Introduction

Dielectric energy storage capacitors are ubiquitous in modern electronics. They are used primarily in pulsed power systems because of the fast charging/discharging speed and ultrahigh power density. Emerging products related to renewable energy, such as electric vehicles, grid-connected photovoltaic (or wind and water) power generation, and underground oil/gas exploration, have created immediate requirements for high-performance ceramic capacitors1,2. A high recoverable energy storage density (Wrec), efficiency (η), and improved temperature stability are hot topics to estimate the industrial applicability of ceramic materials. A large maximum polarization (Pmax), low remnant polarization (Pr), and high breakdown field (Eb) are sought after to attain a greater Wrec and η. Some approaches, such as domain engineering3,4, layered structure design5, grain-size engineering6, high entropy, and defect/doping engineering2,7,8,9,10 have been investigated to achieve this “dual high” condition.

Dielectric capacitors for energy-storage applications can be classified as films11, polymers12, and ceramics-based branches1,3,7,13. Among them, ceramic capacitors score a success by the advantages of thermal stability and mechanical properties. Most current research on energy storage capacitors is concentrated on dielectric materials with perovskite structures, like NaNbO3, Bi0.5Na0.5TiO3, BiFeO3 or lead-based (such as (Pb,La)(Zr,Ti)O3) ceramics4,14,15,16,17,18. Whereas, a higher Wrec (typically 5–20 J cm−3) and η (>80 %) are achieved among bulk ceramics or multilayer devices. However, the volatility, toxicity, and easily reducible nature of some elements (Fe, Bi, Pb, Na, etc) have severely hindered their potential applications in base metal electrode devices19. As the second-largest category of ferroelectrics, tetragonal tungsten bronze structure (TTBs) ceramics are widely considered due to their excellent photoelectric, nonlinear optical, and pyroelectric properties20,21. However, their dielectric energy storage performance is often overlooked because of the low Pmax, poor Eb, and slow dielectric response related to the high sintering temperature, abnormal grain growth, and strong ferroelectricity19,22.

The TTBs has a general chemical formula of (A1)2(A2)4(C)4(B1)2(B2)8O30, where bivalent cations can fully or partially occupy the A site. The B position is always filled by high valence cations (such as Nb5+ and W6+) and connected with the BO6 octahedron as the basic units. The C site is usually empty because of the narrow gap. Existing reports on TTBs-based energy storage generally use the ion doping (A or B site) method to cause lattice structural distortion and modulated relaxor behavior22. For instance, Sr0.425La0.15Ba0.425Nb1.4Ta0.6O6 ceramics with Wrec = 5.895 J cm−3 and η = 85.37 %20, Sr2NaNb3.5Ta1.5O15 with Wrec = 3.99 J cm−3 and η = 91.7 %23, Sr1.82Gd0.12NaNb5O15 with Wrec = 2.37 J/cm−3, η = 94.4 %24, and even some recently reported works on Gd0.03Ba0.47Sr0.455Sm0.02Nb2O6 with Wrec = 9 J cm−3 and η = 84 % and (Sr0.2Ba0.2Pb0.2La0.2Na0.2)Nb2O6 with Wrec = 11 J cm−3 and η = 81.9 %21,25. A lower Eb (generally below 700 kV cm−1) is a key feature of the TTBs-based ceramics concluded from these reports. Despite the significant advancements in these researches, the energy storage performance of TTBs ceramics still lags behind that of perovskite materials.

When sintering composite ceramics, the second phase can play a “pinning effect”, thus significantly inhibiting grain growth26. The reduced grain size and formed segregation phases are conducive to improve the mechanical properties, microstructure stability, and chemical stability. Some oxide systems may derive unique functional properties that enhance the breakdown strength by scattering electron carriers26. This design strategy is common in structural ceramics27. While, it gives us the inspiration that the nonconductive second phase in TTBs ceramics may assist in optimizing the composition, structure, and dielectric properties, thus open a window for future expansion of high-performance energy storage materials.

