Thermal and Electronic Transport Properties of the Half-Heusler Phase ScNiSb

Thermoelectric properties of the half-Heusler phase ScNiSb (space group F4¯3m) were studied on a polycrystalline single-phase sample obtained by arc-melting and spark-plasma-sintering techniques. Measurements of the thermopower, electrical resistivity, and thermal conductivity were performed in the wide temperature range 2–950 K. The material appeared as a p-type conductor, with a fairly large, positive Seebeck coefficient of about 240 μV K−1 near 450 K. Nevertheless, the measured electrical resistivity values were relatively high (83 μΩm at 350 K), resulting in a rather small magnitude of the power factor (less than 1 × 10−3 W m−1 K−2) in the temperature range examined. Furthermore, the thermal conductivity was high, with a local minimum of about 6 W m−1 K−1 occurring near 600 K. As a result, the dimensionless thermoelectric figure of merit showed a maximum of 0.1 at 810 K. This work suggests that ScNiSb could be a promising base compound for obtaining thermoelectric materials for energy conversion at high temperatures.

ScNiSb is a member of the large family of the HH phases, which crystallize with the cubic MgAgAs-type crystal structure (space group F43m, no. 216). The compound was discovered by A. E. Dwight [27]. The first structure refinement from X-ray powder diffraction data confirmed the equiatomic composition of the substance [27,28]. Later, a structure refinement on X-ray single-crystal

Materials and Methods
A polycrystalline sample was synthesized by arc-melting elemental scandium (lumps, 99.9%), nickel (rod, 99.99%), and antimony (lumps, 99.999%) in Ti-gettered argon gas atmosphere. In relation to the intensive evaporation of antimony during the melting, 6% of the nominal mass Sb was added beforehand. The obtained ingots were hand-ground into fine powder. In order to obtain dense bulk samples suitable for thermoelectric property measurements, spark plasma sintering (SPS) was applied (SPS-515 ET, Dr Sinter setup, SDC Fuji, Japan). A consolidation was performed by heating the charge to 950 K at 50 K min −1 under uniaxial pressure of 100 MPa and dwelling this temperature for 10 min. The density of the so-casted pellets, determined by the Archimedes method, was over 98% of the theoretical value.
The prepared material was characterized at room temperature (RT) by X-ray powder diffraction (X pert Pro PANalytical, CuKα radiation, Almelo, Netherlands). Powder diffraction data were collected using an upgraded Huber G670 type Guinier camera with an imaging plate detector. The large focal circle at 360 mm diameter provides for excellent resolution, in particular with hard X-rays. Due to the quite small unit cell for half-Heusler-type compounds, we took advantage of doubling the number of observable Bragg reflections by using the MoKα doublet of the incident beam. As monochromator, a focusing 1D multilayer optics (AXO Dresden, Dresden, Germany) was used. It provides for high usable intensity, along with excellent suppression of the K β component in the direct beam.
The reflection positions obtained by profile deconvolution were corrected for sample displacement. The structure refinement was done by employing the programs FULLPROF (version 6.30) [43] and WinCSD (version 4.19) [44]. Sample composition was checked by energy-dispersive X-ray (EDX) analysis on a FEI scanning electron microscope (FEI, Hillsboro, OR, USA) equipped with an EDAX Genesis XM4 spectrometer.
The Seebeck coefficient and the electrical resistivity of the sintered samples were measured simultaneously under helium atmosphere in the temperature range 350-950 K using the temperature differential and the four-probe methods, respectively, implemented in commercial equipment Linseis LSR-3 (Linseis Messgeraete GmbH, Selb, Germany) and Ulvac ZEM-3 (ULVAC, Methuen, MA, USA). In these measurements, the temperature difference between the ends of each sample was kept equal to 50 K for the LSR-3 device and 20 K, 30 K, and 40 K for the ZEM-3. The thermal diffusivity was measured in the temperature range from 300 K to 923 K using the laser flash method (NETZSCH LFA-457).
