Effects of the Fe/Ni ratio in double half-Heusler composition HfFe_1−xNi_xSb

Abstract

The effects of the Fe/Ni ratio in the double half-Heusler composition HfFe_xNi_1−xSb were investigated. By changing the chemical composition from Ni-rich to Fe-rich in HfFe_xNi_1−xSb, the Seebeck coefficient changes from negative to positive showing a clear n-type to p-type transition. In addition to very low lattice thermal conductivity (κ_L= 1.7 W m⁻¹ K⁻¹) for a half-Heusler material, achieving both p- and n-type materials with similar parent compositions is useful for developing thermoelectric modules as small differences in the thermal expansion coefficient and chemical stability prevent the degradation of thermoelectric modules. The highest thermoelectric figures of merit, zT, were 0.36 and 0.22 at 950 K for n- and p-type respectively.

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1. Introduction

Half-Heusler (HH) compounds, typically represented by the chemical formula XYZ where X and Y are primarily transition metal elements and Z is an element from the 3rd to 6th main groups, have undergone extensive research due to their potential applications in thermoelectrics, spintronics, and magnetic fields. The wide range of compositions available in these materials provides greater flexibility in modifying electronic and phonon structures, which is advantageous for understanding their thermoelectric properties.^1–7

Consequently, research on HH compounds has delved into the understanding of short-range and long-range ordering, disorders, and various types of defects.^8–12 Studies have focused on the properties of common ternary HH phases, which show semiconducting characteristics of valence-balanced compositions. These compositions stabilize the crystal structure by fulfilling a specific electron count in the valence shell, such as a valence electron count (VEC) of 18, under the 18-electron rule.^13–16 For example, 18 VEC ZrNiSn and HfCoSb systems are valence-balanced compositions i.e. net valence NV = 0; ZrNiSn (NV = 4 (Zr⁴⁺ s⁰d⁰) + 0 (Ni⁰ d¹⁰) − 4 (Sn⁴⁻ s²p⁶)) and HfCoSb (NV = 4 (Hf⁴⁺ s⁰d⁰) − 1 (Co¹⁻ d¹⁰) − 3 (Sb³⁻ s²p⁶)). HH compounds have strength as suitable materials for high-temperature thermoelectric applications, attributed to their substantial power factors (PF), mechanical robustness, and thermal stability.^1–4,17 However, their high lattice thermal conductivity (κ_L approximately 15–20 W m⁻¹ K⁻¹) significantly limits their thermoelectric efficiency. To address this issue, alloying and nanostructuring are frequently employed methods aimed at enhancing the thermoelectric properties.^1–7 These techniques primarily focus on reducing lattice thermal conductivity through improved phonon scattering.

The double half-Heusler (also triple half-Heusler and quadruple half-Heusler) compounds have been introduced as a promising approach to reducing lattice thermal conductivity^18–24 while attaining valence-balanced compositions. The double half-Heusler (DHH, formula: X′′X′Y₂Z₂, X₂Y′Y′′Z₂, X₂Y₂Z′Z′′) is created by merging 17-electron and 19-electron systems in a 1 : 1 ratio to achieve a net valence (NV) of 0, i.e. valence balanced composition. For instance, in Hf₂FeNiSb₂, the NV calculation is 0 (e.g. Hf₂FeNiSb₂, NV = 8 (2 Hf⁴⁺ s⁰d⁰) − 2 (Fe²⁻ d¹⁰) + 0 (Ni⁰ d¹⁰) − 6 (2 Sb³⁻ s²p⁶) = 0), derived from its component elements. “Double” denotes the multiplication of the formula unit, similar to the progression from ABO₃ to A₂B′B′′O₆ in double perovskites.²⁵ These DHH materials not only exhibit semiconductor characteristics with NV = 0 but also form stable ordered states at 0 K.

