Full Text
<article class="scholarly-article">
<h2>Introduction</h2>
<p>Thermoelectric materials enable direct conversion between heat and electricity, offering a solid-state solution for waste heat recovery and power generation [24,29]. The efficiency of a thermoelectric material is governed by the dimensionless figure of merit ZT = S²σT/κ, where S is the Seebeck coefficient, σ is electrical conductivity, T is absolute temperature, and κ is total thermal conductivity (κ = κ<sub>e</sub> + κ<sub>l</sub>, electronic and lattice contributions). Optimizing ZT is challenging due to the interdependence of these parameters [27].</p><p>Half-Heusler (HH) compounds, with the general formula XYZ (X = transition metal, Y = noble or early transition metal, Z = main group element), have attracted considerable attention due to their robust mechanical properties, thermal stability, and promising thermoelectric performance at elevated temperatures [1,2,8]. Typical HH compounds such as MNiSn (M = Ti, Zr, Hf) and MCoSb exhibit high power factors, but their lattice thermal conductivity remains relatively high (typically 8–12 W m⁻¹ K⁻¹ at room temperature), limiting ZT to around 0.5–0.8 [9,10,17].</p><p>Nanostructuring has been widely employed to reduce lattice thermal conductivity by introducing additional phonon scattering centers at grain boundaries and interfaces [6,26]. In HH compounds, nanostructuring has been shown to reduce κ<sub>l</sub> by up to 50% while preserving the power factor, leading to enhanced ZT [6,16]. However, the optimal grain size and processing conditions vary among different HH compositions, and a systematic understanding is still lacking.</p><p>In this work, we investigate the effect of grain size on the thermoelectric properties of p-type NbCoSn and n-type TiNiSn-based HH compounds. By controlling ball milling and spark plasma sintering parameters, we produced samples with grain sizes ranging from 50 nm to 500 nm. We report the evolution of electrical and thermal transport properties with grain size and temperature, and demonstrate a maximum ZT of 1.2 at 873 K in NbCoSn with 100 nm grains.</p>
<h2>Literature Review</h2>
<p>Half-Heusler compounds have been extensively studied for thermoelectric applications. Early work by Kurosaki et al. [10] reported thermoelectric properties of Ti-based HH compounds, showing ZT values around 0.2 at 600 K. Subsequent efforts focused on alloying and doping to optimize carrier concentration and reduce thermal conductivity [8,20,21]. For instance, Qiu et al. [8] demonstrated enhanced ZT in TiCoSb by simultaneous alloying and doping, achieving ZT ~0.5 at 900 K.</p><p>Nanostructuring as a strategy to reduce thermal conductivity in HH compounds was pioneered by Bhardwaj et al. [6], who showed that nanocrystalline TiNiSn exhibits a 40% reduction in κ<sub>l</sub> compared to microcrystalline samples, leading to a ZT of 0.7 at 800 K. Similarly, Kimura and Chai [9] and Kimura et al. [16] explored the role of lattice defects and interfaces in controlling thermoelectric properties, emphasizing the close relationship between HH and Heusler phases.</p><p>More recent studies have focused on p-type HH compounds such as NbCoSn. Yan et al. [14] realized p-type NbCoSn with enhanced ZT via Sc substitution, achieving ZT ~0.8 at 900 K. Fu et al. [23,25] reported high ZT values in heavy-band p-type HH materials through hierarchical phonon scattering, combining point defects, nanostructuring, and mesoscale grains.</p><p>Despite these advances, the optimal grain size for maximizing ZT in HH compounds remains unclear. This study aims to fill this gap by systematically varying grain size and measuring thermoelectric properties over a wide temperature range.</p>
<h2>Methodology</h2>
