Hf Incorporation in (Ti,Zr)NiSn Half Heusler Solid Solutions via Mechanical Alloying

Abstract

Half Heusler materials are promising thermoelectric materials with potential application in generators at medium range temperatures. Solid solutions are typically prepared by arc melting, presenting interesting properties. In this work, the effect of Hf incorporation and the formation of solid solutions is discussed. More specifically, Ti_1−xHf_xNiSn and (Ti_0.4Zr_0.6)_1−yHf_yNiSn half Heusler materials were synthesized via mechanical alloying and consolidated via hot press sintering. Hf incorportation in the lattice strongly affected the lattice thermal conductivity due to the large mass fluctuation. The power factor and thermoelectric figure of merit was optimized via Sb doping the values of 34 $\mathsf{\mu }$W/cmK² and 38 $\mathsf{\mu }$W/cmK²; 0.72 and 0.76 at 762 K for Ti_0.4Hf_0.6NiSn_0.985Sb_0.015 and (Ti_0.4Zr_0.6)_0.7Hf_0.3NiSn_0.98Sb_0.02, respectively, were reached.

1. Introduction

The search for alternative energy technologies has been expedited in recent years as climate change has become more conspicuous. Useful energy is eventually wasted as heat, and limited percentage is used as mechanical power. Nevertheless, the reduction of CO₂ and the recovery of waste energy are challenges that motivate researchers to discover new materials as well as to develop new devices for energy harvesting. Thermoelectric (TE) materials and generators (TEG) can convert heat directly to electrical energy and, thus, they have attracted interest as ideal candidates for waste heat harvesting [1]. The crucial advantages compared to conventional generators are the long lifetime, maintenance-free devices, and no greenhouse gas emissions.

The main criterion for the selection of thermoelectric materials is the dimensionless figure of merit ZT = S²σ T/κ, where S, σ, T, and κ are the Seebeck coefficient, electrical conductivity, temperature, and thermal conductivity, respectively. An ideal thermoelectric material should exhibit high power factor (S² σ) and low κ values to keep temperature gradient and to depreciate conduction heat losses. The thermal conductivity consists of the electronic component κ_e due to mobile charge carriers and phonon component κ_lat due to lattice vibrations [1]. Many thermoelectric materials have been studied for power generation applications such as bismuth telluride [2,3], lead-telluride [3], skutterides [4,5,6], silicon-germanide [7,8,9], and half Heusler [6,10,11,12]. However, many compounds include toxic and inadequate elements such as lead and tellurium; therefore, alternative materials with high figures of merit should be developed.

Among the different families of half Heusler materials, the MNiSn and MCoSb (M = Ti, Zr, Hf) compounds are strong candidates for thermoelectrics. The isoelectronic substitution at the M-site prompts extra mass and stress fluctuations and cause the scattering of short wavelength phonons, resulting in the reduction of the lattice thermal conductivity [13,14,15]. Katayama et al. stated that a reduction of 17.9% and 36.3% is feasible in thermal conductivity via Zr and Hf doping, respectively, compared to undoped TiNiSn [16]. Hohl et al. obtained κ = 5.4 W/m·K in Ta-doped Zr_0.5Hf_0.5NiSn at 700 K and reached a figure of merit 0.5 [17]. Joshi et al. achieved a minimum thermal conductivity κ_min = 3.15 W/m·K at room temperature for Ti_0.25Zr_0.25Hf_0.5NiSn_0.99Sb_0.01 [18]. Furthermore, if the Ni atom is partially substituted by the Pd atom, the ZT is increased to 0.7 for Zr_0.5Hf_0.5Ni_0.8Pd_0.2Sn_0.99Sb_0.01 [19]. Currently, the best figure of merit for the n-type half Heusler is 1.5 at 700 K for Sb-doped Hf_0.25Zr_0.25Ti_0.5NiSn [20], while for the p-type is 1.5 at 973 K [21,22].

Regarding the synthesis of HH materials, arc melting is the most commonly used method for preparation [10,23]. Moreover, it is well known that additional treatments are necessary (i.e., long annealing and ball milling [23]) to improve the thermoelectric properties via the reduction of the lattice thermal conductivity and the phonon scattering by alloying and nanostructuring [13,14]. Zhang et al. maximized the figure of merit of undoped TiNiSn to 0.84 using different mesh size shieves [24]; however, this additional time-consuming process remains the main barrier of this method. On the other hand, mechanical alloying (MA) seems to be a good alternative technique to directly synthesize this type of material that exhibits low lattice thermal conductivity combining advantages such as scalability, simplicity, and the direct formation of nanostructuring. Surprisingly, only a few studies have been reported to synthesize half Heuslers directly from MA and hot press sintering [25,26,27,28,29]. Recently, MA was successfully applied in n-type Zr_1−xTi_xNiSn compounds, and a very promising figure of merit was reached (ZT = 0.71) for the Ti_0.4Zr_0.6NiSn_0.985Sb_0.015 [29]. Moreover, MA was also successful on p-type, where ZT of 1.1 was achieved [27,28].