Conventional HH alloys typically only form stable solid solutions at high temperatures, while DHH compounds maintain stability at lower temperatures, specifically near their valence-balanced compositions. This distinct trait sets them apart from the traditionally analyzed quaternary isovalent HH alloys, like TiNiSn–ZrNiSn, although they exhibit similar crystallographic characteristics when they have disordered states. When compared to ternary HHs with similar properties such as average mass per unit cell and the Grüneisen parameter, the more complex, ordered ground state of DHH compounds ensures a decrease in thermal conductivity. This decrease is due to a larger number of atoms in their primitive unit cell (N) at 0 K. In the case of disordered structure, even though the structure is the same as conventional half-Heusler materials, these systems’ mixed sub-lattices lead to reduced lattice thermal conductivity.^{18–24,26–31}

Experimental findings^{18–24,26–31} consistently show notably lower lattice thermal conductivities in disordered crystal structures of DHH and THH, primarily due to alloy scattering. However, there is no experimental evidence yet confirming the existence of an ordered structure in double and triple half-Heusler compounds. When considering random atom distributions at specific sites, the chemical formula for DHH must be adjusted by dividing by the maximum permissible number. For instance, Hf₂FeNiSb₂ becomes HfFe_0.5Ni_0.5Sb. In this research, the notation “double half-Heusler composition” will still be used because of its unique composition stemming from the valence-balanced DHH concept. The broad chemical potential in DHH compositions is drawing considerable interest for further exploration and development in thermoelectrics and other areas of inorganic chemistry.

The flexibility in tuning charge carrier types is another key benefit of DHH compositions. This is achieved by modifying the VEC to favor either electron or hole predominance, thereby controlling the p-type or n-type nature, as depicted in Fig. 1a. In DHH compositions, such as TiNi_0.5Fe_0.5Sb²² and ZrNi_0.5Fe_0.5Sb,²⁸ and in triple half-Heusler³⁰ compositions, p-type to n-type transitions have been reported. For the HfFe_0.5Ni_0.5Sb composition (Fig. 1b), previous studies showed decent p-type thermoelectric performance, with a zT value of around 0.1 for non-doped samples³² and 0.3 with Ti doping.³¹ However, there are no reports investigating the effect of the Fe/Ni ratio in the double half-Heusler composition HfNi_0.5Fe_0.5Sb. In addition, it should be possible to effectively change the charge carrier type by simply adjusting the Fe : Ni ratio in HfFe_xNi_1−xSb. For the development of thermoelectric modules, it is essential to align the physical properties of p-type and n-type materials with similar compositions. And it can be beneficial to not have extrinsic dopants to avoid the complexity of the synthesis process. Differences, particularly in the CTE, can lead to structural damage and reduced performance under significant temperature differences. Designing p- and n-type materials from similar base compositions is, therefore, a critical aspect of developing functional thermoelectric materials.

Fig. 1 (a) Schematic of the pseudo-ternary phase diagram of conventional HH HfCoSb and 2 defective HH HfFeSb and HfNiSb. The DHH composition can be achieved by mixing 17-electron HfFeSb and 19-electron HfNiSb in a ratio of 1 to 1. The connecting composition line from HfCoSb to DHH composition should be valence balanced and deviation from this line can lead to the p-type to n-type transition of the DHH-HfCoSb alloys. (b) Crystal structure of the DHH composition HfFe_xNi_1−xSb with a partially disordered structure. The space group is F4̄3m, which is identical to the conventional ternary HH XYZ phase.

In this study, the change in the majority charge carrier type of HfFe_xNi_1−xSb was demonstrated by changing the Fe : Ni ratio. A large peak value of Seebeck coefficient in both p- and n-type materials was achieved. The thermoelectric figure of merit zT was optimized by changing x in HfFe_xNi_1−xSb for both p- and n-type materials. This outcome highlights the efficacy of using double, triple, and quadruple half-Heuslers not only in creating new compositions but also in developing thermoelectric modules with similar parent compositions in both p- and n-type legs.

