Constructing superrelaxor critical state towards giant energy storage in lead-free dielectric ceramics

Domain: physics
Published: 2026-01-10
Editorial outcome: major_revision

Abstract
Lead-free relaxor ferroelectric ceramics are promising candidates for advanced pulsed power systems owing to their combination of exceptional power density and ultrafast charge-discharge capabilities. However, the simultaneous realization of ultrahigh recoverable energy density (Wrec) and high efficiency (η) remains a persistent challenge, as strategies to enhance polarization typically increase hysteresis losses. To address this issue, we propose a strategy actively constructing a superrelaxor critical state—a crossover from dynamic to static/frozen relaxor states—through targeted compositional tuning and polarization configuration control. Guided by phase-field simulations and first-principles calculations, we introduce BaHfO3 into a Sr0.5Bi0.25Na0.25TiO3 relaxor matrix. This approach successfully shifted the dielectric maximum temperature to room temperature and enhanced the strength of relaxor behavior. Atom-scale structural characterization reveals that this structure weakens local domain interactions within 3−5 nm refined polar nanoregions yet preserving robust polar atomic displacements, effectively bridging the kinetic advantage of superparaelectrics with the dipole magnitude of classical relaxors. As a result, the superrelaxor critical state delivers a giant energy-storage capability, including Wrec of 16.2 J/cm3 with a high η of 92%, outperforming most reported lead-free ceramics. This work establishes a generalizable strategy for engineering critical polarization states in dielectric oxides toward next-generation capacitive energy storage.

Introduction
Dielectric ceramics have garnered great attention for pulsed power systems due to their exceptional power density and rapid charge-discharge capabilities1–5. In these applications, the recoverable energy density (Wrec) and energy-storage efficiency (η) serve as the key performance metrics. The Wrec and η are determined from the polarization-electric field hysteresis loop (P−E loop)6–8, expressed as W = ∫PmaxEdP, where Pmax, Pr, E, and W represent the maximum polarization, remnant polarization, applied electric field, and total energy density, respectively. This relationship dictates that Wrec is governed by both the polarization difference (ΔP=Pmax − Pr) and the breakdown strength (Eb), while the energy dissipation (Wloss) links to η (η=Wrec /(Wrec + Wloss))9,10. In this regard, a persistent challenge lies in the intrinsic trade-off between polarization enhancement and hysteresis suppression, wherein elevated polarization typically exacerbates hysteresis loss11,12, making it difficult to achieve simultaneously high Wrec and η in dielectric ceramics.

Perovskite-type relaxor ferroelectrics are attractive for dielectric energy storage due to their frequency-dispersive dielectric maximum temperature (Tm), which originates from the highly activated polar nanoregions13,14. Below Tm, relaxor (RE) state facilitates strong field-induced polarization; however, it also sustains dipole-dipole correlations that manifest as hysteresis losses. To mitigate this limitation, a variety of optimization strategies, including nanodomain engineering15–17, high-entropy design18–20, local structure modification21–23, and multi-layer design24–26, have been explored to tailor relaxor features, such as size, distribution, configuration, and dynamics of polar nanoregions (PNRs), leading to significantly improved energy-storage performances. In contrast, the superparaelectric (SPE) state appears above Tm, characterized by flatter and nearly dispersion-free dielectric response, reflecting fully dynamic and weakly correlated dipoles that minimize hysteresis and enable ultrahigh-efficiency energy storage14,27,28. Nevertheless, the contrasting dielectric behaviors underscore a fundamental trade-off: the strong correlations within the relatively large PNRs of the relaxor phase restrict dipole dynamics and increase energy loss, especially at elevated electric field, while the weak dipole interactions in the superparaelectric phase limit the achievable polarization strength. Thus, despite considerable progress, simultaneously achieving ultrahigh Wrec and η remains a significant challenge.

To overcome these limitations, we propose the deliberate construction of a room-temperature (RT) superrelaxor critical state, a unique dielectric configuration residing at a crossover between dynamic and static/frozen polar states. In dielectric spectra, this unique state appears where the permittivity maximum flattens, at which thermal fluctuations weaken dipole–dipole correlations while preserving the polarization stability. Such a configuration effectively combines the advantages of dynamic and static/frozen states: it exhibits fast polarization dynamics with minimal hysteresis, reminiscent of a SPE-liked dynamic regime, yet it retains strong dipoles and large polar nanoregions relative to the static or frozen polar state. This intermediate polar state, therefore, provides a promising pathway for advancing dielectric energy-storage performance beyond the inherent limitations of either the relaxor or superparaelectric phases alone.

Results
We first validate our design concept using phase-field simulations and density functional theory calculations, wherein BaHfO3, a typical paraelectric oxide, was selected to incorporate Sr0.5Bi0.25Na0.25TiO3 relaxor ferroelectric matrix to form (1–x)Sr0.5Bi0.25Na0.25TiO3–xBaHfO3 (SBNT–xBH) solid solutions. The phase-field simulations confirm that engineering superrelaxor characteristics in the designed system increase polar vector disorder and optimize nanodomain size (Fig. 1a). Consequently, the dielectric maximum (εm) shifts toward RT, flattening the dielectric response and enhancing the strength of relaxor behavior (Fig. 1b, c). When the εm aligns with ambient temperature, we observe nearly hysteresis-free P−E loops (Fig. 1c, Supplementary Fig. 1), suggesting a viable pathway for minimizing energy loss. To further substantiate these predictions and probe the local structural characteristic, density functional theory (DFT) calculations were carried out for the SBNT–0.3BH composition (Fig. 1d, Supplementary Fig. 2). In the SBNT–xBH system, the introduction of BaHfO3 will induce composition-driven local structural distortion and strongly isotropic polar disorder. Density-functional-theory calculations on relaxed supercells for x=0 and 0.3 reveal enhanced lattice and octahedral distortion in the BaHfO3 modified composition, accompanied by a more isotropic distribution and larger magnitudes of local polar vectors with average polarization of 27 μC/cm2, as illustrated by the polarization arrows overlaid on the atomic models in Fig. 1a. Under an applied electric field, the rotation and alignment of these diverse local polarizations give rise to a large microscopic polarization response while avoiding strong long-range coupling, consistent with the superrelaxor critical state and the coexistence of high recoverable energy density and high efficiency in the SBNT–0.3BH ceramic. These changes promote polar disorder, thereby reducing hysteresis losses, while the increased lattice dimensions provide greater spatial freedom for polarization enhancement29,30. Collectively, such structural modifications fine-tune the original PNRs configuration and favor the emergence of an unusual superrelaxor critical state bridging the dynamic and static/frozen relaxor states.

