Effective Decrease of the Thermal Conductivity Caused by Hf in Fe(V_0.955−xHf_0.045Ti_x)Sb Half-Heusler Phase

Abstract

The thermoelectric properties of the Fe(V_0.955−xHf_0.045Ti_x)Sb half-Heusler (HH) phase were studied in the temperature range from 300 to 800 K. We employed Hf- and Ti-substitutions for V in the FeVSb-based HH phase for reducing the lattice thermal conductivity and tuning the carrier concentration, respectively. The samples prepared with the composition of Fe(V_0.955−xHf_0.045Ti_x)Sb (0.000 ≤ x ≤ 0.075) consisted almost solely of the half-Heusler phase. We succeeded in significantly decreasing the lattice thermal conductivity κ_lat ≈ 2.1 W m⁻¹K⁻¹ for Fe(V_0.88Hf_0.045Ti_0.075)Sb while keeping appropriate carrier concentration for the optimized transport properties. However, the highest ZT value was not significantly increased but kept rather low at 0.55, mainly due to the reduction in the Seebeck coefficient. The mechanism leading to the reduction in Seebeck coefficient was revealed by the means of first principles band calculations.

1. Introduction

Thermoelectric generators are expected to be one of effective technologies for resolving the continuous problem of the fossil energy consumption because of their ability to convert waste heat into electricity. The performance of these thermoelectric devices generally depends on their constituent thermoelectric materials through the dimensionless figure of merit ZT = S²ρ⁻¹/(κ_el + κ_lat), where S, ρ, κ_el, and κ_lat represent the Seebeck coefficient, electrical resistivity, electron and lattice thermal conductivity, respectively. Practical thermoelectric materials, such as PbTe¹⁾ or Bi₂Te₃,²⁾ possess a large value of ZT exceeding unity. However, most of these thermoelectric materials contain rare, expensive, and toxic elements that prevent us from using these materials in various applications. Therefore, new, cheap, non-toxic, and high-performance thermoelectric materials are strongly desired for developing thermoelectric generators so as to construct a low energy consumption and an environmentally friendly sustainable society.

The use of theoretical calculations of electronic structure represents a convenient way to discover new and appropriate materials for thermoelectric generators. Takeuchi³⁾ argued that a practical thermoelectric material should possess the following characteristics: (a) a large band gap exceeding 10 k_BT_A, where T_A indicates the temperature of practical applications, (b) an intense peak in the density of states located a few k_BT_A apart from the edge of energy gap, preferentially consisting by (c) the presence of multiple bands at the same energy range, where the electrons contribute to the electrical transport properties. By the use of first principles calculations, it was found that the FeVSb half-Heusler phase (HH phase) showed an electronic structure satisfying the previous conditions with a band gap of 0.36 eV together with an intense density of states created by two bands at the top of the valence band.⁴⁾ As the FeVSb HH phase consists solely of very cheap, abundant and non-toxic elements, this material can be considered as one of the most promising candidates for the practical thermoelectric materials leading to the wide use of thermoelectric generators.

We calculated, in the previous study,⁴⁾ the thermoelectric properties of FeVSb HH phase, by using the semi-classical Boltzmann transport equation together with the experimentally determined relaxation time and the thermal conductivity. It was found that the FeVSb HH phase is capable of showing ZT = 0.88 at 700 K. This moderately large value of ZT is obtainable only when the Seebeck coefficient possesses a positive sign, i.e. a p-type behavior. In spite of that, the prepared FeVSb HH phase possessed an n-type behavior caused by an excess of electron probably brought about by disordering, such as vacancies and/or anti-site element substitutions. The inappropriate carrier concentration limited its maximum ZT to small values less than 0.40 at 700 K.

More recently, for confirming the prediction of the large ZT exceeding 0.80 at the p-type condition, we prepared Fe(V_1−xTi_x)Sb HH phase with various Ti concentrations for the reduction of its carrier concentration. As a result, the Ti-doped samples transited to the p-type regime with a larger power factor PF = S²ρ⁻¹ of 4.40 × 10⁻³ W m⁻¹K⁻², leading to a maximum ZT value of 0.63 at 700 K for x = 0.20. This measured ZT value was similar to that predicted from calculations (ZT_calc = 0.88). Despite the moderately large ZT value obtained, this value remains lower than that required for industrial applications (e.g.: ZT = 1.40 at 750 K for PbTe¹⁾). Therefore, we need to further increase the figure of merit ZT of FeVSb HH phase by increasing its power factor and/or decreasing its lattice thermal conductivity.