Herein, we designed a high configurational mixed phase SrBaTiNb2O9 (BSTN) ceramic via componential and microstructural engineering. The perovskite Ba1-xSrxTiO3 (BST) phase is formed in the interstitial positions of the matrix phase TTBs Ba1-ySryNb2O6 (BSN) during solidification, which distributes primarily at the edge site of the BSN grains. Introducing Ta5+ in BSTN (BSTN-xTa) allows tuning the relaxation characteristics and promotes the formation of weakly coupled polar nanoregions (PNRs) in the ceramics. An ultrahigh energy density of 12.2 J cm−3 and a remarkable η of 89.5 % at an electric field of 950 kV cm−1 was achieved, surpassing previously reported values for TTBs ceramics. This work offers a route to explore new kind of dielectric materials that are expected to be useful to energy storage devices.

Results

Materials design and energy storage properties

Figure 1a illustrates the unipolar polarization hysteresis (P-E) loops for BSN, BSTN, BSTN-0.1Ta, and BSTN-0.4Ta at the breakdown strength and a frequency of 1 Hz. The corresponding energy storage performance from the P-E loops are shown in Fig. 1b. The polarizability decreases monotonously (under the same electric filed) and the breakdown strength enhances distinctly after adding the BST component in BSN and doping with Ta5+. The Wrec increases from 1.69 to 6.54 J cm−3 from BSN to BSTN, reaching the maximal value for BSTN-0.1Ta (12.20 J cm−3) and then decreasing to 5.95 J cm−3 in BSTN-0.4Ta. Apparently, pure BSN exhibits a typical ferroelectric characteristic with limited electric field tolerance. The compound system of BSTN has a reduced Pr owing to the weak dielectric nonlinearity of the BST component. The Ta5+ doping achieves much slimmer P-E loops and a substantially reduced Pr (improved η to around 89 % for BSTN-0.1Ta/0.4Ta), indicating that substituting Ta5+ for Nb5+ further disrupts the domain ordering and facilitates structural relaxation. However, excessive Ta5+ doping will severely suppress the Wrec because of the weak polarization intensity of Ta ions. Dielectric materials with strong dielectric nonlinearity always lead to a strongly attenuated permittivity and lower stored energy under the operating voltage. By comparison, near linear polarization behaviors sacrifice the Pmax under low electric fields, but a superior Wrec can be acquired from the steadily increasing polarization under a high electric field tolerance. Consequently, a comprehensively optimized energy storage performance may be achieved in a well-balanced component (BSTN-0.1Ta). The P-E loops and Wrec/η fluctuation of BSTN, BSTN-0.1Ta and BSTN-0.4Ta under various electric fields are given in Figs. 1c, d and S1. The designed BSTN-0.1Ta ceramics achieve an ultrahigh Eb of ~950 kV cm−1 with an extraordinary Wrec of 12.2 J cm−3, and a very high efficiency of 89.5 % (Fig. 1d). This value is much higher than state-of-the-art TTBs-based ceramics and even comparable to that of perovskite-structured systems (Fig. 1e)9,15,17,20,21,24,25,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52.

Fig. 1: Energy storage performance and structural analysis of ceramics.
figure 1

a The unipolar P-E loops of BSN, BSTN, BSTN-0.1Ta, and BSTN-0.4Ta ceramics; (b) Wrec and η values derived from the P-E loops; (c, d) The P-E loops, Wrec and η values of BSTN-0.1Ta ceramics under different electric fields; (e) Comparison of the Wrec and η with TTBs-based dielectric ceramics; (f, f1) XRD patterns of series ceramics at room temperature with enlarged views of the (311) and (002) peaks; (g) Raman spectra of series ceramics at room temperature; (h) XRD refinement of the BSTN-0.1Ta ceramics; (i) TEM image of BSTN-0.1Ta ceramics and SAED patterns take along [110]c from BST portion and [100]c from BSN portion.

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Structure, local composition, and mechanism analysis

The crystal structures of BSN, BSTN, BSTN-0.1Ta, and BSTN-0.4Ta ceramics were examined using XRD and Raman spectra to better understand how the energy storage performance develops through the combination of the BST and altering the B-site composition, as shown in Fig. 1f, g. The XRD pattern of BSN exhibits a pure tungsten bronze structure without an impurity. With increasing Sr, Ba, and Ti concentrations, all the patterns (BSTN, BSTN-0.1Ta, and BSTN-0.4Ta) are attributed to a mixture of the tungsten bronze phase and the pseudo cubic perovskite phase, indicating that excessive Sr, Ba, Ti could not successfully enter the BSN matrix to form a single-phase solid solution. The magnified patterns around 32 ° and 46 ° are presented in Fig. 1f2.Tthe diffraction peaks shift to lower 2θ values from BSN to BSTN, BSTN-0.1Ta, and BSTN-0.4Ta. This shift is attributed to differences of the electronegativity between Ta5+ (1.51 Å) and Nb5+ (1.59 Å), leading to a weaker covalent bond20,53.

