Superior energy storage performance with a record high breakdown strength in bulk Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃-based lead-free ceramics via multiple synergistic strategies

Abstract

A high breakdown strength (E_b) together with a large maximum polarization (P_m) is essential for achieving a high recoverable energy density (W_rec) in energy storage dielectric ceramics. However, meeting the urgent need for practical applications remains a challenge due to the intrinsic properties of bulk dielectric ceramics. Herein, a composition and structure optimization strategy combined with a two-step sintering (TSS) process is proposed to design and fabricate (1−x)Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃−xBi(Mg_1/2Sn_1/2)O₃ (BCZT-BMSx-TSS) lead-free ceramics. Highly dynamic locally polar nano-regions (PNRs) are formed via composition optimization, exhibiting a very high P_m and energy storage efficiency (η). Compared to the traditional one-step sintering (OSS) process, the TSS process results in a composition with finer grain size and higher density, dramatically increasing E_b. As a result, an ultrahigh energy storage performance with W_rec ∼ 10.53 J cm⁻³ and η ∼ 85.71% is achieved for the BCZT-BMSx-TSS (x = 0.08) ceramic which is attributed to a record high E_b ∼ 830 kV cm⁻¹ and a large P_m ∼ 44.66 μC cm⁻². Complex impedance spectroscopy revealed that the activation energies of the bulk and grain boundary counterparts significantly increased, suggesting an increase in insulation resistance and a decrease in oxygen vacancies, which is the main reason for the high E_b value. In addition, excellent thermal/frequency stability is achieved in both energy density and efficiency, along with good charge–discharge performance. These findings suggest that BCZT-based lead-free ceramics have the potential for practical use in the future.

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1. Introduction

In recent years, the energy storage field has become an indispensable part of utilizing renewable sources. Dielectric ceramic capacitors are becoming increasingly important due to their excellent properties, such as ultrafast charging/discharging performance, high power density, and long-time stability, which are the key parameters for developing advanced pulsed power electronic systems.^1–5 However, compared to commercial capacitors, the energy storage density of bulk dielectric ceramics is too low for practical applications. To evaluate the energy storage performance (ESP) of dielectric ceramics, the following basic relations are used:

Excellent recoverable energy storage density (W_rec) and efficiency (η) can be simultaneously obtained via achieving a high maximum polarization (P_m) and a low remanent polarization (P_r) as well as enhancing the breakdown strength (E_b).^6,7

Typical ferroelectric (FE) ceramics, such as BaTiO₃ (BT)-based dielectrics, exhibit a nonlinear dielectric response under a certain electric field.^8–15 These ceramics possess a high total energy density (W_tot), but at the cost of a large P_r value. The large P_r and small E_b restrict the improvement of W_rec and η.^11–13 Making a solid solution of BT with a relaxor end-member may enhance E_b and ΔP (ΔP = P_m − P_r) because of the formation of highly dynamic polar nano-regions (PNRs), making it a potential candidate for energy storage applications.^14,15 The formation of highly dynamic PNRs is an effective way to enhance the saturation polarization by improving the structural relaxation and nanodomains. Under an external alternating electric field, the polarity of PNRs can be rapidly reversed, leading to an approximately linear polarization–electric field curve (P–E loop) with large saturation polarization, thereby ensuring high performance for energy storage ceramics.^16–18 Significantly, the quasilinear characteristics of the P–E loop make E_b a more crucial parameter in energy storage ceramics due to the approximate square relationship between E_b and W_rec.^19–21 In other words, while ensuring a high P_m, a higher W_rec can be obtained by improving the E_b value. To maintain a high P_m and low P_r, one effective approach is to make the solid solution of Bi(M)O₃ (M denotes trivalent cations) with BT-based ceramics.^22–25 The introduction of an appropriate amount of a Bi containing “relaxor end-member” can disrupt the B–O coupling of perovskite ceramics and establish A(Bi)–O coupling. This results in the formation of highly dynamic PNRs and P_m, which contributes to achieving the excellent energy storage density.^26–30 Although a relatively large P_m and a smaller P_r can be achieved using this method, the saturated polarization features are more dependent on the ceramics themselves. In other words, instead of further increasing the value of P_m, higher W_rec can be easily obtained by improving E_b.

