Thermoelectric properties of Heusler-type Ru2VAl1−xGax alloys

Intermetallics 92 (2018) 36–41

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Thermoelectric properties of Heusler-type Ru2VAl1−xGax alloys a

a

a,∗

b

c

B. Ramachandran , Y.H. Lin , Y.K. Kuo , C.N. Kuo , A.A. Gippius , C.S. Lue a b c

MARK

b,∗∗

Department of Physics, National Dong Hwa University, Hualien, 97401, Taiwan Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan Department of Physics, Moscow State University, 119991, Moscow, Russia

A R T I C L E I N F O

A B S T R A C T

Keywords: A. Intermetallics B. Thermoelectric properties C. Heat treatment D. Point defect F. X-ray diffraction

Electrical and thermal transport properties of the Heusler-type alloys, Ru2VAl1−xGax (x = 0.0–1.0) were studied by means of the electrical resistivity, Seebeck coefficient, and thermal conductivity measurements. All studied compounds show weak metallic characteristics with a low residual resistivity ratio. In addition, the Ru2VAl1−xGax alloys with x ≤ 0.75 show an n-type thermoelectric conduction from 10 to 300 K, while Ru2VGa displays p-type conduction. The estimated Fermi energy of these materials is higher than 0.5 eV, endorsing their metallic character. From the thermal conductivity study, we noticed that low-temperature thermal conductivity decreases with increasing Ga content for x ≤ 0.5 and then increases with further Ga substitution. This observation is essentially due to the change in the phonon scattering processes as a result of the substitution of heavier Ga atoms into the Al sites of Ru2VAl. It is important that an enhanced thermoelectric figure of merit ZT was found in Ru2VAl0.25Ga0.75, about seven times higher than that in Ru2VAl.

1. Introduction Since the discovery of the first series of Heusler alloys Cu2MnSn, Cu2MnAl, and Cu2MnSb (cubic L21 structure) in 1903 [1,2], more than a thousand compounds have been identified as Heusler alloys. Remarkably, the compounds of this family are suitable materials for various applications, such as half metals [3], ferromagnetic shape memory alloys [4], superconductivity [5,6], and spintronics [7]. However, recent interest is mainly focused on the thermoelectric properties of Heusler-type alloys such as Fe2VAl, Fe2VGa, Fe2MnSi, and Fe2TiSn [8–11]. In particular, Heusler alloys with 24 valence electrons have a narrow band-gap or a pseudogap near the Fermi-level density of states (DOS) and hence they exhibit semimetal characters. According to the Slater-Pauling rule: Mt = Zt - 24, where Mt is the total spin moment per unit cell and Zt is the number of valence electrons per formula unit, the iron-containing alloys such as Fe2VAl and Fe2VGa are nonmagnetic. Nevertheless, due to the presence of a pseudogap near the Fermi energy (EF), the Fe2VAl and Fe2VGa-based materials have generated vast interest towards the optimization of their thermoelectric properties for practical applications [8,9,12–16]. Importantly, the Heusler alloys have the advantage of involving more elements, which allows for more degrees of freedom such as band-gap tuning and multi-functionality [7]. Recently, several new Heusler-type compounds with Zt = 24 have been discovered in the search of thermoelectric materials, namely

∗

Ru2VAl, Ru2VGa, and Ru2NbGa [17–20]. In particular, Kuo et al. [20] reported that the semimetallic Ru2NbGa has a comparable absolute Seebeck coefficient (∼20 μV/K) to that of the promising thermoelectric Heusler alloys such as Fe2VAl and Fe2VGa (∼25 μV/K) at room temperature (RT) [8,9]. Most importantly, the Ru2NbGa compound has a much lower RT thermal conductivity (∼5 W/m K) than those in Fe2VAl and Fe2VGa (> 15 W/m K) [8,9,20]. Although Ru2VAl and Ru2VGa exhibit metallic characteristics [17,18], they have a high resistivity and a low residual resistivity ratio (< 2) as compared to ordinary metals. A recent theoretical investigation by first-principle calculations on the quaternary Ru2VAlxGa1−x (x = 0, 0.25, 0.5, 0.75, 1) alloys revealed a good agreement between the theoretical prediction and experimental results on lattice parameters for Ru2VAl and Ru2VGa alloys at various temperatures [17–19]. The theoretical study disclosed that the electronic density of states of each individual compound has a sharp dip near the Fermi level [19]. According to the model proposed by Mahan and Sofo [21], materials with sharp electronic band features of a few tens of meV from the Fermi level could be potential candidates for efficient thermoelectrics. Hence, both Ru2VAl and Ru2VGa are possible candidates for thermoelectric applications. Nevertheless, the thermoelectric properties such as the Seebeck coefficient and the thermal conductivity of these materials have not been explored yet. In this work, we investigated the temperature-dependent electrical and thermal transport properties of the Ru2VAl1−xGax (x = 0–1.0)

Corresponding author. Corresponding author. E-mail addresses: [email protected] (Y.K. Kuo), [email protected] (C.S. Lue).

