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Engineering relaxors by entropy for high energy storage performance


Relaxor ferroelectrics are the primary candidates for high-performance energy storage dielectric capacitors. A common approach to tuning the relaxor properties is to regulate the local compositional inhomogeneity, but there is a lack of a quantitative evaluation way for compositional fluctuation in relaxors. Here we propose configurational entropy as an index for the quantitative evaluation of local compositional inhomogeneity. Our results reveal that the local inhomogeneity increases with the entropy via scanning transmission electron microscopy, and relaxor features are accordingly modulated. With the deliberate design of entropy, we achieve an optimal overall energy storage performance in Bi4Ti3O12-based medium-entropy films, featuring a high energy density of 178.1 J cm−3 with efficiency exceeding 80% and a high figure of merit of 913. By using the medium-entropy films as dielectric layers, we demonstrate a multilayer film capacitor prototype that outperforms conventional multilayer ceramic capacitors.

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Fig. 1: Enhancing the relaxor properties and energy storage performance through entropy engineering.
Fig. 2: Phase structure and STEM-EDS analysis.
Fig. 3: Evolutions of local inhomogeneity and relaxor features by entropy modulation.
Fig. 4: Energy storage performances of the entropy-modulated films.

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The data supporting the findings of this study are available within the paper and its Supplementary Information files. Source data are provided with this paper and are available at


  1. Chu, B. et al. A dielectric polymer with high-electric-energy density and fast discharge speed. Science 313, 334–336 (2006).

  2. Wang, G. et al. Electroceramics for high-energy density capacitors: current status and future perspectives. Chem. Rev. 121, 6124–6172 (2021).

    Article  Google Scholar 

  3. Li, J. et al. Grain-orientation-engineered multilayer ceramic capacitors for energy storage applications. Nat. Mater. 19, 999–1005 (2020).

    Article  Google Scholar 

  4. Yang, L. et al. Perovskite lead-free dielectrics for energy storage applications. Prog. Mater. Sci. 102, 72–108 (2019).

    Article  Google Scholar 

  5. Pan, H. et al. Ultrahigh energy storage in superparaelectric relaxor ferroelectrics. Science 374, 100–104 (2021).

    Article  Google Scholar 

  6. Kim, J. et al. Ultrahigh-capacitive energy density in ion-bombarded relaxor ferroelectric films. Science 369, 81–84 (2020).

  7. Jayakrishnan, A. R. et al. Are lead-free relaxor ferroelectric materials the most promising candidates for energy storage capacitors? Prog. Mater. Sci. 132, 101046 (2023).

    Article  Google Scholar 

  8. Li, F., Zhang, S., Damjanovic, D., Chen, L.-Q. & Shrout, T. R. Local structural heterogeneity and electromechanical responses of ferroelectrics: learning from relaxor ferroelectrics. Adv. Funct. Mater. 28, 1801504 (2018).

    Article  Google Scholar 

  9. Pan, H. et al. Giant energy density and high efficiency achieved in bismuth ferrite-based film capacitors via domain engineering. Nat. Commun. 9, 1813 (2018).

    Article  Google Scholar 

  10. Shetty, S. et al. Relaxor behavior in ordered lead magnesium niobate (PbMg1/3Nb2/3O3) thin films. Adv. Funct. Mater. 29, 1804258 (2019).

    Article  Google Scholar 

  11. Yang, C. et al. Fatigue-free and bending-endurable flexible Mn-doped Na0.5Bi0.5TiO3-BaTiO3-BiFeO3 film capacitor with an ultrahigh energy storage performance. Adv. Energy Mater. 9, 1803949 (2019).

    Article  Google Scholar 

  12. Chen, J., Qi, H. & Zuo, R. Realizing stable relaxor antiferroelectric and superior energy storage properties in (Na1−x/2Lax/2)(Nb1−xTix)O3 lead-free ceramics through A/6-site complex substitution. ACS Appl. Mater. Interfaces 12, 32871–32879 (2020).

    Article  Google Scholar 

  13. Cantor, B., Chang, I. T. H., Knight, P. & Vincent, A. J. B. Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng. A 375, 213–218 (2004).

    Article  Google Scholar 

  14. Rost, C. M. et al. Entropy-stabilized oxides. Nat. Commun. 6, 8485 (2015).

    Article  Google Scholar 

  15. Yang, B. et al. High-entropy enhanced capacitive energy storage. Nat. Mater. 21, 1074–1080 (2022).

    Article  Google Scholar 

  16. Sarkar, A. et al. High-entropy oxides for reversible energy storage. Nat. Commun. 9, 3400 (2018).

  17. Bérardan, D., Franger, S., Dragoe, D., Meena, A. K. & Dragoe, N. Colossal dielectric constant in high-entropy oxides. Phys. Status Solidi Rapid Res. Lett. 10, 328–333 (2016).

  18. Jiang, S. et al. A new class of high-entropy perovskite oxides. Scr. Mater. 142, 116–120 (2018).

    Article  Google Scholar 

  19. Braun, J. L. et al. Charge-induced disorder controls the thermal conductivity of entropy-stabilized oxides. Adv. Mater. 30, 1805004 (2018).