To further confirm the structural evolution, XRD refinement is performed based on the PDF Card #: 70-3628 and PDF Card #: 39-0265 for all the samples, as given in Fig. 1h and Fig. S2d–f (refined lattice parameters are listed in Table S2, Supplementary Information). Good agreement between the observed and calculated patterns can be obtained with an Rwp < 15 %, indicating the coexistence of two phases belong to Pm3m (cubic crystal system) and P4bm (tetragonal crystal system) space groups in the ceramics. The decreasing tendency of c/a in tetragonal BSN phase points out a suppressed tetragonality with the adding of second phase and doping of Ta. The relaxor behavior of ferroelectrics is always accompanied by a weakened tetragonality.

Raman spectra of the ceramics is fitted basing on the presence of two phases, BSN and BST. The typical vibration modes in these two phases have been denoted in Fig. 1g, and the fitted vibration patterns upon the sample BSTN-0.4Ta are displayed in Fig. S3. Comparing with the pure BSN, new peaks (around 200–310 cm−1 and 500–600 cm−1) are detected in the BSTN and BSTN-Ta samples. The peaks around 200–310 cm−1 correspond to the A1(TO)/E(TO + LO) vibrational modes of the Ti-O bond in BST54,55, and the peaks at 523 and 576 cm−1 correspond to the A1(TO3) and E(TO4) acoustic modes of O-Ti-O along the c-axis within the ab-planes. The peaks below 200 cm−1 are attributed to the displacement of A-site ions in BSN. The v5 mode at around 250 cm−1 is associated with the O-B-O (B=Nb/Ta) bending vibrations and the v2 mode at 630 cm−1 and is related to the B-O stretching vibrations in the NbO6 octahedra24,56. Doping of Ta gives rise to the blueshift and widening of the v2 peak. This matches the mechanism that replacing Nb5+ with Ta5+ weakens the B-O covalent bond and increases the bond length. Peak broadening is caused primarily by distortions in the BO6 octahedra and the breaking of the long-range order. This phenomenon is the structural origin of the low Pr and high-energy storage efficiency.

The microstructures of the samples were examined by SEM (Fig. 2, the grain size distribution is inserted) and TEM (Fig. 1i) to verify the feasibility of the proposed composition design and second phase implanting. Pure BSN displays columnar-shaped grains, similar to that reported in the literatures. The crystals trend to grow along the [001] direction for TTBs-based ceramics40,57. After the adding of BST component, the grain size shrinks sharply from ~2.95 to ~1.62 μm and the amount of spherical-shaped grains have significantly increased. It can be interpreted that the perovskite BST will inhibit the grain growth of BSN. A small amount of Ta doping has further suppressed the grain growth and limited the grain size to ~1.38 μm and ~1.21 μm for BSTN-0.1Ta and BSTN-0.4Ta, respectively. Both the perovskite phase precipitation and Ta5+ doping can significantly inhibit grain growth and increase the proportion of equiaxed grains in the BSTN ceramics. This could be explained by the B-site cation substitution and formation of distorted TaO6 octahedra. Tantalum oxide has a refractory nature, which is more thermodynamically stable than the Niobium oxide. So, the participation of Ta in BSTN will prevent the movement of the grain boundaries during the sintering process, and shrink the grain size58,59. Moreover, component segregation may happen upon the grain boundaries, which has hindered grain coarsening from both energetic and kinetic perspectives. For confirming the uniformity among different technology, morphologies of the thin film samples (TC-samples, BSTN-0.1Ta) and ceramic disks after hot corrosion (BSTN-0.1Ta) are provided in Fig. 2e, f, where almost the same grain feature and size distribution are presented. It illustrates that TC-samples, obtained by tape casting method in this study, will not lead to a grain texture on the surface. The density of the ceramic disks and TC-samples was 6.28 g cm−3 and 6.19 g cm−3, respectively, indicating that excellent densification can also be obtained by the tape casting method.