Low-temperature (2-300 K) measurements of electrical resistivity, specific heat, Seebeck coefficient, and thermal conductivity were carried out on a Physical Property Measurement System (PPMS-9, Quantum Design, San Diego, CA, USA). The electrical resistivity was measured by standard four-point DC technique, where electrical contacts were made from silver wires attached to the sample by silver paste. The heat capacity measurements were carried out using the relaxation method with the two-τ model. For Seebeck and thermal conductivity measurements, gold-plated copper electrodes were attached to the specimen using silver-epoxy paste.

Results and Discussion
First, crystal structure determination was performed with the X-ray powder diffraction pattern obtained using the CuKα radiation (Bragg-Brentano geometry, 2θ max = 90 • , 11 reflections available in the measured range). All the Bragg peaks were well indexed with the cubic system (space group F43m), except traces of impurity phase Sc 2 O 3 , spotted around 31.3 • . The lattice parameter (a = 6.0749(2) Å) obtained is slightly larger than the experimental values reported before in the literature (between 6.0498 Å and 6.0620 Å) [27][28][29]31], yet smaller than the calculated ones [32,34,35]. The differences between experimental values may have resulted from a different level of structural disorder caused, for example, by slightly different stoichiometry (cf. below). The structure refinement was performed first, considering that Sc, Ni, and Sb atoms occupy the 4b ( 1 ⁄2 1 ⁄2 1 ⁄2), 4c ( 1 ⁄4 1 ⁄4 1 ⁄4), and 4a (0 0 0) sites, respectively, and the occupancy factors were assumed to be equal to unity. Despite the obtained low residuals (R I = 0.031, R P = 0.043), the atomic displacement parameters reveal non-systematic change with the atomic masses: B(Sc) = 1.0(1) Å 2 , B(Ni) = 1.3(2) Å 2 , B(Sb) = 0.75(7) Å 2 . An attempt to refine the occupation of the Ni site (vacancy on this position was suggested in [29]) was not successful: R I = 0.031, R P = 0.04; B(Sc) = 0.93(1) Å 2 , B(Ni) = 1.0(2) Å 2 , B(Sb) = 0.78(7) Å 2 ; Occ(Ni) = 0.98(1). Another reason for enhanced B(Ni) may have been the off-center location of the atoms at this position. Indeed, the Ni could be refined at 16e position (xxx) with x = 0.262(2). This did not change the residuals (R I = 0.031, R P = 0.043) but allowed a more logical distribution of the atomic displacement parameters to be obtained (B(Sc) = 0.98(14) Å 2 , B(Ni) = 0.85(15) Å 2 , B(Sb) = 0.75(7) Å 2 ). Despite the low residuals, the used powder diffraction data did not allow a final decision about the structural details in ScNiSb. To shed more light, high-resolution X-ray powder diffraction data were measured, employing Huber G670 type Guinier camera with double radius and using MoKα radiation (2θ max = 100 • , 84 reflections available in the measured range). In this experiment, the application of the ideal atomic distribution on the crystallographic sites confirmed the atomic displacement parameters not following the atomic masses (B(Sc) = 0.64(3) Å 2 , B(Ni) = 0.75(3) Å 2 , B(Sb) = 0.61(2) Å; R I = 0.027, R P = 0.093). An attempt to refine the occupancy of the nickel position did not reveal any vacancies. The stoichiometric composition of the material is in agreement with the lattice parameter, which is clearly larger (a = 6.0761(4) Å) than that for the Ni-defect compositions ScNi 0.87 Sb (a = 6.0521(6) Å) and Sc Ni 0.85 Sb (a = 6.0498(6) Å) [29]. The off-center model with Ni at the 16e position (x = 0.256(2)) yielded similar residuals (R I = 0.024, R P = 0.097). Yet the sequence of the atomic displacement parameters (B(Sc) = 0.66(3) Å 2 , B(Ni) = 0.61(4) Å 2 , B(Sb) = 0.59(2) Å) is in much better agreement with the atomic masses of the elements. The final results of the crystal structure refinement of ScNiSb from powder X-ray diffraction (MoKα radiation) data are presented in Figure 1. Further details of the real crystal structure may be revealed using the high-resolution X-ray single-crystal data at the equiatomic composition. Nonetheless, in most possible scenario with off-center Ni atoms, the crystal structure reveals clear deviation from the translation symmetry, which should reduce the lattice thermal conductivity, as was recently shown for the intermetallic clathrates [45].   The temperature dependencies of the electrical resistivity (ρ) and the Seebeck coefficient (S) of ScNiSb, determined in a wide temperature interval, are shown in Figure 3. At elevated temperatures, the experiments carried out on heating and cooling the specimen yielded very similar results, and hence only the data obtained on cooling are shown. Moreover, it should be noted that near 300 K the measurements performed employing different techniques/equipment (LSR-3, ZEM-3, PPMS) converged to almost the same values. Therefore, in the following discussion, the data collected using LSR-3 will be evaluated.