∗∗

http://dx.doi.org/10.1016/j.intermet.2017.09.012 Received 28 June 2017; Received in revised form 15 September 2017; Accepted 21 September 2017 Available online 27 September 2017 0966-9795/ © 2017 Elsevier Ltd. All rights reserved.

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alloys, grown by an arc-melting method. We noticed that all compounds display weak metallic behavior with a low residual resistivity ratio. The Seebeck coefficient varies noticeably with Ga content (x), due to the substituent induced the modification in the Fermi energy. Notably, the compound Ru2VGa has a p-type thermoelectric conduction from 10 to 300 K, while other compounds including Ru2VAl have n-type conduction. With regard to the thermoelectric performance, the compound of Ru2VAl0.25Ga0.75 shows the highest thermoelectric figure of merit of about 2.7 × 10−3 at RT among this series, mainly due to its relatively high thermoelectric power factor (S2/ρ) of about 0.9 μW/cmK2. 2. Materials and methods The samples of Ru2VAl1−xGax with x = 0, 0.25, 0.5, 0.75, and 1 were synthesized using a standard arc-melting technique [20]. Briefly, the mixture of high purity elemental metals (Ru, V, Al, and Ga) of the respective samples with a stoichiometric ratio was placed in a watercooled copper hearth and melted several times in an argon atmosphere using an arc-melter. We noted that the weight loss during the melting process was less than 0.5% for all samples. To acquire the homogeneity, each obtained ingot was annealed in a vacuum-sealed quartz tube at 1073 K for 48 h and then heated at 673 K for 24 h, following furnace cooling to RT. Such a heat treatment is a typical process to obtain single-phase Heusler alloys [8,9,12,20]. For thermoelectric measurements, each sample was cut into a rectangular parallelepiped shape with a dimension of about 5.0 × 1.5 × 1.5 mm3 by a diamond cutter. The electrical resistivity of the compounds was measured by a standard four-probe method, in the temperature range of 10–300 K. The Seebeck coefficient and thermal conductivity measurements were carried out simultaneously using a direct heat pulse technique. More details about these techniques can be found elsewhere [22–24]. All measurements presented here are recorded with a slow heating rate of about 20 K/h and have reproducibility better than 2%. 3. Results and discussions 3.1. X-ray diffraction Fig. 1. a) The XRD patterns of the polycrystalline Ru2VAl1−xGax samples and b) The calculated lattice constant (a) versus Ga concentration (x). The relative errors in the estimation of lattice constant remarked as the error bars in Fig. 1b, and the solid line is a guide for the eye to illustrate a linear variation of lattice constant with x, according to the Vegard's law.

The powder X-ray diffraction (XRD) patterns of the Ru2VAl1−xGax (x = 0.0–1.0) samples were obtained using the Cu Kα radiation at room temperature and the results are presented in Fig. 1a. The XRD results show that all studied alloys are crystallized in the cubic crystal structure with a space group Fm3m [17,18]. However, the substituted compounds such as Ru2VAl0.75Ga0.25, Ru2VAl0.5Ga0.5, and Ru2VAl0.25Ga0.75 have a minor impurity phase Ru3V, which marked by the asterisks in Fig. 1a. Here, we consider that the presence of the minor impurity phase in the Ga-substituted samples will have little influence on their thermoelectric properties. From the XRD data, we have calculated the lattice constant (a) of the Ru2VAl1−xGax alloys, which is plotted against Ga concentration (x) in Fig. 1b. It is seen that the lattice constant increases rather linearly with increasing Ga content, in accordance with the Vegard's law [23,24]. This finding confirms that Ga atoms are successfully substituted into the Al sites of Ru2VAl.