Fig. 2: Local morphologies of ceramics.
figure 2

a–d SEM images and grain size distributions of BSN, BSTN, BSTN-0.1Ta, and BSTN-0.4Ta ceramics; (e, f) TC-sample and hot corrosive sample of BSTN-0.1Ta.

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The TEM images of the BSTN-0.1Ta ceramic are shown in Figs. 1i1 and S4, S5. The ceramic exhibits heterogeneous microstructure, part of the grains have a core-shell architecture where the second phase (BST) distributing at the shell position and BSN locating in the core. Part of the second phase forms individual grains and mix in the material. The STEM-EDS elemental mapping in Figs. S4 and S5 show that Sr and Ti are rich in the second phase (BST, marked by red dashed circles in Fig. S4). An enrichment of Ta element is observed in the BSN (marked by blue dashed circles in Fig. S4). The selected area electron diffraction (SAED) patterns collected on the BST and BSN portion reveal basic reflections of perovskite structure along the [110] zone axis (Fig. 1i2) and tetragonal tungsten bronze structure along the [100] zone axis (Fig. 1i3). The weak satellite reflections (marked by red arrows in Fig. 1i) indicate an incommensurate modulation in both phases, further proving a facilitated structural relaxation and crystal disorder. In sum, compositional inhomogeneity can be confirmed in the ceramics, which typically induces local structure disorder and interferes with the long-range ferroelectric order, as well as stimulates enhanced relaxor behavior. Benefiting from the aforementioned composition design, the reduced gain size and nonconductive second phase (BST) into the BSTN-Ta ceramics may be the main structural basis and inducement of high breakdown strength.

The atomic-scale local structure of BSTN-0.1Ta was further probed via high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) (Fig. 3) at randomly selected grain boundaries. The HAADF-STEM images verify the core-shell structure of the ceramics, where perovskite BST distributing on the edge of the TTBs BSN grains. They are linked in the form of lattice transition, with no clear interval or amorphous layer between the two phases. This eutectic precipitation phenomenon has been found and mentioned in some metallic and ceramic systems26,27,60,61. Strengthening, toughening, and electric breakdown behavior of ceramics could be re-established by the precipitated second nanophase in ceramic system. For electrostatic energy storage ceramics, the pursuit of simultaneously high polarization, high breakdown strength and low dielectric loss is crucial. As a typical ferroelectric ceramic, the strong polarization of TTBs BSN is usually accompanied with a deteriorated breakdown strength. Here, the interstitial filling and highly insulating second phase (paraelectric state BST) in the main matrix will lead to a higher transport barrier of carriers under an applied electric field and increase the energy storage density due to the escalated polarization under a high electric field.

Fig. 3: Local compositional inhomogeneity of BSTN-Ta ceramics.
figure 3

a Atomic-resolution HAADF-STEM image along [110]c and [001]c of TTBs in BSTN-0.1Ta sample; (b) EDS elemental mapping from (a2); (c, d) Displacement of B-site cations corresponding to different polarization directions in BSN and BST along [110]c.

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The atomic-scaled EDS elemental mapping (Fig. 3b) presents a similar result as the STEM-EDS data (Figs. S4 and S5), where the Sr and Ti are rich in the boundary positions, Nb and Ta are concentrated in the core. The displacement of B-site cations plays a critical role in producing polarization within both the TTBs BSN and perovskite BST. The domain structure and size related to the B-site displacement impact the local dipole moment, thus influence the local polarization and formation of PNRs. The domain structures are determined by marking the B-site (Ti4+ for BST and Nb5+/Ta5+ for BSN-Ta) polarization vectors, as presented in Fig. 3c, d. The PNRs (1–3 nm) with diverse polarization directions are observed along the [110] directions of TTBs BSN-0.1Ta, indicating a multiphasic coexistence of the T and R phases (Fig. 3c)21. The enlarged schematic diagrams on the right side (Fig. 3c2) depict two representative polarization configurations of Nb5+/Ta5+. A wider polarization angle distribution is found in the BST portions along the [110] directions (Fig. 3d), corresponding to a pseudo cubic structure with the coexistence of R, T, and C phases62. The disordered polarization and distribution, chemical inhomogeneity, and insulating boundary layers provide the fundamental structural origin of the dielectric relaxor (large Pmax, negligible Pr, and high η), high Eb, and superior energy storage performance.

