Achieving high thermoelectric performance of triple half-Heusler compositions enabled by high-throughput screening

Abstract

In this study, we have conducted the experimental screening of 90 compositions expected to form DHH/THH compounds. For the high-throughput experiment, liquid phase synthesis was used to check the synthesizability of half Heusler structures. Based on the high-throughput experimental screening, 2 compositions, MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃, were selected and synthesized as bulk materials to measure the thermoelectric properties. Both compositions showed low thermal conductivity as a family of half Heusler compounds and MgV₂Co₃Sb₃ showed the highest zT > 0.7 at 973 K as a triple half Heusler composition.

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1 Introduction

High-throughput experiments have generated considerable interest in the field of intermetallic compounds with their ability to effectively screen a vast number of compositions and identify novel materials with desirable properties. This approach employs a large number of syntheses, characterization techniques, and screening techniques to effectively explore the extensive chemical space of intermetallic systems. By systematically varying elemental compositions and processing conditions, researchers can discover new phases, optimize material properties, and elucidate structure–property relationships. These approaches are significantly effective to accelerate the discovery of new functional materials in various fields such as thermoelectric,¹ magnetic compounds,² and high-efficiency catalysts.³

Half-Heusler (HH) materials are highly promising for thermoelectric applications and other functional materials due to their advantageous combination of composition with tunable properties.^4–10 As thermoelectric materials, HHs have strength in their tunable electronic structure, mechanical robustness, and thermal stability, making them ideal candidates for converting waste heat into electricity across various temperature ranges.^4–10 Their ability to maintain stable thermoelectric properties over a broad range of temperatures is particularly beneficial for practical applications under harsh conditions including high temperature applications with vibrations. Moreover, advancements in alloying, nanostructuring, and the exploration of quaternary half-Heusler compositions provide pathways to further enhance their thermoelectric efficiency by reducing lattice thermal conductivity and optimizing charge carrier mobility.^4–11 With ongoing research efforts focused on optimizing these materials through innovative synthesis and characterization techniques, half-Heusler compounds are expected to play a crucial role in advancing thermoelectric technology for sustainable energy solutions.

Although the conventional ternary HH compositions have been well studied since the late 20th century, the new concept of quaternary HHs (double, triple, and quadruple HHs) opened a new door for the further exploration of this intermetallic system. Conventional ternary HH phase (XYZ) compositions stabilize the crystal structure based on a specific electron count in the valence shell, such as a valence electron count (VEC) of 18, under the 18-electron rule.^11–15 Instead, the double half-Heusler (DHH, formula: X′′X′Y₂Z₂, X₂Y′Y′′Z₂, and X₂Y₂Z′Z′′) was created by merging 17-electron and 19-electron systems in a 1 : 1 ratio to achieve VEC = 18 or a net valence (NV) of 0, e.g. valence balanced composition. For instance, in Hf₂FeNiSb₂, the NV calculation is 0 (e.g. Hf₂FeNiSb₂, NV = 8(2Hf⁴⁺ s⁰d⁰) − 2(Fe⁻² d¹⁰) + 0(Ni⁰ d¹⁰) − 6(2Sb⁻³ s²p⁶) = 0). Similarly, triple and quadruple HH (THH and QHH) compositions are also designed by combining aliovalent substitution of conventional ternary HH by considering 18-electron rules (THH, formula: , , and , QHH, formula: , , and ). Experimental findings^16–34 consistently exhibit notably lower lattice thermal conductivities in disordered crystal structures of double and triple HHs, primarily due to phonon scattering caused by disorder. While 2/3 of possible conventional HH compositions were already studied, only several compositions were explored out of thousands of potential quaternary HH compositions including double and triple HHs.

Integrating quaternary half-Heusler compounds with high-throughput experimental exploration provides substantial advantages in the search for high-performance compositions. With thousands of potential chemical combinations, many of which remain unexplored, the domain of DHH/THH/QHH compositions presents a vast landscape for material discovery. By systematically screening these diverse compositions using high-throughput experiments, it is possible to efficiently identify promising candidates with optimal thermoelectric properties. This approach not only accelerates the discovery of new materials but also enables the identification of compositions with advantageous properties; for example, some may exhibit higher mechanical strength and others may show lower lattice thermal conductivity, or better thermal stability, allowing for more targeted material optimization.