    Article  Google Scholar 

  20. Berardan, D., Franger, S., Meena, A. K. & Dragoe, N. Room temperature lithium superionic conductivity in high-entropy oxides. J. Mater. Chem. A 4, 9536–9541 (2016).

  21. Sarkar, A. et al. High-entropy oxides: fundamental aspects and electrochemical properties. Adv. Mater. 31, 1806236 (2019).

    Article  Google Scholar 

  22. Chen, L. et al. Giant energy-storage density with ultrahigh efficiency in lead-free relaxors via high-entropy design. Nat. Commun. 13, 3089 (2022).

  23. Pu, Y. et al. Dielectric properties and electrocaloric effect of high-entropy (Na0.2Bi0.2Ba0.2Sr0.2Ca0.2)TiO3 ceramic. Appl. Phys. Lett. 115, 223901 (2019).

    Article  Google Scholar 

  24. Yan, B., Chen, K. & An, L. Design and preparation of lead-free (Bi0.4Na0.2K0.2Ba0.2)TiO3-Sr(Mg1/3Nb2/3)O3 high-entropy relaxor ceramics for dielectric energy storage. Chem. Eng. J. 453, 139921 (2023).

    Article  Google Scholar 

  25. Hong, Z. et al. Role of point defects in the formation of relaxor ferroelectrics. Acta Mater. 225, 117558 (2022).

    Article  Google Scholar 

  26. Cummins, S. E. & Cross, L. E. Electrical and optical properties of ferroelectric Bi4Ti3O12 single crystals. J. Appl. Phys. 39, 2268–2274 (1968).

    Article  Google Scholar 

  27. Chon, U., Jang, H. M., Kim, M. G. & Chang, C. H. Layered perovskites with giant spontaneous polarizations for non-volatile memories. Phys. Rev. Lett. 89, 087601 (2002).

  28. Kim, J. et al. Utilization of high-entropy alloy characteristics in Er-Gd-Y-Al-Co high entropy bulk metallic glass. Acta Mater. 155, 350–361 (2018).

  29. Kim, S. J. et al. Direct observation of oxygen stabilization in layered ferroelectric Bi3.25La0.75Ti3O12. Appl. Phys. Lett. 91, 062913 (2007).

    Article  Google Scholar 

  30. Shannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Cryst. 32, 751–767 (1976).

  31. Jiang, B. et al. High-entropy-stabilized chalcogenides with high thermoelectric performance. Science 371, 830–834 (2021).

    Article  Google Scholar 

  32. Su, L. et al. Direct observation of elemental fluctuation and oxygen octahedral distortion-dependent charge distribution in high-entropy oxides. Nat. Commun. 13, 2358 (2022).

  33. Li, F. et al. Giant piezoelectricity of Sm-doped Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals. Science 364, 264–268 (2019).

    Article  Google Scholar 

  34. Wright, A. J. et al. Size disorder as a descriptor for predicting reduced thermal conductivity in medium- and high-entropy pyrochlore oxides. Scr. Mater. 181, 76–81 (2020).

    Article  Google Scholar 

  35. Ma, Z. et al. High thermoelectric performance and low lattice thermal conductivity in lattice-distorted high-entropy semiconductors AgMnSn1−xPbxSbTe4. Chem. Mater. 34, 8959–8967 (2022).

    Article  Google Scholar 

  36. Xiong, W. et al. Low-loss high entropy relaxor-like ferroelectrics with A-site disorder. J. Eur. Ceram. Soc. 41, 2979–2985 (2021).

    Article  Google Scholar 

  37. Pan, H. et al. Ultrahigh-energy density lead-free dielectric films via polymorphic nanodomain design. Science 365, 578–582 (2019).

    Article  Google Scholar 

  38. Kim, C., Pilania, G. & Ramprasad, R. Machine learning assisted predictions of intrinsic dielectric breakdown strength of ABX3 perovskites. J. Phys. Chem. C 120, 14575–14580 (2016).

  39. Yeh J.-W., Chen S.-K., Shih H. C., Zhang Y. & Zuo T. T. in High-Entropy Alloys: Fundamentals and Applications (eds Gao, M. C. et al.) 238–240 (Springer, 2016).

  40. Mu, S. et al. Uncovering electron scattering mechanisms in NiFeCoCrMn derived concentrated solid solution and high-entropy alloys. npj Comput. Mater. 4, 47–54 (2020).

  41. Jin, L. et al. BiFeO3(00l)/LaNiO3/Si thin films with enhanced polarization: an all-solution approach. RSC Adv. 6, 78629–78635 (2016).

    Article  Google Scholar 

  42. Li, M. et al. A family of oxide ion conductors based on the ferroelectric perovskite Na0.5Bi0.5TiO3. Nat. Mater. 13, 31–35 (2014).

    Article  Google Scholar 

  43. Sun Y. et al. Ultrahigh energy storage density in glassy ferroelectric thin films under low electric field. Adv. Sci. (2022).

