Introduction

With the continuous progress in the electronics and automotive industries, there is a growing demand for advanced energy storage materials in electric vehicles (EVs) and power electronics, particularly for pulse power applications1. Dielectric ceramics, renowned for their ultra-fast discharge rates, superior power density, and excellent high-temperature resistance, have garnered considerable interest in energy storage applications. However, their practical implementation is impeded by their low recoverable energy storage density (Wrec) and low efficiency (η)2.

The energy storage performance of a dielectric depends on its dielectric polarization (P) under an externally applied electric field (E), that is, \({W}_{{{{{{\rm{total}}}}}}}={{\int }_{0}^{{{P}}_{{\max }}}}{E}{{{{{\rm{d}}}}}}{P},{{W}}_{{{{{{\rm{rec}}}}}}}={{\int }_{{{P}}_{{{{{{\rm{r}}}}}}}}^{{{P}}_{{\max }}}}{E}{{{{{\rm{dP}}}}}},{\eta }{=}{W}_{{{{{{\rm{rec}}}}}}}/{W}_{{{{{{\rm{total}}}}}}}\cdot 100\%\), where Wtotal, Wrec, η, Pmax and Pr represent the total energy storage density, recoverable energy storage density, efficiency, maximum polarization, and remnant polarization after discharging, respectively3. According to the above definition, the key to achieve excellent energy storage density is to increase Pmax while reducing Pr (i.e., obtaining high ΔP=Pmax-Pr) and enhancing Eb, the breakdown strength, which is closely associated with the maximum applied electric field the ceramics can withstand.

The tetragonal tungsten bronze structure (TTBs), regarded as the second largest family of ferroelectrics, has not attracted sufficient attention due to its complex crystal structure, low breakdown strength and suboptimal property in energy storage. TTBs derive from the perovskite structure but offer enhanced flexibility in customizing local stoichiometry and lattice structures. The unit cell of TTBs, represented by the general formula (A1)2(A2)4(C)4(B1)2(B2)8O30, consists of layers of corner-sharing BO6 octahedra with three types of interstitial channels: quadrilateral A1, pentagon A2, and triangular C channels. TTBs dielectrics are classified into three types based on ion occupancy at lattice sites: fully filled, filled, and unfilled. The intricate crystal structure of TTBs ceramics offers various opportunities for customizing ionic composition, accommodating different charges and radii4.

SrxBa1−xNb2O6 (SBN) is an actively studied composition featuring a tetragonal tungsten bronze structure (TTBs). Unlike filled structures, SBN is classified as an unfilled TTBs due to the presence of a 1/6 vacancy at the A site, which is randomly distributed in the A1 and A2 sites. Typically, the larger Ba2+ ions exclusively occupy the A2-site, while the smaller Sr2+ ions are distributed among both A1 and A2 sites5. The widely accepted explanation for the relaxation behavior in TTB system involves lattice distortion resulting from the randomness of cationic arrangements. The relaxation behavior in SBN, particularly in Sr0.67Ba0.33Nb2O6 material, is attributed to the size mismatch between Sr and Ba ions at A2 sites, displacing adjacent oxygen atoms and thereby inducing a net polarization effect6. Additionally, the specific ion occupancy in the crystal structure reveals that the ferroelectric relaxation phase transition in SBN occurs when more than half of the Sr2+ occupy the A2-site. The transition from normal ferroelectric to relaxor state is gradual, occurring in compositions with x ≥ 0.60 in single crystals and x ≥ 0.53 in ceramics7.

To enhance the energy storage performance in dielectric materials, researchers utilized strategies such as refining grain morphology or grain orientation at a mesoscopic scale8,9 as well as implementing domain engineering at a microscopic level10,11. Despite these efforts, meeting the stringent requirements of modern devices for high-performance and reliable energy storage capacitors remained a formidable challenge. Entropy modulation has emerged as a promising alternative strategy to augment energy storage capacity12. Configurational entropy provides a quantitative measure to assess the heterogeneity of local components, thereby facilitating the optimization of energy storage performance through the manipulation of relaxation characteristics in ferroelectrics13. The configurational entropy of the oxide system can be augmented by increasing the number of elements randomly distributed on the same lattice site14. The molar configurational entropy (ΔSconfig) of oxide systems can be calculated according to Eq. (1)15