Klemens⁶⁾ and Hopkins⁷⁾ reported that phonon scattering mechanisms in alloys are greatly affected by the mass difference between the host and the impurity atoms. Yamamoto⁸⁾ determined that the lattice thermal conductivity of the Al_37.0Mn_30.0−xRu_xRe_xSi_30.0 C54 phase is greatly reduced with increasing the “impurity scattering strength”, becoming larger with a significant mass difference between the host and the impurity atoms.

In order to decrease lattice thermal conductivity of FeVSb-based materials, it would be very plausible to employ the scattering effect with the use of heavy impurity elements. Indeed, by the use of the partial substitution of Nb for V, Fu et al.⁹⁾ succeeded in decreasing the lattice thermal conductivity of the Fe(V_1−xNb_x)Sb HH phase to κ_lat = 5.6 W m⁻¹K⁻¹ at room temperature, that is less than the half of the original value of the FeVSb HH phase (κ_lat = 12.2 W m⁻¹K⁻¹). By knowing that Nb is one of 4d transition metal elements, we expected that the much heavier 5d transition metal elements such as Hf, Ta and W would lead to a stronger impurity phonon scattering leading to a larger reduction of the lattice thermal conductivity of the FeVSb HH phase. Besides, if the lattice thermal conductivity is reduced while keeping the electronic structure unchanged, a large enhancement of ZT would be obtained.

In this study, therefore, we investigated the thermoelectric properties of the Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase in which V was partially and simultaneously substituted by Hf and Ti. We intended to reduce the lattice thermal conductivity by the partial substitution of the heavier Hf for the lighter V and subsequently tuned the carrier concentration by a substitution of the tetravalent valent Ti for the pentavalent V in the range of 0.000 ≤ x ≤ 0.075. The thermoelectric properties were investigated for the prepared samples in the wide temperature range from 300 to 800 K.

2. Experimental Procedure

The first set of samples was prepared in the compositions of Fe(V_1−yHf_y)Sb (0.045 ≤ y ≤ 0.20) to find the solubility limit of Hf. Then, the second set of samples containing the saturated solution of Hf together with a variable concentration of Ti was prepared with the compositions of Fe(V_0.955−xHf_0.045Ti_x)Sb (0.000 ≤ x ≤ 0.075). For the preparation, Fe (purity: 99.9%), V (99.9%), Hf (98%), Ti (99.99%), and Sb (99.999%) were melted together by means of induction melting method in argon atmosphere. We used nominal compositions containing 5 mass% excess of Sb to compensate the evaporation loss of Sb during the preparation. The ingots prepared by the induction melting were crushed into powder and re-melted by arc melting in argon atmosphere at least 2 times for making the solid solution homogeneous. The obtained mother ingots were annealed at 973 K for 72 h in a 10⁻² Pa vacuumed silica tube. The annealed ingots were then crushed into powder and sintered into bulk by hot pressing at 873 K for 15 hours with an applied pressure of 54 MPa in continuous vacuum atmosphere.

The crystal structure and chemical composition of the samples were analyzed by powder X-ray diffraction (XRD) using Cu-Kα radiation (λ = 1.5418 nm) in Bruker D8 Advance, and by scanning electronic microscopy (SEM) combined with energy-dispersive X-ray (EDX) spectroscopy (JEOL JED-2140GS), respectively. The density of bulk samples was determined by the Archimedes’ method using deionized water as working liquid. The measured density of all the samples, displayed in Table 1, exceeded 95% of the theoretical value of the single FeVSb HH phase. The relative densities exceeding 100% for the composition at x = 0.000 and x = 0.075 would be artificially deduced in association with the secondary phases precipitated in the dense matrix of the main phase.

Table 1 Chemical compositions of HH phase and impurity, the lattice constant, and density of Fe(V_0.955−xHf_0.955Ti_x)Sb samples.