As can be inferred from Figure 3, ScNiSb exhibits semiconducting-like behavior, typical for doped semiconductors, with an ionization (or freeze-out) region from 2 K up to about 150 K, an extrinsic (or saturation) region up to about 500 K, and an intrinsic region at higher temperatures. A broad shoulder observed around 50 K has unclear origin. As shown in the inset to Figure 3a, in the intrinsic region, the resistivity can be well described by a standard Arrhenius model: 1/ρ = σ0 + σexp(−Eg/2kBT), where σ0 stands for the residual conductivity, and Eg is the activation energy. The soderived value of Eg amounts to 0.47(1) eV, which is much larger than that reported in the literature [31,35,46].
The thermoelectric power of ScNiSb is positive in the entire temperature range studied, because the number of holes in the valence band far exceeds the number of electrons in the conduction band. Therefore, ScNiSb is a p-type material. The S(T) dependence shows a shoulder-like feature at 120 K and a broad maximum (Smax = 240 μV K −1 ) near T = 450 K. This maximum is related to the The experimental sample density obtained by the Archimedes method is only 1.5% smaller than the theoretical value ( Table 1). The prepared sample of ScNiSb was hard and brittle, as predicted from theoretical calculations [34].  (5) 6.674(2) 6.58 (1) The elements distribution on the polished surface of the specimen is presented in Figure 2. Consistent with the PXRD results, the sample appears fairly homogeneous, except for tiny amounts of scandium-rich phase, probably an oxide. The chemical composition derived as an average over three different points examined on the sample surface is in very good agreement with the nominal one (see Table 1). This supports the off-center position of Ni in the crystal structure.   (5) 6.674(2) 6.58(1) The temperature dependencies of the electrical resistivity (ρ) and the Seebeck coefficient (S) of ScNiSb, determined in a wide temperature interval, are shown in Figure 3. At elevated temperatures, the experiments carried out on heating and cooling the specimen yielded very similar results, and hence only the data obtained on cooling are shown. Moreover, it should be noted that near 300 K the measurements performed employing different techniques/equipment (LSR-3, ZEM-3, PPMS) converged to almost the same values. Therefore, in the following discussion, the data collected using LSR-3 will be evaluated.
As can be inferred from Figure 3, ScNiSb exhibits semiconducting-like behavior, typical for doped semiconductors, with an ionization (or freeze-out) region from 2 K up to about 150 K, an extrinsic (or saturation) region up to about 500 K, and an intrinsic region at higher temperatures. A broad shoulder observed around 50 K has unclear origin. As shown in the inset to Figure 3a, in the intrinsic region, the resistivity can be well described by a standard Arrhenius model: 1/ρ = σ0 + σexp(−Eg/2kBT), where σ0 stands for the residual conductivity, and Eg is the activation energy. The so- The temperature dependencies of the electrical resistivity (ρ) and the Seebeck coefficient (S) of ScNiSb, determined in a wide temperature interval, are shown in Figure 3. At elevated temperatures, the experiments carried out on heating and cooling the specimen yielded very similar results, and hence only the data obtained on cooling are shown. Moreover, it should be noted that near 300 K the measurements performed employing different techniques/equipment (LSR-3, ZEM-3, PPMS) converged to almost the same values. Therefore, in the following discussion, the data collected using LSR-3 will be evaluated. actual one because of breakdown of the Maxwell-Boltzmann law in a material with narrow energy gap or with strong deviation in carriers mobility [48].