Because of the large number of combinations of quaternary HH compositions, combining computational screening and high-throughput experimental screening is an ideal strategy to discover potent quaternary HH compositions. In previous studies, the stability of DHH/THH/QHH phases with competing phases was assessed with the convex hull type analysis by calculating the formation energy.^16,35,36 Some compositions were identified to be stable and can form the DHH/THH/QHH structure at 0 K. However, experimental synthesis always has more obstacles; for example, formation of impurity phases/defects, dopability and so on. Based on these computational screening techniques that estimate the stability of DHH/THH compounds,^16,35,36 in this study, we have conducted the high-throughput experimental exploration of more than 90 potential compositions of DHH and THH to check the synthesizability of half Heusler structures. Based on high throughput screening, 2 compositions (MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃) were discovered with high thermoelectric performance.

2 Results

2.1 Identifying stable composition with high-throughput experiments

Based on the computational screening done by previous studies,^16,35,36 more than 90 DHH/THH compositions were experimentally synthesized with solid–liquid reactions in a stainless-steel container. Some compositions were shown to have a single phase or small amount of impurities with HH compositions based on XRD measurement, while most of the compositions have random peaks from various impurities and alloys. In normal XRD diffraction measurements, phase identification is performed based on the peak position and peak intensity. In this study, the peak position is primarily important since it is sufficient to confirm the formation of the half-Heusler phase. When there are many samples, for example, high-throughput screening in this study, phase identification takes time. In this study, we attempted a notation like the Debye–Scherrer ring, as shown in Fig. 1 (conventional XRD patterns are shown in Fig. S1–S9. A list of the synthesized compositions and sample IDs is shown in Table S1). This notation was applied to 90 samples that were experimentally synthesized to obtain the trend of stability and the formation of the half Heusler phase. The X site of the half-Heusler composition XYZ was used as the basis, and the samples were colored according to the four groups of the periodic table, Mg, Sc, (Ti, Zr, Hf), and (Nb, Ta), as shown in Fig. 2. When comparing the lines corresponding to the half-Heusler in Fig. 2, the lines corresponding to the half-Heusler are concentrated in systems containing Mg at the X site. Although there are some compositions that showed a similar pattern to the half Heusler structure (space group F4̄3m), Mg-containing systems have a strong tendency to form the HH phase. This is partially consistent with previous reports of some DHH compositions with Mg.²⁸ Also, the only report of the experimental synthesis of THH compositions is Mg containing composition (Mg₂VNi₃Sb₃).¹⁷ From Fig. 2, the lines corresponding to the half-Heusler MgNiSb (space group F4̄3m) were observed in the starting compositions Mg₁X_A1Ni₂Sb₂ (X_A = Ti, Zr, Hf) and Mg₂X_B1Ni₃Sb₃ (X_B = V, Nb, Ta). Furthermore, the lines corresponding to the half-Heusler Mg(Pd,Pt)Sb were observed in Mg₁X_C1Pd₂Sb₂ (X_C = Zr, Hf), Mg₁X_D1Pt₂Sb₂ (X_D = Ti, Zr, Hf) and Mg₂Ta₁Pt₃Sb₃. Compositions with Sc, (Ti, Zr, Hf), and (Nb,Ta) at the X site do not show strong tendency of forming the half Heusler phase or a large amount of impurity phases were detected, even though there were some reports showing experimental synthesis of bulk samples. This indicates that the possibility of synthesizing DHH/THH compositions is heavily dependent on the synthesis processes since many compositions contain volatile elements, elements with different melting points, and elements with very high melting points. Thus, the composition successfully synthesized in this screening may not necessarily be stably produced by other synthesis procedures. Conversely, compositions that were not successfully synthesized using the current method may potentially be synthesized as single-phases by refining the synthesis approach.