The microstructural features and intrinsic electrical responses, such as grain size, density, band gap, and/or the distribution of conductive phases, play a key role in affecting E_b.^1,16,31–33 Recent studies show that improving E_b can be effectively achieved by optimizing the processing method and doping strategies.^34–37 It is also reported that the grain size (G_S) of ceramics has an inverse relationship with E_b, i.e., . Dong et al. designed and fabricated BT-based ceramics with a chemical formula of (1−y)[0.9Ba_1−xCa_xTiO₃−0.1Bi(Li_1/3Zr_2/3)O₃]−yBi_0.5Na_0.5TiO₃.³⁸ Results showed that the ceramics exhibited excellent breakdown characteristics, which is attributed to the small and fine grains, leading to a high W_rec ∼ 4.23 J cm⁻³ and η ∼ 93.40%. Similarly, Long et al. obtained a giant E_b by doping and chemical defect strategies, achieving a relatively high P_m and low P_r, resulting in a high W_rec ∼ 5.96 J cm⁻³ and η ∼ 89.5%.³⁹

The above discussion shows that improving E_b is an effective way to enhance the ESP, but the optimization of the sintering process can further enhance the energy storage capability of dielectric ceramics. In several cases, the two-step sintering (TSS) process has been proposed to obtain high-density fine-grain ceramics. Compared with the conventional one-step sintering (OSS) method, the TSS method cleverly controls the change in temperature to suppress the grain boundary migration (which leads to grain growth), while keeping the grain boundary diffusion (which is the driving force of the ceramic body) active to achieve sintering without grain growth. Based on this method, a high E_b (∼750 kV cm⁻¹), ultrahigh W_rec (∼8.4 J cm⁻³), and η (∼90%) were achieved for BiFeO₃–SrTiO₃ ceramics.³⁴ Yang et al. adopted a two-step cold sintering process for Sr_0.7Bi_0.2TiO₃ (SBT) ceramics,³⁵ achieving a sub-micrometer scale grain size along with a uniform and dense morphology, which leads to a high E_b (∼420 kV cm⁻¹) and a superior η (∼92.84%). Similarly, Bai et al. obtained a high E_b of 580 kV cm⁻¹, a large W_rec (∼5.98 J cm⁻³), and an ultrahigh η (∼98.6%) for SBT-based relaxor ferroelectric (RFE) ceramics using the TSS process.³⁶ It is evident from the above discussion that the TSS process in BT-based is an effective strategy to enhance the ESP; therefore, exploring and developing BT-based lead-free ceramics by this process is indispensable.

Inspired by the above discussion, a composition optimization accompanied by a TSS strategy is proposed to improve the ESP of Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃-based ceramics. The Bi(Mg_1/2Sn_1/2)O₃ (BMS) “relaxor end-member” is doped into the BT matrix, with an aim of forming PNRs to ensure a high P_m and a low P_r, followed by a TSS process to further enhance E_b. Furthermore, the introduction of MgO, which possesses high insulating characteristics, is useful to achieve high E_b. This approach resulted in a record high E_b ∼ 830 kV cm⁻¹, accompanied by a large P_m ∼ 44.66 μC cm⁻². The calculated values of W_rec and η were as high as ∼10.53 J cm⁻³ and ∼85.71%, respectively. In addition, the designed and fabricated ceramics showed excellent temperature/frequency stability along with a fast charge–discharge performance. All the desired results demonstrated the potential for practical application of the designed ceramics.