Guided by these theoretical insights, a series of SBNT−xBH (SBNT−xBH, x=0, 0.1, 0.2, 0.3, and 0.35) ceramics were synthesized via a high-temperature solid-state reaction approach (see “Methods” for details) and subjected to comprehensive characterization of their crystal structures and phase components. X-ray diffraction (XRD) patterns confirm that all compositions adopt a pure perovskite structure (Supplementary Fig. 3). The progressive shift of the diffraction peaks toward a lower angle is attributed to the lattice expansion induced by the larger ionic radius of Ba2+ and Hf4+ atoms, as revealed by theoretical calculations. Rietveld refinements (Supplementary Fig. 3) reveal coexisting tetragonal polar and cubic non-polar phases in all SBNT–xBH ceramics. With increasing BaHfO3 content from x=0 to 0.3, the tetragonal fraction decreases while the cubic fraction increases, indicating a composition-driven phase evolution from a tetragonal-dominated polar state toward a mixed tetragonal/cubic state. Energy dispersive spectroscopy-scanning electron microscopy (EDS-SEM) mappings demonstrate uniform distribution of all elements without aggregation or separation (Supplementary Fig. 4), which affirms the successful incorporation of BaHfO3 into the perovskite structure, forming as solid solutions and agreeing well with our DFT calculations.

The relaxor behavior of SBNT−xBH ceramics was examined through temperature-dependent dielectric spectra31,32 (Fig. 2a–d, Supplementary Fig. 5). It can be noted that Tm decreases from 150 °C for x=0 to RT for x=0.3 at 1000 kHz, accompanied by broader diffuse phase transition and reduced temperature dependence, indicative of enhanced relaxor characteristics with increasing BaHfO3 content. This dielectric behavior is consistent with the phase evolution revealed by XRD refinement. As the cubic fraction increases from x=0 to 0.3, Tm shifts toward room temperature, the ε-T curve becomes progressively flatter, and the strength of relaxor behavior is enhanced (Fig. 2d). At the optimal composition x=0.3, a balanced polar and nonpolar phase coexistence, together with composition-induced local distortion and random fields, stabilizes a room-temperature superrelaxor state. Concurrently, the frequency dispersion (the difference of Tm at 1000 kHz and 1 kHz) expands substantially from 3 °C (x=0) to 73.3 °C (x=0.3), while Tm flattening at RT is accompanied by a rise in the relaxor dispersion index (γ) from 1.54 to 1.86. Notably, the Sr0.5Bi0.25Na0.25TiO3–0.3BaHfO3 composition exhibits a flattened dielectric response at RT with a dispersion index γ up to 1.86, consistent with phase-field predictions of the designed superrelaxor critical state. Broadening of Raman peaks further corroborates the enhanced relaxor behavior (Supplementary Fig. 6). Notably, the SBNT−0.3BH composition exhibits a low dielectric constant (εr < 500) and a flattened dielectric–temperature response near Tm = RT, corresponding to our designed RT superrelaxor critical state that bridges the dynamic and static/frozen relaxor states33,34. This dielectric profile suggests a flexible polarization response to the electric field at the superrelaxor critical state (Fig. 2b). Based on these results, a dielectric phase diagram was constructed using Tm (at 1000 kHz) and the Burns temperature (TB) derived from Curie-Weiss relationship, as shown in Fig. 2e. With increasing BaHfO3 content, Tm progressively decreases toward RT, marking a continuous evolution from the conventional relaxor state in SBNT to the superrelaxor regime in SBNT−0.3BH. Remarkably, the Tm of SBNT−0.3BH ceramics lies at the crossover regions involving dynamic and static/frozen relaxor states near RT, while retaining an evident relaxor behavior, closely matching the superrelaxor critical state predicted by phase-field simulations.

To determine the polarization response of the superrelaxor ceramics under an external electric field, we measured the P−E loops. As shown in Fig. 2f, the Pmax and hysteresis loss both decrease under the identical electric fields, leading to progressively slimmer P−E loops. This behavior is attributed to the increased proportion of the weakly ferroelectric C phase. For comparison, the pristine SBNT ceramic exhibits a pronounced hysteresis with high Pr, characteristic of a strong long-range ferroelectric state. Notably, the SBNT−0.3BH composition shows an exceptionally slim P−E loop with minimal hysteresis, originating from weak polar interactions and a flattened Landau free-energy profile1,35,36. Such features are consistent with enhanced structural disorder and reduced domain size, as confirmed by XRD and DFT analyses. Combined with the unique dielectric property and polarization response, SBNT−0.3BH was selected for in-depth local structure characterization.

To elucidate the local structural and polar configuration underlying the observed superrelaxor critical state, atomically resolved scanning transmission electron microscopy (STEM) and quantitative analysis were performed. Low-magnification TEM images display uniform contrast, and the corresponding diffraction pattern matches the pseudocubic structure, being in agreement with XRD results and ruling out the presence of long-range domain ordering in SBNT−0.3BH ceramic37–39 (Supplementary Fig. 8a). Inverse Fourier transform analysis further reveals distinct nanoclusters with significant lattice distortion21, aligning with the phase-field simulation and DFT calculations (Fig. 1, Supplementary Fig. 8b). Figures 3a, b present atom-resolution high-angle annular dark-field (HAADF)-STEM images of SBNT−0.3BH composition along the [001] and [110] zone axes, respectively. No impurity phases are detected, and all atomic columns occupy standard perovskite lattice sites, as denoted by the overlaid crystal model. By precisely determining atomic column positions via two-dimensional Gaussian fitting, the local polar configuration, represented by the off-center cationic displacement relative to the oxygen polyhedral centroid, was calculated and mapped, as shown in Fig. 3c, d. Notably, the SBNT−0.3BH ceramic exhibits numerous polar nanoregions separated by a non-polar cubic matrix and oriented in multiple directions. These nanoregions feature a coherent length of 3−5 nm, smaller than the >5 nm size typical of most relaxor ferroelectrics, yet larger than several unit cells (1−2 nm) observed in superparaelectric system20. The statistical analysis of the polar vectors, including polar angle/magnitude maps and off-centering vector maps, further confirms a strongly isotropic polar disorder in SBNT−0.3BH ceramics (Fig. 3c1-c4, 3d1-d4). This feature originates from the local lattice distortion, as evidenced by the local fluctuation in the corresponding c/a map (Supplementary Fig. 9). Regarding the local polar strength, the nanoregions in SBNT−0.3BH ceramics exhibit an average polar magnitude of 7.01 pm along the [001]pc zone axis and 6.04 pm along the [110]pc zone axis. This polar displacement is higher than that of the previously reported superparaelectric ceramics20 and corresponds to an average polarization of 22.5 μC/cm2 using the Born effective charge method, agreeing well with the spontaneous polarization estimated from the unipolar P−E loop (Fig. 4a). Based on Landau theory40, we can conclude that these polar nanoregions with large polarization magnitude possess a low switching barrier and high polarization responsiveness under electric field, enabling ultrahigh efficiency, negligible hysteresis, and large energy-storage capability in the designed superrelaxor critical state.