for further increasing x (Table 1). Notably, the RRR values of these compounds are quite small (∼1.0–1.3, Table 1), indicating their poor metallic behavior. Furthermore, the compounds Ru2VAl0.75Ga0.25 and Ru2VAl0.5Ga0.5 have a negative temperature coefficient of resistivity (i.e., semiconductor-like behavior) above 75 K and 20 K, respectively. An estimation using the Arrhenius law inferred that both samples have small thermal activation energies of less than 0.6 meV (see Fig. 2b) which is likely due to thermally-excited carriers across the pseudogap [19]. Here, the value of pseudogap is estimated to be about 1.1 and 0.3 meV for Ru2VAl0.75Ga0.25 and Ru2VAl0.5Ga0.5, respectively. With this respect, these two alloys can be classified as semimetals. Overall, all studied samples are poor metals with a small RRR value (less than 1.4, see Table 1). This finding is in good agreement with a recent theoretical work on the Ru2VAl1−xGax systems [19]. The influence of Ga substitution on the physical properties of Ru2VAl will be further examined using the highly sensitive Seebeck coefficient and thermal conductivity measurements in sections 3.3 and 3.4.

3.2. Electrical resistivity Fig. 2a displays the electrical resistivity as a function of temperature, ρ(T), for the Ru2VAl1−xGax compounds. We noticed that Ru2VAl has a lower RT resistivity (ρ300K∼509.0 μΩ cm) and residual resistivity ratio (RRR, ρ300K/ρ10K∼1.2, Table 1) than that of the reported values (ρ300K∼4533 μΩ cm and RRR ∼1.9) in the literature [17,18]. However, Ru2VGa has similar values (ρ300K∼274.0 μΩ cm and RRR ∼1.2) to those in the literature (ρ300K∼277 μΩ cm and RRR ∼1.2) [17,18]. With Ga substitution, both RT resistivity and low-T resistivity (ρ10K) increase considerably with Ga content until x = 0.5 and then decrease markedly

3.3. Seebeck coefficient Fig. 3 shows the Seebeck coefficient data S(T) of the Ru2VAl1−xGax compounds. Seebeck coefficients for all samples (except Ru2VGa, which 37

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Fig. 3. The Seebeck coefficient data, S(T) of the Ru2VAl1−xGax compounds. Inset shows the variation of Seebeck coefficient with respect to the Ga content (x) at 100 K and 300 K.

comparable to those in other Heusler alloys such as Fe2VAl, Fe2VGa, and Ru2NbGa (≥20 μV/K) [8,9,20]. Furthermore, a small peak feature at around 50 K is observed for the Ru2VAl1−xGax samples at low temperatures, presumably due to the phonon-drag effect. Such low-T behavior is usually seen for the metallic compounds [8,9]. It is wellknown that the strong disorder scattering could suppress the phonondrag feature. In this respect, the compound Ru2VGa display a more pronounced phonon-drag peak in the measured S(T) suggesting that this sample is highly ordered in nature, consistent with the x-ray results (Fig. 1). Above 70 K, the S value varies rather linearly with temperature which indicates diffusion thermopower dominating the thermoelectric transport at high temperatures. For normal metals, the relation between Seebeck coefficient and temperature is given by the Mott formula:

Fig. 2. a) Temperature-dependent electrical resistivity, ρ(T) of Ru2VAl1−xGax and b) The Arrhenius law fitting to the high-T ρ(T) of Ru2VAl0.75Ga0.25 and Ru2VAl0.5Ga0.5.

Table 1 The values of the low-temperature resistivity, room-temperature resistivity, residual resistivity ratio (RRR), and the Fermi energy for the Ru2VAl1−xGax alloys. Sample

ρ10K (μΩ cm)

ρ300K (μΩ cm)

ρ300K/ρ10K (RRR)

EF (eV)

Ru2VAl Ru2VAl0.75Ga0.25 Ru2VAl0.5Ga0.5 Ru2VAl0.25Ga0.75 Ru2VGa

409.2 533.7 716.5 276.4 231.8

508.7 536.5 691.3 358.2 274.3

1.24 1.01 0.97 1.30 1.18

1.21 1.29 0.95 0.62 1.25

S=

π 2kB2 T, 2eEF

(1)

where kB is the Boltzmann constant. The estimated EF values of the compounds using Eq. (1) are given in Table 1. As indicated, the Fermi energy of the compounds is greater than 0.5 eV, being consistent with their metallic nature. In addition, the observed variation in the S(T) of Ru2VAl with Ga substitution can be qualitatively described by two-carrier conduction mechanism [8], which is given by the equation:

has p-type carriers) are negative from 10 to 300 K, indicating that the ntype carriers (electrons) dominate their thermoelectric transport. We noted that the RT S value decreases from −13.3 μV/K of Ru2VAl to −10.6 μV/K of Ru2VAl0.75Ga0.25 and then increases gradually with Ga content to −18.2 μV/K for Ru2VAl0.25Ga0.75. Finally, S changes sign to a positive value of ∼8.5 μV/K for Ru2VGa, suggesting that the major charge carriers of this compound are holes. A similar behavior of S versus Ga content (x) is also seen at low temperatures (see the inset of Fig. 3). The observed x-dependence of Seebeck coefficient is presumably due to the rigid-band-like shift of the Fermi level from the center of the pseudogap [25] as a result of the substitution of isoelectronic element Ga into Al sites of Ru2VAl. Since the DOS within the pseudogap is relatively small [19,25], the small change in the carrier concentration induced by substitution could lead to a considerable shift of the Fermi level from the central region of the pseudogap. Hence, the observed variation of S with respect to Ga content and the crossover from n-type (x = 0.75) to p-type of x = 1.0 are witnessed in the presently studied Ru2VAl1−xGax systems. The absolute RT S value (∼18.2 μV/K) of Ru2VAl0.25Ga0.75 is

S=

σn Sn + σp Sp σn + σp

,

(2)

where Sn,p and σn,p are the Seebeck coefficients and the electrical conductivity for n- and p-type carriers, respectively. Hence, the modification in S(T) data of the Ga-substituted Ru2VAl samples can be ascribed to the competition between two types of carriers at a given temperature. Although both substituent and host atoms (Ga and Al) have the same valence electrons, the larger atomic number of Ga results in a higher electronegativity for Ga (1.81, Pauling scale) as compared to the Al (1.61). In addition, Ga has a higher electronegativity than V (1.63) although it has a lower electronegativity compared to Ru (2.2). It should be noted here that the upper and lower valence bands of the Ru2VAl1−xGax are dominated by d orbitals of Ru and V, and s orbitals of Al/Ga, respectively [19]. Thus, the electrical and thermoelectric transport properties of the Ru2VAl are significantly altered by the 38

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Fig. 5. Low-temperature lattice thermal conductivity κL(T) of the Ru2VAl1−xGax compounds, and the solid lines represent the calculated lattice thermal conductivity using the phonon model described in Eqs. (3) and (4). Inset shows a plot of the coefficient of phonon-point-defect scattering (A) versus Ga content (x) and the expected parabolic curve illustrated as solid line for an eye-view.

Fig. 4. The measured thermal conductivity, κ(T) of the Ga-substituted Ru2VAl alloys. The solid lines show the deduced electronic thermal conductivity of the samples from the resistivity data.

substitution of Ga in the Al sites (see Figs. 2 and 3). This is due to the influence of Ga electronegativity, which could facilitate the formation of a strong covalent bonding [26]. As a result, the carrier density near the Fermi-level DOS could move towards high electronegative Ga atoms [27]. This could lead to a shift in EF of Ru2VAl upon Ga substitution which is indeed observed in the present study (Table 1). It has also been proposed that the strong covalent guest-host interactions can cause a localized “cluster vibration” [28], which can affect lattice dynamics along with point defects induced by Ga substitution. As a consequence, the lattice thermal conductivity of the Ga-substituted Ru2VAl compounds would be affected. Such a picture will be further explored in section 3.4.

effects of Ga content (x) on the phonon heat transport of the Ru2VAl1−xGax alloys, we calculated the lattice thermal conductivity using the Debye-Callaway approximation [22,23,29]. Here, the lattice thermal conductivity κL(T) is described by the equation:

κL (T ) =

kB ⎛ kB T ⎞3 2π 2v ⎝ ℏ ⎠

∫0

θD / T

ξ 4e ξ dξ , − 1)2

τ p−1 (e ξ

(3)

where ξ = ћω/kBT is dimensionless, and ω is the phonon frequency, θD is the Debye temperature, and τp−1 is the phonon scattering relaxation time. The term τp−1 is considered as the sum of four scattering mechanisms:

3.4. Thermal conductivity

τ p−1 =

The measured thermal conductivity data κ(T) of the Ru2VAl1−xGax series is presented in Fig. 4. The RT κ value of these samples varies from 9 to 13 W/m K. Importantly, the lowest RT κ value of about 8.8 W/m K was obtained for the Ru2VAl0.5Ga0.5, which is much lower than the promising thermoelectric Heusler alloys Fe2VAl and Fe2VGa (> 15 W/ m K) [8,9]. A peak feature near 50 K is observed for all samples, which is commonly seen in the crystalline solids [8,9,22–24]. However, the low-T phonon peak is reduced considerably for the three quaternary alloys (x = 0.25–0.75) as compared to the end compounds Ru2VAl and Ru2VGa, presumably due to the phonon-impurity scattering. For metallic or semimetallic solids, the total thermal conductivity is usually expressed as a sum of electronic and lattice thermal conductivities, i.e. κ(T) = κe(T) + κL(T). In general, the electronic thermal conductivity and electrical resistivity can be correlated with the Wiedemann-Franz law over certain temperatures: κe(T)ρ(T) = L0T, where ρ(T) is the electrical resistivity and L0 (= 2.45 × 10−8 WΩK−2) is the Lorenz number. The calculated electronic thermal conductivity κe(T) of the Ru2VAl1−xGax samples is illustrated as solid lines in Fig. 4. From this estimation, we noted that κe contributes less than 20% to total κ of the Ru2VAl1−xGax alloys at room temperature, signifying that the thermal conduction is mainly associated with phonons (lattice vibrations). The lattice thermal conductivity κL is obtained by subtracting κe from the measured κ with the result displayed in Fig. 5. To examine the

−θ v + Aω4 + Bω2T exp ⎛ D ⎞ + Cω, L ⎝ 3T ⎠

(4)

where v is the average phonon velocity, L is the mean grain size, and the coefficients A, B, and C are free-fitting parameters. The terms in Eq. (4) are the scattering rates of phonon with boundary, point-defect, phonon, and electron, respectively. The calculated κL of the Ru2VAl1−xGax compounds is illustrated as solid lines in Fig. 5. The used values of θD and v are taken from the theoretical calculations as θD = 546.8 K, 529.2 K, 508.8 K, 489.3 K, and 463.6 K, and v = 4.38 km/s, 4.24 km/s, 4.08 km/s, 3.92 km/s, and 3.73 km/s for Ru2VAl, Ru2VAl0.75Ga0.25, Ru2VAl0.5Ga0.5, Ru2VAl0.25Ga0.75, and Ru2VGa, respectively [19]. The obtained parameters for this series of samples are listed in Table 2. From the fitting (Fig. 5 and Table 2), it is noticed that the phononboundary and phonon-point-defect scattering significantly influence the low-T phonon thermal transport in the Ru2VAl1−xGax alloys. However, the phonon-boundary scattering term (v/L) varies non-systemically with Ga content. In contrast, the phonon-point-defect scattering term (A) increases gradually with Ga content until x = 0.5, and then decreases for x > 0.5. This finding is in agreement with the Klemens model [30] that the prefactor A is directly proportional to x(1−x), where x is the relative concentration of point defects. To demonstrate this correlation, the calculated parameter A versus Ga content (x) is plotted in the inset of Fig. 5. We noticed that the variation of A with x tends to follow an expected parabolic curve [31], which is shown as a 39

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Table 2 The obtained values of free-fitting parameters for the Ru2VAl1−xGax samples from the lattice thermal conductivity fitting. Sample

v/L (108 s−1)

L (μm)

A (10−43 s3)

B (10−19 s/K)

C (10−4)

