Introduction

Dielectric capacitors are extensively used in advanced electronic and electric power systems, benefiting from their superiority of high power density PD, ultrafast charge-discharge rate t0.9, and excellent energy storage stability1,2,3,4. From a practical application standpoint, compared with thin film capacitors, ceramic capacitors offer distinct advantages, including simple fabrication, low cost, high power and energy storage capacity, thus attracting growing attention in the field of dielectric energy storage5,6. The low energy density Ue and suboptimal efficiency η, however, largely limit the long-term development of ceramic capacitors towards miniaturization and low-energy consumption5,7,8. Consequently, extensive efforts have been dedicated to develop ceramic capacitors with outstanding comprehensive energy storage capabilities4,9.

According to the theory of electrostatic energy storage, Ue and η are determined by the polarization P response of dielectrics under an external electric field E, that are, \({U}_{{{{\rm{e}}}}}={\int }_{{P}_{{{{\rm{r}}}}}}^{{P}_{{{{\rm{m}}}}}}E{{{\rm{d}}}}P\) and \(\eta={U}_{{{{\rm{e}}}}}/({U}_{{{{\rm{e}}}}}+{U}_{{{{\rm{loss}}}}})\), where Pm, Pr, and Uloss represent the maximum polarization, remnant polarization, and energy loss, respectively (Supplementary Fig. S1)10. Therefore, the large polarization fluctuation (\(\Delta P={P}_{{{{\rm{m}}}}}-{P}_{{{{\rm{r}}}}}\), large Pm and small Pr) and high breakdown electric field Eb should be effectively controlled to achieve high Ue and η, simultaneously11. Over the past few years, Eb has been greatly enhanced by various approaches, such as improving band gaps, decreasing strain and refining grains, minimizing voids, and mitigating energy loss from the perspectives of intrinsic, electromechanical, partial discharge, and thermal breakdown, respectively, reaching a level up to 80–100 kV mm-15,12,13,14. For controlling the desired polarization fluctuation under external electric fields, on the other hand, the strategies including domain engineering, polymorphic polar nanoregions (PNRs), multistage phase transition have been employed to obtain a large ΔP of 50–60 μC cm-214,15,16,17. It is noteworthy that both Eb and ΔP have nearly approached the upper limits observed in perovskite ceramics prepared by traditional solid-solution method, leading to the unilateral achievement of ultrahigh Ue (10-15 J cm-3). However, the great challenge of realizing ultrahigh energy storage density with simultaneous ultrahigh efficiency still persists in ceramic capacitors.

To overcome the bottleneck in achieving comprehensive energy storage properties, optimizing polarization evolution paths from the perspective of local structure emerges as the critical avenue, particularly at high Eb and large ΔP values. Polarization and oxygen octahedral (BO6) tilt, as two types of local structural units that can be excited by external electric fields, directly and significantly govern the macroscopic polarization response process of dielectrics induced by electric fields. It is recognized that antiferroelectric supercells are coupled by antiparallel polarization and BO6 tilt, offering substantial potential for local structural regulation to realize outstanding energy storage properties18,19. Considering the recent research progresses, however, the regulation of local polarization structure has always been focused on (relaxor) ferroelectrics, lacking exploration and understanding of internal polarization in (relaxor) antiferroelectrics, let alone the meticulous design and synthesis of novel local antiferroelectric polarization landscapes. BO6 tilt can cause severe polarization hysteresis, but it can effectively delay polarization saturation4,20. The control of BO6 tilt configuration is often overlooked in dielectric energy storage, losing another key way to suppress the rapid saturation behavior of relaxor ferroelectrics and solve the large polarization hysteresis of relaxor antiferroelectrics, which have always been a major challenge in designing high-performance dielectrics, especially lead-free antiferroelectrics. If the polarization and BO6 tilt can be synergistically controlled to ingeniously construct diverse local heterostructures, polarization hysteresis is expected to be significantly suppressed while delaying polarization saturation and maintaining a large ΔP, developing high-performance dielectrics for next-generation advanced energy storage applications.