$${{{S}}}_{{{{{{\rm{config}}}}}}}=-{R}\left[{\left({\sum }_{{{i}}=1}^{{{N}}}{{{x}}}_{{{{{{\rm{i}}}}}}}{{{{{{\rm{lnx}}}}}}}_{{{i}}}\right)}_{{{{{{\rm{cation}}}}}}-{{{{{\rm{sit}}}}}}}+{\left({\sum }_{{{j}}=1}^{{{M}}}{{{x}}}_{{{j}}}{{{{{{\rm{lnx}}}}}}}_{{{j}}}\right)}_{{{{{{\rm{anion}}}}}}-{{{{{\rm{sit}}}}}}}\right]$$
(1)

where xi and xj represent the mole fraction of elements present in the cation and anion sites, respectively, and R is the universal gas constant. As per empirical classification, materials can be categorized based on their configurational entropy. Those with ΔSconfig ≥ 1.5 R can be classified as “high entropy”, while materials with 1.5 R >ΔSconfig ≥ 1.0 R fall into the “medium entropy” category, and materials with ΔSconfig < 1.0 R are classified as “low entropy” systems16.

Dielectrics with high entropy possess the distinctive capacity to achieve disordered polarization configurations via meticulously designed local structures12. The high entropy effect augments system disorder by creating a solid solution of multi-component elements, effectively regulating the stability of the entropy-dominated phase. Meanwhile, the increase in atomic disorder induces notable lattice distortion, impedes element diffusion, and triggers a synergistic cocktail effect from multi-component properties14. Due to these characteristics of high-entropy materials, the high entropy strategy has been applied to a variety of material structure systems to enhance energy storage performance, including perovskite structure17, bismuth layer structure18, pyrochlore structure19, and tungsten bronze structure20. For example, Guo et al.21 obtained a Wrec of 10.7 J cm−3 and a efficiency of 89% in Li2CO3-doped Bi0.2Na0.2Ba0.2Sr0.2Ca0.2TiO3 high-entropy ceramics with a perovskite structure. The coexistence of randomly distributed A-site ions and B-site ions facilitates intricate interactions, resulting in the emergence of atomic-scale low crystallographic symmetries. This involved generating multiphase nanoclusters to achieve extremely small polar nanoregions, thereby enhancing the breakdown field, delaying polarization saturation, and significantly improving the energy storage performance22.

Band gap engineering involves adjusting properties through doping to modify the material’s band gap. Increasing the band gap (i.e., raising the energy required for electrons to move from the valence band to the conduction band) can heighten the dielectric breakdown strength by reducing the intrinsic carrier concentration and conductivity, thereby increasing the electric field required for intrinsic breakdown23. This strategy not only significantly improved the energy storage performance but also achieved excellent high-temperature stability.

In this study, we enhance the energy storage performance of tetragonal tungsten bronze structure ceramics, specifically Ba0.4Sr0.6-xCaxNb2-xTaxO6 (BSCNTx, x = 0,0.15,0.3,0.45) ceramics, by employing a combination of high-entropy strategy and band gap engineering. Incorporating oxides with high band gaps, such as CaO and Ta2O5, can elevate the overall band gap of the compound, thereby enhancing the breakdown field. Concurrently, the heightened configurational entropy (from 0.68R to 1.54R) induces the cocktail effect, which is harnessed to optimize the energy storage performance of the Ba0.4Sr0.6Nb2O6 ceramics. This optimization culminates in exceptionally high energy storage properties, characterized by a Wrec of 8.9 J cm−3 and an impressive efficiency of 93%. Crucially, the BSCNT0.30 ceramics can maintain a Wrec of up to 4.9 J cm−3 with a high η of 89% even at elevated temperature of 180 °C. Coupled with its remarkable frequency insensitivity and fatigue resistance, this system shows significant potential for application in advanced pulsed power devices operating in harsh environments.

Results and discussion

Figure 1a shows the P-E loops of different compositions at their respective maximum electric field, i.e., the breakdown field. With the increase of configurational entropy, the breakdown field obviously increases from 360 kV cm−1 to 700 kV cm−1 at high entropy of 1.51R, above which, the breakdown field decreases, this is due to the fact that the excessive addition of Ca/Ta introduces impurities that deteriorate the breakdown field. Meanwhile, the Pr value is negatively correlated with configurational entropy, decreasing from 4.4 to 1.6 μC cm−2. The relationship between the corresponding energy storage performance and configuration entropy is established, as illustrated in Fig. 1b. The transition from low entropy to high entropy is evident in the enhancement of energy storage performance, increasing from 4.3 J cm−3 (BSCNT0) to 8.9 J cm−3 (BSCNT0.30), representing an increase exceeding 100%. Meanwhile the efficiency also improves significantly, rising from 81% to 93%. Despite BSCNT0.45 exhibiting a high efficiency of 93.3%, its low breakdown field and polarization limit its energy storage potential.