The energy storage performance of SBNT−0.3BH ceramics was measured using unipolar P−E loop under varying electric fields (Fig. 4a). As the electric field increasing, the energy density exhibits a parabolic growth trend while maintaining η consistently above 90% (Fig. 4b). Notably, at a high electric field of 68 kV/mm, the SBNT−0.3BH demonstrates an exceptional comprehensive energy storage performance, delivering a Wrec of 16.2 J/cm3 and η of 92%. When compared with representative lead-free ceramics with η exceeding 90% (e.g., Wrec ~13.6 J/cm3 and η~94% for BNT−25BT−0.15BZ, Wrec ~10.1 J/cm3 and η~90% for BBT12), the construction of superrelaxor critical state not only places SBNT−0.3BH in a remarkable position among them but also surpasses previously reported ceramics based on the same parent compounds22,41–44 (Fig. 4c-d, Supplementary Fig. 10 and see detailed data in Supplementary Tables 1–3). Its comprehensive performance is also situated at the upper right corner of the dielectric capacitor performance map, indicating a superior balance of energy density and efficiency. This superior performance is attributed to the synergy of a high applied electric field (68 kV/mm, near the Eb = 68.5 kV/mm), large ΔP (56.3 μC/cm2 with Pmax = 58.8 μC/cm2, Pr = 2.5 μC/cm2), and extremely low hysteresis. The incorporation of larger-radius Ba2+ and Hf4+ enhances local lattice distortion in the matrix, promoting the formation of high-density polar nanoregions with large polarization strength, accounting for the superior energy-storage performance within the superrelaxor state.

Because high insulating properties and strong voltage endurance play pivotal roles in achieving exceptional energy-storage capability, several key and correlated physical parameters of the superrelaxor ceramics were systematically examined, including resistivity, bandgap, grain size, and breakdown strength45. High-temperature impedance spectroscopy shows a pronounced increase in the semicircle radius from x=0 to 0.3, followed by a decrease at x=0.35, indicating the highest resistance at x=0.3. (Fig. 4e, Supplementary Fig. 11). Equivalent-circuit fitting results, by considering the contributions from grain, grain boundary, and electrode-dielectric interface, show that the semicircle at 650 °C is dominated by the grain and grain-boundary resistances. The maximum resistance at x=0.3, dominated by the grain-boundary blocking effect (Fig. 4e, Supplementary Table S4), is consistent with the highest grain boundary at this composition. As shown in Fig. 4f, the activation energy (Ea) of each component, derived from the Arrhenius equation σ=σ0 exp(−Ea/kT) (σ is electrical conductivity, k denotes Boltzmann constant, and T is temperature), increases from 1.21 eV at x=0 to 1.94 eV at x=0.3. The high Ea value in SBNT−0.3BH reflects strong binding capability with charge carriers (e.g., electron and oxygen vacancies), confirming its high insulating property. Bandgap, another key indicator of insulating performance, is determined by the UV-vis absorption spectrum. Figure 4g illustrates the Eg values for each composition, revealing a positive correlation between Eg and x, with Eg of 3.34 eV at x=0.3, owing to the intrinsically wide Eg of BaHfO3 (4.39 eV)46. The larger Eg in the x=0.3 composition significantly hinders electron transitions from the valence band to the conduction band, thereby reducing the leakage current density by approximately three orders of magnitude relative to x=0 and promoting the high breakdown field observed in the x=0.3 ceramic (Supplementary Fig. 12). Grain size statistics from SEM images (Fig. 4h, Supplementary Fig. 13) reveal that SBNT−0.3BH possesses the smallest Gaver of 1.21 μm. This refined microstructure reduces the potential breakdown paths, therefore supporting a higher Eb8 (Supplementary Figs. 13–15). To quantify this, we performed electrical breakdown tests and fitted the results with a two-parameter Weibull distribution47 (Fig. 4i). It can be noted that SBNT−0.3BH achieves the highest Eb among all of the compositions. These results align with its increased Ea, enlarged Eg, small Gaver, and excellent insulating property. These results indicate that the high breakdown strength arises from the synergistic effect of a relatively large bandgap, an increased density of carrier blocking interfaces due to grain refinement, and strong binding/trapping of charge electrons and vacancies upon the introduction of BaHfO3. We note that the x=0.35 composition exhibits a distinct deviation from the trend in dielectric response, electric property, and structural evolution established from x=0 to 0.3. Compared with SBNT–0.3BH, the x=0.35 ceramic shows clear signatures of microstructural (e.g., coarser and more heterogeneous grains, broadened and weakened Raman peak) and electrical degradation (e.g., a reduced bandgap, noticeably higher leakage, and lower thermal activation energy for ion/defect migration). These complementary observations indicate that further increasing the BaHfO3 content pushes the system beyond the optimal solid-solution window, where the possible reasons, including enhanced ionic-size mismatch and defect-related inhomogeneities, degrade local structural and electrical robustness and blur the paraelectric dilution effect. As a result, the x=0.3 composition is identified as the optimal point that provides a balanced combination of robust local structural stability, dense crystalline microstructure, and high voltage endurance, thereby stabilizing the superrelaxor state with the best overall energy-storage performance.

The stability, reliability, and charge/discharge performance of the SBNT−0.3BH ceramic were subsequently assessed, as these are indispensable qualities for practical energy-storage applications. Frequency-dependent energy-storage measurements under 40 kV/mm show minimal variations in Wrec (7.2±0.02 J/cm3) and η (Δη=1.5%) over a wide range of 1−100 Hz (Fig. 5a, Supplementary Fig. 16a). Temperature stability testing at 10 Hz further demonstrates less than 6% degradation in both Wrec and η from 30 to 150 °C (Fig. 5b, Supplementary Fig. 16b). Of equal importance is that the SBNT−0.3BH ceramic maintains a stable Wrec and ultra-low η variation over 108 charge-discharge cycles, retaining a high Wrec of 7.3 J/cm3 and an impressive η of 92% (Fig. 5c, Supplementary Fig. 16c). These exceptional operating stability and reliability arise from the presence of highly dynamic polar nanoregions in the superrelaxor critical state, which bridges dynamic and static/frozen polar states, enabling a rapid polarization switching while minimizing thermal loss1,38.