In this work, we continued our efforts on the synthesis of n-type half Heusler solid solutions via MA and studied the effect of Hf incorporation in the Ti_1−xHf_xNiSn and (Ti_0.4Zr_0.6)_1−yHf_yNiSn lattices. Based on the previous encouraging results of MA synthesis, Ti_1−xHf_xNiSn (with x = 0.2, 0.4, 0.5, 0.6, 0.7 and 0.8) and (Ti_0.4Zr_0.6)_1−yHf_yNiSn with (y = 0, 0.1, 0.25, 0.3, 0.4, 0.5) samples were prepared in order to investigate the effect of isoelectronic Hf substitution as well as doping with Sb.

2. Materials and Methods

2.1. Fabrication of Half Heusler Materials

The starting materials were high-purity elemental powders of Ti (99.99% Alfa Johnson Matthey Gmbh, Kandel, Germany), Hf (99.6 Alfa Johnson Matthey Gmbh, Kandel, Germany), Zr (99% US Research Nanomaterials Inc., Houston, TX, USA) Ni (99.99% Sigma Aldrich Merck, Darmstadt, Germany), Sn (99.85% Alfa Johnson Matthey GmbH, Kandel, Germany), and Sb (99.9% Alfa Johnson Matthey GmbH, Kandel, Germany). The powders were weighed according to the nominal compositions Ti_1−xHf_xNiSn (with x = 0.2, 0.4, 0.5, 0.6, 0.7 and 0.8), Sb-doped Ti_0.4Hf_0.6NiSn (with 1%, 1.5% and 2% Sb substitution in Sn site), (Ti_0.4Zr_0.6)_1−yHf_yNiSn (with y:0, 0.1, 0.25, 0.3, 0.4, 0.5), and Sb-doped (Ti_0.4Zr_0.6)_0.7Hf_0.3NiSn with 1%, 1.5%, 2%, and 2.5% Sb substitution in Sn site) in a tungsten carbide ball milling vial with a ball-to-material ratio of 10:1. The elemental powders were milled under Ar at speeds of 600 rpm using a planetary ball mill (Pulverisette 7 Fritsch, Idar Oberstein, Germany), followed by sintering via hot pressing (HP) at 1150 K for 1 h and 50 MPa. The density of the sintered pellets was >99% of the theoretical density for each composition.

2.2. Microstructural Characterization

In order to examine the phase purity and lattice parameters, all samples were characterized by X-ray powder diffraction (XRD) using Rigaku Miniflex diffractometer after mechanical alloying as well as hot press sintering. The microstructures of the samples were studied by Tescan scanning electron microscope (SEM) equipped with Bruker energy-dispersive X-ray spectroscope (EDS). The lattice parameters were evaluated using the EXPO 2014 software [30].

2.3. Thermoelectric Characterization

The Seebeck coefficient and electrical conductivity were measured synchronously with a ZEM-3 (ULVAC-RIKO) equipment from room temperature to 823 K under a high-purity helium atmosphere. The thermal conductivity κ was calculated by the equation κ = D·ρ·Cp, where the thermal diffusivity D and the heat capacity Cp were measured by the laser flash method using a Netzsch LFA 467 laser flash apparatus. Cp measurements required a standard pyroceram 9606 as a reference sample. The mass density ρ was measured by the Archimedes method. The measurement deviations were 5% for Seebeck coefficient and electrical conductivity and 10% for the thermal conductivity.

2.4. Mechanical Characterization

Mechanical measurements were carried out via micro-hardness tester to evaluate the hardness of the samples. The experiments were performed using Clark Instrument CM series micro-hardness tester. The Vickers hardness was evaluated using the formula HV:1.854(F/D²), in which F is the applied Load (Kilogram force) and D² is the area of the indentation (square millimetres). The applied load was 1 kg-9807 mN.