Fig. 1: Energy storage performance of BSCNTx ceramics.
figure 1

a Unipolar P-E loops under maximum electric field of BSCNTx ceramics. b Energy density and efficiency, calculated based on the P-E loops of BSCNTx ceramics at the maximum electric field, presented as a function of conformational entropy. c Comparison of Eb, ΔSconfig, and energy storage performance of BSCNTx ceramics. d Comparison of the energy storage performance (Wrec and η) of the BSCNT0.30 ceramics with other representative lead-free ceramics and TTBs ceramics reported previously.

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To investigate the effect of configurational entropy on the electric field response of BSCNTx ceramics, the bipolar P-E loops of BSCNTx ceramics with different configurational entropies were measured under the same electric field (150 kV cm−1), as shown in Fig. S1a. The corresponding I-E curves and polarization changes are also illustrated in Fig. S1b, c. With the increase in configuration entropy, both Pmax and Pr exhibit a gradual decrease, indicating weakened ferroelectricity and enhanced relaxation characteristics, which can be substantiated by the gradual flattening of the switching current peak, thereby enabling higher Wrec and ƞ24. To visually demonstrate the impact of entropy on the energy storage capabilities of BSCNTx dielectric ceramics, Fig. 1c compiles data on breakdown strength, ΔP, energy storage performance, and configurational entropy of various compositions. It is evident that BSCNT0.30 ceramics exhibit the most favorable comprehensive energy storage performance, attributed to their exceptionally high Eb and ΔP resulting from elevated configurational entropy. Additionally, Fig. 1d compares the energy storage performance of our study with that of other recently published lead-free dielectric ceramics and TTBs ceramics, from which our findings exhibit a leading comprehensive energy storage performance in TTBs system.

To delineate the influence of configurational entropy on the crystal structure of BSCNTx samples, Fig. 2a depicts the XRD pattern of the BSCNTx ceramics. It is evident that, with the increase in x, the structure of the tetragonal tungsten bronze is maintained; however, some impurities are observed in BSCNT0.45. The secondary phase is mainly composed of CaNb2O6 (PDF#71-2406) and/or Ba6Nb2O11 (PDF#46-0938). These impurities produced by BSCNT0.45 is due to the small ionic radius of Ca2+, which tends to enter the A1 position of the quadrilateral and difficult to enter the A2 position, resulting in limited solubility25. In particular, one third of the A-site is occupied by A1-site, while two-thirds are filled by A2-site. Additionally, in the unfilled structure, one-sixth of the A-sites remain vacant and are randomly distributed between A1 and A2 sites. Therefore, even if all vacancies and Sr2+ ions are located exclusively in the A2-site, the content of Ca2+ can only account for a maximum of one-third of the A-site, corresponding to x = 0.4. Beyond this range will result in the inability to maintain a single phase25,26. In Fig. 2b, a locally amplified XRD pattern is presented. As configurational entropy increases, the peaks corresponding to (211), (530), and (620) gradually shift to the right, indicating lattice shrinkage. Figure 2c illustrates the projection of BSCNT0 and BSCNT0.30 along crystallographic [001] direction. The lattice shrinkage is due to the smaller radius of Ca2+(1.34 Å) compared to Sr2+ (1.44 Å) and Ba2+ (1.61 Å). Moreover, despite the same ionic radius of Ta5+(0.64 Å) and Nb5+ (0.64 Å), the increased electronegativity difference between Ta5+ and O2+ compared to Nb5+ leads to an increase in the polarity of the B-O bond. This, in turn, shortens the B-O covalent bond length, resulting in a contraction of the cell volume27. It is evident that as the configurational entropy increases, a variety of elements occupy both the A-site and B-site, resulting in increased system disorder. The Rietveld refinement results of XRD data for BSCNT0 and BSCNT0.30 are illustrated in Fig. S2. The mean ionic radii of the distinct A-sites within the respective components were computed based on the cationic position and proportion (Tables S1 and S2). The results showcase that the mean ionic radius of BSCNT0 is 1.44 Å and 1.54 Å at A1-sites and A2-sites respectively. For BSCNT0.30, on the other hand, the mean ionic radius is 1.36 Å at the A1-sites and 1.55 Å at the A2-sites. The augmented disparity in radius between A1 and A2 sites is expected to induce lattice distortion, which will affect the polarization and corresponding energy storage performance.