The thermal conductivity of bulk samples was measured by the laser-flash method, using NETZSCH LFA457 Microflash, in the wide temperature range from 300 to 700 K. The thermal diffusivity D was obtained by the method described by Parker et al.¹⁰⁾ The specific heat C_P of the sample was measured by the differential laser flash calorimetry technique using a standard pyroceram pellet.¹¹⁾ Additionally, by using the sample density d, we calculated the thermal conductivity κ according to the following formula.   

\begin{equation} \kappa = C_{P}\times d\times D \end{equation} (1)

The Seebeck coefficient was measured by a hand-made apparatus in the temperature range of 300 K < T < 800 K. The reliability of our apparatus was confirmed by a cross-checking of several samples with the data acquired by ZEM-3, which is commonly used to measure the Seebeck coefficient of various materials, as shown in Fig. 1. Each measurement from our hand-made apparatus showed almost the same values of Seebeck coefficient as that measured with the ZEM-3 apparatus within a deviation of less than 7%. A good reproducibility was also confirmed for different pieces for the same composition sample.

Fig. 1

The temperature dependence of the Seebeck coefficient of Fe(V_0.905Hf_0.045Ti_0.050)Sb HH phase measured by a hand-made apparatus (the solid markers) and a commercial ZEM-3 apparatus (the open markers).

The electrical resistivity was measured with the bulk samples of rectangular shape in the temperature range of 300 K < T < 700 K using a standard four-probe technique in a continuously vacuumed furnace.

We also employed theoretical calculations to reveal the effect of Hf on the electronic density of states of the FeVSb HH phase by use of density functional theory (DFT) calculations in the package software WIEN2k that is based on the full potential linearized augmented plane waves and local orbitals [FP-LAPW+lo]. The generalized gradient approximation developed by Perdew, Burke, and Ernzerhof (GGA-PBE)¹²⁾ was used to express the exchange-correlation potential. A Monkhorst-Pack k-point mesh of 4 × 4 × 4 was used to integrate the first brillouin zone of the structure model with RKmax = 7.

3. Results

The measured powder XRD patterns of Fe(V_1−yHf_y)Sb are plotted in Fig. 2(a). All the prepared samples contained the half-Heusler phase as the dominant phase. Although the Ni₂In-type high-temperature phase^13–15) was absent from the sample, small amounts of unknown phases were detected with several diffractions peaks, marked by arrows in Fig. 2(a). The most apparent peaks, identified at 32.2°, 38.5°, and 46.3°, from the unknown phases increased with increasing Hf concentration. Broad and weak peaks at 56°–58° and 67.5°–68.5° were observed for the highest Hf concentrated sample (y = 0.20). Those peaks possessed a similar pattern than that of the fcc structure of Hf reported by Seelam,¹⁶⁾ hence, the most pronounced secondary phase was safely attributed to compounds involving Hf. With decreasing Hf concentration, the peaks of impurity phase were gradually weakened. Eventually, the precipitation of impurity phase was nearly undetectable in the case of y = 0.045 (= 1.5 at% Hf), and therefore, we identified the solubility of Hf in FeVSb HH phase to be nearly equal to or slightly less than 1.5 at%.

Fig. 2

(a) XRD pattern of Fe(V_1−yHf_y)Sb and (b) Fe(V_0.955−xHf_0.045Ti_x)Sb. Hf related impurities were clearly observed in Hf-rich samples. Presence of another impurity phase, VSb₂, was confirmed for all samples from the peaks at around 33.8° and 38.5° in diffraction angles.

After finding the solubility limit of Hf, the second set of samples with the compositions of Fe(V_0.955−xHf_0.045Ti_x)Sb, involving 1.5 at% Hf and the small amount of Ti in the range of 0.000 ≤ x ≤ 0.075 (0 to 2.5 at% Ti), was prepared. The XRD patterns of prepared samples showed in Fig. 2(b) possessed a nearly single HH phase. A diffraction peak at 33.8° revealed the presence of a small amount of VSb₂ phase, that was commonly reported to precipitate during the preparation of FeVSb HH phase.^14,17) The lattice constant of each composition was calculated with the use of the lattice parameter refinement program CellCalc¹⁸⁾ and summarized in Table 1. The lattice constant was slightly expanded as the Ti concentration increased, proving the solubility of Ti in the FeVSb half-Heusler structure.

SEM images were taken for each sample, and the typical examples of obtained images of Fe(V_0.955Hf_0.045)Sb and Fe(V_0.905Hf_0.045Ti_0.050)Sb are shown in Fig. 3. The SEM image of Fe(V_0.955Hf_0.045)Sb HH phase showed the presence of 1–2 µm grains embedded in the matrix, although its distribution on the surface was very small. By using EDX composition mapping, displayed in Fig. 3(a), we determined that those grains were almost solely composed of Hf. The small volume fraction of these Hf grains presumably prevented us from clearly observing XRD peak shown in Fig. 2(b).