Charging/discharging capabilities were further evaluated using over-damped and under-damped current-time measurements within a practical circuit (Fig. 5d, f, Supplementary Fig. 17a, b). The discharging energy density (Wdis) and power density (PD) can be calculated by Wdis = R/V ∫I2(t)dt and PD = Wdis/t0.9, where R, I, and V represent the load resistance, underdamped current, and ceramic volume48. As shown in Fig. 5d, the SBNT−0.3BH achieves a high Wdis up to 6.56 J/cm3 at 40 kV/mm, a fast discharging time t0.9 (time to release 90% of the stored energy) of 173 ns. Therefore, the results collectively suggest that SBNT−0.3BH ceramic combines superior stability, reliability, and high power capabilities, establishing it as a highly promising candidate for advanced energy-storage devices and applications.

We have demonstrated that the fundamental challenge of concurrently achieving high energy density and efficiency in dielectrics can be overcome by constructing a superrelaxor critical state. The key lies in creating a unique nanoscale architecture where disordered 3−5 nm polar nanoregions significantly suppress remnant polarization and hysteresis, while robust atomic-level polar displacements maintain high polarization strength. This mechanistic understanding, clarifying how local polarization correlation is engineered at a superrelaxor state bridging dynamic and static/frozen relaxor states, directly enabled exceptional performance in the studied model system with Wrec of 16.2 J/cm3 and η of 92%. Therefore, this study provides not just a superior dielectric oxide but a new design paradigm unlocking ultra-high comprehensive energy-storage performance across a broad range of material systems.

Methods
Phase field simulations
In this phase-field simulation, the polarization field P=(px, py, pz) is selected as the order parameter. The polarization field’s temporal evolution is solved by the time-dependent Ginzburg-Landau (TDGL) equation49–51:

γ ∂Pi/∂t + δF/δPi = 0 (1)

where γ is a kinetic coefficient that is related to the domain-wall mobility. F is the total free energy of the system. δF/δPi is the thermodynamic driving force for the polarization evolution, and t is the time.

The total free energy F of the system is the sum of Landau energy (FLand), elastic energy (Felas), electric energy (Felec), and gradient energy (Fgrad). fLand, felas, felec, and fgrad are corresponding energy densities.

F = FLand + Felas + Felec + Fgrad = ∫V (fLand + felas + felec + fgrad) dV (2)

The Landau free energy density is

fLAND = α1(T−T0)P2 + α11P4 + α111P6 + b1(px2py2 + py2pz2 + pz2px2) + b112 [px4(py2 + pz2) + py4(px2 + pz2) + pz4(px2 + py2)] + b123 px2py2pz2 (3)

where α, α11, α111, b1, b11, b111 are the Landau coefficients, and T is the temperature, and T0 is the reference temperature. The electrostatic energy density felec = −EiPi − 1/2 EdiPi, where Ei is the applied electric field, and Ed is the depolarizing electric field.

The elastic energy density

felas = 1/2 cijkl eij ekl = 1/2 cijkl (εij − ε0ij)(εkl − ε0kl) (4)

where cijkl is the elastic stiffness tensor; eij, εij, and ε0ij represent the elastic strain, the total elastic strain, and the eigenstrain, respectively. The eigenstrain is calculated by ε0ij = Qijkl Pk Pl, where Qijkl is the electrostrictive coefficient.

The gradient energy density is given by51

fgrad = 1/2 g11 (P1,12 + P2,22 + P3,32) + g12 (P1,1 P2,2 + P2,2 P3,3 + P1,1 P3,3) + 1/2 g44 [(P1,2 + P2,1)2 + (P2,3 + P3,2)2 + (P1,3 + P3,1)2] + 1/2 g044 [(P1,2 − P2,1)2 + (P2,3 − P3,2)2 + (P1,3 − P3,1)2] (5)

where g11, g12, g44, g044 are the gradient energy coefficients and Pi,j = ∂Pi/∂xj, where xj is the spatial coordinate.

Here in our simulation, the parameters are selected as α1 = 4.125×105 C−2m2NK−1, α11 = −5×108 C−4m6N, α111 = 1.294×108 C−6m10N, b1 = 1.6×107 C−4m6N, b11 = 3×105 C7m10N, b111 = 1.5×107 C−6m10N, c11 = 1.78×1011 Nm−2, c12 = 1.22×1011 Nm−2, c44 = 0.1 C−2m4, Q11 = 0.034 C−2m4, Q12 = 0.029 C−2m4, Q44 = 4×1011 C−2m4N, g11 = g44 = g044 = 2×10−10 C−2m4N. The Landau coefficients and elastic constants are modified from (BNST−BMN)−xBZ52. The grid size is 128dx×128dx, where dx = 1 nm. The local-field effect and local Curie temperature effect caused by the point defects are introduced into the phase field model. There are two sets of local-field and local Curie temperature conditions to simulate different doping ratios of BaHfO3. When x=0, the standard deviation of the local field is 3.5×107 Vm−1; and for T0, the mean value is 155 K, and the standard deviation is 43.3 K. When x=0.1, the standard deviation of the local field is 1×108 Vm−1; for T0, the mean value is 55 K, and the standard deviation is 43.3 K.

Density functional theory calculations
The calculations were performed using the density functional theory (DFT) formalism, specifically implemented in the Cambridge Serial Total Energy Package (CASTEP). Within the framework of Generalized Gradient Approximation (GGA), the Perdew-Burke-Ernzerhof (PBE) function was utilized to define the exchange-correlation energy. A cut-off energy of 520 eV was chosen to ensure convergence, with a minimum energy tolerance set at 10−5 eV per atom and a force tolerance of 0.001 eV/Å. Brillouin zone integration was carried out using the Monkhorst-Pack scheme, employing a 3×3×3 k-point mesh.

Preparation of dielectric ceramics
(1−x)Sr0.5Bi0.25Na0.25TiO3−xBaHfO3 [(1−x)SBNT−xBH] (x=0, 0.1, 0.2, 0.3, 0.35) ceramics were prepared by the solid phase method. Raw materials of Na2CO3 (≥99.8%), Bi2O3 (≥99%), TiO2 (≥98%), SrTiO3 (≥99%), BaCO3 (≥99%), HfO2 (≥98%) (all purchased from Sinopharm Chemical Reagent Co, Ltd, China) were weighed according to the stoichiometric ratio. Use a ball mill to mix the slurry evenly, then put it in the oven for treatment. The dry powder and 3 wt% PVA were mixed and then pressed into pellets with a diameter of 10 mm and a thickness of 1 mm. PVA is then burned at 500 °C for hours and then sintered at 1200−1300 °C for 2 h. Finally, the ceramic is polished to a thickness of 0.06 mm to test its electrical properties.