Fig. 2: Crystal structure analysis of BSCNTx ceramics.
figure 2

a X-ray diffraction patterns of the ceramics with increasing x and (b) enlarge view of selected diffraction peak. c Projection of BSCNT0 and BSCNT0.30 unit taken along [001] (P4bm, solid line). d Raman spectroscopy of BSCNTx ceramics. e The variation in wavenumber v2 and v5 Raman vibration modes were divided by Gaussian-Lorentzian function.

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To understand the changes in the local structure of BSCNTx ceramics with various configuration entropy, the Raman spectrum was measured, as shown in Fig. 2d. Consistent with previous reports, three main regions are observed in the wave number range of 20 to 900 cm−1, (ref. 28). The low wave number region corresponds to the vibration of A-site cations (less than 200 cm−1), the medium wave number region is related to O-B-O bending vibrations (200–400 cm−1), and the high wave number region above 400 cm−1 is closely related to the B-O stretching vibrations29. The sample exhibits a broad and diffuse Raman spectrum mode, which represents the enhancement of elemental disorder and the reduction of unit cell polarity caused by the random distribution of cations at the A and B sites30. Similar to the results of XRD pattern, the Raman spectrum of BSCNT0.45 shows multiple anomalous peaks, which are caused by the secondary phases. At the same time, for a more intuitively understand of the local structure evolution, Gaussian peak fitting was performed on the BSCNTx Raman diagram, as illustrated in Fig. S3. The changes in the wave numbers of the v2 and v5 peaks with x are shown in Fig. 2e. The positions of bands v2 and v5 move toward lower wave numbers with increasing configurational entropy, indicating a decrease in unit cell polarity31.

The breakdown strength stands as a critical factor influencing the energy storage performance of dielectric ceramics. In order to accurately evaluate the breakdown strength of BSCNTx ceramics, breakdown experiments were carried out on 10 samples of each component, and the standard Weibull distribution analysis was calculated according to the results. The fitting results and reliable breakdown electric fields of different components are illustrated in Fig. 3a. The parameter β, denoting the Weibull modulus, serves as an index reflecting the dispersion within the distribution of data.

Fig. 3: Breakdown strength, band gap and impedance spectrum analysis of BSCNTx ceramics.
figure 3

a Weibull distribution analysis of the breakdown strengths of the ceramics. The β is the Weibull modulus. The sample thickness is 70–85 μm and the electrode area is 0.7 mm2. b UV-vis absorption spectra of BSCNTx ceramics. c The Tauc plots of all BSCNTx samples. d Band gap and breakdown strength corresponding to different compositions. e Impedance spectroscopy of BSCNTx at 500 °C (the inset showing the equivalent circuit proposed for impedance data fitting). f The fitting grain boundary activation energy values (Egb) versus the x.

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It is reported that the breakdown strength is closely related to the grain size32, bandgap21, space charge33. Figure S4a–d present scanning electron microscopy (SEM) images showcasing the surface morphology, along with an illustration demonstrating the statistical distribution of grain sizes (Ga) in the corresponding samples. The average grain size of BSCNTx decreases with increasing entropy. Specifically, for BSCNT0.45 ceramics, the average grain size is reduced by 50% compared to BSCNT0, decreasing from 3.4 μm to 1.7 μm. Given their remarkable refractory behavior, oxides of Ta and Ca are extensively employed as grain growth inhibitors to mitigate the average grain size24,34. Furthermore, the lattice distortion induced by the elevated configurational entropy can substantially impede atomic diffusion, thereby further diminishing the average grain size thus higher grain boundary density35. Notably, grain boundaries with higher resistivity play an important role in preventing electric breakdown by absorbing the energy from electric tree expansion within the grains36. Smaller grain sizes correspond to a higher grain boundary density, contributing to an obvious negative correlation between the average grain size and breakdown field, that is Eb∝(Ga)−1,32. Meanwhile, Fig. S4e clearly illustrates that the BSCNT0.30 sample exhibits a uniform distribution of elements without any noticeable segregation, confirming the successful incorporation of Ca2+ and Ta5+ into the lattice. This homogeneous composition, coupled with the refined grain size, contributes to enhancing breakdown strength by altering the electric field distribution within ceramic under applied electric field37.

The intrinsic breakdown mechanism of dielectrics primarily involves electron breakdown, where the band gap serving as the decisive factor. Figure 3b illustrates the UV-visible absorption spectrum of BSCNTx ceramics. while Fig. 3c presents the determination of the direct bandgap of BSCNTx ceramics using the Tauc plot method. The introduction of Ca2+/Ta5+ can elevate the band gap by altering the minimum value of the conduction band38. As anticipated, owing to the wider band gap of Ta2O5(4.3 eV)39 and CaO (7.1 eV)40 in comparison to Nb2O5 (3.4 eV)41 and SrO (6.1 eV)42, the band gap of BSCNTx eventually increases from 3.35 eV (BSCNT0) to 3.46 eV (BSCNT0.30), as shown in Fig. 3d, leading to a significant enhancement in the breakdown strength.

