Modeling and performance characterization methods of half-Heusler thermoelectric devices

ZHANG Yuqian; NIU Chunping; HE Hailong; REN Hongrui; WU Yi

doi:10.7498/aps.74.20250625

Abstract

Due to the ability to directly convert thermal energy into electrical energy, thermoelectric devices operating in the medium-to-high temperature range hold significant potential for applications such as deep space exploration and industrial waste heat recovery. Among candidate materials, half-Heusler alloys have emerged as promising options for device fabrication in this temperature range, owing to their excellent mechanical properties, thermal stability, and favorable thermoelectric performance. However, research on half-Heusler-based thermoelectric devices remains far behind study of the materials, which limits their large-scale industrial application. In this study, high-performance P-type Hf_0.5Zr_0.5CoSb_0.8Sn_0.2 and N-type Hf_0.75Zr_0.25NiSn_0.99Sb_0.01 half-Heusler alloys are firstly synthesized. Then the single-pair thermoelectric module is successfully brazed and assembled by using the graphite mold designed by ourselves. After that, three-dimensional (3D) finite element modeling and one-dimensional (1D) numerical modeling are conducted to simulate the module behaviors, and their results are highly consistent with experimental measurements, thereby validating the accuracy of the simulation models. Using the established simulation models, the influence of geometric parameters on module performance is investigated. The result shows that optimizing the leg height and cross-sectional area ratio is critical for achieving maximum conversion efficiency. Additionally, a self-integrated comprehensive testing system (Model: TE-X-MS) is developed to systematically characterize key thermoelectric properties, including output power and conversion efficiency. The fabricated device achieves a maximum output power of 0.28 W and a peak conversion efficiency of 7.34% at a temperature difference of 538 K, which is comparable to the best-performing devices reported to date. These results provide valuable reference for fabricating, modeling, and characterizing the half-Heusler thermoelectric devices in practical applications.

Keywords:

Authors and contacts

State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China

Corresponding author: HE Hailong, hhlong@xjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 52177159), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. xzy012023163), and the State Key Laboratory of Electrical Insulation and Power Equipment, China (Grant Nos. EIPE23305, EIPE23132, EIPE24207).

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References

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Cited By

图 1 (a) 半赫斯勒热电臂制作流程; (b) 合成材料的热电优值ZT; (c) 单对半赫斯勒热电器件焊接流程

Figure 1. (a) Fabrication process of half-Heusler thermoelectric legs; (b) the ZT values of the synthesized materials; (c) the soldering process of the single-pair half-Heusler thermoelectric device.

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图 2 (a) P型和(b) N型半赫斯勒热电材料XRD图谱

Figure 2. XRD patterns of (a) P-type and (b) N-type half-Heusler thermoelectric.

DownLoad: Full-Size Img PowerPoint

图 3 单对器件三维建模图

Figure 3. Schematic diagram of 3D modeling of single pair device.

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图 4 三维仿真得到的单对半赫斯勒器件温度分布图(a)和电势分布图(b)

Figure 4. Temperature (a) and voltage (b) distribution diagram of single pair half-Heusler thermoelectric device obtained from 3D simulation.

DownLoad: Full-Size Img PowerPoint

图 6 自制热电器件综合性能测试系统

Figure 6. Self-made comprehensive performance testing system for thermoelectric devices.

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图 7 热端温度分别为300 ℃, 400 ℃, 500 ℃, 600 ℃时单对器件在不同电流负载下的特性变化　(a) 电压; (b) 输出功率; (c) 转换效率. (d) 本文不同温差下的最大转换效率与其他文献中报道的半赫斯勒器件的最大效率的对比

Figure 7. Characteristic curves of a single pair of devices under different current loads when the hot end temperatures are 300 ℃, 400 ℃, 500 ℃ and 600 ℃ respectively: (a) Voltage; (b) output power; (c) conversion efficiency. (d) Comparison between the maximum conversion efficiency under different temperature differences in this work and other literatures.