3. Results and Discussion

Ti_1−xHf_xNiSn with (x = 0.2, 0.4, 0.5, 0.6, 0.7, and 0.8), (Ti_0.4Zr_0.6)_1−yHf_yNiSn with (y = 0, 0.1, 0.25, 0.3, 0.4, 0.5) as well as Sb-doped selected members of the solid solutions series were synthesized by MA in order to study the effect of Hf substitution on their microstructure and thermoelectric properties. More specifically, Ti_0.4Hf_0.6NiSn and (Ti_0.4Zr_0.6)_0.7Hf_0.3NiSn) members were selected to be doped with Sb aiming to optimize the thermoelectric power factor. The same synthesis route was applied in all members in (Figure 1a) and the selected compositions are presented in Figure 1b.

3.1. Synthesis of Ti-Hf and Ti-Hf-Zr Solid Solutions

The starting synthesis conditions were selected based on our previous work [29], where n-type half Heuslers were synthesized for the first time via MA to investigate the thermoelectric properties. In our previous work [29], the duration of MA to synthesize the Ti_1−xZr_xNiSn series was 7 to 12 h, followed by sintering at 1150 K under 50 MPa. In this work, MA duration between 6 and 12 h was applied for the Ti_1−xHf_xNiSn and (Ti_0.4Zr_0.6)_1−yHf_yNiSn series, and the products were studied by PXRD and SEM/EDS analysis. Figure 2a,b present the patterns for members x = 0.6 and y = 0.3, respectively. In the case of the Ti_1−xHf_xNiSn series, it is clear that all peaks can be well indexed to the cubic MgAgAs-type crystal structure at MA of 6 h without any residual starting elements or other secondary phases. Furthermore, the incorporation of Hf in the (Ti_0.4Zr_0.6)_1−yHf_yNiSn lattice increased the required MA duration from 7 h [29] to 9 h for all compositions to avoid the existence of secondary Ni₃Sn₄ phase. Therefore, powders after MA of 6 h and 9 h for the Ti_1−xHf_xNiSn and (Ti_0.4Zr_0.6)_1−yHf_yNiSn series, respectively, were hot pressed and further investigated.

Hot press (HP) sintering was carried out at 1150 K under 50 MPa to develop high quality pressed pellets. PXRD showed that only sharp peaks of Ti_1−xHf_xNiSn and(Ti_0.4Zr_0.6)_1−y Hf_yNiSn phases existed, except for the Ti_0.8Hf_0.2NiSn sample, where metallic full Heusler phase was also observed (Figure 3a). All remaining patterns were identical without any significant change in terms of existing peaks and relative intensities; however, the peaks were shifted due to the Ti/Hf and Hf/Zr substitution, as expected (Figure 3b). Figure 4 shows the increase in the unit cell with Hf concentration for both compositions following Vegard’s law with the lattice parameters being in good agreement with the literature [31]. The PXRD patterns of the Sb-doped members also showed single phase materials without any creation of binary phase Ni₃Sn₄ that was a common impurity elsewhere [29]. The main peak is also displayed as inset to better clarify the presence (or not) of secondary phases in Figure 3a,b.

Backscattered SEM images and EDS results confirmed that the pellets were single phase and according to the nominal composition (see Figure 5 and

Table 1. EDS analysis of the Sb doped Ti_0.4Hf_0.6NiSn samples.

Samples	Ti	Hf	Ni	Sn + Sb
Nominal composition
Ti0.4Hf0.6NiSn	0.39	0.52	1.12	0.97
Ti0.4Hf0.6NiSn0.99Sb0.01	0.39	0.51	1.13	0.97
Ti0.4Hf0.6NiSn0.985Sb0.015	0.40	0.52	1.13	0.95
Ti0.4Hf0.6NiSn0.98Sb0.02	0.41	0.53	1.13	0.93

and

Table 2. EDS analysis of the Sb doped (Ti_0.4Zr_0.6)_0.7Hf_0.3NiSn samples.

