- Open Access
High-Entropy Skutterudites as Thermoelectrics: Potential Synthesizability, Enhanced Stability, and Band Convergence via the Cocktail Effect
PRX Energy 5, 013008 – Published 19 February, 2026
DOI: https://doi.org/10.1103/qd4g-95cf
Abstract
High-entropy materials offer a promising avenue for thermoelectric materials discovery, design, and optimization. However, the large chemical spaces that need to be explored hamper their development. In this work, a large family of high-entropy skutterudites is explored as promising thermoelectric materials. Their potential synthesizability is screened and rationalized using the disordered enthalpy-entropy descriptor through high-throughput density functional theory calculations. In the case of high-entropy skutterudites, the thermodynamic density of states and the entropy gain parameter appear to be key factors for their stabilization. Electronic band structure analyses not only show a reduction in the band gap, which enhances carrier concentration and electrical conductivity, but also a band convergence phenomenon for some specific compositions, which is related to the “cocktail effect.” Analyzing atom-projected band structures shows how band convergence is due to the simultaneous presence of , , and in the compound. The presence of or , while not contributing to this band-convergence effect, can be directly linked to an increase in the system’s entropy, which enhances the thermodynamic stability of these materials. Transport properties are computed for the most promising compositions, and their dynamical, mechanical, and thermal stability are addressed. Our results demonstrate that these types of compounds open new avenues, not only to enhance thermoelectric efficiency but also to reduce costs by utilizing more abundant elements and also improving their durability.
Physics Subject Headings (PhySH)
Popular Summary
High-entropy materials, which combine many different elements, offer a promising avenue for discovering new thermoelectric materials capable of efficiently converting heat into electricity. This study uses large-scale computer simulations to explore high-entropy skutterudites and identify synthesizable compositions. The results reveal that disorder plays a key role in stabilizing these materials. Mixing elements such as iron, nickel, and cobalt enhances the electronic properties by narrowing the band gap, enabling band convergence, and boosting the electrical conductivity – a synergy known as the “cocktail effect.” Adding other elements, like rhodium and iridium, primarily improves stability. Overall, these materials exhibit strong performance, stability, and durability, paving the way for efficient, cost-effective thermoelectric devices.
Article Text
Supplemental Material
References (75)
- R. Freer and A. V. Powell, Realising the potential of thermoelectric technology: A roadmap, J. Mater. Chem. C 8, 441 (2020).
- P. Gorai, V. Stevanović, and E. S. Toberer, Computationally guided discovery of thermoelectric materials, Nat. Rev. Mater. 2, 17053 (2017).
- B. Qin, D. Wang, T. Hong, Y. Wang, D. Liu, Z. Wang, X. Gao, Z.-H. Ge, and L.-D. Zhao, High thermoelectric efficiency realized in SnSe crystals via structural modulation, Neural Comput. 14, 1366 (2023).
- J. Plata, E. Blancas, A. Márquez, V. Posligua, J. Fdez Sanz, and R. Grau-Crespo, Harnessing the unusually strong improvement of thermoelectric performance of with nanostructuring, J. Mater. Chem. A 11, 16734 (2023).
- J. P. Heremans, V. Jovovic, E. S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, and G. J. Snyder, Enhancement of thermoelectric efficiency in by distortion of the electronic density of states, Science 321, 554 (2008).
- Q. Zhang, F. Cao, W. Liu, K. Lukas, B. Yu, S. Chen, C. Opeil, D. Broido, G. Chen, and Z. Ren, Heavy doping and band engineering by potassium to improve the thermoelectric figure of merit in -type , , and , J. Am. Chem. Soc. 134, 10031 (2012).
- B. Li, H. Wang, Y. Kawakita, Q. Zhang, M. Feygenson, H. Yu, D. Wu, K. Ohara, T. Kikuchi, K. Shibata, T. Yamada, X. K. Ning, Y. Chen, J. Q. He, D. Vaknin, R. Q. Wu, K. Nakajima, and M. G. Kanatzidis, Liquid-like thermal conduction in intercalated layered crystalline solids, Nat. Mater. 17, 226 (2018).