Here, we propose a hierarchical heterostructure design strategy that controls favorable polarization evolution through the synergistic regulation of polarization and BO6 tilt, aiming to enhance energy storage properties (Fig. 1)21. High-bandgap NaNbO3 (NN, tolerance factor: t = 0.967) ceramic with antiferroelectric nature is selected as the implementation target, in which antiparallel off-centering cation displacements in adjacent unit cells and BO6 distortions existed22,23. To preserve the energy storage advantages of antiferroelectrics, low-t (<1) modifiers are chosen to stabilize antiferroelectric order. Considering the solubility limitations, 10 mol% of the low-t (0.914) and nonpolar CaZrO3 (CZ) is first doped into NN to form an NN-CZ antiferroelectric matrix. This can decrease polarization displacement and enhance component disorder as much as possible to break long-range antiferroelectric polarization order, transforming the concave polarization rising path into a convex one20,24,25. However, the ordered BO6 distortion with large tilt angles can be obtained by doping CZ, which can deteriorate Pm and η despite effectively delaying polarization saturation20. To ensure polarization evolution with negligible hysteresis and a large ΔP, we introduce large-t (0.975) and high-spontaneous polarization (Ps) Bi0.5Na0.5TiO3 (BNT) into NN-CZ matrix to synthesize (1-x)(NN-CZ)-xBNT (NN-CZ-xBNT; x = 0 to 0.25) solid solutions to further localize polarization, enhance local polar distortion, and weaken BO6 order7,26,27. Such designs are desired to synthesize hierarchical heterostructures with diverse antiferroelectric nanoclusters and order-disorder BO6 tilts, thereby improving the comprehensive energy storage performance of the dielectrics.

Fig. 1: Schematic diagram of designing hierarchical heterostructures for enhancing energy storage properties.
Fig. 1: Schematic diagram of designing hierarchical heterostructures for enhancing energy storage properties.The alternative text for this image may have been generated using AI.
Full size image

a Component design strategy for designing hierarchical heterostructures21. b Designing hierarchical heterostructures to optimize polarization evolution paths in NaNbO3-based lead-free antiferroelectrics.

Results and discussion

General structure features

We first demonstrate that all the ceramics are pure perovskite structure without any secondary phase through X-ray and neutron diffraction patterns (Supplementary Fig. S2). Both in-phase and anti-phase BO6 tilts are further identified in all dielectrics, evidenced by the appearance of three superlattice peaks corresponding to (ooe)/2 and (ooo)/2 (o is odd and e is even) based on the conclusions by Glazer20,23,26,28,29. The weakened superlattice peaks with increasing BNT means the abatement of BO6 tilts and antiferroelectric nature, which can also be confirmed by the gradually flattening and decreasing current peaks (Supplementary Fig. S3), indicating the enhanced local component fluctuations. The enhanced relaxation behavior exhibiting more diffuse phase transitions and weaker temperature dependence of dielectric constant with increasing BNT can be revealed by temperature-dependent dielectric spectra (Supplementary Fig. S4). All samples show the superparaelectric state with low loss characteristic, where ultrasmall weakly coupled polarization nanoclusters exist30,31. Specifically, the temperature coefficient of capacitance (ΔCp/ΔCp,25 °C) can be significantly improved by increasing BNT, enabling the x = 0.25 ceramic to satisfy the X9R specification (−55 to 200 °C, ΔCp/ΔCp,25 °C ≤ ± 15%) for ceramic capacitors while maintaining ultralow dielectric loss (≤0.01)32,33. The above phenomena represent great potential for x = 0.25 ceramic to achieve excellent energy storage performance.