Fig. 1 Conversion of XRD patterns into Debye–Scherrer representation. Numbers in the compositions were not subscripted for visibility reasons. For example, Mg₁X₁Pt₂Sb₂ indicates Mg₁X₁Pt₂Sb₂.

Fig. 2 Debye–Scherrer patterns of high-throughput screening. Numbers in the compositions were not subscripted for visibility reasons. For example, Mg₁X₁Pt₂Sb₂ indicates Mg₁X₁Pt₂Sb₂. A list of the synthesized compositions and sample IDs is shown in Table S1. Conventional XRD patterns are also shown in the SI in Fig. S1–S9.

Overall, high-throughput synthesis suggests that the compositions containing Mg at the X site and Sb at the Z site tend to be synthesized as a half Heusler phase. However, not all systems are single-phase samples. For example, in Mg₂Ta₁Ni₃Sb₃, while the half-Heusler phase was mainly formed, the binary compound NiSb and unreacted Ta remained as the impurity phase based on the composition analysis. A line corresponding to the XRD peak of Ta was seen at 2θ = ∼29° to the left of the 220 line in Fig. 2. This line was seen in many samples containing Ta. This is partially due to the synthesis method, which is used to prepare samples by mixing and sintering powders. There were many patterns in which elemental Ta remained unreacted due to its high melting temperature. This also indicates that the purity and homogeneity of the sample will heavily depend on the synthesis route. Mg-containing compositions tend to have a half Heusler structure, which is partially attributed to the stabilization based on the band gap opening with the d–d interaction as discussed in the previous study.²⁸ Therefore, in this study, we focused on the Mg system, in which many half-Heusler phases were formed in high-throughput screening and previous reports.^17,28,33 We have selected MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃ because these two compositions were practically possible to experimentally synthesize in terms of toxicity, cost, and melting temperature. Additionally, the XCoSb system is well known as a good thermoelectric, and both TiCoSb and V_1−xCoSb were previously reported implying the high stability and performance of these compositions.

2.2 Electronic performance of synthesized THH compositions

After the experimental screening of 90 compositions, two Mg containing compositions (MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃) were selected to synthesize the bulk sample. To get a larger pellet and homogenized sample for the detailed physical property measurements, arc-melting, ball milling and high temperature sintering were conducted instead of a solid–liquid reaction. X-ray diffraction (XRD, Fig. 3) measurements and scanning electron microscope energy dispersive spectroscopy (SEM-EDS, Fig. 4) measurements were performed to obtain the status of the bulk materials of MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃. XRD patterns for both compositions were indexed to the HH peak positions (space group 216: F4̄3m) which indicated the successful synthesis of homogenized bulk samples. Impurity peaks were much smaller than the high-throughput synthesis result as the combination of ball milling and arc melting is more precise in terms of composition control, and it also provided a larger quantity of powders in one batch. Based on the SEM and XRD results, the impurity arises from CoSb and Co–V in MgV₂Co₃Sb₃ and NiSb and Ni–Nb alloys in Mg₂NbNi₃Sb₃. However, the overall composition matches the nominal composition as the amount of the impurity phase is small. The quality of the XRD peak was not high as the experiment was conducted on a lab-scale XRD, but the overall fraction of impurity phases should be around or less than 5% by combining the results of SEM and XRD. Also, the matrix phase showed a homogeneous distribution of each element indicating the homogenized microstructure of MgV₂Co₃Sb₃.

Fig. 3 XRD patterns of synthesized MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃ bulk samples. The XRD peaks for HH, CoSb, and NiSb were added for reference.

Fig. 4 (a) SEM image of synthesized MgV₂Co₃Sb₃ bulk sample. EDS mapping of MgV₂Co₃Sb₃ showing the compositional distribution of (b) Mg, (c) Co, (d) Sb, and (e) V. There are some unreacted impurity phases such as V-rich and Co-rich phases. SEM data for Mg₂NbNi₃Sb₃ can be found in the SI (Fig. S10).