To delve deeper into the high Eb exhibited by the BSCNTx ceramics, complex impedance spectra are presented in Fig. S5a–d, covering temperatures ranging from 450 °C to 650 °C. Figure 3e gives the impedance spectrum of BSCNTx at 500 °C. It is apparent that as the configurational entropy increases, the radius of impedance spectrum arc gradually increases, highlighting a gradual rise in resistance. This observation implies that higher configurational entropy enhances the insulation performance of ceramics. The block ceramic-electrode system can be simplified as a brick structure consisting of grain boundaries and grains. Two sets of equivalent R-C circuit elements, representing grains and grain boundaries, were connected in series to fit the impedance data, as illustrated in the inset of Fig. 3e. The activation energy of conduction for the grain boundary (Egb) of the BSCNTx ceramic system can be calculated by the Arrhenius formula43, as showcased in Fig. 3f. The increase in Egb indicates a decrease in the concentration of oxygen vacancies at these grain boundaries, resulting in higher resistivity of the boundaries. The activation energy of conduction was positively correlated with the breakdown strength44. By incorporation of Ca2+ and Ta5+ into Ba0.4Sr0.6Nb2O6 ceramics, Egb exceeding 1.58 eV can be achieved in BSCNT0.30 samples, significantly enhancing the breakdown strength. Nevertheless, in the BSCNT0.45 ceramics, the solid solubility limitation of Ca2+ ions within the SBN matrix gives rise to secondary phases, such as Ca2Nb2O6 and/or Ba6Nb2O11. Notably, oxygen vacancy exists in Ba6Nb2O11 to maintain electrical neutrality45. Since the activation energy inversely correlates with the concentration of oxygen vacancies44, BSCNT0.45 exhibits a lower activation energy, which is further supported by the decreased breakdown field observed in BSCNT0.45.

In addition to breakdown strength, the high saturation polarization and low remanent polarization of relaxor ferroelectrics are the favorable characteristics for their applications in energy storage. Therefore, enhancing the relaxation characteristics of dielectrics is a crucial approach to optimize their energy storage performance, which can be achieved by high entropy strategy2. To investigate the evolution of relaxation behavior in the BSCNTx ceramics, the relative permittivity (εr) and loss tangent (tanδ) were measured over a temperature range of −100 to 250 °C and a frequency range from 10 Hz to 2 MHz, as depicted in Fig. S6a–h. The observed less steep dielectric peaks, along with significant frequency dispersion behavior, suggest a typical dispersion phase transition characteristic of relaxor ferroelectrics46. In Fig. S7a, the temperature dependence of the εr and tanδ of BSCNTx samples at 1 kHz is presented. As configurational entropy increases, the maximum dielectric constant in BSCNTx samples decreases, and the temperature corresponding to the maximum dielectric constant (Tm) shifts to a lower temperature. Frequency dispersion behavior, indicating an increase in Tm with rising frequency, is a crucial characteristic of relaxor ferroelectrics. As illustrated in Fig. S7b, △Tm (Tm 2MHz-Tm 10Hz) notably rises from 17 K to 59 K with an increase in configurational entropy, signifying that increased entropy is beneficial for enhancing relaxor component in BSCNTx. Furthermore, the semi-quantitative evaluation of the relaxation properties can be achieved by fitting the diffusion coefficient γ based on the modified Curie-Weiss equation47, exhibiting an increasing trend from 1.35 to 1.73, as given in Fig. S7c, indicating a stronger relaxation behavior in high entropy BSCNT0.30 ceramics. The introduction of multiple elements into equivalent lattice positions via the high entropy strategy increases chemical complexity, disrupts long-range ordering in the ferroelectrics, and enhances the relaxor characteristics of BSCNT0.3048.

The relaxation dynamic behaviors in BSCNTx ceramics were assessed using the Vogel-Fulcher model49. The fitting outcomes are demonstrated in Fig. S6, while the computed activation energy (Ea) is depicted in Fig. S7d. The Ea escalates from 0.013 eV (BSCNT0) to 0.073 eV (BSCNT0.30) with increasing configurational entropy. The increase in activation energy suggests a weakening of the coupling between polar clusters in the system, making it more challenging to form ordered polarized regions50. This phenomenon presents an advantage for energy storage, as it corresponds to delayed polarization saturation under high electric fields and maintain a thinner P-E loop49.