2. Results and discussions

2.1. p-type to n-type transition in HfFe_xNi_1−xSb

The crystal structure and microstructure of the synthesized DHH compositions with different Fe : Ni ratios, HfFe_xNi_1−xSb (x = 0.3–0.7), were analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX) measurements. The main peaks of XRD were indexed as peaks from the HH crystal structure (space group 216: F4̄3m) in all synthesized samples (XRD, Fig. 2). This further suggests that the ordered structure was not verified through lab-scale XRD under the conditions of synthesis or even at room temperature, which is consistent with previous DHH^18,20–22 and THH studies.^19,30 The energy difference between the ordered structure and the disordered HH structure is small, indicating that stabilizing the ordered structure in this system may be challenging, which is also consistent with previous reports.¹⁸ However, future research should be conducted with a detailed analysis of the order–disorder structure on a localized scale. Additionally, the presence of small peaks was observed when the compositions deviated from the valence-balanced composition (x > 0.6 or x < 0.35) from HfFe_0.5Ni_0.5Sb. The scanning electron microscope and energy dispersive spectroscopy (SEM-EDS, Fig. 3) results show a homogeneous distribution of the elements in the matrix phase of HfFe_0.5Ni_0.5Sb. Some unreacted Hf or Fe-rich phases exist, but overall compositions of the matrix phases agreed with the nominal composition (Table 1). The measured density of the x = 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, and 0.7 samples were 10.89, 11.02, 10.74, 11.8, 10.30, 10.80, 10.25, 9.94, and 10.12 g cm⁻³ respectively. Even though there are some deviations depending on the composition due to the presence of the impurity phases, these values are consistent with the density of the referenced ternary half-Heusler HfCoSb (10.83 g cm⁻³).

Fig. 2 XRD patterns of different Fe : Ni ratios in HfFe_xNi_1−xSb (x = 0.3–0.7). Most peaks were identified to be the HH peaks and there were peaks from impurity only for samples with large or small x (x = 0.3, 0.65, 0.7) because these compositions highly deviated from the valence balanced composition of HfFe_0.5Ni_0.5Sb.

Fig. 3 (a) SEM figure of the polished surface of HfFe_0.5Ni_0.5Sb. EDS mapping of HfFe_0.5Ni_0.5Sb showed the homogeneous compositional distribution of (b) Hf, (c) Fe, (d) Ni, and (e) Sb in the matrix phase indicating the successful synthesis of the single phase with a homogeneous microstructure. There are some unreacted impurity phases such as Fe and Hf rich phases.

Table 1 Compositions of HfFe_xNi_1−xSb (x = 0.3–0.7) measured by EDX compared to the nominal compositions

x	0.3		0.35		0.4		0.45		0.5		0.55		0.6		0.65		0.7
	Nominal	Measured	Nominal	Measured	Nominal	Measured	Nominal	Measured	Nominal	Measured	Nominal	Measured	Nominal	Measured	Nominal	Measured	Nominal	Measured
Hf	33.3	32.2	33.3	33.0	33.3	32.8	33.3	29.6	33.3	32.4	33.3	31.7	33.3	32.8	33.3	32.4	33.3	32.6
Fe	10	10.7	11.7	12.2	13.3	14.0	15.0	14.9	16.7	18.0	18.3	19.4	20.0	21.7	21.7	22.5	23.3	24.6
Ni	23.3	24.6	21.7	22.5	20.0	20.7	18.3	17.4	16.7	17.6	15.0	15.4	13.3	14.7	11.7	12.1	10.0	10.5
Sb	33.3	32.5	33.3	33.0	33.3	32.5	33.3	38.2	33.3	32.0	33.3	33.5	33.3	30.9	33.3	33.0	33.3	32.4

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The impact of the Fe : Ni ratio on thermoelectric properties was explored to facilitate the transition from p- to n-type in HfFe_xNi_1−xSb (Fig. 4). The valence-balanced composition (HfFe_0.5Ni_0.5Sb) shows weak p-type characteristics with S = 8 μV K⁻¹ at 300 K. Changing x leads to the transition from p-type to n-type without using any external dopants. By deviating the composition from HfFe_0.5Ni_0.5Sb, the Seebeck coefficient has peaked on both Ni-rich and Fe-rich composition. For x > 0.5, it peaks at x = 0.55 with S = 125 μV K⁻¹ at 300 K. For x< 0.5, the Seebeck coefficient peaks at x = 0.45 with S = −81 μV K⁻¹ at 300 K. As you can see in Fig. 4, an increase in Fe content (x) in HfFe_xNi_1−xSb led to a shift from a negative to a positive Seebeck coefficient. Taking the valence-balanced composition HfFe_0.5Ni_0.5Sb (or HfCoSb) as the reference, the Fe-rich composition corresponds to the hole-dominated charge transport as Fe addition provides 1 hole per atom. In contrast, the Ni-rich composition corresponds to the electron-dominated charge transport due to the added electron per Ni atom. For the p-type and n-type, the highest absolute Seebeck coefficient S was 138 and −125 μV K⁻¹ for a Fe-rich (x = 0.6) and Ni-rich composition (x = 0.35) leading to a power factor of 0.6–0.7 mW m⁻¹ K⁻² around 650 K.