The apparent domain structures in pure BSN and BSTN-0.1Ta are observed by HRTEM and displayed in Fig. S6 (Supplementary Information). Distinct domain structures with a size of several tens of nanometers could be found in pure TTBs crystals (Fig. S6a). However, no visible domains were detected in BSTN-0.1Ta under the resolution of HRTEM. Piezoresponse force microscopy (PFM) is used to evaluate the dynamic response of domains in the ceramics. The out-of-plane phase images of BSN and BSTN-0.1Ta are compared after tip voltages of +12 and −12 V within a 3 × 3 μm2 area (Fig. 4a, b). The contrast evolution indicates that domain switching occurs faster in the BSTN-0.1Ta, with a relaxation time of <3 min. The room temperature ferroelectricity of pure BSN is reaffirmed as the signal contrast barely changes within 9 min. The decreased domain size and fast back switching favor an easier polarization reorientation and benefit a slimmer P–E loop.

Fig. 4: Phase-field simulation, breakdown strength and impedance spectrum analysis of ceramics.
figure 4

a, b The out of plane phase image of pure BSN (a) and BSTN-0.1Ta (b) after a writing voltage of ±12 V; (c–e) Phase-field simulations on dielectric breakdown of the BSN (c) and BSTN-Ta (d), corresponding nominal electric field-charge-density relation (e); (f) Weibull distribution of experimental breakdown strength; (g) Impedance spectra of BSTN-0.1Ta ceramics at a temperature region of 460–560 °C; (h) The fitted activation energy of grains and grain boundaries.

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Phase-field simulations and cycling stability

Dielectric breakdowns of both BSN and BSTN-Ta are pre-evaluated via phase-field simulations to determine the benefits of the multiscale optimization strategy, especially the mixture phase and grain size modulation. During propagation, the breakdown path of BSTN-Ta ceramics passes across the insulating BST layers or grains and dissipates more energy, leading to a greater breakdown strength (Fig. 4c, d). The largest nominal breakdown strength of BSTN-Ta ceramics is nearly a 170 % increment over BSN, supporting the introduction of insulating BST shells and enhanced grain boundaries to significantly improve the Eb of ceramics (Fig. 4e). The statistical Eb of these two samples was also derived from the standard Weibull distribution (Fig. 4f). The calculated data are around 330 and 980 kV cm−1 for BSN and BSTN-0.1Ta, respectively, consistent with the simulation results. The temperature-dependent impedance measurements were conducted for all samples to further verify the carrier transport dynamics into the ceramics. The Cole-Cole plots of the electrical impedance are shown in Figs. 4g and S7 (Supplementary Information). Two R–C elements are set as an equivalent circuit to fit the spectra. The activation energy (Ea) of the grains and grain boundaries are represented in Fig. 4h. Overall, the Ea of the grain boundaries is higher than that of the grains, confirming that grain boundaries still dominate the ceramics’ resistance. Both Ea values for the grain boundaries and grains exhibit a rising tendency either from the BST combination or Ta doping. A more significant optimization occurs in the grain boundaries or shells of the ceramics due to the lower conductivity of the pseudo cubic BST and carrier transportation barrier caused by lattice distortion. The maximal Ea in the Ta doping BSTN is an essential factor in uplifting the breakdown strength of the samples.

The initial capacity of the energy storage devices and temperature stability play vital roles in practical applications. Fig. S8 illustrates the temperature-dependent dielectric permittivity (εr) and loss tangent (tan δ) of the ceramics under various frequencies. The pure BSN ceramic has sharp dielectric peaks and significant dielectric loss (Fig. S8a). The broadening Tm peaks (temperature corresponding to maximum εr) and shifting to higher temperatures for greater frequencies indicates the relaxor behaviors of the BSTN by excessively adding Sr, Ba, and Ti and embedding of the BST second phase (Fig. S8b). The Tm peaks further move to a temperature below −100 °C in BSTN-0.1Ta/0.4Ta, inferring the apparent relaxation behavior at room temperature in the samples. The dielectric loss curves of BSTN-0.1Ta/0.4Ta are flat in the temperature range from −100 to 150 °C, with a value <0.2 % (1 kHz). Thereby, introducing Ta5+ and the resulting ionic disorder and chemical inhomogeneity in BSN can further destroy the long-range-ordered domains and favor easier polarization reorientation. This agrees with the variations in the P-E loops in Fig. 1a, where a minimal Pr and maximal η are obtained in the BSTN-0.1Ta/0.4Ta ceramics.