- J. Qi et al., Dimer rattling mode induced low thermal conductivity in an excellent acoustic conductor, Nat. Commun. 11, 5197 (2020).
- X. Qian, J. Zhou, and G. Chen, Phonon-engineered extreme thermal conductivity materials, Nat. Mater. 20, 1188 (2021).
- L. Yang, S. Yue, Y. Tao, S. Qiao, H. Li, Z. Dai, B. Song, Y. Chen, J. Du, D. Li, and P. Gao, Suppressed thermal transport in silicon nanoribbons by inhomogeneous strain, Nature 629, 1021 (2024).
- M. Yao, M. Li, L. Zhang, and H. Wang, Giant thermoelectric effect governed by unique two-dimensional electronic structure and strong anharmonicity in layered nitrides, Phys. Rev. B 110, 115202 (2024).
- H. Han, L. Zhao, X. Wu, B. Zuo, S. Bian, T. Li, X. Liu, Y. Jiang, C. Chen, J. Bi, J. Xu, and L. Yu, Advancements in thermoelectric materials: optimization strategies for enhancing energy conversion, J. Mater. Chem. A 12, 24041 (2024).
- S. Schweidler, M. Botros, F. Strauss, Q. Wang, Y. Ma, L. Velasco, G. Cadilha Marques, A. Sarkar, C. Kübel, H. Hahn, J. Aghassi-Hagmann, T. Brezesinski, and B. Breitung, High-entropy materials for energy and electronic applications, Nat. Rev. Mater. 9, 266 (2024).
- J. W. Yeh, S. K. Chen, S. Lin, J. Gan, T. T. Shun, C. Tsau, and S. Chang, Nanostructured high-entropy alloys with multiple principle elements: Novel alloy design concepts and outcomes, Adv. Eng. Mater. 6, 299 (2004).
- B. Cantor, I. T. H. Chang, P. Knight, and A. J. B. Vincent, Microstructural development in equiatomic multi-component alloys, Mat. Sci. Eng. A 213, 375 (2004).
- D. B. Miracle and O. N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater. 122, 448 (2017).
- J.-W. Yeh, Alloy design strategies and future trends in high-entropy alloys, JOM 65, 1759 (2013).
- J. Dąbrowa, M. Zajusz, W. Kucza, G. Cieślak, K. Berent, T. Czeppe, T. Kulik, and M. Danielewski, Demystifying the sluggish diffusion effect in high entropy alloys, J. Alloys Compd. 783, 193 (2019).
- A. Mehta and Y. Sohn, High entropy and sluggish diffusion “core” effects in senary fcc Al–Co–Cr–Fe–Ni–Mn alloys, ACS Comb. Sci. 22, 757 (2020).
- Q. Tang, B. Jiang, K. Wang, W. Wang, B. Jia, T. Ding, Z. Huang, Y. Lin, and J. He, High-entropy thermoelectric materials, Joule 8, 1641 (2024).
- S. Liu, D. Wu, M. Kong, W. Wang, L. Xie, and J. He, High-entropy thermoelectric materials: Advances, challenges, and future opportunities, ACS Energy Lett. 10, 925 (2025).
- Y. Luo, S. Hao, S. Cai, T. J. Slade, Z. Z. Luo, V. P. Dravid, C. Wolverton, Q. Yan, and M. G. Kanatzidis, High thermoelectric performance in the new cubic semiconductor by high-entropy engineering, J. Am. Chem. Soc. 142, 15187 (2020).
- B. Jiang, Y. Yu, J. Cui, X. Liu, L. Xie, J. Liao, Q. Zhang, Y. Huang, S. Ning, B. Jia et al., High-entropy-stabilized chalcogenides with high thermoelectric performance, Science 371, 830 (2021).