Ru2VAl Ru2VAl0.75Ga0.25 Ru2VAl0.5Ga0.5 Ru2VAl0.25Ga0.75 Ru2VGa

1.9 12.2 3.7 3.2 10.0

23.1 3.5 11.0 12.3 3.7

14.2 16.5 22.0 18.0 7.5

16.0 3.4 7.5 9.0 5.0

1.6 0.4 2.4 2.2 0.4

6 × 10−3 at 400 K. This value is twice higher than that the value (2.7 × 10−3) at 300 K, but it is still much lower compared to that of the state-of-the-art thermoelectric materials such as Bi2Te3 (ZT ∼ 0.8) [32]. While the thermoelectric ZT value of Ru2VAl has been demonstrated to be enhanced by the substitution of Gain Al sites, a further improvement in the thermoelectric performance is needed. This could be achieved through the modification in the electronic band structure, e.g. by incorporating antisite disorders in the system. For example, an absolute S value as high as ∼130 μV/K at RT for the off-stoichiometric compound Fe1.95V1.05Al was reported [33]. Recently, we have also demonstrated that the ZT value can be effectively enhanced through off-stoichiometric approach in semimetallic Heusler compound Ru2TaAl [34]. Moreover, the slight addition of heavier elements such as Rh and Ir onto the Fe sites of Fe1.95V1.05Al led to further increase in the absolute S value of about 170 μV/K for the Fe1.92Rh0.03V1.05Al and Fe1.92Ir0.03V1.05Al compounds [35]. For the reduction of the lattice thermal conductivity, a common strategy is to introduce the disorders/ distortions into the lattice by substituting a larger size and heavier element. It is worthwhile mentioning that our early study of a new Heusler-type compound of Ru2NbGa shows an intrinsic low κL of about 5W/m K at RT [20]. On this basis, the substitution of Nb at the V sites or In at the Al sites seems to be a feasible approach to reduce κL in Ru2VAl. In fact, a reduction of κL almost by one half in the Nb-substituted Fe2VAl was achieved, i.e. κL ∼13 W/m K for Fe2V0.9Nb0.1Al as compared to κL ∼25 W/m K for Fe2VAl [36]. From the above-mentioned developments, further investigations of the thermoelectric properties of the Ru2VAl-based compounds are in order.

solid line in the inset of Fig. 5. Here, the phonon-point-defect scattering produced by Ga substitution is mainly due to the mass fluctuations between host Al and substituent Ga, since their mass difference is very high (> 150%). However, the strain field scattering also contributes to the phonon-point-defect scattering, as the difference in atomic sizes of Al and Ga is about 5.6%. Other lattice imperfections, such as impurities, vacancies, and other crystallographic defects, may also contribute to the phonon-point-defect scattering. On the other hand, the phononphonon scattering contributes significantly to phonon thermal transport of the Ru2VAl1−xGax alloys above the low-T phonon peak. However, the phonon-electron scattering has additional contributions to the κL(T) of three quaternary alloys (x = 0.25–0.75) as T > 150 K.

3.5. Figure of merit, ZT Fig. 6 illustrates the thermoelectric figure of merit, ZT (= S2T/ρκ) versus temperature for the Ru2VAl1−xGax alloys, estimated using the measured ρ(T), S(T), and κ(T). The highest ZT value of about 2.7 × 10−3 was obtained for the n-type Ru2VAl0.25Ga0.75 at RT, which is about seven times larger than that of parent Ru2VAl. In this respect, the n-type Ru2VAl0.5Ga0.5 and p-type Ru2VGa samples have the RT ZT value of about 0.8 × 10−3 and 0.6 × 10−3, respectively. However, these values are more than one orders of magnitude smaller that of the Fe2VAl and Fe2VGa-based compounds [8,9,14,15]. This observation is mainly due to the low thermoelectric power factor (S2/ρ ≤ 1.0 μW/ cmK2) of these Ru2VAl1−xGax alloys. It is seen that the ZT value of the optimized compound Ru2VAl0.25Ga0.75 varies rather linearly with temperature above 200 K. Hence, a realistic extrapolation of the ZT data of this sample to higher temperatures yields a ZT value of about

4. Conclusion The temperature-dependent electrical resistivity, Seebeck coefficient, and thermal conductivity of the Ru2VAl1−xGax alloys were measured to investigate their thermoelectric properties. Our study revealed that these Heusler-type alloys are poor metals with a low residual resistivity ratio of about 1.0–1.3. In particular, the compounds Ru2VAl0.75Ga0.25 and Ru2VAl0.5Ga0.5 show semiconductor-like behavior above 75 K and 20 K, respectively, with the small thermal activation energy (less than 0.6 meV). Such a behavior is associated with the thermally-excited carriers across the small pseudogap arising from the Ga substitution in Ru2VAl. All compounds (except Ru2VGa, which has a p-type transport) have the majority n-type carriers that dominate thermoelectric conduction. The thermal conductivity study unveiled that the low-temperature phonon peak in lattice thermal conductivity is suppressed substantially with Ga substitution. This is attributed to the modification in phonon-point-defect scattering by Ga substitution via mass fluctuation. For the thermoelectric improvement, an enhanced room-temperature ZT has been achieved in Ru2VAl0.25Ga0.75, about seven times larger than that of Ru2VAl. Acknowledgments This work was supported by the Ministry of Science and Technology of Taiwan under Grant Nos. MOST-103-2112-M-259-008-MY3 (Y.K.K.), MOST-103-2112-M-006-014-MY3 (C.S.L.), and MOST-105-2923-M006-002-MY3 (C.S.L.). A.A.G. acknowledges the support by the Russian

Fig. 6. The thermoelectric figure of merit, ZT values of the studied compounds.