Fig. 4 (a) Seebeck coefficient depending on the Fe content x in HfFe_xNi_1−xSb (x =0.3–0.7). An n-type to p-type transition was achieved by changing the composition from Ni-rich to Fe-rich compositions in HfFe_xNi_1−xSb. The yellow region is a guide to the eyes. (b) The temperature dependency of the Seebeck coefficient in HfFe_xNi_1−xSb (x = 0.3–0.7).

Electrical conductivity is also enhanced in the deviated compositions (both x> 0.5 and x < 0.5) because of the larger carrier concentration (Fig. 5a). If x is closer to 0.5, the samples were not well-doped and showed low electrical conductivity. Most deviated compositions x = 0.3 and 0.7 showed the highest electrical conductivity. However, when you calculate the power factor by combining the temperature dependence of Seebeck coefficient and electrical resistivity measured by using ZEM3, x = 0.35 and 0.6–0.65 have the highest power factor for p- and n-type compositions due to the higher Seebeck coefficient (Fig. 4b). As the power factor heavily depends on the carrier concentration and Fermi level, weighted mobility often provides more valuable information for the evaluation of the potential electrical performance.^33,34 Also, Hall mobility is a well-known parameter for assessing electronic properties. However, in our material, it is difficult to measure Hall mobility because of low carrier mobility and the high carrier concentration. Instead, weighted mobility provides more insights for evaluating the electronic performance of thermoelectric materials. Weighted mobility is defined as where μ₀ is the mobility parameter, m_DOS is the density of state effective mass, and m_e is the mass of an electron. It was calculated from the measured temperature dependence of the Seebeck coefficient and electrical resistivity based on this analytical equation:^33,34

Fig. 5 The temperature-dependent (a) electrical conductivity, (b) power factor, and (c) weighted mobility of HfFe_xNi_1−xSb (x = 0.3–0.7). And (d) a change in the weighted mobility in different Fe : Ni ratios in HfFe_xNi_1−xSb at 350 K and 600 K. The yellow region is a guide to the eyes.

A higher weighted mobility implies higher power factor values when the carrier concentration is ideally optimized. Similar to electrical conductivity and power factor, when the x value is closer to 0.5, the samples possessed low weighted mobility. Samples with a high power factor (ex. x = 0.35, 0.6. 0.65) have higher weighted mobility, but n-type samples tend to have higher mobility which might be due to the band structure e.g. the conduction band having a sharper and/or degenerated band. In general, high-performance thermoelectric materials have T^−3/2 dependency on weighted mobility with the acoustic phonon scattering, while an increasing trend of weighted mobility at lower temperatures in high mobility samples (ex. x = 0.35, 0.6). This might be due to the electrically resistive grain boundary^35,36 or different scattering mechanisms of carriers implying potential improvement of the electrical performance at lower temperatures by optimizing microstructure and defect characteristics. When the composition dependence of the weighted mobility is evaluated, there are two peaks of weighted mobility at x = 0.35 and 0.6 as shown in Fig. 5d. Each peak corresponds to the p- and n-type compositions, and it shows both p- and n-type have optimal compositions located around x = 0.35 and 0.6 for the higher weighted mobility.