To confirm the weakly coupled features of polar clusters in the BSCNTx ceramics and elucidate the origin of relaxation, field emission transmission electron microscopy (TEM) observations were conducted on BSCNT0 and BSCNT0.30 samples, as depicted in Fig. 4a, b. The BSCNT0 sample (Fig. 4a) exhibits noticeable long-range continuous polarization, manifesting as ferroelectric domains with widths extending up to tens of nanometers. Dramatically divergent, the BSCNT0.30 sample lacks such discernible ferroelectric domain structures, as shown in Fig. 4b. Figure 4c, d depict the corresponding selected area electron diffraction (SAED) patterns for BSCNT0 and BSCNT0.30 along the [110] zone axis. Alongside the Bragg reflections corresponding to the TTB structure, additional superlattice spots associated with structural modulation (indicated by white arrows) emerge in the SAED patterns, signifying the presence of incommensurate modulation in BSCNTx ceramics at room temperature51. The presence of a commensurate modulation is strongly associated with the long-range ordering and demonstrates ferroelectric properties. Conversely, the existence of an incommensurate modulation suggests a pronounced relaxation characteristics52. The incommensurate modulation wave vectors were calculated as (1/4 + δ)(a-b)+1/2c, where a, b, and c are the vectors in reciprocal space and δ is the parameter that describes the deviation from commensurate periodicity53. δ is calculated using the formula δ = (x − y)/(x + y), where x and y represent the distances from the adjacent incommensurate diffraction spots, as determined by measuring the positions of weak reflections52. The measurement method for determining incommensurability parameter δ is presented in inset of Fig. 4d. It can be obtained by calculating the weak reflections: δBSCNT0 = 0.18 ± 0.04 (300 K), δBSCNT0.30 = 0.28 ± 0.06 (300 K). The increased incommensurability parameter arises from the A-site disorder, consequently leading to diffused satellite reflection points53. Hence, the larger δ observed in BSCNT0.30 is ascribed to the random occupancy of Ba2+, Sr2+, and Ca2+ in the A-site, accounting for the enhanced relaxation behavior54. Simultaneously, the addition of Ta5+ causes unavoidable distortion of the oxygen octahedron, leading to local lattice distortion. This suggests that B-site ion doping tends to promote incommensurate modulation31.

Fig. 4: TEM characterization and out-of-plane PFM phase images of BSCNT0 and BSCNT0.30 ceramics.
figure 4

a, b TEM image patterns take along [110] zone from BSCNT0 and BSCNT0.30 samples, (c, d) SAED patterns take along [110] zone from BSCNT0 and BSCNT0.3 samples. The inset of (d) displays the measurement schematic for determining the incommensurate superlattice incommensurability parameter δ. The white arrows indicate the appearance of the satellite reflections for incommensurate modulation in b and d. e Atomic-resolution HAADF-STEM image along [110] of the BSCNT0.30 ceramic, and the arrows show the displacement of B-site cations corresponding to different polarization directions. f, g Out-of-plane PFM phase images of samples BSCNT0 and BSCNT0.30 after poling treatment with ±10 V and then measuring after a certain relaxation time.

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To further illustrate the presence of weakly coupled polar nanoregions (PNRs) and the influence of high entropy effect on local polarization distribution, high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) experiments were conducted on the high-entropy BSCNT0.30 sample, as depicted in Fig. 4e. In the HAADF-STEM images, A-site atoms were observed to occupy highly symmetric positions, showing minimal relative movement among them. In contrast, B-site atoms exhibited multi-directional displacement from the central position between two neighboring atoms, as evidenced by the lower left images in Fig. 4e. Since the polarization of TTBs stems from the displacement of B-site ions55, examining the movement of the central B-site cation in relation to adjacent B-site cations allows for the determination of local polarization direction. As illustrated in Fig. 4e, the displacement of B-site atoms in the BSCNT0.30 sample appeared highly disordered, lacking consistent displacement directions. This disorder results in the formation of highly segmented PNRs and weak coupling effects among them. Such a disordered structure significantly impedes the long-range order of the ferroelectrics, ultimately contributing to the enhanced relaxation and thereby excellent energy storage performance18. Meanwhile, such localized ordered structures are more conducive to polarization realignment under the influence of an applied electric field, reduce the domain-switching energy barriers, resulting in reduced heat generation and thereby enhancing thermal breakdown strength36.