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(2013), pp. 978–979. [19] H. Abbassa, S. Hadjri-Mebarki, B. Amrani, T. Belaroussi, K.D. Khodja, P. Aubert, Theoretical investigation of new Heusler alloys Ru2VGa1-xAlx, J. Alloys Compd. 637 (2015) 557. [20] C.N. Kuo, H.W. Lee, C.M. Wei, Y.K. Lin, Y.K. Kuo, C.S. Luo, Ru2NbGa: a Heusler compound with semimetallic characteristics, Phys. Rev. B 94 (2016) 205116. [21] G.D. Mahan, J.O. Sofo, The best thermoelectric, Natl. Acad. Sci. U.S.A. 93 (1996) 7436–7439. [22] Y.K. Kuo, B. Ramachandran, C.S. Lue, Optimization of thermoelectric performance of SrSi2-based alloys via the modification in band structure and phonon-point-defect scattering, Front. Chem. 2 (2014) 106. [23] C.S. Lue, C.N. Kuo, J.Y. Huang, H.L. Hsieh, H.Y. Liao, B. Ramachandran, Y.K. Kuo, Enchancementof thermoelectric performance driven by Ge substitution in SrSi2 alloy, J. Phys. D. Appl. Phys. 46 (2013) 315303. [24] C.S. Lue, S.F. Wong, J.Y. Huang, H.L. Hsieh, H.Y. Liao, B. Ramachandran, Y.K. Kuo, Chemical pressure effect on thermoelectric properties of Ca and Ba substituted SrSi2 alloys, J. Appl. Phys. 113 (2013) 013710. [25] Y. Nishino, S. Deguchi, U. Mizutani, Thermal and transport properties of the Heusler-type Fe2VAl1-xGex (0 ≤ x ≤ 0.20) alloys: effect of doping on the lattice thermal conductivity, electrical resistivity, and Seebeck coefficient, Phys. Rev. B 74 (2006) 115115. [26] T.M. Bhat, D.C. Gupta, Robust thermoelectric performance and high spin polarization in CoMnTiAl and FeMnTiAl compounds, R. Soc. Chem. Adv. 6 (2016) 80302–80309. [27] A.H. Reshak, Transport properties of Co-based Heusler compounds Co2VAl and Co2VGa: spin-polarized DFT+U, R. Soc. Chem. Adv. 6 (2016) 54001–54012. [28] B. Duan, J. Yang, J.R. Salvador, Y. He, B. Zhao, S. Wang, P. Wei, F.S. Ohuchi, W. Zhang, R.P. Hermann, O. Gourdon, S.X. Mao, Y. Cheng, C. Wang, J. Liu, P. Zhai, X. Tang, Q. Zhang, J. Yang, Electronegative guest in CoSb3, Energy Environ. Sci. 9 (2016) 2090–2098. [29] B. Ramachandran, J.Y. Jhiang, Y.K. Kuo, C.N. Kuo, C.S. Lue, Electrical and thermal transport properties of Nb and Ru substituted Mo3Al2C superconducting compounds, Supercond. Sci. Technol. 29 (2016) 035003. [30] P.G. Klemens, The scattering of low-frequency lattice waves by static imperfections, Proc. Phys. Soc. Lond. Sect. A68 (1959) 1113–1128. [31] A. Petersen, S. Bhattacharya, T.M. Tritt, S.J. Poon, Critical analysis of lattice thermal conductivity of half-Heusler alloys using variations of Callaway model, J. Appl. Phys. 117 (2015) 035706. [32] H. Scherrer, S. Scherrer, D.M. Rowe (Ed.), CRC Handbook of Thermoelectrics, CRC, Boca Raton, FL, 1995. [33] C.S. Lue, Y.K. Kuo, Thermoelectric properties of the semimetallic Heusler compounds Fe2-xV1+xM (M=Al, Ga), Phys. Rev. B 66 (2002) 085121. [34] C.W. Tseng, C.N. Kuo, H.W. Lee, K.F. Chen, R.C. Huang, C.M. Wei, Y.K. Kuo, C.S. Lue, Semimetallic behavior in Heusler-type Ru2TaAl and thermoelectric performance improved by off-stoichiometry, Phys. Rev. B 96 (2017) 125106. [35] T. Sugiura, Y. Nishino, Doping effects of transition metals on thermoelectric properties of off-stoichiometric Fe2VAl alloys, J. Jpn. Inst. Met. 73 (2009) 846–851. [36] C.S. Lue, R.F. Liu, M.Y. Song, K.K. Wu, Y.K. Kuo, Chemical pressure effect on the transport and electronic band structure of Fe2V1-xNbxAl, Phys. Rev. B 78 (2008) 165117.