Fig. 3

SEM images of (a) Fe(V_0.955Hf_0.955)Sb and (b) Fe(V_0.905Hf_0.045Ti_0.050)Sb sintered pellets. The EDX element mappings of the selected area specified by the dashed lines in the SEM image in (a1), were depicted in the right panels (a2)–(a5). We confirmed that a small amount of Hf was not dissolved in the matrix and precipitated in Fe(V_0.955Hf_0.955)Sb. A small amount of impurity VSb₂-phase, highlighted by a light gray color in the (b2) BSE image and indicated by arrows, was also precipitated as small grains of 0.10–5.00 µm in diameter in Fe(V_0.905Hf_0.045Ti_0.050)Sb together with the similar size of Hf grains.

The composition analysis of the main phase, displayed in Table 1, showed that the Hf solubility limit was found to be more than 1 at% but less than 1.5 at%, showing very good consistency with that concluded from the XRD analysis. Some other grains of 1–2 µm in size were scattered over the sample surface. Their chemical compositions were determined to be Sb:V ≈ 2:1, and therefore, we safely identified these particles as the VSb₂-phase precipitated during the sample preparation. The composition of the main phase in all samples showed a deficiency of Fe compensated by an excess of Sb, probably caused by the precipitation of the VSb₂ impurity phase. Nevertheless, from the small volume fraction and the homogenous distribution of isolated impurity phase over the matrix of HH phase, we consider that the effect of those phases on the transport properties would be negligible to be safely ignored.

The thermal conductivity of Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase is shown in Fig. 4. The thermal conductivity of samples monotonically decreased with increasing Ti concentration towards the lowest value of κ = 3.2 W m⁻¹K⁻¹ for Fe(V_0.88Hf_0.045Ti_0.075)Sb. By use of the Wiedemann-Franz law, we roughly calculated the lattice thermal conductivity κ_lat of samples at 700 K, and compared with that of Fe(V_1−xTi_x)Sb HH phase.⁵⁾ The lattice thermal conductivity κ_lat of Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase decreased with increasing x towards the minimum value κ_lat = 2.1 W m⁻¹K⁻¹ at x = 0.075. Notably, this value is less than half of the lowest κ_lat = 2.1 W m⁻¹K⁻¹ reported for the Hf-free Fe(V_0.80Ti_0.20)Sb HH phase⁵⁾ and Fe(V_1−xNb_x)Sb HH phase.⁹⁾ It then confirmed, in this analysis, that the phonon scattering in association with Hf effectively reduced the lattice thermal conductivity of HH phase.

Fig. 4

(a) Temperature dependence of thermal conductivity of Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase and Fe(V_1−xTi_x)Sb HH phases [REF 5]. (b) Lattice thermal conductivity at 700 K estimated using κ_lat = κ − κ_el, where the electrical thermal conductivity κ_el was roughly determined by the Wiedemann-Franz law κ_el = LσT.

As we successfully decreased the lattice thermal conductivity of Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase by introducing Hf, we intended next to optimize the carrier concentration for the best electron transport properties by employing the Ti partial-substitution for V.

The Seebeck coefficient of Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase is shown in Fig. 5(a). All the samples showed a positive sign of the Seebeck coefficient. This fact clearly proved that the electron concentration was effectively reduced by Ti-substitution for V. At low temperatures, it increased with increasing temperature regardless of Ti concentrations, but unfortunately, the magnitude of the Seebeck coefficient showed a decreasing tendency at high temperatures above 460 K presumably due to the bipolar effect. Notably, this bipolar effect was not observed for Hf-free samples up to 700 K which possessed a maximal Seebeck coefficient value of S = 324 µV K⁻¹ at 700 K for Fe(V_0.80Ti_0.20)Sb.⁵⁾ The samples showed a maximal magnitude of the Seebeck coefficient of 227.67 µV K⁻¹ at 573 K for Fe(V_0.905Hf_0.045Ti_0.050)Sb HH phase.

Fig. 5

Temperature dependence of (a) Seebeck coefficient, (b) electrical resistivity, and (c) power factor of Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase and Fe(V_0.80Ti_0.20)Sb HH phase [REF 5]. The power factor at 700 K is plotted in (d) as a function of Ti concentration x.