2. Experimental

(1−x)Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃−xBi(Mg_1/2Sn_1/2)O₃ (abbreviated as BCZT-BMSx-TSS, x = 0.03, 0.06, 0.08, 0.10) ceramics were fabricated through the TSS method. Analytical reagent grade (>99.0%) BaCO₃, CaCO₃, ZrO₂, Bi₂O₃, MgO and SnO₂ purchased from Sinopharm Chemical Reagent Co., Ltd and TiO₂ (Shanghai Yuejiang Powders, anatase) were weighed according to the molar ratios of the compositions. The powders were ball milled for 16 h in anhydrous ethanol using a planetary milling machine at 230 rpm. After drying, the mixed powders were calcined at 950–1100 °C for 3 h at a heating rate of 300 °C h⁻¹. An 8 wt% polyvinyl alcohol (PVA) was added to the calcined powders and then pressed into cylindrical discs, using a uniaxial press. The PVA was removed at 600 °C for 2 h. The discs were sintered by TSS technology to form densified ceramics. The obtained discs were initially heated to 1420 °C in air at a heating rate of 200 °C h⁻¹ then straight down to 1320 °C and held at 1320 °C for 10 h to achieve maximum possible densification. The densified pellets were ground/polished to a thickness of about ∼0.1 mm, and Au electrodes with a diameter of 2 mm or 3 mm were sputtered on both surfaces to evaluate the energy storage performance. The thickness of ∼0.8 mm samples was sputtered Au as electrodes to measure dielectric properties and the electrode area is 5 mm × 5 mm.

X-ray diffraction patterns for the samples were collected using an X-ray diffractometer (DX-2700, Dandong Haoyuan). Lattice parameters were calculated by MS Modeling (Accelrys) using Cu Kα1 radiation (λ = 1.540562 Å). The Raman spectra of the samples were recorded at room temperature (RT), using a LabRAM XploRA Raman spectrometer (Horiba Jobin Yvon). The surface morphologies of the sintered discs were examined using a Scanning Electron Microscope (SEM, EVOMA 10, Zeiss). To examine the domain structure of the samples, a JEOL JEM-F200 Transmission Electron Microscope (TEM, Japan) was used. The dielectric properties, P–E ferroelectric loops, and charging/discharging properties were measured using a Dielectric/Impedance spectrometer (Concept 41, Novocontrol, Germany), ferroelectric analyzer (TF2000E, aixACCT Inc., Germany), and charging/discharging measurement system (CFD-003, Shanghai Tongguo instruments technology, China), respectively. Unless otherwise stated, all the tests were carried out at room temperature in air.

3. Results and discussion

XRD patterns of the samples recorded at RT are shown in Fig. 1(a), which shows the formation of a single phase perovskite structure, confirming the solubility of Bi, Mg, and Sn in the Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃ lattice. Meanwhile, there is a symmetric diffraction peak without significant splitting in the range of 44 and 46°, indicating that all the doped samples have a pseudo-cubic structure. With an increase in x from 0.03 to 0.10, a slight shift towards a lower 2θ value occurs, indicative of a relative expansion of the unit-cell, which is due to the difference in the ionic radii of the doping elements. Although the ionic radius of Bi³⁺ (∼1.38 Å) is less than that for (Ba_0.85Ca_0.15)²⁺ (∼1.569 Å) at the A-site but at the B-site, the doping cations (Mg_1/2Sn_1/2)³⁺ (∼0.71 Å) have larger ionic radii than (Zr_0.1Ti_0.9)⁴⁺ (∼0.62 Å) which increases the volume of the BO₆ octahedron, causing lattice expansion which is more prominent.^22,30,40 And the unit cell volume (V₀) is 64.43 ų, 64.56 ų, 64.66 ų, and 64.69 ų for BCZT-BMSx-TSS (x = 0.03, 0.06, 0.08, 0.10), respectively.

Fig. 1 (a) XRD patterns, (b) Raman spectra, and (c) temperature-dependent Raman spectra for BCZT-BMSx-TSS ceramics.