Characterizations of lattice structure and polar configuration
The phase and microstructure of the ceramics were characterized by X-ray diffractometer (XRD, D8 ADVANCE-A25, Bruker, Germany) and scanning electron microscope (Germany’s Zeiss Gemini SEM 300), and EDS (Oxford Instruments X-Max NSN78861). The grain size of ceramics was measured using by ImageJ software. The HAADF-STEM experiments were conducted using an aberration-corrected scanning transmission electron microscope (STEM; FEI Titan Cubed Themis G2 300, Thermo Fisher Scientific, USA). Selected area electron diffraction (SAED) measurements were performed on an image-aberration-corrected STEM operating at an accelerating voltage of 200 kV. The Ultraviolet and visible (UV-Vis) absorption spectra were acquired using a UV-vis spectrometer (UV-9000, METASH, China) in the wavelength range of 300−700 nm, with BaSO4 serving as the reference material.

Measurements of electric properties and dielectric energy storage
Bipolar P−E loops at low electric fields and room temperature were recorded using a ferroelectric analyzer (PolyK Technologies, USA). The temperature-dependent dielectric properties (εr) and dielectric loss (tanδ) were measured by an LCR meter (DMS-1000, BALAB, China). AC impedance spectroscopy was measured using an Electrochemical Workstation (VSP, Bio-Logic, France) in the temperature range of 350−650 °C. The unipolar P−E loops under various electric fields, frequencies, temperatures, and cycle numbers were measured utilizing a ferroelectric tester (Radiant Technologies Inc., USA). The overdamped (390 Ω) and underdamped (1 Ω) charge/discharge tests were conducted according to Tongguo (TG) technology (CFD003, China).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript reports mixing BaHfO3 into (Sr,Bi,Na)TiO3 to tune the dielectric-maximum temperature Tm to room\ntemperature, and claims a combination of high recoverable energy density (16.2 J/cm2) and efficiency (92%). While the\nreported values are impressive, the discussion about the physical mechanism is less convincing. Therefore, it would require\na major revision and a few pieces of supplementary data before the manuscript could be recommended for publication in\nNature Communications.\n1. Line 31 “a phase boundary between relaxor and superparaelectric phases” Line 63 “Below Tm, relaxor (RE) state …” Line\n69 “In contrast, the superparaelectric (SPE) state appears above Tm …”\nThe authors should be cautious when talking about a “phase boundary” at Tm. In relaxor ferroelectrics, Tm should be never\ntaken as an actual phase-transition temperature, as Tm strongly depends on measurement condition (i.e., probe\nfrequency). Instead, it has been established since the ‘90s that, in order to extract the actual transition temperature, the\nfrequency dependency of Tm must be fitted to Vogel-Fulcher law, which yields the actual phase-transition temperature,\nTf. For an original reference of the idea, please refer to [Viehland, Dwight, et al. \"Freezing of the polarization\nfluctuations in lead magnesium niobate relaxors.\" Journal of Applied Physics 68, 2916 (1990)]. For a modern understanding of phase transitions\nin relaxor ferroelectrics, please read [Takenaka, Hiroyuki, et al. \"Slush-like polar structures in single-crystal relaxors.\" Nature\n546, 391 (2017)].\nTo be consistent with the mainstream understanding of relaxor ferroelectrics and to avoid confusion from future readers, the\nauthors should avoid using the term of “phase boundary” and instead use descriptions such as “the crossover from dynamic\nto static/frozen relaxor states”. This adaption should be made not only at Line 31, 63, and 69, but throughout the manuscript.\n2. Line 85, “it exhibits faster dynamics and minimal akin to SPE state” This sentence is hard to understand. Some words\nmight be missing.\n3. Line 86, “relative to the RFE state”. Please use consistent abbreviations throughout the manuscript, either “RE” or\n“RFE”.\n4. Line 98, “relaxor degree” is not considered good English. Please consider switching to another expression such as\n“strength of relaxor behavior”.\n5. Line 110, “the increased lattice dimensions provide greater spatial freedom for polarization enhancement”. This is an\ninteresting point. Is this supported by the polarization value extracted from DFT?\n6. Left, Fig. 1a. Is this illustration based on phase-field simulations? If so, what are the compositions of the materials\nsimulated, for the top and bottom panels, respectively? Please describe in the figure/legend.\nRight, Fig. 1a. Again, assuming this illustration is from DFT, please describe the material compositions for such\ncalculations. Plus, please provide a legend for the colors of the atoms.\n7. Top, Fig. 1b. Again, please specify which chemical compositions these simulations correspond to.\nBottom, Fig. 1b. If this data is from experiment, it should be clearly labelled. Plus, the abbreviations ER and NER should be\ndefined.\n8. Fig. 1c. Are the dielectric-temperature curve and the P-E loop from real experiments, or simulations? Please specify.\nEither way, the material compositions and measurement conditions (frequency, temperature) should be labelled in\nfigure/legend.\n9. Top, Fig. 1d. The lattice expansion is highly exaggerated. Please label the actual expansion percentage. Also, it would\nbe a good idea to label the composition in figure/legend as well.\n10. Line 147, “a rise in the relaxor dispersion index (γ) rises from …” Please fix the grammar.\n11. Line 147, “… rises from 1.54 to 1.84.” Based on Supplementary Fig. 5, x = 0.3 does not fit well to the given model. Please\nrefrain from using this value.\n12. Fig. 2b-2c. The significant difference between x = 0.3 and x = 0.35 is unexpected. First off, there is only a small\ndifference in chemical composition. Second, BaHfO3 is a paraelectric and, naively, one would expect adding more\nBaHfO3 should lead to decreasing Tm. Is there any structural difference (density, grain size, phase separation, etc.) that\nleads to this difference?\n13. Fig. 2e. How is Burns temperature (TB) extracted? Please provide a plot of these fittings.\nAll the dielectric data presented in this work are from temperatures lower than TB, but TB is only meaningful if extracted from\nthe high-temperature side. See, for example, [Bokov, A. A., and Z-G. Ye. \"Recent progress in relaxor ferroelectrics with\nperovskite structure.\" Journal of materials science 41, 31 (2006)].\n14. Figs. 3c4 and 3d4. Can the authors provide an estimate of local polarization (in μC/cm2) based on the local atomic\ndisplacement? This value defines the maximum polarization that can be achieved in this system via polarization rotation\nunder electric field.\n15. Fig. 4g. What is the connection between bandgap and breakdown field? If the logic is “large bandgap -> low leakage\ncurrent -> high breakdown field”, please show a comparison of the leakage current (I-V curve) in each case.