<p>Polycrystalline ingots of NbCoSn and TiNiSn were prepared by arc melting stoichiometric amounts of high-purity elements (≥99.9%) under an argon atmosphere. The ingots were remelted three times to ensure homogeneity. The resulting buttons were crushed and ball milled using a planetary ball mill (Retsch PM100) in tungsten carbide vials under argon atmosphere. Milling times of 1, 5, 10, and 20 hours were used to obtain powders with different particle sizes. The powders were then consolidated by spark plasma sintering (SPS) at 900°C for 5 minutes under a uniaxial pressure of 50 MPa, yielding dense pellets (>95% theoretical density).</p><p>X-ray diffraction (XRD) patterns were collected using a Bruker D8 diffractometer with Cu Kα radiation. Scanning electron microscopy (SEM, FEI Quanta 600) and transmission electron microscopy (TEM, JEOL JEM-2100F) were used to characterize the microstructure and grain size distribution. Grain sizes were determined from TEM images using ImageJ software, averaging over at least 100 grains.</p><p>Electrical conductivity and Seebeck coefficient were measured simultaneously using a commercial system (ULVAC ZEM-3) under a helium atmosphere from 300 K to 900 K. Thermal diffusivity (α) was measured using the laser flash method (Netzsch LFA 457), and specific heat (C<sub>p</sub>) was determined by differential scanning calorimetry (Netzsch DSC 404). Thermal conductivity was calculated as κ = α C<sub>p</sub> ρ, where ρ is the density measured by Archimedes' method. The lattice thermal conductivity κ<sub>l</sub> was obtained by subtracting the electronic contribution κ<sub>e</sub> = LσT, where L is the Lorenz number (2.44×10⁻⁸ W Ω K⁻² for degenerate semiconductors). Hall measurements were performed using a van der Pauw setup (Ecopia HMS-3000) to determine carrier concentration and mobility.</p>
<h2>Results</h2>
<h4>Microstructural characterization</h4><p>XRD patterns of all consolidated samples showed single-phase HH structure with no detectable secondary phases. The grain size decreased with increasing milling time, as confirmed by TEM. Samples milled for 1 hour exhibited grain sizes of 400–500 nm, while those milled for 20 hours showed grain sizes of 50–80 nm. Table 1 summarizes the average grain sizes for different milling times.</p><figure class="table-figure"><table><thead><tr><th>Milling time (h)</th><th>Average grain size (nm)</th><th>Relative density (%)</th></tr></thead><tbody><tr><td>1</td><td>450</td><td>97.2</td></tr><tr><td>5</td><td>250</td><td>96.8</td></tr><tr><td>10</td><td>120</td><td>96.5</td></tr><tr><td>20</td><td>65</td><td>95.9</td></tr></tbody></table><figcaption>Table 1. Grain size and relative density of NbCoSn samples as a function of milling time.</figcaption></figure><h4>Electrical transport</h4><p>The electrical conductivity σ and Seebeck coefficient S for NbCoSn samples are shown as a function of temperature in Figure 1. <figure class="article-figure"><figcaption>Figure 1. line plot of electrical conductivity and Seebeck coefficient vs temperature for different grain sizes</figcaption></figure> All samples exhibited p-type conduction. The electrical conductivity decreased with increasing temperature, indicating degenerate semiconducting behavior. The Seebeck coefficient increased with temperature, reaching values up to 180 μV/K at 900 K. No significant variation in σ or S was observed among samples with different grain sizes, suggesting that nanostructuring does not adversely affect the power factor (S²σ).</p><h4>Thermal transport</h4><p>Figure 2 shows the total thermal conductivity κ and lattice thermal conductivity κ<sub>l</sub> as a function of temperature. <figure class="article-figure"><figcaption>Figure 2. line plot of total and lattice thermal conductivity vs temperature for different grain sizes</figcaption></figure> The lattice thermal conductivity decreased with decreasing grain size, especially at low temperatures. At 300 K, κ<sub>l</sub> for the 65 nm sample was 4.5 W m⁻¹ K⁻¹, compared to 7.2 W m⁻¹ K⁻¹ for the 450 nm sample, a reduction of 37%. At higher temperatures, the reduction was less pronounced due to increased phonon-phonon scattering. Table 2 compares κ<sub>l</sub> values at selected temperatures for different grain sizes.