2.2. Reduced thermal conductivity in HfFe_xNi_1−xSb

The thermal conductivity of HfFe_xNi_1−xSb is significantly lower than that of conventional ternary HH materials (Fig. 6a and b). To compare the material's inherent properties, the lattice thermal conductivity κ_L (Fig. 6b) was estimated by subtracting the electrical contribution of thermal conductivity κ_E from the total thermal conductivity κ_Tot according to the Wiedemann–Franz law. The lattice thermal conductivity of HfFe_xNi_1−xSb is much smaller (κ_L = 2.0–4.0 W m⁻¹ K⁻¹) than that of well-known high-performance HH materials such as ZrNiSn^37,38 (κ_L = 8–10 W m⁻¹ K⁻¹), NbCoSn³⁹ (κ_L = 8–10 W m⁻¹ K⁻¹), TiCoSb¹⁸ (κ_L = 20 W m⁻¹ K⁻¹) or DHH TiFe_0.5Ni_0.5Sb (κ_L = 9 W m⁻¹ K⁻¹)^18,22 at 300 K. Alloy scattering at the Fe/Ni sites plays a crucial role, as evidenced by the flat temperature dependence of the lattice thermal conductivity. The dependence of κ_L in x was plotted in Fig. 6c, showing an increasing trend of κ_L with increasing amount of Fe content x in HfFe_xNi_1−xSb. This is partially understood by the mass difference between Ni and Fe. As Ni atoms have heavier characteristics, the lattice thermal conductivity is reduced in Ni-rich compositions. This means that as the x becomes smaller, the lattice thermal conductivity is reduced. The x = 0.4 sample has the lowest value of both total and lattice thermal conductivity with 2.0 W m⁻¹ K⁻¹ at 300 K. At higher temperatures where more acoustic phonon scattering is dominant, the minimum value of the lattice thermal conductivity reached as low as 1.7 W m⁻¹ K⁻¹ at 650 K. Multiple mechanisms likely influence the reductions in thermal conductivity of HfFe_xNi_1−xSb, yet uncovering these combined effects necessitates a more detailed analysis across various systems. The reason why the lattice thermal conductivity increases after decreasing x = 0.4 is attributed to the presence of impurity phases. As XRD data suggested, compositions that deviated too far from the valence-balanced compositions have some impurity phases. These impurities have higher thermal conductivity with metallic characteristics which increase the lattice thermal conductivity with an effective medium perspective.

Fig. 6 Temperature dependence of (a) the total thermal conductivity, (b) the lattice thermal conductivity, and (c) the lattice thermal conductivity with different Fe content x in HfFe_xNi_1−xSb (x = 0.3–0.7). The yellow region is a guide to the eyes.

The temperature-dependent thermoelectric properties of HfFe_xNi_1−xSb determine the improved thermoelectric figure of merit zT as shown in Fig. 7a. With a large enough band gap, the zT values of x = 0.35 and 0.6 increase with the increase in temperature. The highest zT values for p-type and n-type materials were both around 0.15 at 700 K. Enhancing the efficiency of thermoelectric materials requires improving the figure of merit, zT. As we discussed in the weighted mobility section, the complexity arises from the interconnected nature of properties that contribute to zT, particularly through the Fermi level and carrier concentration. Increasing a material's electrical conductivity often also increases its thermal conductivity, since charge carriers contribute to heat transfer. Moreover, achieving optimal performance can be challenging if the material is either excessively doped, resulting in too high a carrier concentration, or insufficiently doped, which results in too low a carrier concentration. These factors must be carefully balanced to maximize zT without compromising the material's overall performance.³³ To tackle this challenge, quality factor analysis was employed to evaluate an intrinsic characteristic of the material that should not be affected by the Fermi level and carrier concentration. This approach helps separately understand the material's inherent properties, providing a clearer picture of its thermoelectric suitability independent of external modulation factors like doping.

Fig. 7 (a) Thermoelectric figure of merit zT and (b) thermoelectric quality factor B of HfFe_xNi_1−xSb (x = 0.3–0.7) from 300 K to 673 K.