To further understand the local structure, Raman spectroscopy of the samples was carried out at RT. The obtained spectra were divided into four main parts as shown in Fig. 1(b). With an increase in x, the peaks located near ∼113 cm⁻¹ and ∼287 cm⁻¹ become stronger, demonstrating that the A-site ion fluctuations and B–O vibration mode are intensified.^23,41 This is because the local lattice distortion increases, which further confirms the occupancy of dopants at their sites. In addition, ν₁ and ν₂ peaks between 400 and 800 cm⁻¹ shift toward a low wavenumber, which is related to the vibrations of BO₆ octahedra, thus reflecting the enhanced pseudo-cubic symmetry.^33,42,43 The emerging vibrational mode of ν₃ is an indication of local short-range ordered structures and is often associated with enhanced relaxor behavior. Moreover, the broadening of Raman peaks indicates that long-range FE ordered is disrupted, which promotes the formation of PNRs and enhances the relaxor behavior.^23,44

Temperature-dependent (from −180 °C to 180 °C) Raman spectra for BCZT-BMSx-TSS ceramics are shown in Fig. 1(c), which reflect the evolution of the local structure as a function of temperature. As the temperature increases, the Raman mode broadens and the typical ν₁ mode tends to shift to a lower wavenumber, which can be ascribed to an increase in the local structural disorder and the weakening of B–O bonds.^2,45,46 The cation disorders can enhance domain dynamics, inducing PNRs, and resulting in an improvement in ESP. More importantly, all the samples show similar Raman active modes, suggesting the formation of RFE behavior and the stability of local structural symmetry within the measured temperature range.

Dielectric constant (ε′) as a function of temperature at different frequencies (f) of 1 kHz–1 MHz for all the samples is shown in Fig. 2(a)–(d). All the doped ceramics show a similar trend for the maximum ε′, that is the (corresponding to T_m) decreases with an increase in the frequency, and T_m moves to high temperatures, displaying a typical dielectric relaxation behavior.^9,39,47,48 The f dispersion is an important feature for relaxed ferroelectrics, and the degree of f dispersion can be characterized by calculating ΔT_relaxor as follows:

Fig. 2 Temperature-dependence of ε′ and tan δ for BCZT-BMSx-TSS with x = (a) 0.03, (b) 0.06, (c) 0.08, and (d) 0.10, (e) T_m as a function of x, and the inset shows the ΔT_relaxor for BCZT-BMSx-TSS ceramics; (f) temperature-dependence of ε′ measured at 1 kHz for BCZT-BMSx-TSS ceramics, and the inset shows the TCC of BCZT-BMS8-TSS; (g) a plot of ; (h) TEM image for the BCZT-BMS8-TSS ceramic.

As shown in Fig. 2(e), T_m initially decreases and then slightly increases with an increase in x, which may be due to the octahedral distortion caused by the introduction of BMS in the host lattice.^13,18 The value of ΔT_relaxor increases from ∼29 °C to ∼64 °C, indicating that the dispersion phase transformation behavior is gradually enhanced with the increase in doping concentration, which further indicates the transition from the ferroelectric state to the relaxation state.^38,49,50 The f dispersion and diffused phase transition behavior lead to the formation of PNRs, which is crucial to achieve a high η. One further key is all samples have a very low dielectric loss (tan δ ∼ 0.004) at RT, which is beneficial for improving E_b.^51,52

In Fig. 2(f), the temperature-dependence of ε′ measured at 1 kHz for BCZT-BMSx-TSS ceramics is presented. With an increase in x, the dielectric curves become broader and the ε′ of the BCZT-BMSx-TSS ceramics decreased slightly. In particular, the BCZT-BMS8-TSS material shows a moderate RT permittivity and near independence with variation in temperature, indicating that the ceramic has a low variation in temperature coefficients of capacitance (TCC) and meets the requirements of X5R specification (−55–85 °C, ). In addition, an optimal ε′ can effectively enhance E_b by reducing the likelihood of electromechanical breakdown, because ε′ is inversely related to E_b. The excellent dielectric performance and relaxor characteristics of the BCZT-BMS8-TSS ceramic can be ascribed to the compression of BO₆ octahedra and the restriction of B-site cation activity after difference ionic doping, which is the basis for achieving high energy storage performance.