The temperature dependence of the power factor (PF = S 2 /ρ) calculated from the measured data of ScNiSb is presented in Figure 3c. On increasing temperature, PF starts growing above about 50 K and reaches a maximum of 0.90(4) × 10 −3 W m K 2 at 810 K. This value is similar to those determined for other RE-based HH phases [3,5,[38][39][40][41][42] and other thermoelectric materials [49]. In order to inspect the conduction mechanism in ScNiSb, a Jonker plot was constructed ( Figure  4) [50]. The observed linear relationship between the thermopower and logarithm of the electrical conductivity is a characteristic feature of semiconductor in its intrinsic region, with charge carriers scattered mainly on acoustic phonons [51]. At low temperatures, the slope of the straight line is positive, while at high temperatures it is negative. However, in both temperature regions, slope has a constant value of ±86.15 μV K −1 . The switch in the sign of the Jonker-type correlation occurring near 450 K suggests that the temperature variations of the Seebeck coefficient and the electrical conductivity in ScNiSb are governed mainly by changes in the carrier concentration. As can be inferred from Figure 3, ScNiSb exhibits semiconducting-like behavior, typical for doped semiconductors, with an ionization (or freeze-out) region from 2 K up to about 150 K, an extrinsic (or saturation) region up to about 500 K, and an intrinsic region at higher temperatures. A broad shoulder observed around 50 K has unclear origin. As shown in the inset to Figure 3a, in the intrinsic region, the resistivity can be well described by a standard Arrhenius model: 1/ρ = σ 0 + σexp(−E g /2k B T), where σ 0 stands for the residual conductivity, and E g is the activation energy. The so-derived value of E g amounts to 0.47(1) eV, which is much larger than that reported in the literature [31,35,46].
The thermoelectric power of ScNiSb is positive in the entire temperature range studied, because the number of holes in the valence band far exceeds the number of electrons in the conduction band. Therefore, ScNiSb is a p-type material. The S(T) dependence shows a shoulder-like feature at 120 K and a broad maximum (S max = 240 µV K −1 ) near T = 450 K. This maximum is related to the compensation effect, when the electron concentration starts to overcome the holes concentration. Using the relationship [47] S max = E g /2eT max (e stands for elementary charge) one finds E g = 0.22 eV, in good agreement with the theoretical data [35,46], however more than twice smaller than that determined from the ρ data. It should be noted that the so-obtained value of E g may differ from the actual one because of breakdown of the Maxwell-Boltzmann law in a material with narrow energy gap or with strong deviation in carriers mobility [48].
The temperature dependence of the power factor (PF = S 2 /ρ) calculated from the measured data of ScNiSb is presented in Figure 3c. On increasing temperature, PF starts growing above about 50 K and reaches a maximum of 0.90(4) × 10 −3 W m K 2 at 810 K. This value is similar to those determined for other RE-based HH phases [3,5,[38][39][40][41][42] and other thermoelectric materials [49].
In order to inspect the conduction mechanism in ScNiSb, a Jonker plot was constructed (Figure 4) [50]. The observed linear relationship between the thermopower and logarithm of the electrical conductivity is a characteristic feature of semiconductor in its intrinsic region, with charge carriers scattered mainly on acoustic phonons [51]. At low temperatures, the slope of the straight line is positive, while at high temperatures it is negative. However, in both temperature regions, slope has a constant value of ±86.15 µV K −1 . The switch in the sign of the Jonker-type correlation occurring near 450 K suggests that the temperature variations of the Seebeck coefficient and the electrical conductivity in ScNiSb are governed mainly by changes in the carrier concentration. The low-temperature (T < 300 K) specific heat (Cp) of ScNiSb is featureless, except for little hump near 3 K (see Figure 5). Possibly, the latter anomaly appears because of the impurity phase detected in the PXRD and EDX studies. Generally, the Cp(T) of ScNiSb has a shape typical for nonmagnetic compounds and can be analyzed by Debye formula: where n is the number of atoms per formula unit, R is the gas constant, ΘD is the Debye temperature, and x = hν/kBT. The first term of Equation (1) corresponds to the electronic part, while the second one corresponds to the phonon contribution to the Cp. The electronic specific heat was described using a simple Sommerfeld term Cel = γT; the fit in the range 4.5-7 K yields γ = 0.5(1) mJ mol −1 K −2 (Inset of Figure 5). By fitting the experimental data over the whole temperature range, we derived the ΘD = 354(1) K. Close to room temperature, Cp is approaching the Dulong-Petit limit of 74.8 J mol −1 K −1 . The temperature dependence