased with increasing of Hf contents for x ≤ 0.2. The reduction could be attributed to the mass defect which caused by the large Hf ions [41], and then increased as x was further increased. The increment of electrical conductivity at x = 0.3 might be ascribed to the appearance of an impurity phase with highest carrier concentration value of 9.41×1019 cm-3 as shown in Table. 3. The electrical conductivity value for pure FeVSb is about 7.5×104 Ω-1 cm-1 near room temperature which is comparable to that reported by Chenguang Fu et al [42]. a)

b)

c)

Fig. 6 Temperature dependence of the thermoelectric properties of FeV1−xHfxSb system; a) electrical conductivity, b) Seebeck coefficient and c) power factor. Fig. 6 (b) shows the temperature dependence of the thermoelectric power (Seebeck coefficient) of the FeV1−xHfxSb alloys. The Seebeck coefficient of the pure FeVSb sample possesses negative values which corresponds to n-type electrical transport behaviour thus demonstrated that the dominating charge carriers are electrons, which is in good accordance with the results obtained by Hall coefficient measurements shown in Table 3. The absolute Seebeck coefficient value |S| of the FeVSb alloy is 110 µV/K near room temperature and reached a maximum value of 133 µV/K at 500 K and then slightly decreases with increasing temperature due to the intrinsic excitation of minority carriers. It is worth mentioning that, the value of |S| in our work is higher than that reported by Young et al (-70 µV/K near room temperature and -80 µV /K at 500 K) [21] and comparable to that reported by Jodin et al (-110 µV/K at room temperature) [20]. On the other hand, the S values of FeV1−xHfxSb become positive with further increasing in the Hf content, which is attributed to the fact that Hf has one less electron than V, accordingly, the number of holes increases with increasing the Hf content [43]. Consequently, the material is now p-type with majority carriers of holes, with a large value of 127 µV/K near room temperature for the Hf content x = 0.1. At higher temperature (500 K) the value reached about 144 µV/K which is the maximum observed Sebeeck coefficient value among all the studied samples. Fig. 6 (c) shows the temperature dependence of power factor of FeV1−xHfxSb alloys. The power factor increases with temperature increasing, reaching a maximum value at certain temperature, depending on the amount of Hf, and decreasing again beyond. This behaviour can be ascribed to the behaviour of the Seebeck coefficient and electrical

conductivity. The maximum power factor was obtained for x = 0.0 with a value of 1.07 mWm−1 K−2 at 420 K. Table 3: Room-temperature electrical conductivity (σ), Seebeck coefficient (S), Hall coefficient (RH), carrier concentration (n), carrier mobility (µ) of FeV1−xHfxSb system. σ (104 (Ω-1m-1)

S (µV. K-1)

RH (cm3·C-1)

n (1019 cm-3)

µ (cm2V-1s-1)

0.0

7.52

-110

-0.629

0.994

473

0.1

4.42

127

0.088

7.10

39

0.2

3.29

86

0.127

4.93

42

0.3

6.42

52

0.066

9.41

43

Nominal composition, x

3.3 Thermal transport property Thermal conductivity (k), which is the summation of the contributions of the crystal lattice (kl) and the electronic thermal conductivity (ke), where (ke) can be calculated from the Well-known Wiedemann-Franz law as ke = LσT ( is the Lorenz factor = 2.45 × 10–8 V2 K–2 for degenerate semiconductors) was investigated. Temperature dependence of the thermal conductivity measurements of the FeV1−xHfxSb alloys was studied over the temperature range of 300 to 600 K. Due to the relatively high density of FeVSb, the thermal conductivity showed highest value of 10.46 Wm-1K-1 near room temperature which is lower than the previously reported value for the same alloy by Chenguang Fu et al [34]. Moreover, the thermal conductivity decreases rapidly with increasing Hf doping value, which led to a notable scattering due to the presence of point defects adapted by heavy elements substitution featured with the discrete differences in atomic mass and size between host atoms (V) and impurity atoms (Hf) [44]. Disorder scattering parameter Гm due to mass fluctuations between host atoms (V) and impurity atoms (Hf) for the ternary half-Heusler compounds was calculated. The parameter Гm is given by the equation [45]. Гm = = = Where

,

,

, and



x (1-x) x+ +

(2)

(1-x) +



(3) (4)

are the atomic weights of V, Hf, Fe, and Sb, respectively. Dependence of

the disorder scattering parameter Гm on the Hf content is presented in Fig. 7 (a). It is clear that Гm

increases with increasing Hf doping level which in turn leads to a reduction in the values of lattice thermal conductivity (kl) as shown in Fig. 7 (b). Therefore, mass fluctuations enhance the phonon scattering and play an important role in the reduction of kl as reported by Yang et al [45]. Moreover, nano-size particles and fine grains which obtained by MA and SPS process also participated in enhancing the phonon scattering during introducing large number of defects in the grains [30, 31]. Thus, the thermal conductivity (k) decreased by ~ 54% which was obtained for the sample with x = 0.2 and is about 4.31 Wm-1K-1 near room temperature as represented in Fig. 7 (d). The higher thermal conductivity recorded for x = 0.3 than that of x =0.2 is related to the higher relative density of (x = 0.3) than (x = 0.2) as observed in Table 2. Additionally, it can be clearly seen that the lattice thermal conductivity kl is dominant in the FeV1−xHfxSb system, compared to the electronic thermal contribution ke, which indicates that the alloy scattering due to mass fluctuations is an effective way to reduce the total thermal conductivity of the FeVSb compound. a)

c)

b)

d)