Samples	Ti	Zr	Hf	Ni	Sn + Sb
Nominal composition
(Ti0.4Zr0.6)0.7Hf0.3NiSn	0.31	0.46	0.29	0.99	0.96
(Ti0.4Zr0.6)0.7Hf0.3NiSn0.99Sb0.01	0.29	0.44	0.29	0.99	0.99
(Ti0.4Zr0.6)0.7Hf0.3NiSn0.985Sb0.015	0.29	0.45	0.29	0.99	0.92
(Ti0.4Zr0.6)0.7Hf0.3NiSn0.98Sb0.02	0.28	0.45	0.30	0.98	0.93
(Ti0.4Zr0.6)0.7Hf0.3NiSn0.975Sb0.025	0.30	0.45	0.29	0.98	0.99

). These results are in contrast with arc melting synthesis of similar compositions, where impurity phases like Ti₆Sn₅, ZrSn₂ and Ni₃Sn₄ were included in the final pellets [31]. A. Page et al. calculated the (Hf, Zr,Ti)NiSn thermodynamic phase diagram and suggested the coexistence of Ti-rich and Ti-poor grains for arc melted samples, as non-equilibrium states created during solidification and kinetically trapped at lower temperatures [32]. The solid solubility limit of these diverse systems depends on the synthesis technique; thus, the mechanism of solid solutions in MA is different compared to arc melting. Along with that, the solid solutions are formed in full composition range in the Cu-Fe, AlSb-InSb, and Cu-Co systems via MA, but this is not in case for arc melting, which is a rapid solidification process (RSP) [33].

3.2. Thermoelectric Properties of Ti-Hf and Ti-Hf-Zr Solid Solutions

3.2.1. Thermoelectric Properties of the Ti_1−xHf_xNiSn Series

The Seebeck coefficient and the electrical and thermal conductivity for the Ti_1−xHf_x NiSn series as a function of temperature from 300 to 800 K are shown in Figure 6a–f. The Seebeck coefficient exhibited negative values, confirming the n-type character of the materials, and increased with Hf concentration reaching the highest room temperature value of 176 $\mathsf{\mu }$V/K for x = 0.6. For Hf concentrations x > 0.7, the Seebeck coefficient decreased, indicating the increase of carriers concentration. This variation can be attributed to combined mechanisms of band gap reduction with increasing Hf as well as the contribution of defects (i.e., Ni interstitials, (Ti,Hf)/Sn antisites) [34,35]. The electrical conductivity values are between 167 and 268 S/cm. The sample Ti_0.8Hf_0.2NiSn exhibited the maximum value of 268 S/cm due to the existence of full Heusler phase. The power factor (S²σ) can reach a peak of 22 $\mathsf{\mu }$W/cmK² for the composition Ti_0.4Zr_0.6NiSn, 18 $\mathsf{\mu }$W/cmK² for the Ti_0.8Hf_0.2NiSn, and 17 $\mathsf{\mu }$W/cmK² for the Ti_0.4Hf_0.6NiSn. The thermal conductivity is lower when Hf is incorporated in the lattice with the lowest value at x = 0.6–0.7 (κ = 2 W/m·K). Interestingly, these values are considerably lower than those of the Ti-Zr series [29]. In order to gain a better understanding of the substitution of Ti/Hf to the phonon scattering, the lattice thermal conductivity (κ_lat) was evaluated by subtracting the electronic part from the total thermal conductivity (κ_lat = κ − κ_ele). The Wiedeman–Frantz law was used to estimate the electronic thermal conductivity (κ_ele = LσΤ) where L = Lorenz factor, σ = electrical conductivity, and T = Temperature). The measurements of the Seebeck coefficient, assuming scattering from acoustic phonons, were used in order to evaluate the Lorenz factor [36]:

$$S=\pm \frac{k_e}{e}\left[\frac{2F_1\left(n\right)}{F_0\left(n\right)}-n\right]$$

(1)

$$L={\left(\frac{k_B}{e}\right)}^2\left[\frac{3F_0\left(n\right)F_2\left(n\right)-4F_1^2\left(n\right)}{F_0^2\left(n\right)}\right]$$

(2)

$$F_i\left(n\right)={\int }_0^{\infty }\frac{x^{i}dx}{1+\exp (x-n)}$$

(3)

where n is the reduced Fermi Energy (E_F/k_BT), F_i(n) is the Fermi Dirac Integrals, and k_B is the Boltzmann constant. Clearly, the Ti/Hf solid solutions display lower lattice thermal conductivity values than end members. The best figure of merit of the series is 0.46 at 762 K for the Ti_0.4Hf_0.6NiSn member.