\nIn fact, bandgap would be a good indicator of leakage only if the conductivity is determined by intrinsic excitations. In\nperovskite oxides, however, the case of intrinsic excitation is relatively rare, and in most cases the leakage is determined\nby extrinsic factors such as doping or trap states.", "reviewer_2": "This report outlines a strategy to simultaneously achieve an exceptional comprehensive energy storage performance, Wrec\nof 16.2 J/cm3 and η of 92% at a high Eb of 68 kV/mm, by actively constructing a super-relaxor critical state—a phase\nboundary between relaxor and super-paraelectric phases—through targeted compositional tuning and polarization\nconfiguration control. The approach incorporates both phase-field simulations and first-principle calculations to explore\nthe influence of BaHfO3 integration into the Sr0.5Bi0.25Na0.25TiO3 relaxor matrix. The study presents promising result and\ncould make a significant contribution to the ceramic community if further questions are clarified and refined as follows:\n1. In the first paragraph of the Results and Discussion, the authors stated that the addition of larger substituent ions, such as\nBa2+ and Hf4+ can expand the volume of the Sr0.5Bi0.25Na0.25TiO3 unit cell, and the increased lattice dimension can\nprovide greater spatial freedom for polarization enhancement. This description is a problematic assumption without clear\nevidence. Instead, the composition-driven enhancement induced by the strongly isotropic polar disorder via the BaHfO3\ndoping should be the main reason for providing greater spatial freedom for the polarization enhancement, rather than the\nincreased lattice dimension. The authors should give more evidences to support this conclusion.\n2. The temperature-dependent dielectric permittivity curves (Fig. 2d), Raman scattering spectra (Fig. S6, Supplementary\nInformation) and P−E loops (Fig. 2f), as well as the high-temperature impedance response (Fig. 4e) show different trends for\nx = 0.35 composition. The authors should describe their correlations and give explanation for the observed change in trend.\nAlso, the authors should show the reliability of experimental data.\n3. To understand the relationship between the dielectric properties and phase structures in SBNT−xBH ceramics, please\nprovide the complete XRD refinement analyses for all compositions. Moreover, specifically explain the roles of the cubic and\ntetragonal structures play in enhancing the energy storage characteristics, particularly in relation to the emergence of the\nsuper-paraelectric/ super-relaxor state.\n4. Why is the c/a map of SBNT−0.3BH in the Fig. S8 (Supplementary Information) done along the [110]pc zone axis rather\nthan [100]pc zone axis? Is there any specific consideration?\n5. In the Nyquist plots (Z' vs. -Z'') plots as shown in Fig. 4e and Fig. S10 (Supplementary Information), the same intervals\nof Z’ and -Z” should be applied for semicircle comparison and to estimate the resistances. What type of resistance contribute to\nthe semicircle (for example, grain bulk, grain boundary, or interface between electrode and ceramic)?\n6. Abbreviations should be given with full names or chemical formula while they appear first time in the text, such as\nDFT (density functional theory) and BBT12.\n7. The label ‘Density grain’ in Fig. S7a (Supplementary Information) should be corrected to ‘Dense grain’."}, "author_response": "Responses to specific comments raised by the reviewers\n------------------------------------------------------------------------\nReport of Reviewer 1\n------------------------------------------------------------------------\nRecommendation: Major revisions.\nComments:\nThis manuscript reports mixing BaHfO into (Sr,Bi,Na)TiO to tune the dielectric-maximum temperature T to room\n3 3 m\ntemperature, and claims a combination of high recoverable energy density (16.2 J/cm2) and efficiency (92%). While the\nreported values are impressive, the discussion about the physical mechanism is less convincing. Therefore, it would\nrequire a major revision and a few pieces of supplementary data before the manuscript could be recommended for\npublication in Nature Communications.\nWe sincerely thank the reviewer for the recognition of our work and for his/her invaluable comments and\nsuggestions, which have helped us significantly enhance our work.\n1. Line 31 “a phase boundary between relaxor and superparaelectric phases” Line 63 “Below T , relaxor (RE) state …”\nm\nLine 69 “In contrast, the superparaelectric (SPE) state appears above T …”\nm\nThe authors should be cautious when talking about a “phase boundary” at T . In relaxor ferroelectrics, Tm should be\nm\nnever taken as an actual phase-transition temperature, as T strongly depends on measurement condition (i.e., probe\nm\nfrequency). Instead, it has been established since the ‘90s that, in order to extract the actual transition temperature, the\nfrequency dependency of T must be fitted to Vogel-Fulcher law, which yields the actual phase-transition temperature,\nm\nT. For an original reference of the idea, please refer to [Viehland, Dwight, et al. \"Freezing of the polarization\nf\nfluctuations in lead magnesium niobate relaxors.\" Journal of Applied Physics 68, 2916 (1990)]. For a modern\nunderstanding of phase transitions in relaxor ferroelectrics, please read [Takenaka, Hiroyuki, et al. \"Slush-like polar\nstructures in single-crystal relaxors.\" Nature 546, 391 (2017)].\nTo be consistent with the mainstream understanding of relaxor ferroelectrics and to avoid confusion from future\nreaders, the authors should avoid using the term of “phase boundary” and instead use descriptions such as “the crossover\nfrom dynamic to static/frozen relaxor states”. This adaptation should be made not only at Line 31, 63, and 69, but\nthroughout the manuscript.\nResponse: Thank you very much for this insightful comment. We fully agree with the reviewer that, in relaxor\nferroelectrics, the temperature of the dielectric maximum T , should not be regarded as a true thermodynamic phase\nm\ntransition, since T is strongly frequency dependent and reflects the measurement timescale. We acknowledge that our\nm\noriginal wording of “a phase boundary between relaxor and superparaelectric phases” at T , could be misleading. To\nm\navoid confusion and to be consistent with the mainstream relaxor framework, we have carefully revised the terminology\nas “the crossover from dynamic to static/frozen relaxor states” accordingly throughout the manuscript.\nRevision: MS, Page 2, Lines 29-32, a sentence has been amended.\nTo address this issue, we propose a strategy actively constructing a superrelaxor critical state located at the crossover\nfrom dynamic to static/frozen relaxor states, achieved through targeted compositional tuning and polarization\nconfiguration control.\nNotably, the SBNT−0.3BH composition exhibits a low dielectric constant (ε < 500) and a flattened dielectric–\nr\ntemperature response near T = RT, corresponding to our designed RT superrelaxor critical state situated at the\nm\ncrossover between dynamic and static/frozen relaxor regimes.33,34\nRevision: MS, Page 7, Lines 177-178, a sentence has been amended.\nRemarkably, the T of SBNT−0.3BH ceramics lies within this dynamic-static/frozen relaxor crossover region near\nm\nRT, while retaining an evident relaxor behavior, closely matching the superrelaxor critical state predicted by phase-field\nsimulations.