of the thermal conductivity (κ) in ScNiSb was calculated with the T > 300 K data derived from the measured thermal diffusivity (D), using the relationship κ = DCpd, where Cp = 3nR represents the specific heat (n is a number of atoms in formula unit, and R is the gas The low-temperature (T < 300 K) specific heat (C p ) of ScNiSb is featureless, except for little hump near 3 K (see Figure 5). Possibly, the latter anomaly appears because of the impurity phase detected in the PXRD and EDX studies. Generally, the C p (T) of ScNiSb has a shape typical for nonmagnetic compounds and can be analyzed by Debye formula: where n is the number of atoms per formula unit, R is the gas constant, Θ D is the Debye temperature, and x = hν/k B T. The first term of Equation (1) corresponds to the electronic part, while the second one corresponds to the phonon contribution to the C p . The electronic specific heat was described using a simple Sommerfeld term C el = γT; the fit in the range 4.5-7 K yields γ= 0.5(1) mJ mol −1 K −2 (Inset of Figure 5). By fitting the experimental data over the whole temperature range, we derived the Θ D = 354(1) K. Close to room temperature, C p is approaching the Dulong-Petit limit of 74.8 J mol −1 K −1 .
where n is the number of atoms per formula unit, R is the gas constant, ΘD is the Debye temperature, and x = hν/kBT. The first term of Equation (1) corresponds to the electronic part, while the second one corresponds to the phonon contribution to the Cp. The electronic specific heat was described using a simple Sommerfeld term Cel = γT; the fit in the range 4.5-7 K yields γ = 0.5(1) mJ mol −1 K −2 (Inset of Figure 5). By fitting the experimental data over the whole temperature range, we derived the ΘD = 354(1) K. Close to room temperature, Cp is approaching the Dulong-Petit limit of 74.8 J mol −1 K −1 . The temperature dependence of the thermal conductivity (κ) in ScNiSb was calculated with the T > 300 K data derived from the measured thermal diffusivity (D), using the relationship κ = DCpd, where Cp = 3nR represents the specific heat (n is a number of atoms in formula unit, and R is the gas constant), while d denotes the density of the material. The overall magnitude of κ is greater than in the literature results [31]. A small increase of κ above about 600 K can be related to heat loses during the measurement or/and some contribution due to bipolar thermal conductivity [52]. At lower The temperature dependence of the thermal conductivity (κ) in ScNiSb was calculated with the T > 300 K data derived from the measured thermal diffusivity (D), using the relationship κ = DC p d, where C p = 3nR represents the specific heat (n is a number of atoms in formula unit, and R is the gas constant), while d denotes the density of the material. The overall magnitude of κ is greater than in the literature results [31]. A small increase of κ above about 600 K can be related to heat loses during the measurement or/and some contribution due to bipolar thermal conductivity [52]. At lower temperatures we observed a well-exposed peak at~50 K, which is related to the interplay between different types of phonon-scattering processes, and suggests high quality of our sample.
Assuming the validity of the Wiedemann-Franz law, κ el = LσT, where L is the Lorenz number, one can calculate the electronic contribution (κ el ) to total κ. Shown in Figure 6 is the estimate of κ el in ScNiSb, derived with L = 1.5 + exp(−|S|/116), as given in Ref. [53]. The so-obtained κ el is fairly small and slightly increasing with increasing temperature. This result implies that the thermal conductivity in ScNiSb is dominated in the whole temperature range studied by the lattice contribution (κ lat ). Remarkably, the magnitude of κ lat is much larger than the minimum thermal conductivity calculated using the Cahill model [54]. This finding opens a prospective of significant reducing κ lat by proper alloying and forming composite materials based on ScNiSb. The values between 5 and 10 W m −1 K −1 above RT are typical for the HH phases [55,56]. The deviations from the translational symmetry found during the crystal structure determination do not reduce markedly the thermal conductivity, as was found recently in intermetallic clathrates [45], raising once more the question of the real atomic structure of the HH phases, as was already discussed for example TiGePt [57,58]. On the other hand, the good thermal conductivity may be understood from the point of view of chemical bonding. The latter characterized by the presence of three-center Sc-Ni-Sb and two-center Sc-Ni interactions. Due to the predominant role of the first type, the bonding may be considered as pseudo homogeneous, i.e., all interactions are same or similar. The regular distribution of similar bonds in the crystal structure of the chemical bonding is described as isotrop. This characteristic of bonding should not influence the thermal conductivity [59].