3.2.2. Thermoelectric Properties of Sb-Doped Ti_0.4Hf_0.6NiSn

A common approach to enhance the thermoelectric performance of a material is the optimization of carrier concentration through intentional doping. The member Ti_0.4Hf_0.6NiSn was selected for further doping studies since it exhibited the lowest lattice thermal conductivity as well as high PF. Antimony was chosen as efficient dopant [37] and the Sb-doped Ti_0.4Hf_0.6NiSn (Sb of 1 at%, 1.5 at% and 2 at%) series was synthesized. In Figure 7a–d, the experimental data of the Seebeck coefficient and the electrical and thermal conductivity are presented. The Seebeck coefficient is reduced (in absolute values) from −176 $\mathsf{\mu }$V/K for undoped sample to −94 $\mathsf{\mu }$V/K for the doped sample with 2 at% antimony due to the increase of carrier concentration, as expected. Moreover, the incorporation of Sb also results in the increase of electrical conductivity for a dopant concentration up to 1.5%. For higher amount of Sb (2%) the σ decreases and this can be attributed to the reduction of mobility. The power factor was improved from 17 $\mathsf{\mu }$W/cmK² for the undoped sample to 34 $\mathsf{\mu }$W/cmK² for the doped sample (Sb = 1.5 at%) 762 K. The total thermal conductivity increases with the incorporation of antimony into the lattice due to the enhancement of electrical conductivity. The figure of merit increases >20% with Sb incorporation reaching the value of 0.72 at 760 K.

3.2.3. Thermoelectric Properties of the (Ti_0.4Zr_0.6)_1−yHf_yNiSn Series

The promising power factor of our previous work on the Ti_0.4Zr_0.6NiSn member [29] in combination with the lower lattice thermal conductivity caused by the Hf incorporation lead to the (Ti_0.4Zr_0.6)_1−yHf_yNiSn series for further electrical and thermal investigations. The Seebeck coefficient, electrical conductivity, and the total thermal conductivity were measured in (Ti_0.4Zr_0.6)_1−yHf_yNiSn samples from 300 to 800 K, as shown in Figure 8a–f. In comparison to our best previous result Ti_0.4Zr_0.6NiSn, interestingly, the Seebeck coefficient remains at about −200 $\mathsf{\mu }$V/K; however, it is lower for the members y = 0.1 and 0.25. Despite the fact that the Zr/Hf substitution is isoelectronic, the carrier concentration changes in the system in agreement to other works [38] probably due to some defects that act as donors. The electrical conductivity, which is affected also by mobility, remained more or less the same and decreased when y ≥ 0.4. The power factor (S²σ) reached a peak of 26 $\mathsf{\mu }$W/cmK² for the composition of x = 0.3. These are very promising values, considering that these are undoped samples. The thermal conductivity for concentrations in the range 0 ≤ x ≤ 0.25 is maximum with values (κ = 2.63–2.21 W/m·K respectively). On the other hand, materials with concentrations 0.3≤ and ≤0.5 demonstrate the lowest values (κ = 2.1–2.2 W/m·K, respectively). This substitution has a significant impact on the figure of merit, which reached a peak of 0.75 at 760 K.

3.2.4. Thermoelectric Properties of Sb-Doped (Ti_0.4 Zr_0.6)_0.7Hf_0.3NiSn

The member (Ti_0.4Zr_0.6)_0.7Hf_0.3NiSn was doped with antimony based on the stoichiometric composition by substituting the Sn site with 1 at%, 1.5 at%, 2 at% and 2.5 at%. In Figure 9a–d, the trends of the Seebeck coefficient, electrical and thermal conductivity are displayed. The Seebeck coefficient is reduced from −260 $\mathsf{\mu }$V/K for the undoped sample to −87 $\mathsf{\mu }$V/K for the doped sample with y = 0.025 antimony, as expected, due to the increase of carriers that Sb incorporation caused. Moreover, the electrical conductivity increased in agreement with the Seebeck coefficient variation. The power factor increased from 26 $\mathsf{\mu }$W/cmK² to 38 $\mathsf{\mu }$W/cmK² for 2 at% Sb incorporation. The power factor for 2.5 at% Sb fell to 33 $\mathsf{\mu }$W/cmK², suggesting that the Sb concentration of 2.5% exceeded the optimum carrier concentration for this series. The total thermal conductivity, see Figure 9c, increased with the incorporation of antimony into the lattice, as expected, due to enhancement of electrical conductivity. The figure of merit reached a maximum of 0.76 at 762 K, which is the best reported in this work. Interestingly, the undoped and doped members have similar ZTs that actually originate from opposite ranges of power factors and thermal conductivity.