\nReferences:\n[33] Viehland, Dwight, et al. Freezing of the polarization fluctuations in lead magnesium niobate relaxors. J. Appl. Phys.\n68, 2916 (1990)\n[34] Takenaka, Hiroyuki, et al. Slush-like polar structures in single-crystal relaxors. Nature 546, 391 (2017).\n2. Line 85, “it exhibits faster dynamics and minimal akin to SPE state” This sentence is hard to understand. Some words\nmight be missing.\nResponse: Thank you very much for this helpful comment. We agree that the original sentence was incomplete and\nthus hard to follow. To clarify this point and improve readability, we have rewritten the sentence accordingly in the\nrevised manuscript.\nRevision: MS, Page 4, Lines 84-87, a sentence has been revised.\nSuch a configuration effectively combines the advantages of dynamic and static/frozen states: it exhibits fast\npolarization dynamics with minimal hysteresis, reminiscent of a SPE-like dynamic regime, yet it retains strong dipoles\nand large polar nanoregions relative to the static or frozen polar state.\n3. Line 86, “relative to the RFE state”. Please use consistent abbreviations throughout the manuscript, either “RE” or\n“RFE”.\nResponse: Thank you very much for pointing out this inconsistency. In the revised manuscript, we have unified the\nabbreviation and now consistently use “RFE” for “relaxor ferroelectric” throughout the manuscript. The term is clearly\ndefined at its first occurrence, and all previous instances of “RE” have been corrected to “RFE” in the main text, figure\nlabels, captions, and Supplementary Information.\n4. Line 98, “relaxor degree” is not considered good English. Please consider switching to another expression such as\n“strength of relaxor behavior”.\nResponse: Thank you very much for this helpful comment and for suggesting a more appropriate expression. Following\nthe reviewer’s suggestion, we have replaced “relaxor degree” with the more precise phrase “strength of relaxor behavior”\nin the revised manuscript to improve the clarity and professionalism of the description.\nRevision: MS, Page 2, Lines 34-36, an expression has been revised.\nstrength of relaxor behavior.\nRevision: MS, Page 4, Lines 98-99, an expression has been revised.\nConsequently, the dielectric maximum (ɛ ) shifts toward RT, flattening the dielectric response and enhancing the\nm\nstrength of relaxor behavior\n5. Line 110, “the increased lattice dimensions provide greater spatial freedom for polarization enhancement”. This is an\ninteresting point. Is this supported by the polarization value extracted from DFT?\nResponse: Thank you very much for this important comment. We agree that this statement needs to be substantiated by\nquantitative analysis. In the revised manuscript, we have further clarified this point using polarization vectors extracted\nfrom our density-functional-theory calculations. Specifically, we evaluated the spontaneous polar configuration of\nrelaxed supercells using the Born effective charge method. With BaHfO incorporation, the supercell shows evident\n3\nlocal structural distortion and lattice expansion. Under this framework, the atomic polar vectors exhibit a higher degree\nof orientational disorder and enhanced local polar magnitudes within the distorted oxygen polyhedral, as illustrated by\nthe overlaid polar vectors on the colored atoms in Fig. 1a. Consequently, under an applied electric field, the reorientation\nof these diverse local polarizations mainly contributes to a large microscopic polarization response. We also extracted\nthe average polarization value from the supercells and found that the local spontaneous polarization (27 μC/cm2) is\nhigher than that of the SBNT-based unit cell (16 μC/cm2), which is contributed by large lattice distortion and, in turn,\nleads to more isotropic, disordered polar configurations. Taken together, these results clarify that the key effect of\nBaHfO doping in local structure is a composition-driven enhancement of polar disorder and local distortion, rather than\n3\na simple geometric lattice expansion, and this enhanced polar disorder underpins the coexistence of high recoverable\nenergy density and high efficiency in the designed superrelaxor critical state. Therefore, we have revised our discussion\non this local structure feature accordingly.\nRevision: MS, Page 4, Lines 104-114, a new discussion has been added.\nIn the SBNT–xBH system, the introduction of BaHfO will induce composition-driven local structural distortion and\n3\nstrongly isotropic polar disorder. Density-functional-theory calculations on relaxed supercells for x = 0 and 0.3 system\nreveal enhanced lattice and octahedral distortion in the BaHfO -modified composition, accompanied by a more isotropic\n3\ndistribution and larger magnitudes of local polar vectors with average polarization of 27 μC/cm2, as illustrated by the\npolarization arrows overlaid on the atomic models in Fig. 1a. Under an applied electric field, the rotation and alignment\nof these diverse local polarizations give rise to a large microscopic polarization response while avoiding strong long-\nrange coupling, consistent with the superrelaxor critical state and the coexistence of high recoverable energy density\nand high efficiency in the SBNT–0.3BH ceramic.\n6. Left, Fig. 1a. Is this illustration based on phase-field simulations? If so, what are the compositions of the materials\nsimulated, for the top and bottom panels, respectively? Please describe in the figure/legend.\nRight, Fig. 1a. Again, assuming this illustration is from DFT, please describe the material compositions for such\ncalculations. Plus, please provide a legend for the colors of the atoms.\ncompositions of the schematic illustrations in Fig. 1a in the original submission. For the left panel of Fig. 1a, the domain\nconfigurations are indeed obtained from phase-field simulations. The top schematic corresponds to the conventional\nrelaxor ferroelectric (RFE) state of the parent SBNT composition (x = 0), whereas the bottom schematic represents the\ndesigned superrelaxor state of the BaHfO -modified composition (x = 0.3). For the right panel of Fig. 1a, the atomic-\n3\nscale illustration is based on DFT-relaxed crystal structures that are used to compare the local structural difference in\nthe x = 0 and 0.3 compositions. Therefore, we have explicitly labeled these compositions, states, and a color legend that\nspecifies different atomic species in the figure and described them in the figure caption to avoid ambiguity.\nRevision: MS, Page 4, missed labels in Figure 1 have been added.\nFig. 1 | Schematic illustration of superrelaxor critical state design based on phase field simulations and density\nfunctional theory calculations. (a) Conceptual framework for constructing a superrelaxor critical state, integrating\nphase-field simulations and crystal structure calculations to compare relaxor ferroelectric and superrelaxor domain\nstructures. (b) Experimental temperature-dependent dielectric constant spectra for relaxor ferroelectric and superrelaxor\nstates and composition-dependent evolution of the temperature corresponding to the T . (c) Temperature-dependent\nm\ndielectric constant spectrum calculated by phase-field simulation at 1 kHz, wherein the insets show the schematic P−E\nloops and polar configurations for relaxor ferroelectric, superrelaxor ferroelectric, and paraelectric states. (d) Crystal\nstructure of superrelaxor in density-functional-theory calculations.