the good thermal conductivity may be understood from the point of view of chemical bonding. The latter characterized by the presence of three-center Sc-Ni-Sb and two-center Sc-Ni interactions. Due to the predominant role of the first type, the bonding may be considered as pseudo homogeneous, i.e., all interactions are same or similar. The regular distribution of similar bonds in the crystal structure of the chemical bonding is described as isotrop. This characteristic of bonding should not influence the thermal conductivity [59]. The experimental data collected for ScNiSb allowed us to calculate the thermoelectric figure of merit (ZT = S 2 T/ρκ), and the result is shown in Figure 7. With increasing temperature, ZT increased, reaching the maximum ZT = 0.10 at 810 K. This value is smaller than ZT reported for well-established p-type thermoelectrics [60], however it is similar to those found for other RE-based HH phases [1,3,51]. At room temperature ZT = 0.01, which is almost two times smaller than the value reported before for an arc-melted sample [31], yet four times larger when compared with ZT of our sample, prepared by high-pressure high-temperature (HPHT) sintering [42]. The main reason for the reduced ZT values is very low electrical conductivity, opening a way for enhancing the thermoelectric figure of merit by appropriate substitutions. The experimental data collected for ScNiSb allowed us to calculate the thermoelectric figure of merit (ZT = S 2 T/ρκ), and the result is shown in Figure 7. With increasing temperature, ZT increased, reaching the maximum ZT = 0.10 at 810 K. This value is smaller than ZT reported for well-established p-type thermoelectrics [60], however it is similar to those found for other RE-based HH phases [1,3,51]. At room temperature ZT = 0.01, which is almost two times smaller than the value reported before for an arc-melted sample [31], yet four times larger when compared with ZT of our sample, prepared by high-pressure high-temperature (HPHT) sintering [42]. The main reason for the reduced ZT values is very low electrical conductivity, opening a way for enhancing the thermoelectric figure of merit by appropriate substitutions.

Conclusions
As an extension of the literature data for T < 400 K, the thermoelectric properties of the HH antimonide ScNiSb were determined from 2 K up to 950 K. Although this material has a high positive value of the Seebeck coefficient (up to 240 μV K −1 at 450 K), its thermoelectric properties are moderate. Because of a high electrical resistivity (~100 μΩm around RT) and a relatively high value of thermal conductivity (>6 W m −1 K −1 ), the maximum PF and ZT values of 0.91(4) × 10 −3 W m −1 K −2 and 0.1 at 810 K were established, respectively.
The results obtained for ScNiSb are similar to the data reported for many other RE-bearing HH phases and for pure RE-free HH phases. It appears plausible that proper modification of this material (nanostructurization, substitution, composite formation, etc.) may lead to significant improvement of its thermoelectric performance.

Conclusions
As an extension of the literature data for T < 400 K, the thermoelectric properties of the HH antimonide ScNiSb were determined from 2 K up to 950 K. Although this material has a high positive value of the Seebeck coefficient (up to 240 µV K −1 at 450 K), its thermoelectric properties are moderate. Because of a high electrical resistivity (~100 µΩm around RT) and a relatively high value of thermal conductivity (>6 W m −1 K −1 ), the maximum PF and ZT values of 0.91(4) × 10 −3 W m −1 K −2 and 0.1 at 810 K were established, respectively.
The results obtained for ScNiSb are similar to the data reported for many other RE-bearing HH phases and for pure RE-free HH phases. It appears plausible that proper modification of this material (nanostructurization, substitution, composite formation, etc.) may lead to significant improvement of its thermoelectric performance.