Synthesized bulk pellets of triple half-Heusler compositions MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃ were measured in LFA and ZEM to obtain thermoelectric properties from room temperature to higher temperature up to approximately 950 K. MgV₂Co₃Sb₃ showed n-type characteristics and a large absolute value of the Seebeck coefficient (>|200| μV K⁻¹) and monotonically decreasing electrical conductivity (Fig. 5a and b). In contrast, Mg₂NbNi₃Sb₃ showed a relatively small positive value of the Seebeck range from 25–60 μV K⁻¹ in the temperature range of 300–650 K. Even with similar composition, the major carrier type is different between MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃ due to the different defect formation. Also, previously reported triple half Heusler composition Mg₂VNi₃Sb₃ showed a p-type conduction¹⁷ same as Mg₂NbNi₃Sb₃.

Fig. 5 The temperature dependent (a) Seebeck coefficient, (b) electrical conductivity, and (c) power factor of Mg_1−xV_2+xCo₃Sb₃ and Mg_2−yNb_1+yNi₃Sb₃. An error bar was added to the x = 0.3 sample. The relative uncertainties of the Seebeck coefficient and electrical resistivity are estimated to be within 5%.

To further optimize the electronic properties of MgV₂Co₃Sb₃, the effect of the Mg/V ratio was investigated with the different x in Mg_1−xV_2+xCo₃Sb₃. As MgV₂Co₃Sb₃ can be treated as the combination of 16-electron MgCoSb and 19-electron VCoSb ternary compositions, V-rich compositions lead to electron-rich characteristics and potentially change the band structure. As you can see in Fig. 5a and b, the higher x samples showed a higher electrical conductivity compared to the x = 0 sample. Also, the peak temperature of the Seebeck coefficient and power factor shifted to slightly higher temperature. These might be caused by the combination of band structure change and the bipolar effect. Further detailed analysis on band structure change and carrier concentration measurement would be required to fully understand the transport mechanism of these compositions. Peak power factor values of Mg_1−xV_2+xCo₃Sb₃ are about 3 times higher than that of the reported THH composition Mg₂VNi₃Sb₃ (ref. 17) (Fig. 5c).

Similarly, by changing Nb content y in Mg_2−yNb_1+yNi₃Sb₃, the carrier concentration is decreased and Seebeck coefficient reaches 110 μV K⁻¹ in Mg_1.9Nb_1.1Ni₃Sb₃, which is quite similar to that of the previously reported THH composition Mg₂VNi₃Sb₃.¹⁷ In this case, Mg₂NbNi₃Sb₃ can be treated as the combination of 17-electron MgNiSb and 20-electron NbNiSb ternary compositions in a ratio of 2 : 1. Nb-rich composition will lead to electron-rich characteristics, meaning reduced hole carrier concentrations to achieve a higher Seebeck coefficient. While Mg₂NbNi₃Sb₃ showed a similar Seebeck coefficient to previously reported Mg₂VNi₃Sb₃, Mg₂VNi₃Sb₃ shows a higher power factor due to the higher electrical conductivity which can be attributed to the higher hole mobility.¹⁷

To understand the electronic band structure and origin of semiconducting characteristics of the synthesized MgV₂Co₃Sb₃, density functional theory (DFT) calculations were performed (Fig. 6). While the exact THH composition MgV₂Co₃Sb₃ (Mg_1/3V_2/3CoSb) was not calculated because this specific ratio is difficult to calculate in a supercell, the results of Mg_1/4V_3/4CoSb and Mg_3/4V_1/4CoSb should give a general understanding of how the band structure changes depending on the V content. The calculated result of MgCoSb (Fig. 6a) exhibits a gapless metallic electronic structure, while Mg_1/4V_3/4CoSb (Fig. 6c) displays a pseudo-gap electronic structure. In Mg_1/4V_3/4CoSb the pseudo-gap near the Fermi level is relatively shallow, resulting not only in a reduced density of states at E_F but also in a steep energy-dependent rise of DOS just above E_F. This combination of low N(E_F) and large dN/dE serves to enhance the Seebeck coefficient at elevated temperatures. Furthermore, as more V is added, the gap increases which might be attributed to the hybridization of Co-d and V-d orbitals. This is consistent with the previous report that d orbital interaction is necessary for band gap opening in valence-balanced half Heusler compositions.²⁸