In quality factor analysis, the emphasis is placed on weighted mobility (μ_W) and lattice thermal conductivity (κ_L) as you can see in the definition.^33,34,40

This framework provides a means to individually evaluate a material's electronic and thermal properties through μ_W and κ_L, respectively.^33,34,40 The quality factor B is proportional to the ratio μ_W and κ_L, representing weighted mobility divided by lattice thermal conductivity. This ratio effectively highlights the interplay between a material's electronic and thermal properties and shows the potential of the thermoelectric material. The zT that an optimally doped material can achieve is proportional to the thermoelectric quality factor B. The estimated quality factor for HfFe_xNi_1−xSb shown in Fig. 6b is consistent with the zT values. The optimized values of zT for high zT compositions were not far from the current zT values, however, a small amount of dopant or fine adjustment in the Fe content x potentially improves the zT values of these materials.

Based on the zT values and quality factor analysis, x = 0.35 for n-type, and x = 0.6 for p-type, should have the highest potential for thermoelectric performance. Also, as you can see the increasing trend in both zT and B, the performance can be even better at higher temperature. Sample 2 for each composition was synthesized to check the high-temperature performance and reproducibility. As there is no significant hysteresis or reaction after both thermal and electrical measurements up to 950 K (Fig. 8), the compounds were stable even at this temperature range. Both x = 0.35 and x = 0.6 showed consistent values between samples 1 and 2, indicating reproducibility with a slight change in the carrier concentration. Thermal conductivity has a small discrepancy, however, lattice thermal conductivity values merge at higher temperatures, which indicates differences are mainly attributed to the grain boundary scattering and microstructure. And the lattice thermal conductivity of x = 0.35 and x = 0.6 reaches 2.0 and 2.5 W m⁻¹ K⁻¹ at 950 K. These values are small compared to the conventional ternary HHs and other double HH materials. As we discussed in the previous section, Ni is a heavier element compared to Fe, and the lattice thermal conductivity of the Ni rich sample x = 0.3 showed slightly smaller values than that of the Fe rich sample (x = 0.6). The thermoelectric figure of merit zT of HfFe_xNi_1−xSb (x = 0.35, 0.6) can reach 0.36 and 0.22 at 950 K, respectively. Unlike the previous report (purple: HfFe_0.5Ni_0.5Sb,³² and green: Hf_0.875Ti_0.125Fe_0.5Ni_0.5Sb³¹) which showed only p-type properties for HfFe_1−xNi_xSb, we obtained n-type behavior and a decently high zT value for a Ni-rich composition of this compound. The difference in the properties can also be due to the synthesis route as previous studies conducted melt spinning and hand grinding to prepare samples. Nevertheless, we have successfully shown p-type to n-type transition with decent zT values in HfFe_xNi_1−xSb by just adjusting the Fe : Ni ratio without external dopants.

Fig. 8 (a) Seebeck coefficient, (b) electrical conductivity, (c) total and lattice thermal conductivity and (d) thermoelectric figure of merit zT of HfFe_xNi_1−xSb (x = 0.35, 0.6) up to 950 K. Sample 2 was synthesized and measured for higher temperature and showed consistent values compared to sample 1 to check the reproducibility. Also, data from previous reports (purple: HfFe_0.5Ni_0.5Sb,³² and green: Hf_0.875Ti_0.125Fe_0.5Ni_0.5Sb³¹) were added for comparison.

As shown above, we have demonstrated that the DHH composition HfFe_xNi_1−xSb can possess a substantially low lattice thermal conductivity and tunable p-type/n-type characteristics. While the overall zT and performance are not very high compared to the commercialized materials such as Bi₂Te₃, the proof of the effectiveness of the double half-Heusler concept is beneficial for the further investigation of large compositional space. First, the mechanical robustness of half-Heusler compounds and stability at higher temperatures are beneficial to fabricating the module (the result of repeated high-temperature measurements is shown in Fig. S1, ESI†), especially for high-temperature applications such as car applications⁴¹ and biochar plants.^42,43 Some other compounds with volatile elements such as Mg or Te are struggling with high temperature stability even though they show higher performance.^44,45 Secondly, when designing thermoelectric modules for practical applications, factors beyond output power and conversion efficiency often need prioritization depending on specific use cases and requirements, for instance, in applications like low-energy electronics and sensors,⁴⁶ and module-standardization.⁴⁷ Within this framework, DHH compositions emerge as particularly advantageous options. The strategy of utilizing both p-type and n-type legs derived from the same parent composition can be extended to explore thousands of quaternary half-Heusler compositions including DHH that remain largely untouched but may offer significantly enhanced thermoelectric properties.