Fig. 7 a) The dependence of disorder scattering parameter Гm on Hf content, b) lattice thermal conductivity (kl), c) eelectronic thermal conductivity (ke) and d) thermal conductivity (k) of FeV1−xHfxSb (0.0 ≤ x ≤ 0.3) system. 3.4 ZT value Temperature dependence of the dimensionless parameter ZT of the FeV1−xHfxSb alloys is shown in Fig. 8. Notably, the ZT values of all samples increase significantly with temperature increasing. The values samples are grown remarkably with presenting the Hf atoms into the FeVSb system at x = 0.1. whilst, ZT value for x ≥ 0.2 decreased because of the reduced power factor despite of reduction of the thermal conduction. A maximum ZT value of 0.08 is obtained at 600 K for x = 0.1 due to the increased of power factor and the related reduction of thermal conductivity which is higher than that reported by Rahidul Hasan et al (ZT = 0.03 at 573 K for FeV1−xTixSb with x = 0.1) [43]. In the view of the previous work, it would be possible to further enhance the TE efficiency of the Hf-doped FeVSb system by multi-substituting. For example, a combination of Hf and Ti is thought to be more effective in reducing the lattice thermal conductivity, to increase the effect of larger atomic mass and size differences of Hf and Ti on stronger alloy scattering of phonons. In addition, the formation of nanocomposite refinement would greatly increase grain surface densities and therefore greatly scatter phonons and consequently achieve higher ZT as reported by Giri Joshi et al [46].

Fig. 8: Temperature dependence of the dimensionless parameter ZT in the FeV1−xHfxSb alloys.

4 Conclusions Thermoelectric samples of FeVSb HH compound materials with fine grains have been successfully synthesized by the induction melting followed by mechanical alloying and spark plasma sintering. The samples after that were annealed. Hf doping was carried out to enhance the phonon scattering. Thermoelectric properties were investigated as a function of temperature in the range from room temperature to 600 K. As well, transport properties including Hall coefficient, Hall mobility and charge carrier concentration were investigated at room temperature. It was shown that substitution of V with Hf can change the sign of Seebeck coefficient from negative to positive, due to one less valence electron of Hf. The thermal conductivity was decreased by ~ 54% in the sample of x = 0.2, due to point defect scattering adapted by heavy elements substitution and the formation of nanocomposite with ultrafine grain sizes via the used synthesis method. The maximum Seebeck coefficient was obtained at about 144 µV/K at 500 K while a maximum ZT value of 0.08 at 573 K for the sample with x = 0.1 was obtained due to the increased of power factor and related reduction of thermal conductivity. Acknowledgments The authors gratefully acknowledge the financial support from the Ministry of Science and Higher Education of the Russian Federation in the framework of Increase Competitiveness Program of NUST“MISiS” (grant No. K3-2017-061), implemented by a governmental decree dated 16th of March 2013, N 211. VK acknowledges Act 211 Government of the Russian Federation, contract No. 02.A03.21.0011. References [1] M. Zou, J.F. Li and T. Kita, Thermoelectric properties of fine-grained FeVSb half-Heusler alloys tuned to p-type by substituting vanadium with titanium, J. Solid State Chem. 198 (2013) 125–130. [2] N.V. Du, J.U. Rahman, E.J. Meang, C.H. Lim, W.H. Shin, W.S. Seo, P.T. Huy, M.H. Kim, S. Lee, Synthesis and thermoelectric properties of Ti-substituted (Hf0.5Zr0.5)1- xTixNiSn0.998Sb0.002 HalfHeusler compounds, J. Alloys Compd. 773 (2019) 1141-1145. [3] N.S. Chauhan, S. Bathula, B. Gahtori, Y.V. Kolen’ko, R. Shyam, N.K. Upadhyay and A. Dhar, Spinodal decomposition in (Ti, Zr)CoSb half-Heusler: A nanostructuring route toward high efficiency thermoelectric materials J. Appl. Phys. 126 (2019) 125110. [4] A.M. Adam, A. El-Khouly, A.P. Novitskii, E.M.M. Ibrahim, A.V. Kalugina, D.S. Pankratova, A.I. Taranova, A.A. Sakr, A. Trukhanov, M.M. Salem, V. Khovaylo, Enhanced thermoelectric

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Highlights 1- Thermoelectric samples of FeVSb HH compound materials with fine grains have been successfully synthesized. 2- Hf doping was carried out to enhance the phonon scattering. 3- The thermal conductivity decreased by ~ 54%. 4- ZT value of 0.08 at 573 K for the sample with x = 0.1.

Transport and thermoelectric properties of Hf-doped FeVSb half-Heusler alloys Authors of the manuscript contributed equally to the manuscript work.

Manuscript title: Transport and thermoelectric properties of Hf-doped FeVSb halfHeusler alloys

The authors whose names are listed below certify that they have no conflict of interest.