From the perspective of P-E loop variations, BSTN-0.1Ta exhibits excellent stability against temperature, frequency, and fatigue (Figs. 5a–c and S9). Over a temperature range from 20 to 160 °C at 600 kV cm−1 and 1 Hz, there are Wrec variations <0.5 J cm−3 and an η degradation <5 % (Fig. 5a). In the operating frequency window of 0.01–100 Hz, Wrec remains stable at 5.5 ± 0.1 J cm−3, and η remains consistent at 89.5 ± 1 % (Fig. 5b). Moreover, this ceramic exhibits an impressive fatigue resistance ability. After being subjected to up to 106 cycles, a negligible degradation of η and even an optimized Wrec are obtained (Fig. 5c).

Fig. 5: Stability of energy storage performance of BSTN-0.1Ta ceramics.
figure 5

a–c Wrec and η of BSTN-0.1Ta ceramics at different temperature (a), frequencies (b), and cycle numbers (c); (d, e) The overdamped discharge and underdamped discharge curves of BSTN-0.1Ta ceramics at 150–500 kV cm−1 (the Wdis as a function of time, CD, PD values as a function of electric field are inserted).

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The energy discharge behavior (overdamped discharge) of the pulsed discharge electric current-time curves as functions of the applied voltage are shown in Fig. 5d. The integral Wdis curve is inserted in Fig. 5d, with an ultrafast t0.9 of 20.7 ns. This short discharging time is promising for pulsed power capacitors. The temperature-dependent overdamped discharging curves from 20 to 180 °C and Wdis fluctuation (<15 %) reflects a superior temperature stability of the ceramics under actual working conditions (Fig. S9d, e). The underdamped discharge current density curve exhibits a uniform waveform shape (Fig. 5e). The calculated current density (CD) and power density (PD) are inserted, with values up to 730 A cm−2 and 180 MW cm−3, indicating good discharge capabilities of the ceramic. The comprehensive performance indicates that BSTN-0.1Ta ceramics are a suitable candidate for pulse dielectric capacitors.

Discussion

The TTBs BSN ceramic is a suitable matrix for regulating relaxation ferroelectrics in high-performance energy storage devices. An energy density of 12.2 J cm−3 with an efficiency of 89.5 % was achieved in the BSTN-0.1Ta ceramic via multi-strategy design of second phase precipitation, core-shell structural configuration, B-site substitution, and the consequent size effect and high entropy state. Atomic-scale polarization and elements mapping revealed that weak coupling PNRs and chemical inhomogeneity are successfully embedded in the BSTN-0.1Ta matrix, acting as a fundamental origin for the large Wrec and η. Notably, the BSTN-0.1Ta ceramic exhibits excellent thermal stability (20–160 °C), fatigue resistance (>106 cycles), power density (180 MW cm−3), and an ultrafast discharge rate (t0.9 = 20.7 ns). This work is an innovative exploration beyond the extensively studied perovskite-structured ferroelectrics and provides a promising candidate for energy storage performance based on the TTBs groups.

Methods

Material preparation

Sr0.5Ba0.5Nb2O6, SrBaTiNb2O9, SrBaTiNb1.9Ta0.1O9, SrBaTiNb1.6Ta0.4O9 (abbreviated as BSN, BSTN, BSTN-0.1Ta, and BSTN-0.4Ta) ceramics were prepared by a conventional solid state method using BaCO3 (99.95 %), SrCO3 (99.9 %), TiO2 (99.9 %), Nb2O5 (99.9 %), and Ta2O5 (99.99 %) as raw materials. The raw materials were weighed in stoichiometric ratio and mixed by a ball milling process for 12 h. These slurries were then dried and calcined at 1100 °C for 2 h. Then, the powders were dispersed again by a ball milling. After drying in air, the powders were mixed with polyvinyl alcohol (PVA) solution, and pressed into disks with a diameter of 10 mm under a pressure of 12 MPa. Finally, the ceramic disks were sintered in air at 1350 °C for 3 h (with a heating rate of 10 °C min−1) and cooled down with a temperature rate of 2 °C min−1 from 1350 ~ 1200 °C, and then followed a furnace cooling. The thinner ceramic film samples (TC-samples) were prepared via tape casting method. The weighed powders with dispersant, binder, and plasticizer were rolled using zirconia balls for 24 h. Continuous ceramic tapes with a thickness of approximately 70 µm were fabricated by a roll-to-roll process on a tape casting machine (CMD-S1.7/D/4.OH/3-778, Yasui Seiki Co., Japan). The TC-samples were then burned out in air at 600 °C for 3 h to remove the binder, and subsequently sintered following the same process that of the disks. Silver electrodes (8.04 mm2) on both the ceramic disks and TC-samples were deposited by a magnetron sputtering method before electric testing. The thickness of the silver electrode was about 100 nm with a depositing speed of 0.1 nm per second.