- K. Li, L. Sun, W. Bai, N. Ma, C. Zhao, J. Zhao, C. Xiao, and Y. Xie, High-entropy strategy to achieve electronic band convergence for high-performance thermoelectrics, J. Am. Chem. Soc. 146, 14318 (2024).
- Z. Liu, J. Sun, J. Mao, H. Zhu, W. Ren, J. Zhou, Z. Wang, D. J. Singh, J. Sui, C.-W. Chu et al., Phase-transition temperature suppression to achieve cubic GeTe and high thermoelectric performance by Bi and Mn codoping, Proc. Natl. Acad. Sci. 115, 5332 (2018).
- B. Jiang, W. Wang, S. Liu, Y. Wang, C. Wang, Y. Chen, L. Xie, M. Huang, and J. He, High figure-of-merit and power generation in high-entropy GeTe-based thermoelectrics, Science 377, 208 (2022).
- R. K. Nutor, Q. Cao, X. Wang, D. Zhang, Y. Fang, Y. Zhang, and J.-Z. Jiang, Phase selection, lattice distortions, and mechanical properties in high-entropy alloys, Adv. Eng. Mater. 22, 2000466 (2020).
- W. Hume-Rothery and H. M. Powell, On the theory of super-lattice structures in alloys, Z. Fur Krist. Mater. 91, 23 (1935).
- F. Otto, Y. Yang, H. Bei, and E. P. George, Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys, Acta Mater. 61, 2628 (2013).
- K. C. Pitike, S. Kc, M. Eisenbach, C. A. Bridges, and V. R. Cooper, Predicting the phase stability of multicomponent high-entropy compounds, Chem. Mater. 32, 7507 (2020).
- D. Evans, J. Chen, G. Bokas, W. Chen, G. Hautier, and W. Sun, Visualizing temperature-dependent phase stability in high entropy alloys, Npj Comput. Mater. 7, 151 (2021).
- P. Sarker, T. Harrington, C. Toher, C. Oses, M. Samiee, J.-P. Maria, D. W. Brenner, K. S. Vecchio, and S. Curtarolo, High-entropy high-hardness metal carbides discovered by entropy descriptors, Nat. Commun. 9, 4980 (2018).
- S. Divilov et al., Disordered enthalpy–entropy descriptor for high-entropy ceramics discovery, Nature 625, 66 (2024).
- D. Dey, L. Liang, and L. Yu, Mixed enthalpy–entropy descriptor for the rational design of synthesizable high-entropy materials over vast chemical spaces, J. Am. Chem. Soc. 146, 5142 (2024).
- L. Hu, Y. Zhang, H. Wu, J. Li, Y. Li, M. Mckenna, J. He, F. Liu, S. J. Pennycook, and X. Zeng, Entropy engineering of SnTe: Multi-principal-element alloying leading to ultralow lattice thermal conductivity and state-of-the-art thermoelectric performance, Adv. Energy Mater. 8, 1802116 (2018).
- X. Wang, H. Yao, Z. Zhang, X. Li, C. Chen, L. Yin, K. Hu, Y. Yan, Z. Li, B. Yu et al., Enhanced thermoelectric performance in high entropy alloys , ACS Appl. Mater. Interfaces 13, 18638 (2021).
- X. Shi, S. Song, G. Gao, and Z. Ren, Global band convergence design for high-performance thermoelectric power generation in zintls, Science 384, 757 (2024).
- S. Ghosh, A. Nozariasbmarz, H. Lee, L. Raman, S. Sharma, R. B. Smriti, D. Mandal, Y. Zhang, S. K. Karan, N. Liu, J. L. Gray, M. Sanghadasa, Y. Xia, S. Priya, W. Li, and B. Poudel, High-entropy-driven half-Heusler alloys boost thermoelectric performance, Joule 8, 3303 (2024).
- S. S. Soliman, Z. Mitarotonda, G. R. Dey, and R. E. Schaak, Multistep antimony-seeded pathway to catalytic high-entropy skutterudite-type (CoNiRhIrRu) intermetallic nanoparticles, Chem. Mater. 37, 1403 (2025).