Hierarchical heterostructures

To validate our ideas, we describe the internal structure using transmission electron microscope (TEM) and selected area electron diffraction (SAED). We find striped nanodomains with weak contrast in x = 0 ceramic, which is confirmed to be incommensurate modulated antiferroelectric structures exhibiting uniform fringes with alternating widths of 5 and 6 unit cells, as well as satellite spots of (001)/5 and (001)/6 (Supplementary Fig. S5)34. Interestingly, two heterostructure regions at the micro-scale, named regions I and II (IIa and IIb), can be discovered and separated by SAED patterns in the grains of x = 0.25 (Fig. 2a–c and Supplementary Fig. S6). The elongated host lattice diffraction points along [010]c and [001]c, together with (011)/2 superlattices, can be detected in region I. The region II can be further distinguished as regions IIa and IIb by vertically elongated (001)/2 and (010)/2 superlattices, respectively. Further observation reveals that vertically intersecting striped nanodomains rather than disordered blotched nanodomains (regions IIa and IIb) can be clearly found in region I (Fig. 2d). However, blotched nanodomains can also be captured in small amounts in region I, indicating that the coexisting striped and blotched nanodomain heterostructure has been established at the mesoscale (Supplementary Fig. S7). It is well established that blotched nanodomains are an important feature for relaxors35. The emergence of vertically intersecting striped nanodomains means the disruption of long-range antiferroelectric ordering, especially in the regions showing disordered blotched domains, which also signifies the enhanced ferroelectirc distortion with increasing BNT.

Fig. 2: Hierarchical heterostructures and BO6 tilts.
Fig. 2: Hierarchical heterostructures and BO6 tilts.The alternative text for this image may have been generated using AI.
Full size image

a Heterostructure in one grain for x = 0.25 along [100]c. Yellow dashed areas are named region I, while the rest is designated as region II, which is distinguished into two regions, IIa and IIb, based on the orientation of the superlattice diffraction points. SAED patterns of regions (b) I and (c) IIa from (a). Yellow arrows, red circles and blue rectangles represent the elongated host lattice diffraction points, (011)/2, and vertically elongated (001)/2 or (010)/2 superlattice diffraction points, respectively. d Amplified domain morphologies of the marked green square area from (a). Atomic-resolution ABF-STEM images and the calculated BO6 tilts for regions (e) I and (f) II. Red, blue, and white square indicate the clockwise, anticlockwise, and no tilt of BO6, respectively. g Statistical distributions of BO6 tilt angles for regions I and II.

The designs are more intuitively reflected in the local-scale fluctuations of cation displacements and BO6 tilts. We first characterize the atomic-scale microstructure using atomic-resolution scanning transmission electron microscope (STEM) with annular bright-field (ABF) mode to study BO6 distortions of x = 0.25 (Fig. 2e-g). We identify the long-range ordering characteristic with small disturbances of strictly periodically alternating clockwise and anticlockwise BO6 tilts in region I, which can be further proved by the similar clockwise (Average tilt angle: Ac-ave = 6.43°) and anticlockwise tilt angles (Aa-ave = −6.28°) as well as symmetric distribution behavior from the statistical data (Fig. 2e, g). The ordered BO6 tilt structure is similar to that of the CZ modified NN ceramic exhibiting strong (anti)ferrodistortion characteristics20, which contributes to the emergence of (011)/2 superlattices. Disordered BO6 tilts showing irregular alternations of clockwise and anticlockwise rotation, however, can be detected in region II accompanied by randomly distributed tilt angles with a large difference (Ac-ave = 2.11° and Aa-ave = −1.39°, Fig. 2f, g). Compared to ordered BO6 tilts, the disordered BO6 tilts with largely decreased tilt angle verify the enhanced composition disorder and weakened BO6 distortion. Therefore, we have established a heterodistortion exhibiting order-disorder BO6 tilts at a local scale.