The dynamic response of PNRs to external electric fields is closely related to the energy storage properties of dielectric materials56, which was investigated using piezoelectric response force microscopy (PFM). As shown in Fig. 4f1-f5 and g1-g5, after being written with DC voltages of +10 V and −10 V, respectively, read scans were performed every 4 min. It was observed that the polarization of BSCNT0.30 returned to its initial highly random state much faster compared to BSCNT0. Notably, as depicted in Fig. 4g5, BSCNT0.30 exhibited almost no identifiable PNRs after 12 min of polarized writing, highlighting the weak coupling between polar clusters. This suggests the presence of more dynamic PNRs in BSCNT0.30 ceramics, a significant characteristic of enhanced relaxation. The rapid reversibility of PNRs leads to reduced Pr, delayed polarization saturation, and ultimately exceptional energy storage performance57.

Given the advantage of excellent high-temperature resistance in dielectric ceramics, the temperature stability of their energy storage performance is of paramount importance. To assess the energy storage performance of BSCNT0.30 at different temperatures, the P-E loop was tested at 500 kV cm−1 across temperature range of 30 °C to 180 °C, as shown in Fig. 5a. The corresponding energy storage performance at different temperatures is depicted in Fig. 5b. Across the tested temperature range, Wrec and η consistently maintained high values, with Wrec ranging from 5.1 to 4.9 J cm−3 and η ranging between 89-92%. The change rates were less than 5% and 3%, respectively. This outcome illustrates that, owing to the high-entropy effect, the energy storage performance of BSCNT0.30 exhibits excellent temperature stability. To delve deeper into the reason behind the high-temperature stability of BSCNT0.30, its structural changes with temperature were tested. Figure 5c displays the XRD pattern from −70 to 350 °C, revealing minimal changes in the peak position and width of each diffraction peak. Similarly, as shown in Fig. 5d, the Raman test pattern obtained in the temperature range of −70 to 350 °C demonstrates that although the peak intensity decreases at the wave number of ~600 cm−1, the peak position remains largely unchanged. The excellent temperature stability of BSCNT0.30’s energy storage performance is attributed to the temperature insensitivity of its crystal structure (as shown in Fig. 5c, d) and the ultra-low dielectric loss of <0.003 across the temperature range up to 180 °C. Moreover, the complex impedance spectrum indicates that BSCNT0.30 maintains extremely high resistance (~2MΩ) even at 450 °C, demonstrating its excellent high-temperature insulation properties. The excellent temperature stability may also be attributed to the superparaelectric (SPE) state of BSCNT0.30. The temperature-driven SPE in relaxors was report to maintain nonlinear polarization with high Pmax and minimal hysteresis, which is desirable for achieving both high Wrec and η in dielectric capacitors58. At 180 °C, the increase in Pmax is attributed to additional charge from increased leakage at high temperatures, while the increase in Pr may result from conduction losses due to thermal stimulation, ultimately leading to lower efficiency59.

Fig. 5: Temperature stability of energy storage performance of BSCNT0.30 ceramics.
figure 5

a P-E loops with different temperatures at 500 kV cm−1. b Variation of recoverable energy density and efficiency with temperature. c XRD patterns of BSCNT0.30 ceramics at different temperature. d Raman spectra of BSCNT0.30 ceramics at different temperature. e Comparison of this work with other recently published TTBs ceramics for variable temperature energy storage performance.

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Figure 5e illustrates the comparison of the recoverable energy storage density of the studied compositions with recently published TTBs ceramics across different temperature ranges24,28,29,55,60,61. In comparison to these works, the BSCNT0.30 exhibits higher energy storage density over a wider temperature range up to 180 °C, making it suitable for applications in high-temperature environments.

In addition to temperature usage range and stability of the energy storage performance, cycling reliability is another crucial consideration for real applications. Figure S8a, b depict the P-E loops of BSCNT0.30 after various cycles at 350 kV cm−1. These loops maintain a slimmed shape with minimal hysteresis and high Pmax over the cycle range of 100–105, accompanied by negligible changes in Wrec (3-3.1 J cm−3) and η (93-96%), showcasing excellent fatigue resistance and superior cycling reliability. Figure S8c, d shows the P-E loop of BSCNT0.30 across various frequencies (5–500 Hz) and the associated energy storage performance at 350 kV cm−1. The Wrec and η values remain stable at approximately 3 J cm−3 and 87–93%, respectively, indicating excellent frequency insensitivity properties.