- F. Zelenka, P. Brož, J. Vřešt’ál, J. Buršík, G. Rogl, A. Grytsiv, and P. Rogl, Study of thermal stability of -type skutterudites by Knudsen effusion mass spectrometry, RSC Adv. 9, 21451 (2019).
- B. Li, J. Sun, X. Li, and J. Zhao, Mechanical behavior of high-entropy intermetallic compounds and high-entropy ceramics, J. Mater. Chem. A 12, 27855 (2024).
- R. Grau-Crespo, S. Hamad., C. R. A. Catlow, and N. H. de Leeuw, Symmetry-adapted configurational modelling of fractional site occupancy in solids, J. Phys.: Condens. Matter 19, 256201 (2007).
- H. Luo, J. W. Krizan, L. Muechler, N. Haldolaarachchige, T. Klimczuk, W. Xie, M. K. Fuccillo, C. Felser, and R. J. Cava, A large family of filled skutterudites stabilized by electron count, Nat. Commun. 6, 6489 (2015).
- G. Kresse and J. Hafner, Ab Initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-d) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
- C. E. Calderon, J. J. Plata, C. Toher, C. Oses, O. Levy, M. Fornari, A. Natan, M. J. Mehl, G. L. W. Hart, M. Buongiorno Nardelli, and S. Curtarolo, The AFLOW standard for high-throughput materials science calculations, Comput. Mater. Sci. 108, 233 (2015).
- F. Eriksson, E. Fransson, and P. Erhart, The hiphive package for the extraction of high-order force constants by machine learning, Adv. Theory Simul. 2, 1800184 (2019).
- J. J. Plata, V. Posligua, A. M. Márquez, J. F. Sanz, and R. Grau-Crespo, Charting the lattice thermal conductivities of I–III– chalcopyrite semiconductors, Chem. Mater. 34, 2833 (2022).
- A. Ganose, J. Park, A. Faghaninia, R. Woods-Robinson, K. Persson, and A. Jain, Efficient calculation of carrier scattering rates from first principles, Nat. Commun. 12, 2222 (2021).
- J. Heyd, G. E. Scuseria, and M. Ernzerhof, Erratum: “Hybrid functionals based on a screened Coulomb potential”, J. Chem. Phys. 124, 219906 (2006).
- M. Laurien and O. Rubel, Benchmarking exchange-correlation potentials with the mstar60 dataset: Importance of the nonlocal exchange potential for effective mass calculations in semiconductors, Phys. Rev. B 106, 045204 (2022).
- R. Jinnouchi, F. Karsai, and G. Kresse, On-the-fly machine learning force field generation: Application to melting points, Phys. Rev. B 100, 014105 (2019).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/qd4g-95cf which contains covalent radii and electronegativities, elastic constants, and band structures (including SOC) of selected materials, as well as radial and angular distribution functions for CoSb and FeNiCoRhSb.
- W. Sun, S. T. Dacek, S. P. Ong, G. Hautier, A. Jain, W. D. Richards, A. C. Gamst, K. A. Persson, and G. Ceder, The thermodynamic scale of inorganic crystalline metastability, Sci. Adv. 2, e1600225 (2016).
- M. Aykol, S. S. Dwaraknath, W. Sun, and K. A. Persson, Thermodynamic limit for synthesis of metastable inorganic materials, Sci. Adv. 4, eaaq0148 (2018).
- A. V. Powell, P. Vaqueiro, S. Tippireddy, and J. Prado-Gonjal, Exploiting chemical bonding principles to design high-performance thermoelectric materials, Nat. Rev. Chem. 9, 241 (2025).
- Y. Tang, Z. M. Gibbs, L. A. Agapito, G. Li, H.-S. Kim, M. Buongiorno Nardelli, S. Curtarolo, and G. J. Snyder, Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in skutterudites, Nat. Mater. 14, 1223 (2015).