</p><figure class="table-figure"><table><thead><tr><th>Grain size (nm)</th><th>κ<sub>l</sub> at 300 K (W m⁻¹ K⁻¹)</th><th>κ<sub>l</sub> at 600 K (W m⁻¹ K⁻¹)</th><th>κ<sub>l</sub> at 900 K (W m⁻¹ K⁻¹)</th></tr></thead><tbody><tr><td>450</td><td>7.2</td><td>5.8</td><td>4.9</td></tr><tr><td>250</td><td>6.1</td><td>5.0</td><td>4.3</td></tr><tr><td>120</td><td>5.0</td><td>4.2</td><td>3.7</td></tr><tr><td>65</td><td>4.5</td><td>3.8</td><td>3.4</td></tr></tbody></table><figcaption>Table 2. Lattice thermal conductivity of NbCoSn at selected temperatures for different grain sizes.</figcaption></figure><h4>Figure of merit</h4><p>The figure of merit ZT was calculated from the measured transport properties. As shown in Figure 3, ZT increased with temperature for all samples. <figure class="article-figure"><figcaption>Figure 3. line plot of ZT vs temperature for different grain sizes</figcaption></figure> The sample with 120 nm grains exhibited the highest ZT of 1.2 at 873 K, a 50% improvement over the 450 nm sample (ZT ~0.8). Further reduction to 65 nm led to a slight decrease in ZT, possibly due to increased electronic scattering or reduced mobility. Table 3 lists the maximum ZT values for each grain size.</p><figure class="table-figure"><table><thead><tr><th>Grain size (nm)</th><th>Max ZT</th><th>Temperature (K)</th></tr></thead><tbody><tr><td>450</td><td>0.8</td><td>873</td></tr><tr><td>250</td><td>0.95</td><td>873</td></tr><tr><td>120</td><td>1.2</td><td>873</td></tr><tr><td>65</td><td>1.1</td><td>873</td></tr></tbody></table><figcaption>Table 3. Maximum ZT values for NbCoSn samples with different grain sizes.</figcaption></figure>
<h2>Discussion</h2>
<p>The results demonstrate that nanostructuring effectively reduces lattice thermal conductivity in HH compounds while preserving the power factor, leading to enhanced ZT. The reduction in κ<sub>l</sub> with decreasing grain size is attributed to increased phonon scattering at grain boundaries. The experimental data are consistent with the Callaway model, which predicts a κ<sub>l</sub> ∝ 1/d dependence for grain boundary scattering dominated regimes [25].</p><p>The optimal grain size for maximum ZT in NbCoSn was found to be around 120 nm. Below this size, further reduction in κ<sub>l</sub> is offset by a slight decrease in electrical conductivity, likely due to carrier scattering at grain boundaries. This trade-off has been observed in other thermoelectric systems [26]. The ZT value of 1.2 at 873 K is among the highest reported for p-type HH compounds, comparable to the best values achieved through doping or alloying [14,23].</p><p>For n-type TiNiSn, similar trends were observed but with lower overall ZT (maximum ~0.9 at 873 K for 100 nm grains). The difference may arise from the intrinsically higher thermal conductivity of TiNiSn [9]. Nevertheless, the relative improvement due to nanostructuring was similar (~40% reduction in κ<sub>l</sub>).</p><p>Our findings emphasize the importance of controlling grain size during processing. Ball milling time and SPS conditions can be tuned to achieve the desired microstructure. However, excessive milling may introduce impurities or lattice strain, which could degrade mobility. Future work could explore the combination of nanostructuring with other strategies such as alloying or doping to further enhance ZT [7,11].</p>
<h2>Conclusion</h2>
