Balancing the Competing Effects of Carrier and Phonon Transport Mechanisms to Enhance the Thermoelectric Properties of p-Type Ti₂Zr_2−xHf₂Nb₂Fe_5.6Ni_2.4Sb₈ Double Half-Heusler Alloys via Cation Vacancy Engineering

Abstract

Boosting thermoelectric performance is challenging due to the intricate interplay between electrical and thermal transport properties. This study focuses on Zr vacancy-filled p-type Ti₂Zr₂Hf₂Nb₂Fe_5.6Ni_2.4Sb₈-based thermoelectric materials to explore how Zr vacancies affect their structural and transport characteristics. Density functional theory calculations demonstrate that Zr vacancies induce proximal contraction/distal relaxation, strengthening lattice distortion while preserving the intrinsically intense phonon scattering in Ti₂Zr₂Hf₂Nb₂Fe_5.6Ni_2.4Sb₈ samples. The intensified asymmetric electron localization between adjacent anions and the cation vacancies softens local chemical bonds. Microscopic investigations reveal that Ti₂Zr_2−xHf₂Nb₂Fe_5.6Ni_2.4Sb₈ alloys with an optimal number of Zr vacancies balance the competing effects of carrier and phonon transport mechanisms by regulating multi-scale defects. Introducing appropriate Zr vacancies optimizes both the Seebeck coefficient and κ_L without greatly affecting electrical conductivity and weight mobility, achieving a 23% maximum power factor improvement and roughly 10% κ_L reduction. The bipolar diffusion effect is effectively suppressed to negligible levels by energy filtering effects, thus ensuring high-temperature stability. The maximum ZT of Ti₂Zr_1.97Hf₂Nb₂Fe_5.6Ni_2.4Sb₈ and Ti₂Zr_1.95Hf₂Nb₂Fe_5.6Ni_2.4Sb₈ is 30% higher than that of pristine samples without Zr vacancies. These findings are the first demonstration of vacancy engineering as a promising strategy in p-type double half-Heusler alloys to enhance their thermoelectric performance and decouple intertwined transport parameters.

Keywords

double half-Heusler / multi-principal-element alloying / thermoelectric / vacancy-filling

References

[1] N. Li, Z. S. Wang, X. R. Yang, Z. Y. Zhang, W. D. Zhang, S. B. Sang, H. L. Zhang, Adv. Funct. Mater. 2024, 34, 2314419.

[2] N. Li, Z. S. Wang, Y. Niu, Y. Li, S. Y. Wen, H. L. Zhang, Z. H. Lin, Adv. Sci. 2025, 12, e05873.

[3] Z. S. Wang, N. Li, X. R. Yang, Z. Y. Zhang, H. L. Zhang, X. J. Cui, Microsyst. Nanoeng. 2024, 10, 55.

[4] X. Shi, Z. Tian, Q. Jiang, Y. Yan, H. Kang, E. Guo, Z. Chen, T. Wang, J. Mater. Chem. A 2024, 12, 18104.

[5] N. Li, H. Zhu, W. He, B. Zhang, W. Cui, Z.-Y. Hu, X. Sang, X. Lu, G. Wang, X. Zhou, J. Mater. Chem. C 2020, 8, 3156.

[6] J. N. Kahiu, S. K. Kihoi, H. Kim, U. S. Shenoy, D. K. Bhat, H. S. Lee, ACS Appl. Energy Mater. 2023, 6, 4305.

[7] Z. Liu, S. Guo, Y. Wu, J. Mao, Q. Zhu, H. Zhu, Y. Pei, J. Sui, Y. Zhang, Z. Ren, Adv. Funct. Mater. 2019, 29, 1905044.

[8] Q. Wang, X. Li, C. Chen, W. Xue, X. Xie, F. Cao, J. Sui, Y. Wang, X. Liu, Q. Zhang, Phys. Status Solidi A 2020, 217, 2000096.

[9] C. Wang, Z. Dong, J. Chen, Z. Li, L. Gan, J. Yang, J. Zhang, J. Luo, Sci. China Mater. 2023, 66, 3230.

[10] R. Hasan, S. Jo, W. Shi, S. Y. Lee, W.-S. Seo, V. C. S. Theja, R. A. L. Vellaisamy, K. T. Kim, S.-I. Kim, S. W. Kim, H.-S. Kim, K. H. Lee, J. Alloys Compd. 2023, 938, 168572.

[11] C. Wang, X. Zhou, D. Cong, G. Tang, J. Yang, Mater. Today Phys. 2023, 36, 101172.

[12] C. Wang, D. Cong, G. Tang, X. Zhou, J. Li, Chem. Eng. J. 2024, 496, 154313.

[13] K. Xia, Y. Liu, S. Anand, G. J. Snyder, J. Xin, J. Yu, X. Zhao, T. Zhu, Adv. Funct. Mater. 2018, 28, 1705845.