In practical applications, assessing the charge and discharge capabilities holds paramount importance. To evaluate the real charge and discharge performance of BSCN0.30 ceramics, both under-damped and over-damped charge and discharge tests were conducted. Additionally, the alterations in charge and discharge performance at various temperatures were thoroughly evaluated. The results are presented in Figs. S9 and S10. The findings reveal that BSCNT attains an impressive current density (CD) of up to 1500 A cm−2, a power density (PD) of 280 MW cm−3, a discharge energy storage density (Wdiss) of 2.6 J cm−3, and a discharge speed of t0.9 = 69.4 ns. Notably, BSCNT0.30 showcases remarkable temperature stability, underscoring its immense potential for use in demanding operational environments, such as high-temperature settings.

In summary, by controlling configurational entropy and band gap within tetragonal tungsten bronze-structured BSCNT ceramics, we have successfully achieved a remarkable recoverable energy density (Wrec) of 8.9 J cm−3 and an efficiency of 93% in the Ba0.4Sr0.3Ca0.3Nb1.7Ta0.3O6 TTBs ceramic. Notably, the excellent temperature stability enables BSCNT0.30 ceramics to maintain an energy storage density of greater than 4.9 J cm−3 at 180 °C while achieving an efficiency of up to 89%. The comprehensive structural characterization proves that the random cation occupancy caused by the high entropy effect breaks the long-range order of the ferroelectric, resulting in highly dynamic and weakly coupled polar nano regions. Meanwhile the high entropy effect restricts the grain growth and increases the overall resistivity of the ceramics, together with the increased band gaps, contributing to an extremely high breakdown strength. The optimized polarization ΔP behavior and increased Eb are responsible for the greatly improved energy storage performance in the TTBs ceramics, hold great potential for energy storage application across a broad temperature range.

Methods

Ceramics fabrication

In this research, a series of BSCNT ceramics were fabricated through a high-temperature solid-state reaction method. The ceramics with the composition Ba0.4Sr0.6-xCaxNb2-xTaxO6 (BSCNTx, 0 ≤x ≤ 0.45) were developed using high-purity powders: Ba2CO3 (99.8%), SrCO3 (99%), CaCO3 (99.99%), Nb2O5 (99.9%), and Ta2O5 (99.9%). The powders were accurately measured based on their stoichiometric proportions and then combined with zirconia grinding media and anhydrous ethanol. This mixture was subjected to ball milling at 400 rpm for 12 h in a polyethylene vessel to achieve uniform mixing. Following this, the dried powder was pre-sintered at 1100 °C for 2 h and underwent a second ball milling under the same conditions. The resulting fine powder was then compacted into 10 mm diameter discs using cold isostatic pressing at 200 MPa for 60 seconds. The compacted samples were finally sintered in an alumina crucible at temperatures ranging from 1300 °C to 1370 °C for 2 h.

Structural characterization

The crystal structures of samples were analyzed using X-ray diffraction (XRD, SMARTLAB, Japan) with Cu Kα-0.1541 nm. Surface morphology and elemental distribution were examined by a field emission scanning electron microscope (Gemini SEM 500, Carle Zeiss, Germany). Raman spectrometry (HR800, Horiba JOBIN YVON) with a wavelength of 532.3 nm was employed to acquire detailed information about doping effect on the structural change of BSCNT ceramics. The HAADF-STEM images were taken by an aberration-corrected (scanning) transmission electron microscope (JEM-ARM300F2, JEOL, Japan). UV-Vis absorption spectra were obtained by a UV-Vis Spectrometer (PerkinElmer Lambda 950).

Electrical properties characterizations

The dielectric properties of the samples were measured using an LCR meter (E4980A, Agilent). The samples were polished to ~0.6 mm thick, coated with conductive silver paste and sintered at 550 °C for 30 min. The P-E hysteresis loops and current-electric field (I-E) curves under different electric fields were measured by Precision Premier II from Radiant Technologies, connected to a high voltage amplifier. The samples are polished down to 70–85 μm in thickness, then coated with platinum electrode with a thickness of ~40 nm and a diameter is 0.95 mm by magnetron sputtering for P-E hysteresis loops measurements. Diamond polishing liquids with particle sizes of 3 µ, 2 µ, and 0.5 µ were used for polishing to ensure low surface roughness. Piezoresponse force microscopy (PFM) measurements were conducted using Park Systems XE7 AFM. Under-damped and over-damped (with a load resistance of 300 Ω) charge/discharge measurements were carried out by capacitor charge-discharge system (CFD-001, Gogo Instruments, China). The sample thickness for charging/discharging test is ~150 μm, with an electrode diameter of 2 mm.