To further verify the relaxation behavior of the samples, the modified Curie–Weiss law is used to achieve the relaxation coefficient (γ), shown in Fig. 2(g).⁵³ The γ values of all the doped ceramics are higher than 1.6, confirming the phase transition of the doped BMS samples having typical relaxation and dispersion characteristics.^51,53,54 TEM analysis is employed to confirm the existence of the PNRs (Fig. 2(h)). The HR-TEM micrograph of the BCZT-BMS8-TSS ceramic shows that very small strip-like nano-domains of about 1.2–1.8 nm (marked by white ellipses) are evenly distributed in the sample. This complex domain pattern is usually composed of randomly distributed PNRs in the matrix with weak contrasts, which indicates the destruction of long-range ferroelectric domains and the formation of PNRs after doping the Bi-based relaxor end-member.^55,56 PNRs have highly dynamic characteristics and a fast response speed under the external field, which is crucial for a slim P–E loop and a high E_b, leading to both a high W_rec and η.

The unipolar P–E loops measured at maximum breakdown strength for BCZT-BMSx-TSS ceramics are shown in Fig. 3(a). With an increase in BMS content, the P–E loops gradually become slimmer, and the maximum polarization intensity (P_m) slightly decreases, which is consistent with the relaxation characteristics observed in the dielectric spectrum (Fig. 2). More importantly, the breakdown strength (E_b) is significantly increased. For x = 0.08, the E_b of the BCZT-BMS8-TSS ceramic reaches the maximum value of ∼830 kV cm⁻¹, which is the record high value in bulk BT-based ceramics.^4,11–15,42 A high P_m ∼ 44.66 μC cm⁻² and negligible remanent polarization (P_r ∼ 2.92 μC cm⁻²) make a large polarization difference (ΔP) for BCZT-BMS8-TSS, which is conducive to improving the energy storage density.

Fig. 3 (a) P–E loops, (b) W_rec, W_tot, and η at maximum electric fields, (c) Weibull distribution of E_b for BCZT-BMSx-TSS ceramics, and (d) the comparison of W_rec and E_b of the recently reported ceramics with BCZT-BMS8-TSS ceramic.^{2–6,8,9,11–15,17,18,25,26,28,32–34,36,38,39,42,45–49,58,59}

Fig. 3(b) illustrates that the BCZT-BMS8-TSS ceramic exhibits an ultra-high W_rec ∼ 10.53 J cm⁻³ and excellent η ∼ 85.71%, which is superior to mostly lead-free energy storage ceramics (Fig. 3(d)). To further confirm the reliability of E_b, Weibull distribution is employed as shown in Fig. 3(c). After linear fitting of the Weibull distribution, the value of β for all the samples is higher than 9, indicating that the data are highly reliable.^18,22,57 The average E_b value for the BCZT-BMS8-TSS ceramic is ∼800.3 kV cm⁻¹, which is higher than most of the reported ceramics (Fig. 3(d)).

In order to evaluate the effect of the TSS process and BMS doping on the microstructure of BCZT-based ceramics, the surface morphology and average grain size distribution are investigated (Fig. 4). All the specimens have a dense microstructure. Importantly, the BCZT-BMS8-TSS ceramic has better grain uniformity and smaller porosity than other samples, which helps to enhance the E_b.^16,20,55 The energy dispersive spectroscopy (EDS) spectrum confirms that all elements are uniformly distributed in the x = 0.08 ceramic (Fig. 4(g–n)), indicating that the system has a high degree of chemical composition uniformity. With the further increase in doping concentration, the grain size of the BCZT-BMS10-TSS ceramic increases, which is ascribed to the low melting point of Bi₂O₃. Grain size has a significant impact on the electrical performance, ESP, and dielectric compatibility of the ceramics by regulating the internal stress, tetragonality, and phase transition temperature. The dense fine-grain ceramics have high grain boundary barriers, which hinder the electrons from crossing the barrier, leading to a high E_b.⁵⁸

Fig. 4 SEM images of BCZT-BMSx-TSS with x = (a) 0.03, (b) 0.06, (c) 0.08, and (d) 0.10, respectively; (e) EDS, (f) SEM and (g–n) elemental mapping for x = 0.08 ceramic.