3. Method

3.1. Synthesis and sintering

Pure elemental materials of hafnium plates (Hf, 99.9%, Strem Chemicals), antimony grains (Sb, 99.999%, Kojundo Chemical Lab.), nickel grains (Ni, 99.9%, Kojundo Chemical Lab.), and iron grains (Fe, 99.999%, Chempur) were weighed according to the nominal composition, to evaluate the effect of the Fe : Ni ratio. After arc melting, each sample with different compositions was loaded into a stainless-steel container inside an argon-filled glove box (O₂ < 1.0 ppm). Mechanical reaction and homogenization were conducted by high energy ball milling (SPEX 8000D, SPEX) for 2 h (30 min pause every 30 min). The powder was extracted from the jar and transferred into a graphite die under an argon atmosphere to prevent oxidation. Subsequently, the powder was sintered (SPS-622A, Fuji Electronic Industrial) at 1073 K for 20 min under a uniaxial pressure of 65 MPa under a dynamic vacuum to prepare pellet-shaped samples. The samples were gradually cooled down to room temperature after releasing the pressure.

3.2. Characterization

The Seebeck coefficient and electrical conductivity of the sintered samples were measured using a commercial system (ZEM-3, Advance-Riko) under a helium atmosphere. The thermal diffusivity D was measured by using the flash method (Netzsch LFA 467) under an argon flow. The thermal conductivity κ_Tot was calculated by κ_Tot = D × C_p × d, where C_p is the specific heat capacity estimated from the empirical model,⁴⁸ and d is the sample density determined by the Archimedes method. The lattice thermal conductivity κ_L was estimated by subtracting the electrical contribution of thermal conductivity κ_E = LσT from the total thermal conductivity κ_Tot according to the Wiedemann–Franz law, where L is the Lorenz number estimated from the measured Seebeck coefficient.⁴⁹ Microstructure analysis was performed by SEM (TM3030Plus, Hitachi and Helios 5 Hydra CX, Thermo Fisher Scientific). XRD measurements were conducted using Rigaku MiniFlex600 with Cu-Kα radiation.

4. Conclusions

The adjustment of Fe/Ni ratio in the double half-Heusler composition HfFe_xNi_1−xSb leads to a p-type to n-type transition. By changing the chemical composition from Ni-rich to Fe-rich in HfFe_xNi_1−xSb, the Seebeck coefficient changes from negative to positive values indicating the successful demonstration of the p-type to n-type transition. In addition to HfFe_xNi_1−xSb exhibiting very low lattice thermal conductivity (κ_L = 1.7 W m⁻¹ K⁻¹ at 650 K) for a half-Heuler material, achieving both p- and n-type materials with similar parent compositions is useful for developing reliable thermoelectric modules. Compared to the zT values of the valence balanced composition (x = 0.5, zT = 0.004 at 675 K), the highest thermoelectric figure of merit zT = 0.36 and 0.22 at 950 K for n- and p-type respectively was demonstrated with the composition HfFe_xNi_1−xSb.

Author contributions

K. I. and P. S. did the experiments, analyzed the data, and wrote the manuscript. K. I., P. S. and M. M. discussed the results. M. O., T. I. and A. Y. supervised the project. All authors edited the manuscript.

Data availability

All data reported or analyzed during this work is included in this article.

Conflicts of interest

M. O. and A. Y. are cofounders of Mottainai Energy Co., Ltd. Mottainai Energy Co., Ltd. does not fund the work or participate in its execution. K. I., P. S., T. I., M. O. and A. Y. are inventors on a patent application related to this work filed by the AIST (application no. 2022–075176, 28 April 2022).

Acknowledgements

This work was supported by JSPS KAKENHI Grant Numbers JP22K14468 and JSPS Overseas Research Fellowships. The authors express thanks to Mr Takeo Tanita, of AIST for their assistance in sample preparation and measurements.

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Footnote

† Electronic supplementary information (ESI) available: Repetitive measurements of the Seebeck coefficient and power factor. See DOI: https://doi.org/10.1039/d4tc03206c

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