We also explore the local polarization configurations of x = 0.25 by analyzing cation displacements using high-angle annular dark-field (HAADF) STEM (Fig. 3 and Supplementary Fig. S8–9). In region I, we can observe vertically intersecting polarization nanoclusters in different directions, manifested as each antiferroelectric nanoclusters are vertically embedded with polarization regions in other directions, which form polarization interlocking structure (Fig. 3a, e and Supplementary Fig. S8). Combined with the striped nanodomains with different widths (Supplementary Fig. S7), the disturbed antiparallel polarization regions with periodicities of n = 5 to 7 demonstrate the existence of antiferroelectric nature in region I (Supplementary Fig. S8–9), contributing to the elongated host lattice diffraction points that are a series of satellite spots. In region II, we can find alternating striped polarization regions with periodicities of n = 2 along [001]c and short-range alternating striped polarization regions with multiple periodicities along [010]c. These features display fishbone polarization configuration derived from incommensurate supercells, which accounts for the appearance of (001)/2 superlattices with vertical elongation characteristic (Fig. 3c, f and Supplementary Fig. S8). The ultrafine fishbone polarization structure, coupled with disordered BO6 tilts, exhibits a relaxation characteristic of blotched domain morphologies at the mesoscale. Note that the antiferroelectric nanoclusters featuring interlocked polarization structure and fishbone polarization configuration are different from traditional nanodomains or PNRs in relaxor ferroelectrics, which typically exhibit ellipsoidal shapes free in nonpolar matrices35,36,37. The distinctive antiferroelectric nanoclusters are expected to enable large polarization fluctuations while delaying polarization saturation. Furthermore, the polarizations in region I are approximately uniformly distributed at various angles, which is related to the interlocking characteristics of the different polarization regions and cannot be found in region II (Fig. 3g). The polarization magnitudes in regions I and II are randomly distributed, revealing the polar regions embedded in the nonpolar matrix (Fig. 3b, d). The approximately equal average polarization magnitudes (Mave) and statistical distribution behaviors in regions I and II indicate that the local diverse polarization heterostructure can be formed through roughly similar polarization units arranged and combined in different directions and positions (Fig. 3g, h). To sum up, the hierarchical heterostructures, without obvious element segregation (Supplementary Fig. S10), signifying at the micro-scale (grains), mesoscale (domains), and local scale (BO6 tilts and polarizations), are successfully established in x = 0.25 ceramic by synergistically controlling polarization and BO6 tilt.

Fig. 3: Local polarization structure.
Fig. 3: Local polarization structure.The alternative text for this image may have been generated using AI.
Full size image

Atomic-resolution HAADF-STEM image of the x = 0.25 ceramic with the corresponding (a) cation displacement vectors showing polarization interlocking structure and (b) polarization magnitudes for region I. Atomic-resolution HAADF-STEM image of the x = 0.25 ceramic with the corresponding (c) cation displacement vectors showing fishbone polarization configuration and (d) polarization magnitudes for region II. Two-dimensional contours of polarization angles for regions (e) I and (f) II. The color bars are the same as those in (a) and (c). Statistical distributions of (g) polarization angles and (h) polarization magnitudes for regions I and II.

Energy storage performance

To explore the full potential of the synthesized NN-CZ-xBNT ceramics for applications, we investigate their energy storage properties under electric fields until breakdown from P-E loops (Fig. 4a and Supplementary Figs. S11–12). The Ue reaches a maximum of 21.0 J cm−3 under 90 kV mm−1 for x = 0.25 with hierarchical heterostructures exhibiting the desired polarization evolution path, which is approximately four times the energy density (Ue = 5.6 J cm−3) of x = 0 ceramic with long-range incommensurate modulated antiferroelectric structure, especially with the large improvement of η from 77% to 90%. In general, dielectrics with large energy density but low efficiency will lead to severe energy dissipation and subsequent thermal effect, significantly shortening the service life of the capacitors4,12. Compared to other samples, it can be noted that the η of x = 0.25 ceramic presents the minimum fluctuation during the continuous increase of electric field and remains above 90% until breakdown. Specifically, in comparison with other bulk ceramic dielectrics including lead-free and lead-based systems, x = 0.25 ceramic exhibits significant superiorities for overcoming the bottleneck of simultaneously achieving ultrahigh Ue (≥20 J cm-3) along with ultrahigh η (≥ 90%) (Fig. 4b, Supplementary Fig. S13, and Table S1)7,14,19,38,39,40,41,42, making a breakthrough progress in comprehensive energy storage performance.