As shown in Fig. 5(b), all the prepared sample exhibited small values less than 5.0 mΩ cm in the whole temperature range of measurement. Notably, Fe(V_0.955Hf_0.045)Sb HH phase seemed to show a typical behavior of metallic electrical resistivity, increasing with temperature below 580 K. Then the electrical resistivity slowly decreased at high temperatures above 580 K. This behavior would correspond to the electron-hole excitation. For other compositions, the presence of Ti shortened the mean free path of conduction electrons to a minimum value comparable to the interatomic distance a of the metal, filling the Ioffe-Regel-Mott criterion,¹⁹⁾ and cannot be furthermore reduced as the thermally-induced scattering of electrons were increased. As a consequence, the measured electrical resistivity reached a saturated limit, independent from the temperature, at the value of ρ ≈ 1.80 mΩ cm.

The calculated power factor PF = S²/ρ is displayed as a function of temperature in Fig. 5(c), and its magnitude at 700 K are replotted in Fig. 5(d). Notably, a large magnitude of PF exceeding 3.00 mW m⁻¹K⁻² were observed over a wide temperature range from 400 K to 700 K for Fe(V_0.905Hf_0.045Ti_0.050)Sb. Despite this value of power factor was smaller than that of PF = 4.40 × 10⁻³ W m⁻¹K⁻² at 700 K for Fe(V_0.80Ti_0.20)Sb HH phase,⁵⁾ this characteristic would be very important for practical applications. We also note here that the carrier concentration best suited for thermoelectric applications was obtained at Fe(V_0.905Hf_0.045Ti_0.050)Sb.

Finally, we plotted the figure of merit ZT in Fig. 6. Despite that we succeeded in effectively reducing the lattice thermal conductivity of Fe(V_0.87Hf_0.045Ti_0.075)Sb HH phase by the Hf-substitution for V, the figure of merit ZT did not show any enhancement from the ZT value of 0.63 of the Hf-free Fe(V_0.8Ti_0.2)Sb to stay below 0.55, that was observed at 700 K for Fe(V_0.87Hf_0.045Ti_0.075)Sb. The absence of the effective increase of the ZT is caused by the reduction in the Seebeck coefficient. It is explained, in other words, that the substitution of Hf for V altered the electronic structure of FeVSb HH phase to prevent us from obtaining the value of large ZT.⁴⁾ Therefore, the effect of Hf-substitutions on the electronic structure of the FeVSb HH phase are revealed and discussed in the following section.

Fig. 6

(a) Figure of merit ZT of Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase plotted as a function of temperature. (b) ZT of Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase plotted as a function of chemical potential at 700 K together with that of calculation [REF 4] and the Fe(V_1−xTi_x)Sb [REF 5].

4. Discussions

In this section, we discuss the effect of Hf substitution on the electronic structure of the FeVSb HH phase. To estimate the Fermi energy from the various compositions of substituted Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase (0.000 ≤ x ≤ 0.075), we deduced the number of electrons of each nominal composition, assuming 1 at% Hf integrated into the half-Heusler structure (as indicate the SEM-EDX analysis compositions). Then the Fermi energy of each composition was retrieved using the integrated electron density of states of the original FeVSb HH phase. We also calculated the temperature dependence of chemical potential using the Sommerfield theory according to the following formula.   

\begin{equation} \mu(T) = \varepsilon_{f} - \frac{\pi^{2}}{6}(k_{B}T)^{2}\frac{N'(\varepsilon_{f})}{N(\varepsilon_{f})} \end{equation} (2)

Where μ, ε_f, k_B, N(ε_f) represent the chemical potential, the Fermi energy, the Boltzmann constant, and the density of state, respectively. The measured S and ρ of the Hf-free FeV_1−xTi_xSb HH phase are plotted as a function of chemical potential together with that of the FeVSb HH phase in Fig. 7.

Fig. 7

(a) Electronic density of states near the valence band top. (b) Seebeck coefficient, and (c) electrical resistivity at 700 K of Fe(V_1−xTi_x)Sb [REF 5] and Fe(V_0.955−xHf_0.045Ti_x)Sb HH phases plotted a function of chemical potential, μ − ε_VBT. The transport properties calculated from the electronic structure of the FeVSb HH phase were also plotted in (b) and (c).