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图 5 随热电臂高度和P型N型热电臂面积比(A_P/A_N)变化而变化的单对器件(a) 转换效率和(b) 输出功率

Figure 5. Variation of conversion efficiency (a) and output power (b) of a single pair of devices with variation of thermoelectric arm height and P-type/N-type thermoelectric arm area ratio (A_P/A_N).

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表 1 单对器件建模参数

Table 1. Single pair device’s modeling parameters.

参数	数值
陶瓷基板长度L_s/mm	8
陶瓷基板宽度W_s/mm	3
陶瓷基板厚度D_s/mm	0.6
覆铜层长度L_Cu/mm	7
覆铜层宽度W_Cu/mm	3
覆铜层厚度D_Cu/mm	0.3
P型热电臂宽度W_p/mm	2.1
P型热电臂高度H_p/mm	6
N型热电臂宽度W_n/mm	2
N型热电臂宽度H_n/mm	6

DownLoad: CSV

表 2 热电材料物性参数

Table 2. Physical parameters of thermoelectric materials.

	参数	温度相关表达式
P型	S/(μV·K^–1)	$-2.37478\times 10^{-13}T^3+2.00399\times 10^{-10} T^2 + 1.45119\times 10^{-7} T + 0.0000646145 $
	σ/(S⋅cm^–1)	$-6.40884\times 10^{-9}T^3+0.0000127913T^2 -0.00898933T + 6.35472 $
	κ/(W⋅m^–1⋅K^–1)	$-0.000461149T^3 + 1.02189T^2 -825.929T +327500.0 $
N型	S/(μV⋅K^–1)	$2.37915\times 10^{-13}T^3 -1.39249\times 10^{-10}T^2 -2.14638\times 10^{-7} T -0.0000648974 $
	σ/(S⋅cm^–1)	$-1.25489\times 10^{-8} T^3 + 0.0000285845T^2 -0.0223619T +10.403 $
	κ/(W⋅m^–1⋅K^–1)	$0.0000727835T^3 + 0.0782446T^2 -271.589T +266246.0$