Foundation for Basic Research under Grant 16-53-52012. References [1] F. Heusler, About magnetic manganese alloy, Verh. Deut. Phys. Gesell. 5 (1903) 219. [2] F. Heusler, W. Starck, E. Haupt, On synthesis of ferromagnetic manganese alloy, Verh. Deut. Phys. Gesell. 5 (1903) 220. [3] E. Sasioglu, L.M. Sandratskii, P. Bruno, I. Galanakis, Exchange interactions and temperature dependence of magnetization in half-metallic Heusler alloys, Phys. Rev. B 72 (2005) 184415. [4] H. Ishikawa, Y. Sutou, T. Omori, K. Ishida, A. Yoshikawa, R.Y. Umetsu, R. Kainuma, Pd-In-Fe shape memory alloy, Appl. Phys. Lett. 90 (2007) 261906. [5] T. Klimczuk, C.H. Wang, K. Gofryk, F. Ronning, J. Winterlik, G.H. Fecher, J.C. Griveau, E. Colineau, C. Felser, J.D. Thompson, D.J. Safarik, R.J. Cava, Superconductivity in the Heusler family of intermetallics, Phys. Rev. B 85 (2012) 174505. [6] B. Wiendlocha, M.J. Winiarski, M. Muras, C. Zvoriste-Walters, J.C. Griveau, S. Heathman, M. Gazda, T. Klimczuk, Pressure effects on the superconductivity of the HfPd2Al Heusler compound: experimental and theoretical study, Phys. Rev. B 91 (2015) 024509. [7] C. Felser, H. Atsufumi, Heusler Alloys: Properties, Growth and Applications, Springer, Cham, Switzerland, 2016, p. 3. [8] C.S. Lue, C.F. Chen, J.Y. Lin, Y.T. Yu, Y.K. Kuo, Thermoelectric properties of quaternary Heusler alloys Fe2VAl1-xSix, Phys. Rev. B 75 (2007) 064204. [9] C.S. Lue, J.W. Huang, D.S. Tsai, K.M. Sivakumar, Y.K. Kuo, Effects of Ge substitution on the thermoelectric properties and pseudogap characteristics of Fe2VGa, J. Phys. Condens. Matter 20 (2008) 255233. [10] A.H. Reshak, Fe2MnSixGe1-x: influence thermoelectric properties of varying the germanium content, R. Soc. Chem. Adv. 4 (2014) 39565–39571. [11] A. Ślebarski, J. Deniszczyk, W. Borgieł, A. Jezierski, M. Swatek, A. Winiarska, M.B. Maple, W.M. Yuhasz, Electronic structure and thermodynamic properties of the Heusler alloys Fe2Ti1-xVxSn, Phys. Rev. B 69 (2004) 155118. [12] Y. Nishino, T.B. Massalski, P.E. Turchi (Eds.), The Science of Complex Alloys, TMS, Warrendale, 2005, p. 325. [13] A. Ślebarski, J. Goraus, Electronic structure and thermodynamic properties of Fe2VGa, Phys. Rev. B 80 (2009) 235121. [14] M. Mikami, Y. Kinemuchi, K. Ozaki, Y. Terazawa, T. Takeuchi, Thermoelectric properties of tungsten-substituted Heusler Fe2VAl alloy, J. Appl. Phys. 111 (2012) 093710. [15] P.C. Wei, T.S. Huang, S.W. Lin, G.Y. Guo, Y.Y. Chen, Thermoelectric properties optimization of Fe2VGa by tuning electronic density of states via titanium doping, J. Appl. Phys. 118 (2015) 165102. [16] H. Miyazaki, M. Inukai, Y. Nishino, Effect of Ta substitution on the electronic structure of Heusler-type Fe2VAl-based alloy, J. Appl. Phys. 120 (2016) 125106. [17] S. Mondal, C. Mazumdar, R. Ranganathan, Ru2VAl and Ru2VGa: two new Heuslertype compounds, AIP Conf. Proc. vol. 1536, (2013), pp. 825–826. [18] S. Mondal, C. Mazumdar, R. Ranganathan, Structural and transport properties of two new Heusler type Ru2VAl and Ru2VGa compounds, AIP Conf. Proc. vol. 1512,

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