  44. Wang, K. et al. Superparaelectric (Ba0.95,Sr0.05)(Zr0.2,Ti0.8)O3 ultracapacitors. Adv. Energy Mater. 10, 2001778 (2020).

    Article  Google Scholar 

  45. Bin, C. et al. Flexible lead-free film capacitor based on BiMg0.5Ti0.5O3-SrTiO3 for high-performance energy storage. Chem. Eng. J. 445, 136728 (2022).

    Article  Google Scholar 

  46. Yang, S., Kim, T., Yoon, J.-G. & Noh, T. Nanoscale observation of time-dependent domain wall pinning as the origin of polarization fatigue. Adv. Funct. Mater. 22, 2310–2317 (2012).

    Article  Google Scholar 

  47. Glaum, J. & Hoffman, M. Electric fatigue of lead-free piezoelectric materials. J. Am. Ceram. Soc. 97, 665–680 (2014).

  48. Chen, X., Huang, B., Liu, Y., Wang, W. & Yu, P. High energy density and high efficiency achieved in the Ca0.74Sr0.26Zr0.7Ti0.3O3 linear dielectric thin films on the silicon substrates. Appl. Phys. Lett. 117, 112902 (2020).

    Article  Google Scholar 

  49. Shvartsman, V. V. & Lupascu, D. C. Lead-free relaxor ferroelectrics. J. Am. Ceram. Soc. 95, 1–26 (2012).

    Article  Google Scholar 

  50. Hong, K., Lee, T. H., Suh, J. M., Yoon, S.-H. & Jang, H. W. Perspectives and challenges in multilayer ceramic capacitors for next generation electronics. J. Mater. Chem. C 7, 9782–9802 (2019).

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We thank Z. Zhou and J. Qi for fruitful discussions. L.-Q.C. acknowledges the generous support by the Hamer Foundation through a Hamer Professorship at Penn State. This work was financially supported by the National Key Research Program of China (grant numbers 2021YFB3800601, Y.-H.L.); the Basic Science Center Project of the National Natural Science Foundation of China (NSFC) (grant number 52388201, Y.-H.L. and C.-W.N.); the Guangdong Basic and Applied Basic Research Foundation (2022A1515110048, B.Y.); the NSFC (grant numbers 52025025, 52072400 and 52103284, Q.Z., L.G and F.M.); the NSFC (grant number 51972028, H.H.).

Author information

Authors and Affiliations



Y.-H.L. and B.Y. conceived this study. B.Y. performed this study with the supervision of Y.-H.L. C.-W.N. H.H., W.Z. and L.-Q.C. performed the phase-field simulations. B.W. performed the first-principles calculation. B.Y., S.L. and Yiqian Liu prepared the samples and measured the electrical properties. Q.Z., F.M. and L.G. performed the STEM characterizations. Yiqun Liu and L.Y. discussed the results. B.Y. wrote the first draft of the paper. H.P., Y.-H.L. and C.-W.N. revised the paper. All authors discussed the results and commented on the paper.

Corresponding authors

Correspondence to Ce-Wen Nan or Yuan-Hua Lin.

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Nature Energy thanks Lane Martin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Temperature dependent permittivity and loss tangent.

Temperature dependent permittivity and loss tangent of the films. a, x = 0.0. b, x = 0.4. c, x = 1.0. d, x = 1.5. e, x = 2.0 and f, x = 2.2.

Source data

Extended Data Fig. 2 Comparison of the Pm/Pr and Uloss.

Comparison of the Pm/Pr and Uloss of these entropy-modulated films at electric field of 2 MV cm−1.

Source data

Extended Data Fig. 3 Bipolar P-E loops.

Bipolar P-E loops at 10 kHz of these entropy-modulated films at electric field up to breakdown field. a, x = 0.0. b, x = 0.4. c, x = 1.0. d, x = 1.5. e, x = 2.0. f, x = 2.2.

Source data

Extended Data Fig. 4 The cross-section microstructure and breakdown property of the multilayer film capacitors.

a, Cross-sectional SEM image of the multilayer film capacitor. b and c, EDS-SEM images show the elemental distributions of Bi (b) and Au (c) elements, showing clear interfaces between dielectric layers and inner electrode layers. d, Weibull distribution analysis of the characteristic breakdown fields of the multilayer film capacitors.

Source data

Supplementary information

Supplementary Information

Supplementary Notes 1–4, Figs. 1–14, Tables 1–3 and References.

Source data

Source Data Fig. 1

Polarization, energy density, efficiency and figure of merit source data.

Source Data Fig. 2

XRD source data.

Source Data Fig. 3

Relaxor features, polarization and energy storage source data.

Source Data Fig. 4

Breakdown and energy storage source data.

Source Data Extended Data Fig. 1

Dielectric properties source data.

Source Data Extended Data Fig. 2

Polarization source data.

Source Data Extended Data Fig. 3

P–E loops source data.

Source Data Extended Data Fig. 4

Breakdown field source data.

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Yang, B., Zhang, Q., Huang, H. et al. Engineering relaxors by entropy for high energy storage performance. Nat Energy 8, 956–964 (2023).

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