Fig. 4: Energy storage and charge-discharge performance of the NN-CZ-xBNT ceramics.
Fig. 4: Energy storage and charge-discharge performance of the NN-CZ-xBNT ceramics.The alternative text for this image may have been generated using AI.
Full size image

a Energy density and efficiency of the NN-CZ-xBNT ceramics. b Comparisons of energy density between our ceramic and other reported lead-free bulk ceramics with η ≥ 90% and Ue ≥ 1.0 J cm-3 (AN: AgNbO3, BF: BiFeO3, BKT: Bi0.5K0.5TiO3, BT: BaTiO3, KNN: (K,Na)NbO3, ST: SrTiO3). The references are provided in Supplementary Table S1. c Weibull distribution analysis of the breakdown fields of the NN-CZ-xBNT ceramics. d Temperature-dependent energy storage performance of x = 0.25 at an electric field of 60 kV mm-1. e Time-dependent overdamped discharge energy density of x = 0.25. f Charge-discharge performance under different electric fields of x = 0.25.

Enhancement mechanisms of capacitive energy storage

The excellent capacitive energy storage should be attributed to the enhanced Eb, increased polarization fluctuation, and delayed polarization saturation behaviors with minimal hysteresis. The statistical Eb derived from Weibull distribution is 96 kV mm-1 for x = 0.25, which is more than twice that (45 kV mm−1) for x = 0 ceramic (Fig. 4c). The Weibull modulus β values of all ceramics are larger than 10, demonstrating the high sample quality and high reliability. According to the exponential decay relationship between Eb and average grain size Ga43, the decreased Ga from 3.18 (x = 0) to 2.05 μm (x = 0.25) serves as the vital external contribution to enhance Eb by increasing the density of high-resistance grain boundaries (Supplementary Fig. S14), which can build depletion space charge layers acting as barriers for the migration of charge carriers. Furthermore, thermal breakdown strength can be improved by the less heat generation caused by low dielectric loss, small polarization hysteresis, and high η. Compared to energy storage ceramics, it is widely recognized that higher Ue can be universally obtained in thin films through achieved higher Eb values2. The x = 0.25 ceramic exhibits outstanding breakdown resistance strength and a larger Eb than that of the most reported energy storage ceramics4,15, which can build a bridge to achieve high energy storage properties closer to thin films.