[14] T. Fang, K. Xia, P. Nan, B. Ge, X. Zhao, T. Zhu, Mater. Today Phys. 2020, 13, 100200.

[15] F. Luo, J. Wang, C. Zhu, X. He, S. Zhang, J. Wang, H. Liu, Z. Sun, J. Mater. Chem. A 2022, 10, 9655.

[16] W. Li, S. Lin, X. Zhang, Z. Chen, X. Xu, Y. Pei, Chem. Mater. 2016, 28, 6227.

[17] W. Ren, W. Xue, S. Guo, R. He, L. Deng, S. Song, A. Sotnikov, K. Nielsch, J. van den Brink, G. Gao, S. Chen, Y. Han, J. Wu, C. W. Chu, Z. Wang, Y. Wang, Z. Ren, Nat. Commun. 2023, 14, 4722.

[18] C. Wu, X. L. Shi, L. Wang, W. Lyu, P. Yuan, L. Cheng, Z.-G. Chen, X. Yao, ACS Nano 2024, 18, 31660.

[19] Y. Jiang, J. Dong, H. L. Zhuang, J. Yu, B. Su, H. Li, J. Pei, F. H. Sun, M. Zhou, H. Hu, J. W. Li, Z. Han, B. P. Zhang, T. Mori, J. F. Li, Nat. Commun. 2022, 13, 6087.

[20] T. Lu, L. Chen, X. L. Shi, W. Liu, M. Li, Y. Wang, X. Zeng, P. Song, J. Bell, G. J. Snyder, Z. G. Chen, M. Hong, Small Struct. 2025, 6, 2400694.

[21] Q. Deng, F. Zhang, X. Yang, R. Li, C. Xia, P. Nan, Y. Chen, B. Ge, R. Ang, J. He, Energy Environ. Sci. 2024, 17, 9467.

[22] Z. Chen, B. Ge, W. Li, S. Lin, J. Shen, Y. Chang, R. Hanus, G. J. Snyder, Y. Pei, Nat. Commun. 2017, 8, 13828.

[23] M. Y. Kim, D. Lee, J. H. Lee, D. Lee, G. Y. Kim, S. Y. Choi, J. P. Heremans, H. Jin, Adv. Sci. 2025, 12, 2502892.

[24] G. Liang, T. Lyu, L. Hu, W. Qu, S. Zhi, J. Li, Y. Zhang, J. He, J. Li, F. Liu, C. Zhang, W. Ao, H. Xie, H. Wu, ACS Appl. Mater. Interfaces 2021, 13, 47081.

[25] X. L. Shi, J. Zou, Z. G. Chen, Chem. Rev. 2020, 120, 7399.

[26] Z. Huang, K. Hayashi, W. Saito, H. Li, J. Pei, J. Dong, T. Chiba, X. Nan, B. P. Zhang, J. F. Li, Y. Miyazaki, Small Methods 2025, 2500385.

[27] L. C. Yin, W. D. Liu, M. Li, Q. Sun, H. Gao, D. Z. Wang, H. Wu, Y. F. Wang, X. L. Shi, Q. Liu, Z. G. Chen, Adv. Energy Mater. 2021, 11, 2102913.

[28] J. Q. He, J. R. Sootsman, S. N. Girard, J. C. Zheng, J. Wen, Y. Zhu, M. G. Kanatzidis, V. P. Dravid, J. Am. Chem. Soc. 2010, 132, 8669.

[29] G. J. Snyder, A. H. Snyder, M. Wood, R. Gurunathan, B. H. Snyder, C. Niu, Adv. Mater. 2020, 32, 2001537.

[30] G. Tan, L. D. Zhao, M. G. Kanatzidis, Chem. Rev. 2016, 116, 12123.

[31] F. R. Lillie, H. Wang, Proc. Natl. Acad. Sci. USA 1940, 26, 67.

[32] F. Li, X. Liu, N. Ma, L. Chen, L. M. Wu, Angew. Chem. Int. Ed. 2022, 61, e202208216.

[33] G. Kresse, J. Non-Cryst. Solids 1995, 192, 222.

[34] G. K. A. J. Furthmuller, Phys. Rev. B 1996, 54, 169.

[35] G. Kresse, J. Furthmüller, J. Hafner, Phys. Rev. B 1994, 50, 13181.

[36] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865.

[37] P. E. Blöchl, Phys. Rev. B 1994, 50, 17953.

[38] A. Zunger, S. H. Wei, L. G. Ferreira, J. E. Bernard, Phys. Rev. Lett. 1990, 65, 353.

RIGHTS & PERMISSIONS

2025 The Author(s). Energy & Environmental Materials published by John Wiley & Sons Australia, Ltd on behalf of Zhengzhou University.