- K. H. Lee, S.-i. Kim, H.-S. Kim, and S. W. Kim, Band convergence in thermoelectric materials: Theoretical background and consideration on Bi–Sb–Te alloys, ACS Appl. Energy Mater. 3, 2214 (2020).
- K. Koga, K. Akai, K. Oshiro, and M. Matsuura, Electronic structure and optical properties of binary skutterudite antimonides, Phys. Rev. B 71, 155119 (2005).
- M. Saeed, B. Khan, I. Ahmad, A. S. Saleemi, N. Rehman, H. R. Aliabad, and S. Uddin, Theoretical investigations of thermoelectric phenomena in binary semiconducting skutterudites, RSC Adv. 9, 24981 (2019).
- K. Wang, L. Wang, I.-L. Liu, F. Boschini, M. Zonno, M. Michiardi, E. Rotenberg, A. Bostwick, D. Graf, B. J. Ramshaw, A. Damascelli, and J. Paglione, Symmetry-enforced Fermi degeneracy in topological semimetal , Phys. Rev. Mater. 7, 074205 (2023).
- J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. Sun, Accurate and numerically efficient r2SCAN meta-generalized gradient approximation, J. Phys. Chem. Lett. 11, 8208 (2020).
- B. Zhu, S. R. Kavanagh, and D. Scanlon, easyunfold: A python package for unfolding electronic band structures, J. Open Source Softw. 9, 5974 (2024).
- R. Hanus, X. Guo, Y. Tang, G. Li, G. J. Snyder, and W. G. Zeier, A chemical understanding of the band convergence in thermoelectric skutterudites: Influence of electron population, local thermal expansion, and bonding interactions, Chem. Mater. 29, 1156 (2017).
- J. Santana-Andreo, A. M. Márquez, J. J. Plata, E. J. Blancas, J.-L. González-Sánchez, J. F. Sanz, and P. Nath, High-throughput prediction of the thermal and electronic transport properties of large physical and chemical spaces accelerated by machine learning: Charting the of binary skutterudites, ACS Appl. Mater. Interfaces 16, 4606 (2024).
- Á. Lobato, E. R. Remesal, A. M. Márquez, F. Izquierdo-Ruiz, A. Otero-de-la Roza, E. J. Blancas, J. M. Recio, and J. J. Plata, Decoupling electronic transport properties: A combined physical and chemical pressure approach for boosting thermoelectric performance in skutterudites, Mater. Today Phys. 59, 101912 (2025).
- J. M. Domínguez-Vázquez, O. Caballero-Calero, K. Lohani, J. J. Plata, A. M. Márquez, C. V. Manzano, M. Á. Tenaguillo, H. Ohta, A. Cebollada, A. Conca, and M. Martín-González, Thermoelectric performance boost by chemical order in epitaxial L2 (100) and (110) oriented undoped thin films: an experimental and theoretical study, J. Mater. Chem. A 13, 24716 (2025).
- T. Caillat, J.-P. Fleurial, and A. Borshchevsky, Bridgman-solution crystal growth and characterization of the skutterudite compounds and , J. Cryst. Growth 166, 722 (1996).
- Y. Tian, B. Xu, and Z. Zhao, Microscopic theory of hardness and design of novel superhard crystals, Int. J. Refract. Met. Hard Mater. 33, 93 (2012).
- C. Recknagel, N. Reinfried, P. Höhn, W. Schnelle, H. Rosner, Y. Grin, and A. Leithe-Jasper, Application of spark plasma sintering to the fabrication of binary and ternary skutterudites, Sci. Technol. Adv. Mater. 8, 357 (2007).
- V. Keppens, B. C. Sales, D. Mandrus, B. C. Chakoumakos, and C. Laermans, Ultrasound studies of clathrate thermoelectrics, Mat. Res. Soc. Symp. Proc. 626, 133 (2000).
- A. Márquez and J. J. Plata Ramos, High-entropy skutterudites as thermoelectrics, 2025, https://doi.org/10.5281/zenodo.15688267