The polarization fluctuation, saturation, and hysteresis behaviors can be effectively controlled by synthesizing hierarchical heterostructures to optimize the polarization evolution pathways. Firstly, the large Pm can be stimulated by the striped nanodomains, while the blotched nanodomains induce small Pr44,45. In addition, the presence of blotched nanodomains within the striped ones reduces stress during domain switching, leading to the enhanced polarization texture along high electric fields and yielding large Pm4. Secondly, the polarization interlocking structure exhibits remarkable capability in simultaneously enhancing Pm, reducing Pr, and delaying polarization saturation with minimal hysteresis. The anomalous increase in polarization with increasing electric field should be attributed to the gradual release of polarization interlock driven by high electric field (Supplementary Figs. S11 and S15–16), which accelerates more polarization units to align along the direction of electric field and significantly enhances Pm, conquering the inverse correlation between the Pm and Eb46. Moreover, the presence of antiferroelectric nanoclusters with interlocking characteristic delays polarization saturation during charging process. This structure also provides a polarization restoring force after removal of the electric field, facilitating a quick and efficient return to the initial state (Supplementary Fig. S16). The optimized polarization recovery path can largely eliminate the hysteresis loss caused by polarization rotation and the (diffuse) antiferroelectric-ferroelectric phase transition in (relaxor) antiferroelectrics during discharging progress, thereby significantly reducing Pr and improving η (Supplementary Figs. S11 and S16–17). Thirdly, fishbone polarization structure in region II can also contribute to high Pm and small Pr, but its effectiveness in delaying polarization saturation is inferior to that of polarization interlocking structure. This limitation can be proved by the almost disappeared satellite spots perpendicular to the (010)/2 superlattice points under low electric fields (Supplementary Fig. S16). Lastly, the heterostructure of order-disorder BO6 tilts can absorb partial electric energy and provide excess resistance for forming long-range polarizatin order under electric fields4,20, delaying polarization saturation. The disordered BO6 distortion with small tilt angles effectively compensates for the deficiency of ordered oxygen distortion with large tilt angles, which can enhance Pm and decrease Pr4,20, thereby achieving a good balance between polarization fluctuation and saturation regulation. Consequently, an optimal polarization evolution path for excellent comprehensive energy storage performance can be achieved in hierarchical-heterostructure relaxor antiferroelectrics.

Stability and charge-discharge properties

Stability and charge-discharge characteristics are also the important application index for dielectric capacitors. The x = 0.25 ceramic shows good stability over a wide temperature range (25 to 100 °C) with Ue variation of <4% and η variation of <2% under 60 kV mm-1, which is related to the temperature-insensitive dielectric constant and phase structure (Fig. 4d and Supplementary Fig. S18–19). The excellent frequency stability with Ue variation of <7% and η variation of <4% can also be obtained at 60 kV mm-1 from 1 to 200 Hz (Supplementary Figs. S18 and S20). The increase and decrease in polarization with increasing temperature and frequency, respectively, should be mainly attributed to the polarization interlocking structure, which is easier to unlock at high temperatures and more difficult to unlock at high frequencies (Supplementary Fig. S21). Furthermore, the cyclic fatigue stability of x = 0.25 ceramic under a electric field of 60 kV mm−1 is also considered (Supplementary Fig. S20). After 106 consecutive electrical cycling tests, the variations of Ue and η for the x = 0.25 ceramic are less than 2% and 1%, respectively, demonstrating the outstanding fatigue stability. We can also discover the regular underdamped and overdamped discharge waveforms in x = 0.25 ceramic under the electric fiels from 10 to 40 kV mm−1 (Supplementary Fig. S22). The PD and discharge energy density UD increase with increasing electric field, which reach the maximum of 460 MW cm−3 and 7.0 J cm−3 at 40 kV mm−1, respectively (Fig. 4e, f). The ultrahigh UD can be released by 90% in a very short time of 32 ns, making a good application prospect for advanced capacitors (Supplementary Table S2).

In summary, we develop hierarchical heterostructures in NaNbO3-based lead-free antiferroelectrics by synergistically controlling cation displacements and BO6 tilts to form antiferroelectric nanoclusters with polarization interlocking structure and fishbone polarization configuration, as well as order-disorder BO6 tilts at local scale. The hierarchical heterostructures can effectively optimize polarization evolution pathways to increase polarization fluctuation and delay polarization saturation with minimal hysteresis, achieving a large improvement of overall energy storage performance in ceramic capacitors. The strategy should be applicable to other material systems such as thin films and composites. Generally, this strategy can be extended to other functionalities involving the development of materials through multi-scale heterostructural regulation.