To further investigate the effect of the sintering process on the energy storage performance, the P–E loops of BCZT-BMS8 obtained using both the OSS⁶⁰ and TSS methods are shown in Fig. 5(a) and (b), respectively. Compared to the BCZT-BMS8-OSS ceramic, the BCZT-BMS8-TSS ceramic has a larger P_m and E_b, indicating a higher W_rec. This can be explained on the basis of the TSS process, which contributes to the formation of smaller grains and lower porosity (the inset of Fig. 5(a) and (b)). Actually, the relative density of BCZT-BMS8-OSS and BCZT-BMS8-TSS is ∼93% and ∼95% of the theoretical density, and the average grain size is ∼3.8 μm and ∼1.72 μm, respectively. Fig. 5(c) presents the sintering process curve for BT-based specimens sintered by OSS and TSS, respectively. For the TSS process, the sample was heated at a high temperature (T₁) to obtain a medium density (greater than 75%). It is then cooled and kept at a lower temperature (T₂). The different kinetics between densification diffusion and grain boundary network mobility leave a kinetic window that can be utilized in the second-step sintering.^36,37,61 Due to the slow kinetics process, grain growth during the second-step sintering is completely suppressed, which is conducive to obtaining dense fine-grained ceramics, improving E_b and ESP.⁶¹

Fig. 5 P–E loops of (a) BCZT-BMS8-OSS and (b) BCZT-BMS8-TSS ceramic; (c) sintering process curve for BaTiO₃-based specimens by OSS and TSS.

Complex impedance spectroscopy was carried out to understand the defect chemistry and the mechanism of high E_b of the prepared BCZT-BMSx-TSS sample.^38,55 As shown in Fig. 6(a–d), there is no semicircle at a low frequency (for electrode response), indicating the good ohmic contact between the electrode and ceramics. All the samples exhibit two well-resolved semicircles at 500–600 °C, which can be fitted by the two in-series R//CPE equivalent circuit model.^55,62 The two semicircles can be ascribed to the grain and grain boundary response which is in accordance with the internal barrier layer capacitor model.⁶³ Also, all the semicircles exhibit some degree of depression and distortion, meaning the presence of a non-Debye type of relaxation phenomenon.^63,64 BCZT-BMS8-TSS ceramic has the largest resistivity, which can be extracted by the intersection of the x-axis with the semicircular arc at low frequency.^23,62 The real impedance decreases with the increase of measuring temperature, which is reflected in the decrease of semicircle diameter. It also can be seen that the arc of the impedance has a contraction tendency as the temperature rises, which presents a typical thermally activated relaxor process. In order to explore the conduction mechanism, the activation energy (E_a) is calculated using the fitted resistance as a function of temperature. According to the Arrhenius relationship:

where σ₀ is a constant, σ is the bulk conductivity, k is the Boltzmann constant, and T is the temperature in Kelvin. E_a is determined from the slope of ln(1/R) − 1000/T curves. The inset of Fig. 6(a–d) shows the Arrhenius plots for BCZT-BMSx-TSS ceramics. The activation energy of the grain boundary (E_GB) is greater than that of grains (E_G), and the grain boundary resistance is dominant at high temperatures. With an increase in BMS content, the E_GB and E_G increase, indicating that the insulation properties of ceramics are enhanced. The largest E_GB of ∼1.70 eV is obtained for the BCZT-BMS8-TSS ceramic, which is significantly higher than that of most reported BT-BiMO₃ systems dominated by the grain boundary.^14,65 In addition, the BCZT-BMS8-TSS ceramic has the highest E_G, which is attributed to its compact and uniform microstructure, small grain size, and a decrease in oxygen vacancy concentration.^57,62 It can also be considered that the semiconducting grains in BCZT ceramics gradually transform into insulation grains with the increase of BMS doping concentration. Generally, the higher E_a denotes a higher barrier for oxygen vacancy jumping in the grain boundary, leading to a lower concentration of oxygen vacancies at the grain boundary, which is conducive to achieve a higher E_b. Thus, the high E_b for the sample with x = 0.08 is due to the dense microstructure with fine grain size and a high E_a.

Fig. 6 Complex impedance and activation energy (inset) for BCZT-BMSx-TSS ceramics with x = (a) 0.03, (b) 0.06, (c) 0.08, and (d) 0.10, respectively; (e) UV-Vis absorbance spectra and (f) the curves of (αhv)² as a function of hv for BCZT-BMSx-TSS ceramics.

Fig. 6(e) and (f) present UV-vis absorption spectra and the calculated band gap (E_g) for BCZT-BMSx-TSS ceramics. The E_g value can be obtained from the following equation:^23,45,66

(αhv)² = A(hv − E_g) (6)

where α, A, and hv are the absorbance coefficient, constant, and energy of the electromagnetic waves, respectively. As shown in Fig. 6(f), with the increase of BMS content, the E_g of BCZT-BMSx-TSS ceramics increases from 3.21 eV to 3.29 eV. The increase in E_g may be due to the doping of wider band gap SnO₂ (∼3.5 eV) and MgO (∼7 eV),^67,68 leading to the change of the band structure, which improves the intrinsic breakdown strength and reduces the energy loss at high electric fields. In addition, the comparison of E_g and E_a shows that intrinsic conduction takes place at the grain boundary because E_g ∼ 2E_a.^69,70 The values further suggest that the concentration of oxygen vacancies decreases with an increase in x which improves the barrier strength and hence E_b.

To evaluate the operating stability of dielectric capacitors, the frequency stability and temperature stability of the BCZT-BMS8-TSS ceramic at a fixed electric field intensity of 250 kV cm⁻¹ are studied. As shown in Fig. 7(a and b), as the frequency increases from 2 Hz to 500 Hz, neither the P–E loops nor the polarization intensity changes significantly. The W_rec and η values calculated at different frequencies show high frequency stability, and the PNRs that can quickly and reversibly switch have high dynamic characteristics in the external electric field, which is the main reason for the high frequency stability of ESP. In addition, temperature-dependent ferroelectric tests were performed at a fixed frequency of 250 kV cm⁻¹ and 10 Hz to evaluate the thermal stability of the ceramics in the temperature range of 30–130 °C. Fig. 7(c and d) demonstrate that the variation in W_rec is less than ±4.3%, and the η value is slightly decreased in the entire temperature range, which is due to the thermally activated conduction promoting P–E hysteresis loops and the increase of leakage current at high temperatures.^18,19 In general, the BCZT-BMS8-TSS ceramic has good stability and reliability and broad application prospects in the field of energy storage.

Fig. 7 (a) Frequency and (c) temperature-dependence of P–E loops of BCZT-BMS8-TSS ceramic; (b) and (d) show the values of W, W_rec, and η as a function of frequency and temperature, respectively.

In order to further evaluate the actual working ability of the BCZT-BMS8-TSS ceramic, the charge–discharge performance of the ceramic is evaluated from overdamped and underdamped discharge current curves. The underdamped discharge current curve at different electric field intensities is shown in Fig. 8(a). The relationship between current density (C_D = I_max/S, S being the sample electrode area) and power density (P_D = EI_max/2S) and electric field intensity is shown in Fig. 8(b).^6,28 The values of C_D and P_D increase monotonically with an increase in electric field intensity from 52 A cm⁻² and 0.52 MW cm⁻³ at 20 kV cm⁻¹ to 371.6 A cm⁻² and 29.73 MW cm⁻³ at 160 kV cm⁻¹, respectively. In addition, in the temperature range of 333–453 K (Fig. 8(c and d)), the values of C_D and P_D decreased slightly with an increase in temperature, and the change rate is controlled within ±4.8%.