Fig. 6 Density functional theory (DFT) calculations of (a) MgCoSb, (b) Mg_3/4V_1/4CoSb (c) Mg_1/4V_3/4CoSb and (d) VCoSb. Data for Mg₂NbNi₃Sb₃ can be found in the SI (Fig. S11).

2.3 Reduced thermal conductivity with THH compositions

Both MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃ showed very low thermal conductivity among HH materials (Fig. 7a and b). To compare the material's inherent properties, the lattice thermal conductivity κ_L was estimated by subtracting the electrical contribution of thermal conductivity κ_E from the total thermal conductivity κ_Tot according to the Wiedemann–Frantz law. The lattice thermal conductivities of MgV₂Co₃Sb₃ and Mg₂NbNi₃Sb₃ are much smaller (κ_L < 2.5 W m⁻¹ K⁻¹) than those 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), TiCoSb (κ_L = 20 W m⁻¹ K⁻¹) or double half Heusler Ti₂FeNiSb₂ (κ_L = 9 W m⁻¹ K⁻¹)^16,40 at 300 K. In particular, we have plotted TiCoSb as a comparison in Fig. 7b as TiCoSb is considered to be a referenced ternary composition of MgV₂Co₃Sb₃. MgV₂Co₃Sb₃ is designed by substituting the Ti site in TiCoSb with Mg and V while retaining valence balance composition. Also, DHH Ti₂FeNiSb₂ showed reduced lattice thermal conductivity compared to TiCoSb; however, the lattice thermal conductivity of THH MgV₂Co₃Sb₃ was significantly lower than the value of Ti₂FeNiSb₂. Even though the ordered structure of the THH phase was not confirmed, the random occupancy of the X site with Mg and V or Nb is effective to reduce the lattice thermal conductivity which is consistent with previous double and triple half Heusler compositions.^17,41 Even with the heavier element of Nb than V in Mg₂VNi₃Sb₃,¹⁷ the lattice thermal conductivity is almost the same. This implies that the origin of low thermal conductivity is not only from the mass difference in the composition but also from the microstructure and the presence of impurity phases.

Fig. 7 Temperature dependence of (a) the total thermal conductivity, (b) the lattice thermal conductivity, (c) thermoelectric quality factor B and (d) thermoelectric figure of merit zT of Mg_1−xV_2+xCo₃Sb₃ and Mg_2−yNb_1+yNi₃Sb₃. An error bar was added to the x = 0.3 sample. The relative uncertainty of thermal conductivity is estimated to be within 8%, considering the uncertainties for D, C_P, and d. The combined relative uncertainty for all measurements involved in the calculation of zT is around 12%.

2.4 Thermoelectric performance of Mg_1−xV_2+xCo₃Sb₃ and Mg_2−yNb_1+yNi₃Sb₃

Enhancing the efficiency of thermoelectric materials requires improving the material's figure of merit, zT. 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 also 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.⁴² 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.^42,43 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.