The estimated chemical potential of the Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase (x ≥ 0.025) was located near the top edge of the valence band regardless of Ti concentration, whereas the chemical potential of Hf-free samples was determined to stay slightly lower energies inside the valence band. We considered from this fact that some extra impurity states were introduced in the vicinity of the Fermi energy in association with Hf, which acted as a barrier retaining the chemical potential of samples to higher energies.

We also note here that the slope of the Seebeck coefficient S(μ) showed nearly the same value for calculation and Fe(V_1−xTi_x)Sb HH phase, while Hf-substituted Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase possessed a slightly different slope with reduced magnitudes. Thus, the linear increase of S(μ) at x < 0.050 indicated us that the decrease of the carrier concentration with increasing the Ti concentration didn’t interact with the Hf element, as demonstrating the slope of the measured figure of merit ZT, in Fig. 6(b), showing the same behavior than that of Hf-free composition as the calculation predicted. These facts strongly suggested that the electronic structure of Hf-substituted Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase would be different from that of FeVSb HH phase near the valence band top. In a good agreement with S(μ), the decreased magnitude of the resistivity ρ(μ) in the Hf-substituted samples also suggested the presence of impurity states.

In order to confirm the hypothesis, that is the formation of Hf impurity states near the top of the valence band, we calculated the electronic density of states of the FeVSb HH phase containing one Hf atom in the unit cell by use of the first principles calculations. To simulate the partial substitution of V for 1 at% Hf, a Fe₃₂V₃₁Hf₁Sb₃₂ supercell structure was constructed from a 2 × 2 × 2 supercell of FeVSb HH phase (or Fe₃₂V₃₂Sb₃₂ supercell), as described in Fig. 8(a), in which the central V atom was replaced by Hf. The obtained electronic density of states is shown in Fig. 8(b) together with that of FeVSb HH phase. The states containing Hf-5d component were created near the edge of the valence band, where the chemical potential of Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase was located. We also confirmed that the band gap is also slightly reduced in good consistency with the enhanced bipolar effect in Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase.

Fig. 8

(a) Structure of the Fe₃₂V₃₁Hf₁Sb₃₂ supercell used for calculating the impurity states of Hf. The original FeVSb HH phase is duplicated to the 2a × 2a × 2a axis, respectively. The central V of the supercell is manually replaced by Hf (b). The density of states N(ε) of the Fe₃₂V₃₁Hf₁Sb₃₂ supercell (thick solid curve) and FeVSb (thin solid curve). Each N(ε) is plotted as a function of ε-ε_VBT where ε_VBT represents the top of the valence band. The detailed N(ε) near the ε_VBT is plotted in (c).

In summary, we revealed that the presence of the Hf in the half-Heusler structure certainly altered the electronic structure of the original FeVSb HH phase by creating impurity states in the vicinity of the valence band edge. The change of electronic structure prevented us from obtaining a large magnitude of ZT of the Fe(V_0.955−xHf_0.045Ti_x)Sb HH phase even under the significantly reduced lattice thermal conductivity. It is argued, in other words, that we might have much larger ZT of FeVSb-based HH phase if we used a heavy element that does not modify the electronic structure in the vicinity of the chemical potential. We are now in progress for finding such an element by means of band calculations and for producing FeVSb based HH phases possessing a larger value of ZT.

5. Conclusions

In this study, we prepared the polycrystalline Fe(V_0.955−xHf_0.045Ti_x)Sb half-Heusler phase in the Ti-concentration range of 0.000 ≤ x ≤ 0.075, and investigated the thermoelectric properties in the wide temperature range from 300 K to 700 K. The presence of the heavy Hf in the half-Heusler structure significantly decreased the lattice thermal conductivity down to κ_lat = 2.1 W m⁻¹K⁻¹ for Fe(V_0.88Hf_0.045Ti_0.075)Sb. Unfortunately, the formation of impurity states in the electronic density of states near the edge of the valence band reduced the magnitude of Seebeck coefficient especially at high temperatures above 500 K, leading to a limited ZT value less than 0.55. This experimentally revealed fact led us to a consideration that a higher value of ZT should be obtained by the use of other heavy element that does not alter the electronic structure near the band edge on the substitution for constituent element of FeVSb based half-Heusler phase.

Acknowledgments

We thank the Professor H. Miyazaki and Professor Y. Nishino from Nagoya Institute of Technology for their help in the measurement of Seebeck coefficient using the ZEM-3 system. One of the authors was financially supported by MEXT/JSPS KAKENHI Grant Number 18H01695.

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