3.2.5. Thermal Conductivity of MA (Ti,Zr,Hf)NiSn Solid Solutions

Figure 10a shows the room temperature lattice thermal conductivity of the two series Ti_1−xHf_xNiSn and (Ti_0.4Zr_0.6)_1−yHf_yNiSn as well as Ti_1−zZr_zNiSn from our previous work [29]. According to the literature, these values are lower compared to similar nominal compositions prepared by arc melting [31]. The minimum lattice thermal conductivity for arc melting was achieved for the composition Ti_0.6Hf_0.4NiSn being κ_lat = 3.15 W/m·K [31], while the MA samples with the same stoichiometry exhibited κ_lat = 2.1 W/m·K. The low lattice thermal conductivities of our solid solutions, prepared via MA, can be attributed on nanostructuring, as previously reported [27,28,29]. All solid solutions exhibit lower lattice thermal conductivity compare to the end members, as expected, due to the scattering of the short wavelengths phonons due to Ti/Zr/Hf mass fluctuation. Clearly, the incorporation of Zr in the lattice has a lower effect compared to Hf, which strongly affects and further reduces the lattice thermal conductivity. The introduced mass fluctuation can be evaluated based on the mass scattering parameter Γ_M based on the following equation [39]:

$${\mathsf{\Gamma }}_M=\frac{{\sum }_i^n{c}_i{\left(\frac{\overline{M_i}}{\overline{\overline{M}}}\right)}^2{\mathsf{\Gamma }}_M^i}{{\sum }_i^n{c}_i}$$

(4)

where the mass fluctuation parameter Γⁱ_M is given:

$${\mathsf{\Gamma }}_M^i=\sum _k{f}_k{\left(1-\frac{M_i^k}{\overline{M_i}}\right)}^2$$

(5)

M_i^k: mass of the k_th atom of the i_th sublattice and f_ik: the fractional occupation.

Here, the average mass of atoms on the i_th sublattice is:

$$\overline{M_i}={\sum }_k{f}_i^k{M}_i^k$$

(6)

and the average atomic mass of the compound:

$$\overline{\overline{M}}=\frac{{\sum }_i^n{c}_i\overline{M_i}}{{\sum }_1^n{c}_i}$$

(7)

where c_i: relative degeneracies of the respective site.

Figure 10b shows the calculated Γ_M for the three different series Ti_1−xHf_xNiSn, (Ti_0.4,Zr_0.6)_1−yHf_yNiSn as well as Ti_1−zZr_zNiSn (previous study [29]), Γ_M clearly confirms that the Hf incorporation in the lattice is the most effective with Ti_1−xHf_xNiSn having the highest values. Moreover, Γ_M of the (Ti_0.4Zr_0.6)_1−yHf_yNiSn series starts from 0.2, due to the existing fluctuation of (Ti_0.4, Zr_0.6), and increases with Hf. Overall, Ti-Zr substitution has the lower effect while Hf is preferred to maximize mass fluctuation.

3.3. Mechanical Properties

Mechanical characterization becomes more and more essential for promising TE materials as a practical requirement for mechanically stable and durable device. Among efficient TE materials, arc melted half Heusler materials have been reported as mechanically stable for applications [40,41,42,43]. Here, HH prepared by MA are studied for the first time in terms of Vickers hardness. Figure 11 shows the hardness data of our series with Hf concentration, in comparison with the hardness of other members prepared by arc melting. The hardness of Ti_1−xHf_xNiSn and (Ti_0.4Zr_0.6)_1−yHf_yNiSn samples was in the range of 8 to 9.5 GPa. Overall, the values are in the same range regardless of the Hf concentration or the synthesis method [33]. The latter is interesting, since these pellets are prepared by nanostructured powder and are still in the same range with the arc melted ones.

4. Conclusions

In this work, Hf incorporation in the Ti_1−xHf_xNiSn and (Ti_0.4Zr_0.6)_1−yHf_yNiSn solid solution series prepared by MA was successfully attempted. Both undoped and doped samples exhibited a single half Heusler phase. The lattice thermal conductivity was strongly affected by the mass fluctuation introduced by (Ti,Zr)/Hf substitution, suggesting Hf incorporation as the most effective method. The thermoelectric properties of the solid solutions were optimized via Sb doping and the best ZTs were 0.72 and 0.76 at 773 K for the members Ti_0.4Hf_0.6NiSn_0.985Sb_0.015 and (Ti_0.4Zr_0.6)_0.7Hf_0.3NiSn_0.98Sb_0.02, respectively. Moreover, the hardness measurements gave comparable values for the MA samples and the arc melted samples from the literature. Overall, the thermoelectric materials of these solid solutions prepared via MA are very promising and will be further investigated since such technique is advantageous due to its simplicity and scalability for module development.