In quality factor analysis, the emphasis is placed on weighted mobility (μ_W) and lattice thermal conductivity (κ_L). This framework provides a means to individually evaluate a material's electronic and thermal properties through μ_W and κ_L, respectively.^42,43 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 thermoelectric materials. A higher material quality factor B suggests the potential for elevated zT values when the carrier concentration is optimally adjusted. Almost unchanged quality factors in Mg_1−xV_2+xCo₃Sb₃ indicate that the Mg : V ratio does not significantly change the intrinsic thermoelectric performance. At higher temperatures, x = 0 data deviate from the other two compositions which can be attributed to the smaller band gap or the bipolar effect which is due to the thermal excitation of the carrier due to the lower carrier concentration (Fig. 7c and d). The highest zT value over 0.7 can be obtained with the x = 0.2 sample (Mg_0.8V_2.2Co₃Sb₃) at 950 K, which is about 5 times higher than reported peak zT values among triple half Heusler compositions.^17,33 With the increasing trend of the zT value with temperature, an even higher zT value can be achieved when it goes to higher temperature, but the thermal stability must be checked for the higher temperature measurement as reported in other Mg containing materials^44–46 even though we confirmed the stability of the sample up to 950 K (Fig. S12). Mg_2−yNb_1+yNi₃Sb₃ showed a slightly higher value of zT by changing y. However, due to the lower power factor compared to Mg_1−xV_2+xCo₃Sb₃ and Mg₂VNi₃Sb₃,¹⁷ the maximum zT value is lower than 0.1 at 675 K.

As shown above, we have demonstrated the effectiveness of exploring new quaternary half Heusler compositions by using a high-throughput screening. MgV₂Co₃Sb₃ can possess substantially low lattice thermal conductivity and high thermoelectric performance. These are examples of high-performance quaternary half Heusler compositions and in this study we demonstrate a strategy for identifying new compositions. While the zT is still not comparable to that of commercialized materials such as Bi₂Te₃,⁴⁷ thermal and mechanical stability of half Heusler compounds in general are beneficial for fabricating the thermoelectric module, especially for high-temperature applications such as car applications⁴⁸ and pyrolysis plants.^49,50 Not limited to Mg_1−xV_2+xCo₃Sb₃ and Mg_2−yNb_1+yNi₃Sb₃, other compositions listed in Fig. 2 can be a guideline for discovering other DHH/THH compounds that could show better thermoelectric performance. In addition, factors beyond output power and conversion efficiency are often prioritized in the practical design of thermoelectric modules. This requirement depends on specific use cases, for example, in applications such as low-energy electronics and sensors⁵¹ and module-standardization.⁵² Within this framework, a large number of choices in DHH/THH compositions are advantageous to develop next-generation thermoelectric technologies.

3 Methods

3.1 High throughput synthesis and screening

The samples for identifying stable composition with high throughput experiments were synthesized by the direct solid–liquid reaction of each elemental powder. Raw materials other than precious metals were obtained from Kojundo Chemical Laboratory Co., Ltd, and precious materials, Ru, Rh, Ir, Pd, and Pt were purchased from TANAKA Kikinzoku Kogyo K. K. Co., Ltd. The powders of raw materials used in this experiment are shown with their purity: Mg (99.5%), Sc (99%), Ti (99.99%), Zr (98%), Hf (98%), V (99.5%), Nb (99.9%), Ta (99.9%), Fe (99.9%), Co (99.9%), Ni (99.9%), Al (99.99%), Ga (99.99%), In (99.99%), Sn (99.99%), Sb (99.9%), Bi (99.9%), Ru (99.9%), Rh (99.9%), Ir (99.9%), Pd (99.9%), and Pt (99.95%). These powders were weighed in the listed molar ratios (list of the compositions is shown in Table S1) and gently mixed in an agate mortar. The mixed powder was pelletized into a columnar shape (Φ 5 mm diameter, ∼1 mm height) using a die and placed in a boron nitride (BN) crucible (Zikusu Industry Co., Ltd, 99.7%, 8.5 mm outer diameter, 6.5 mm inner diameter, 18 mm depth), in air. Then, in an Ar-filled glove box (O₂ and H₂O < 1 ppm), the crucible containing the sample was placed in a one-end welded stainless-steel tube (SUS316, 12.7 mm outer diameter, 10.5 mm inner diameter, 80 mm height) and sealed with a stainless-steel cap (SUS316). A photograph and schematic diagram of this stainless-steel container were previously reported.⁵³ To synthesize the sample, this container was heated at 1173 K for 24 h in an electric furnace in an air atmosphere. The samples containing Mg were heated at 973 K for 48 h to prevent Mg evaporation. The crystalline phases present in the synthesized samples were identified through powder X-ray diffraction (XRD), utilizing a Bruker D2-Phaser system with CuKα radiation at 30 kV and 10 mA.