DownLoad: CSV

[1]	王雅宁, 陈少平, 樊文浩, 郭敬云, 吴玉程, 王文先 2020 物理学报 69 246801 Google Scholar Wang Y N, Chen S P, Fan W H, Guo J Y, Wu Y C, Wang W X 2020 Acta Phys. Sin. 69 246801 Google Scholar
[2]	杨士冠, 林鑫, 何俊松, 翟立军, 程林, 吕明豪, 刘虹霞, 张艳, 孙志刚 2023 物理学报 72 228401 Google Scholar Yang S G, Lin X, He J S, Zhai L J, Chen L, Lü M H, Liu H X, Zhang Y, Sun Z G 2023 Acta Phys. Sin. 72 228401 Google Scholar
[3]	谢忠祥, 喻霞, 贾聘真, 陈学坤, 邓元祥, 张勇, 周五星 2023 物理学报 72 124401 Google Scholar Xie Z X, Yu X, Jia P Z, Chen X K, Deng Y X, Zhang Y, Zhou W X 2023 Acta Phys. Sin. 72 124401 Google Scholar
[4]	He H L, Fang Z X, Niu C P, Wu Y, Rong M Z 2021 Energy Convers. Manag. 241 114314 Google Scholar
[5]	Yu K, Wu Y, He H L, Niu C P, Rong M Z, Wu D, Liu S X, Zhang Y Q 2021 J. Alloys Compd. 885 161378 Google Scholar
[6]	Zhang P, Ouyang T, Tang C, He C Y, Li J, Zhang C X, Zhong J X 2021 Chin. Phys. B 30 128401 Google Scholar
[7]	许易, 许小言, 张薇, 欧阳滔, 唐超 2019 物理学报 68 247202 Google Scholar Xu Y, Xu X Y, Zhang W, Ouyang T, Tang C 2019 Acta Phys. Sin. 68 247202 Google Scholar
[8]	Lu J Y, Cui C F, Ouyang T, Li J, He C Y, Tang C, Zhong J X 2023 Chin. Phys. B 32 048401 Google Scholar
[9]	Zhang P, Ouyang T, Tang C, He C Y, Li J, Zhang C X, Zhong J X 2020 Chin. Phys. B 29 118401 Google Scholar
[10]	Ovik R, Long B D, Barma M C, Riaz M, Sabri M F M, Said S M, Saidur R 2016 Renewable Sustainable Energy Rev. 64 635 Google Scholar
[11]	Eddine A N, Chalet D, Faure X, Faure X, Chessé P 2018 Energy 143 682 Google Scholar
[12]	Haddad C, Périlhon C, Danlos A, François M X, Descombes G 2014 Energy Procedia 50 1056 Google Scholar
[13]	Shen Z G, Tian L L, Liu X 2019 Energy Convers. Manag. 195 1138 Google Scholar
[14]	Holgate T C, Bennett R, Hammel T, Caillat T, Keyser S, Sievers B 2015 J. Electron. Mater. 44 1814 Google Scholar
[15]	柏胜强, 廖锦城, 夏绪贵, 陈立东 2020 深空探测学报 7 525 Google Scholar Bai S Q, Liao J C, Xia X G, Chen L D 2020 J. Deep Space Explor. 7 525 Google Scholar
[16]	Xiao Y, Zhao L D 2018 npj Quantum Mater. 3 55 Google Scholar
[17]	Rogl G, Rogl P 2017 Curr. Opin. Green Sustainable Chem. 4 50 Google Scholar
[18]	Huang L H, Zhang Q Y, Yuan B, Xiang L, Yan X, Ren Z F 2016 Mater. Res. Bull. 76 107 Google Scholar
[19]	Gelbstein Y, Gotesman G, Lishzinker Y, Dashevsky Z, Dariel M P 2008 Scr. Mater. 58 251 Google Scholar
[20]	Rull-Bravo M, Moure A, Fernández J F, Martín-González M 2015 RSC Adv. 5 41653 Google Scholar
[21]	Rogl G, Grytsiv A, Gürth M, Tavassoli A, Ebner C, Wünschek A, Puchegger S, Soprunyuk V, Schranz W, Bauer E, Müller H, Zehetbauer M, Rogl P 2016 Acta Mater. 107 178 Google Scholar
[22]	Silpawilawan W, Kurosaki K, Ohishi Y, Muta H, Yamanaka S 2017 J. Mater. Chem. C 5 6677 Google Scholar
[23]	Poon S J 2018 Metals 8 989 Google Scholar
[24]	He H L, Zhao Y B, Ren H R, Niu C P, Fang Z X, Wu Y, Rong M Z 2022 Appl. Therm. Eng. 215 118900 Google Scholar
[25]	Nozariasbmarz A, Saparamadu U, Li W, Kang H B, Dettor C, Zhu H T, Poudel B, Priya S 2021 J. Power Sources 493 229695 Google Scholar
[26]	Yu J J, Xing Y F, Hu C L, Huang Z J, Qiu Q Y, Wang C, Xia K Y, Wang Z Y, Bai S Q, Zhao X B, Chen L D, Zhu T J 2020 Adv. Energy Mater. 10 2000888 Google Scholar
[27]	Xing Y F, Liu R H, Liao J C, Zhang Q H, Xia X G, Wang C, Huang H, Chu J, Gu M, Zhu T J, Zhu C X, Xu F F, Yao D X, Zeng Y P, Bai S Q, Uher C, Chen L D 2019 Energy Environ. Sci. 12 3390 Google Scholar
[28]	苗圃, 韩屾, 高梓恒, 付晨光, 朱铁军 2022 中国材料进展 41 1029 Google Scholar Miao P, Han S, Gao Z H, Fu C G, Zhu T J 2022 Mater. Chin. 41 1029 Google Scholar
[29]	Moh'd A A N, Tashtoush B M, Jaradat A A 2015 Energy 90 1239 Google Scholar
[30]	Chen W H, Huang S R, Wang X D, Wu P H, Lin Y L 2017 Energy 133 257 Google Scholar
[31]	Meng F K, Chen L G, Sun F R 2016 Low-Carbon Technol. 11 375 Google Scholar
[32]	Ouyang Z, Li D 2016 Sci. Rep. 6 24123 Google Scholar

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