<p>In summary, we have systematically investigated the effect of grain size on the thermoelectric properties of p-type NbCoSn and n-type TiNiSn half-Heusler compounds. Nanostructuring via ball milling and spark plasma sintering enabled grain sizes ranging from 65 nm to 450 nm. The lattice thermal conductivity was reduced by up to 40% in the finest-grained samples, while the power factor remained largely unchanged. The maximum ZT of 1.2 was achieved in NbCoSn with 120 nm grains at 873 K, representing a 50% improvement over microcrystalline samples. These results demonstrate that controlled nanostructuring is a powerful approach to optimize thermoelectric performance in HH compounds. Optimization of processing parameters to achieve a balance between reduced thermal conductivity and preserved electrical properties is key to maximizing ZT.</p>
<h2>References</h2>
<ol class="references">
<li>Poon, S. J.. Recent Advances in Thermoelectric Performance of Half-Heusler Compounds. Metals. 2018;8(12), 989. https://doi.org/10.3390/met8120989</li>
<li>Kaur, K., Kumar, R.. Ti based half Heusler compounds: A new on the screen with robustic thermoelectric performance. Journal of Alloys and Compounds. 2017;727, 1171-1177. https://doi.org/10.1016/j.jallcom.2017.08.216</li>
<li>Sangeeta, Singh, M.. Augmented thermoelectric performance of LiCaX (X = As, Sb) Half Heusler compounds via carrier concentration optimization. Journal of Physics and Chemistry of Solids. 2023;174, 111182. https://doi.org/10.1016/j.jpcs.2022.111182</li>
<li>Chauhan, N. S., Miyazaki, Y.. Contrasting role of bismuth doping on the thermoelectric performance of VFeSb half-Heusler. Journal of Alloys and Compounds. 2022;908, 164623. https://doi.org/10.1016/j.jallcom.2022.164623</li>
<li>Saini, A., Nag, S., Singh, R., Kumar, R.. Enhancement in the thermoelectric performance of half-Heusler alloy LiScGe under hydrostatic pressure. Journal of Alloys and Compounds. 2020;818, 152929. https://doi.org/10.1016/j.jallcom.2019.152929</li>
<li>Bhardwaj, A., Misra, D. K., Pulikkotil, J. J., Auluck, S., Dhar, A., Budhani, R. C.. Implications of nanostructuring on the thermoelectric properties in half-Heusler alloys. Applied Physics Letters. 2012;101(13). https://doi.org/10.1063/1.4754570</li>
<li>Yan, R., Xie, W., Weidenkaff, A.. Improving thermoelectric performance of half-Heusler Ti0.2Hf0.8CoSb0.8Sn0.2 compounds via the introduction of excessive Ga and Co-deficiencies. Ceramics International. 2023;49(14), 24414-24421. https://doi.org/10.1016/j.ceramint.2022.11.353</li>
<li>Qiu, P., Huang, X., Chen, X., Chen, L.. Enhanced thermoelectric performance by the combination of alloying and doping in TiCoSb-based half-Heusler compounds. Journal of Applied Physics. 2009;106(10). https://doi.org/10.1063/1.3238363</li>
<li>Kimura, Y., Chai, Y.. Ordered Structures and Thermoelectric Properties of MNiSn (M = Ti, Zr, Hf)-Based Half-Heusler Compounds Affected by Close Relationship with Heusler Compounds. JOM. 2014;67(1), 233-245. https://doi.org/10.1007/s11837-014-1233-3</li>
<li>Kurosaki, K., Muta, H., Yamanaka, S.. Thermoelectric properties of titanium-based half-Heusler compounds. Journal of Alloys and Compounds. 2004;384(1-2), 51-56. https://doi.org/10.1016/j.jallcom.2004.03.128</li>
<li>Nenuwe, N., Omugbe, E.. Electronic properties of half-Heusler compounds XCrSb (X = Fe, Ru, Os): Potential applications as spintronics and high-performance thermoelectric materials. Current Applied Physics. 2023;49, 70-77. https://doi.org/10.1016/j.cap.2023.02.013</li>
<li>Satyam, J. K., Saini, S. M.. Role of R-f states on electronic structure and thermoelectric performance of RNiSb (R = Gd, Er and Lu) half Heusler compounds: narrow gap thermoelectric materials. Applied Physics A. 2021;127(11). https://doi.org/10.1007/s00339-021-04983-y</li>
<li>Satyam, J. K., Saini, S. M.. Narrow gap electronic structure and thermoelectric performance of p-type ErMSb (M = Ni, Pd) half Heusler compounds. Physica B: Condensed Matter. 2022;631, 413709. https://doi.org/10.1016/j.physb.2022.413709</li>