Methods

Sample synthesis

A series of (1-x)(0.9NaNbO3-0.1CaZrO3)-xBi0.5Na0.5TiO3 (abbreviated as NN-CZ-xBNT; x = 0 to 0.25) ceramics were synthesized by a conventional solid-state reaction method. High-purity Na2CO3 (Aladdin, 99.99%), Bi2O3 (Aladdin, 99.99%), CaCO3 (Aladdin, 99.9%), Nb2O5 (Aladdin, 99.9%), ZrO2 (Aladdin, 99.99%), and TiO2 (Aladdin, 99.8%) were used as the raw materials, and 0.5 mol% MnO2 (Aladdin, 99.0%) was used as a sintering aid. The dried raw materials were mixed at the designed stoichiometric ratios by planetary ball milling with alcohol for 24 h and then calcined twice at 800 °C for 5 h. Subsequently, the calcined powders were remixed with 0.5 wt% PVB binders through high-energy ball milling under 700 r min-1 for 15 h. The mixed powders were uniaxially pressed into pellets with diameters of 10 mm under 400 MPa. After being covered with sacrificial powders of the same compositions, the pellets were sintered at 1200–1390 °C in closed double crucibles for 2 h at a heating rate of 5 °C min−1 after excluding PVB binders at 550 °C for 2 h. The surface of ceramics was carefully polished and coated with silver electrodes, which were fired at 550 °C for 30 min for measuring electrical properties.

Structure characterizations

The phase structures of the ceramic powders were detected using an X-ray diffractometer (XRD, Smartlab, Rigaku) with Co target (λ = 1.79 Å). The room-temperature neutron total scattering data were collected at Nanoscale-Ordered Materials Diffractometer (NOMAD) in the Spallation Neutron Source (SNS), Oak Ridge National Laboratory. The grain morphologies were detected through a scanning electron microscope (SEM, LEO1530, ZEISS SUPRA 55), and grain size was analyzed by Nano Measure software. The finely polished ceramics below 40 µm were thinned using an ion milling system (PIPS, Model 691, Gatan Inc., Pleasanton) with a liquid nitrogen-cooled stage for transmission electron microscope measurement. Domain morphologies, selected area electron diffraction (SAED), and element distribution analysis were performed on a field-emission transmission electron microscope (TEM, JEM-2100, JEOL, Japan) with an accelerating voltage of 200 kV. The atomic-scale HAADF-STEM and ABF-STEM images were carried out on Cs-corrected Hitachi HF5000 microscope. The microscope settings were: probe size in UHR mode and convergence semi-angle of 20 mrad, and collection semi-angle of 60–320 mrad (HAADF) and 11–22 mrad (ABF). The images were acquired under conditions of fast scanning and cross-correlation summing of multiple frames to minimize sample drift. The atomic column positions at picometer-precision fitting were performed using the MATLAB code for calculating the polarization vectors with different polarization magnitudes and polarization angles, as well as oxygen octahedral tilts.

Electrical property characterizations

The room-temperature, temperature- and frequency-dependent P-E loops as well as room-temperature J-E loops of the sintered ceramics with a thickness of about 35-60 μm and an electrode diameter of about 0.8-1.0 mm were tested using a ferroelectric analyzer (aix ACCT, TF Analyzer 1000). Temperature-dependent capacitance and dielectric spectra were measured using a precision LCR meter (Keysight E4990A). The charge-discharge performance under different electric fields was characterized by a commercial charge-discharge platform (CFD-003, Gogo Instruments Technology).

Weibull distribution

The Weibull experiments of the NN-CZ-xBNT ceramics can be calculated by the following equations:

$${P}_{i}=i/(n+1)$$
(1)
$${X}_{i}={{\mathrm{ln}}}\left({E}_{i}\right)$$
(2)
$${Y}_{i}={{{\mathrm{ln}}}}({{{\mathrm{ln}}}}(1/(1-{P}_{i})))$$
(3)

where Ei is the specific breakdown electric field of each sample, i means the ordinal number of each sample, and n is the total amount of ceramic for each sample (n = 10 in this work). The intersection of the fitted line and Yi = 0 should be the theoretical Eb value. Weibull parameter β evaluates the distribution of Ei.