3.2 Bulk synthesis and sintering of Mg_1−xV_2+xCo₃Sb₃ and Mg_2−yNb_1+yNi₃Sb₃

Pure elemental materials of magnesium grains (Mg, 99.9%, Kojundo Chemical Lab), antimony grains (Sb, 99.999%, Kojundo Chemical Lab), nickel grains (Ni, 99.9%, Kojundo Chemical Lab), cobalt block (Co, 99.9%, Stream Chemicals Inc), niobium grains (Nb, 99.9%, Kojundo Chemical Lab), and vanadium pieces (V, 99.7%, Alfa Aesar) were weighed according to the nominal composition. To evaluate the effect of the Mg stoichiometry, weighed V, Ni, Co, Nb and Sb were melted in an arc-melting furnace (arc current: around 50 A) and a nominal amount of Mg was added after arc melting, before ball milling. Afterward, each sample with different compositions was loaded into a stainless-steel container inside an argon-filled glove box. 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 with a heating rate of 20 °C min⁻¹. A uniaxial pressure of 65 MPa was applied during both the heating and temperature holding under dynamic vacuum to prepare pellet-shaped samples. Samples gradually cooled down to 473 K at a rate of 20 K min⁻¹ over 30 minutes and naturally cooled down to room temperature after that. During the cooling process, the pressure was gradually released over 30 minutes until it reached 0 MPa.

3.3 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 argon flow. The thermal conductivity κ_Tot was calculated using κ_Tot = D × C_p × d, where C_p is the specific heat capacity estimated from the empirical model⁵⁴ 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 coefficient⁵⁵ by using eqn (1), which is usually a better estimation than using a constant value of 2.44 × 10⁻⁸ W Ω K⁻² to reduce the overestimation of L (i.e. under estimation of κ_L)

Microstructure analysis was performed by SEM (Hitachi TM3030Plus). XRD measurements were conducted using a Rigaku MiniFlex600 with Cu-Kα radiation.

3.4 Calculation conditions

The electronic band structures were calculated using the full-potential linearized augmented plane-wave method and the generalized gradient approximation in the form of the Perdew–Burke–Ernzerhof functional,⁵⁶ as implemented using the WIEN2k package.⁵⁷ The equilibrium crystal structure was determined by minimizing the total energy through relaxation of the lattice parameters. The energy convergence criterion was set to ΔE < 1 × 10⁻⁶ Ry. The detailed discussion on structural stability is described in the SI (Tables S1, S2 and Fig. S13, S14).

Author contributions

K. I., F. H., H. M., and P. S. did the experiments, and H. M. performed the DFT calculations. K. I., F. H., H. M., P. S., and M. M. analyzed and discussed data. K. I. and H. M. wrote the manuscript, and all authors edited the manuscript. K. I., Y. K., and H. M. conceptualized and M. O., T. I., Y. K., and A. Y. supervised the project. Funding acquisition: K. I. and Y. K.

Conflicts of interest

K. I., 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).

Data availability

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

Supplementary information: XRD results from high throughput synthesis, SEM data, DOS of Mg₂NbNi₃Sb_3, repetitive measurement of the Seebeck coefficient and electrical conductivity of Mg_0.8V_2.2Co₃Sb₃ (x = 0.2 sample), sample IDs corresponding to each composition, and the details of the stability calculations. See DOI: https://doi.org/10.1039/d5ta05156h.

Acknowledgements

This work was supported by JSPS KAKENHI Grant Numbers JP24KK0263 and JP22K14468, the Japan Science and Technology Agency (JST) CREST (Grant No. JPMJCR19J1) and JSPS Overseas Research Fellowships. The computation was performed using Research Center for Computational Science, Okazaki, Japan (Project: 24-IMS-C168, 25-IMS-C338). The authors express thanks to Mr Takeo Tanita of AIST for their assistance in sample preparations and measurements.

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