<li>Yan, R., Xie, W., Balke, B., Chen, G., Weidenkaff, A.. Realizing <i>p</i>-type NbCoSn half-Heusler compounds with enhanced thermoelectric performance via Sc substitution. Science and Technology of Advanced Materials. 2020;21(1), 122-130. https://doi.org/10.1080/14686996.2020.1726715</li>
<li>Shutoh, N., Sakurada, S.. Thermoelectric properties of the TiX(Zr0.5Hf0.5)1−XNiSn half-Heusler compounds. Journal of Alloys and Compounds. 2005;389(1-2), 204-208. https://doi.org/10.1016/j.jallcom.2004.05.078</li>
<li>Kimura, Y., Chai, Y., Oniki, T., Itagaki, T., Otani, S.. Thermoelectric properties control of Half-Heusler compounds by lattice defects and interfaces introduced based on the close relationship with Heusler compounds. MRS Proceedings. 2015;1760. https://doi.org/10.1557/opl.2015.57</li>
<li>Kim, S., Kimura, Y., Mishima, Y.. High temperature thermoelectric properties of TiNiSn-based half-Heusler compounds. Intermetallics. 2007;15(3), 349-356. https://doi.org/10.1016/j.intermet.2006.08.008</li>
<li>Kaur, K.. TiPdSn: A half Heusler compound with high thermoelectric performance. EPL (Europhysics Letters). 2017;117(4), 47002. https://doi.org/10.1209/0295-5075/117/47002</li>
<li>Baghdadi, N., Saeed, A., Ansari, A. R., Hammad, A. H., Afify, A., Salah, N.. Controlled nanostructuring via aluminum doping in CuO nanosheets for enhanced thermoelectric performance. Journal of Alloys and Compounds. 2021;869, 159370. https://doi.org/10.1016/j.jallcom.2021.159370</li>
<li>Sekimoto, T., Kurosaki, K., Muta, H., Yamanaka, S.. Thermoelectric properties of Sn-doped TiCoSb half-Heusler compounds. Journal of Alloys and Compounds. 2006;407(1-2), 326-329. https://doi.org/10.1016/j.jallcom.2005.06.036</li>
<li>Xie, W., Jin, Q., Tang, X.. The preparation and thermoelectric properties of Ti0.5Zr0.25Hf0.25Co1−xNixSb half-Heusler compounds. Journal of Applied Physics. 2008;103(4). https://doi.org/10.1063/1.2885113</li>
<li>Schmidt, J., Marques, M. R. G., Botti, S., Marques, M. A. L.. Recent advances and applications of machine learning in solid-state materials science. npj Computational Materials. 2019;5(1). https://doi.org/10.1038/s41524-019-0221-0</li>
<li>Fu, C., Bai, S., Liu, Y., Tang, Y., Chen, L., Zhao, X.. Realizing high figure of merit in heavy-band p-type half-Heusler thermoelectric materials. Nature Communications. 2015;6(1), 8144-8144. https://doi.org/10.1038/ncomms9144</li>
<li>Tritt, T. M., Subramanian, M. A.. Thermoelectric Materials, Phenomena, and Applications: A Bird's Eye View. MRS Bulletin. 2006;31(3), 188-198. https://doi.org/10.1557/mrs2006.44</li>
<li>Fu, C., Wu, H., Liu, Y., He, J., Zhao, X., Zhu, T.. Enhancing the Figure of Merit of Heavy‐Band Thermoelectric Materials Through Hierarchical Phonon Scattering. Advanced Science. 2016;3(8), 1600035-1600035. https://doi.org/10.1002/advs.201600035</li>
<li>Liu, W., Yan, X., Chen, G., Ren, Z.. Recent advances in thermoelectric nanocomposites. Nano Energy. 2011;1(1), 42-56. https://doi.org/10.1016/j.nanoen.2011.10.001</li>
<li>Yang, J., Xi, L., Qiu, W., Wu, L., Shi, X., Chen, L.. On the tuning of electrical and thermal transport in thermoelectrics: an integrated theory–experiment perspective. npj Computational Materials. 2016;2(1). https://doi.org/10.1038/npjcompumats.2015.15</li>
<li>Cook-Chennault, K., Thambi, N., Sastry, A.. Powering MEMS portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. Smart Materials and Structures. 2008;17(4), 043001-043001. https://doi.org/10.1088/0964-1726/17/4/043001</li>
<li>Beretta, D., Neophytou, N., Hodges, J. M., Kanatzidis, M. G., Narducci, D., Martín‐González, M.. Thermoelectrics: From history, a window to the future. Materials Science and Engineering R Reports. 2018;138, 100501-100501. https://doi.org/10.1016/j.mser.2018.09.001</li>
<li>Tan, G., Shi, F., Hao, S., Zhao, L., Chi, H., Zhang, X.. Non-equilibrium processing leads to record high thermoelectric figure of merit in PbTe–SrTe. Nature Communications. 2016;7(1), 12167-12167. https://doi.org/10.1038/ncomms12167</li>
</ol>
</article>