Fig. 8 The underdamped discharge current curves at (a) room temperature and (c) the temperature range of 333–453 K, and (b) and (d) the calculated C_D and P_D; the overdamped pulsed discharge current curves at (e) room temperature and (f) the temperature range of 333–453 K, and the inset of (e) shows the corresponding W_D as a function of time for BCZT-BMS8-TSS ceramic.

Fig. 8(e) shows the overdamped discharge current curves of the BCZT-BMS8-TSS ceramic at different electric fields. The discharge energy density (W_D) can be calculated from the formula of , where R (200 Ω) and V represent the load resistance and sample volume, respectively.^42,63 The inset of Fig. 8(e) is the curve between W_D and time (t). With the gradual increase in electric field intensity, the maximum current (I_max) and W_D value rapidly increase. The time corresponding to the 90% saturation W_D value is defined as the discharge time (t_0.9), and the shorter the t_0.9 of the capacitor, the more favorable the application in the pulse power supply system. According to the overdamped discharge current curve, W_D is 0.62 J cm⁻³ at 160 kV cm⁻¹, and the ultra-fast discharge time of t_0.9 ∼ 142 ns. It should be noted that there is a significant difference between W_D and W_rec when the electric field intensity is the same, that is,the W_rec measured from the P–E loops is higher than that of the W_D measured from the charging–discharging curves, mainly due to the difference of testing frequency. The BCZT-BMS8-TSS ceramic shows both high ESP and fast discharging speed, which is superior to the most reported lead-free ceramics in terms of comprehensive energy storage performance (Fig. 3(d)).

4. Conclusion

In this work, a record high breakdown strength (E_b) of ∼830 kV cm⁻¹ has been achieved in BT-based ceramics via composition optimized and a two-step sintering (TSS) process. The results show that the introduction of BMS can effectively destroy the ferroelectric long order and form PNRs, which improves the dielectric behavior and polarization response process of the ceramics. Meanwhile, a finer grain size and higher density of ceramics are achieved by the TSS process. In addition, the doping of wider band gap MgO and SnO₂ can further enlarge the E_g of the optimized ceramics, and the activation energies of the bulk and grain boundary counterparts significantly increased in the BCZT-BMS8-TSS ceramic. Benefiting from the above optimization, an unprecedented W_rec ∼ 10.53 J cm⁻³ and η ∼ 85.71% are achieved in the BCZT-BMS8-TSS ceramic, which is superior to the most reported ceramics. Moreover, all the samples exhibited excellent thermal/frequency stability and charge–discharge performance. In summary, the collaborative optimization strategy within this study is effective to enhance the comprehensive performance of energy storage ceramics, which provides a feasible way to develop other high ESP materials.

Author contributions

Changhao Wang and Dandan Han: conceptualization, methodology, investigation, data curation, writing – original draft, visualization, and funding acquisition. Jiaxi Hao and Longxiao Duan: investigation, formal analysis, and data curation. Jianfan Zhang, Wenfeng Yue and Zhenhao Fan: data curation. Raz Muhammad and Fanxu Meng: writing – review & editing. Dawei Wang: supervision and writing – review & editing.

Data availability

The data that support the findings of this study are available from the corresponding author and first author upon reasonable request.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Projects of the Jilin Provincial Science and Technology Department (Grant No. YDZJ202201ZYTS420), the Projects of the Jilin Provincial Education Department (Grant No. JJKH20230298KJ), and the National Science Foundation for Yong Scientists China (Grant No. 62004081). The authors acknowledge the assistance of the JLICT Center of Characterization and Analysis.

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