Structural characterization

The crystal structures were characterized by using X-ray diffractometer (XRD) with Cu Ka radiation (λ = 1.5406 Å) (6 °/min, D8 Advance, Bruker, Karlsruhe, Germany) and Raman spectroscopy with a laser wavelength of 532 nm (LabRAM HR Evolution, HORIBA Scientific, France). The XRD patterns for refinement was recorded at a scanning speed of 2 °/min (Rigaku, D/max-2550, Japan). Le bail refinement was used to extract the lattice parameters based on the PDF card #70-3628 (Ba0.6Sr0.4TiO3) and PDF card #39-0265 (Sr0.52Ba0.48Nb2O6), without considering the occupancy factor. The Leb Bail fitting is a qualitative analysis, and the function type used in the Leb Bail fitting is Pseudo-Voigt, which is a linear combination of Gaussian and Lorentzian functions, which gives information about the space groups and cell parameters in the material system. Before the XRD and Raman characterization, the sintered ceramic disks were ground to powders and compacted in sample holder. The microstructure of the samples was observed by a scanning electron microscope (SEM, MERLINVP Compact, Zeiss GmbH, Germany) and a transmission electron microscope (TEM, FEI Talos F200X, USA). For a more accurate view by SEM, hot corrosion was carried out on a polished disk at 1250 °C for 1 h. Density of both the ceramic disks and TC-samples was measured by a drainage method. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images were taken by a condenser spherical aberration-corrected transmission electron microscope (FEI-Titan Cubed Themis G2 300).

Properties measurement

The dielectric constant and dielectric loss as well as the impedance of the ceramics were pre-estimated on polished ceramic disks by using an impedance analyzer (E4980A, Agilent, the sample thickness is 0.15 mm and electrode area is 8.04 mm2). The response of the structural domains after a certain relaxation time was studied using a piezo-response force microscope (Park Systems XE7 PFM) with the writing voltage of ±12 V. Polarization-electric field loops were measured by using a TF ANALYZER 2000E ferroelectric measurement system at different electric fields, temperatures, and frequencies. (aixACCT Systems GmbH, Aachen, Germany). The charge-discharge performance of the samples was investigated using a charge-discharge platform (CFD-001, Gogo Instruments Technology, Shanghai, China) with a given discharge resistance and capacitive load circuit (RLC). All the energy storage characteristics were carried out on TC-samples with a thickness of 0.06 mm and an electrode area of 8.04 mm2.

The plot of Weibull distribution is tested on TC-samples and described by the formulas62,63:

$${{{\rm{ln}}}}\left\{{{{\rm{ln}}}}[1/(1-{P}_{i})]\right\}=m{ \, {{\mathrm{ln}}}}({E}_{i}-{E}_{U})-{{{\mathrm{ln}}} \, }({E}_{b}^{m})$$
(1)
$${P}_{i}=^{(i-0.375)}/N+0.25$$
(2)

Where, N is the total number of test samples, Pi is the cumulative breakdown probability of the sample i, Ei is the dielectric breakdown strength of the sample i with the order of breakdown electric field strength from low to high. EU is the breakdown strength when the breakdown probability is 0 (usually identified as 0). Eb is the average breakdown field strength obtained by Weibull statistical distribution.

Phase-field simulation

Phase-field breakdown model: to analyze the mechanism for the enhanced breakdown strength caused by the mixture phase method, a scalar spatially and temporally dependent damage field s (x, t) is introduced to characterize the breakdown process of the BSN ceramic and BSTN-Ta ceramics, respectively. More details about the phase-field breakdown model and equations can be found in the Supplementary Information.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.