\n5\n7. Top, Fig. 1b. Again, please specify which chemical compositions these simulations correspond to Bottom, Fig. 1b. If\nthis data is from experiment, it should be clearly labelled. Plus, the abbreviations ER and NER should be defined.\nResponse: Thank you very much for this careful comment. For the top panel of Fig. 1b, the dielectric permittivity–\ntemperature curves are obtained from simulations and correspond to representative x = 0 and 0.3 compositions. In the\nrevised figure, we have explicitly labeled these simulated curves with their chemical compositions to make the\ncorrespondence unambiguous. In addition, the abbreviations “ER” and “NER” have been replaced by their full forms\n“ergodic state” and “non-ergodic state” to avoid the unclear expression. Please refer to our response to comment #6 for\nthe revised Figure 1.\n8. Fig. 1c. Are the dielectric-temperature curve and the P-E loop from real experiments, or simulations? Please specify.\nEither way, the material compositions and measurement conditions (frequency, temperature) should be labelled in\nfigure/legend.\nResponse: Thank you very much for this helpful comment and for pointing out the ambiguity in our original figure.\nFig. 1c, the dielectric–temperature curve using phase-field simulations based on x = 0.3 composite with a temperature\nrange from -150°C to 250 °C and a frequency of 1 kHz, wherein the inserts show the schematic diagrams of P-E loops\nbefore, near, and above the dielectric maximum temperature. In the revised manuscript, we have explicitly indicated the\nmaterial composition and the simulation conditions accordingly to avoid the possible uncertainty. Please refer to our\nresponse to comment #6 for the revised Fig. 1.\n9. Top, Fig. 1d. The lattice expansion is highly exaggerated. Please label the actual expansion percentage. Also, it would\nbe a good idea to label the composition in figure/legend as well.\nResponse: Thank you very much for this constructive suggestion. We fully agree that the lattice expansion in the\noriginal schematic of Fig. 1d was qualitatively exaggerated and could therefore be misleading if not properly annotated.\nIn the revised manuscript, we have redrawn the lattice models in Fig. 1d and explicitly indicated the actual lattice\nexpansion ratio derived from our structural analysis. Please refer to our response to comment #6 for the revised Fig. 1.\n10. Line 147, “a rise in the relaxor dispersion index (γ) rises from …” Please fix the grammar.\nResponse: Thank you very much for pointing out this grammatical issue. We have corrected the sentence accordingly\nand have also carefully checked the grammar and language throughout the manuscript to ensure consistency and\ncorrectness.\nRevision: MS, Page 6, Lines 162-163, a sentence has been amended.\nT flattening at RT is accompanied by a rise in the relaxor dispersion index (γ) from 1.54 to 1.84.\nm\n11. Line 147, “… rises from 1.54 to 1.84.” Based on Supplementary Fig. 5, x = 0.3 does not fit well to the given model.\nPlease refrain from using this value.\nResponse: Thank you very much for this important comment. To address this concern, we have re-measured the\n6\ndielectric permittivity–temperature curves and performed the Curie-Weiss fitting for the x = 0.3 ceramic. In the revised\nSupplementary Fig. 5, we present the updated fitting results, wherein the relaxor dispersion for x = 0.3 is determined as\nγ =1.86, showing a clear and robust increase relative to the x = 0. Therefore, we have accordingly revised the\ncorresponding sentence in the manuscript.\nRevision: SI, page 6, a figure, Supplementary Figure 5, has been revised.\nSupplementary Figure 5. Temperature-dependent ε and tan δ of (a) SBNT and (b) SBNT−0.2BH ceramics under\nr\nvarious frequencies, (c) the modified Curie-Weiss distributions at x = 0 and x = 0.3, an increased γ value in x = 0.3\nindicates an increase in relaxor.\nRevision: MS, Page 6, Lines 162-163, a sentence has been amended.\nT flattening at RT is accompanied by a rise in the relaxor dispersion index (γ) from 1.54 to 1.86.\nm\n12. Fig. 2b-2c. The significant difference between x = 0.3 and x = 0.35 is unexpected. First off, there is only a small\ndifference in chemical composition. Second, BaHfO is a paraelectric and, naively, one would expect adding more\n3 m\nleads to this difference?\nResponse: Thank you very much for the comments. We agree that the small difference in chemical composition between\nx = 0.3 and 0.35 composites. As per the reviewer’s suggestions, we performed additional structural and electrical\ncharacterizations. As shown in the newly added Supplementary Figure 15, x = 0.35 exhibits coarser and more\nheterogeneous grains than x = 0.30, indicating increased microstructural inhomogeneity. Regarding lattice structure, the\nRaman spectra, which are highly sensitive to local atomic vibrations, bonding topology, and crystallinity, display weaker\nand significantly broadened peaks for the x = 0.35 composition, even though the long-range average perovskite phase\nis still maintained in the XRD patterns. In addition, the x = 0.35 composition shows a slightly smaller bandgap, a\nsignificantly higher leakage current density (please refer to our response to comment #15 and the newly added\nSupplementary Figure S13) as well as a lower thermal activation energy for ion and defect immigrations compared with\nx = 0.30. These results suggest that further increasing the BaHfO content pushes the system beyond the optimal solid-\n3\nsolution window, where effects such as enhanced ionic-size mismatch, possible defect configuration, and poor chemical\nreaction may begin to degrade the local structure and electrical robustness, blurring the paraelectric dilution induced by\nthe BaHfO phase. Importantly, these observations further identify the x = 0.30 ceramic as the optimal composition,\n3\nproviding a balanced combination of robust local structural stability, dense crystalline microstructure, and high voltage\nendurance, thereby realizing superior energy-storage performance. Therefore, we have added a discussion based on\nthese experimental findings in the revised manuscript.\nRevision: MS, Pages 12-13, Lines 309-322, a discussion has been added.\nWe note that the x = 0.35 composition exhibits a distinct deviation from the trend in dielectric response, electric\nproperty, and structural evolution established from x = 0 to 0.3. Compared with SBNT–0.3BH, the x=0.35 ceramic\nshows clear signatures of microstructural (e.g., coarser and more heterogeneous grains, broadened and weakened Raman\npeak) and electrical degradation (e. g. a reduced bandgap, noticeably higher leakage, and lower thermal activation\nenergy for ion/defect migration). These complementary observations indicate that further increasing the BaHfO content\n3\npushes the system beyond the optimal solid-solution window, where the possible reasons, including the enhanced ionic-\nsize mismatch and defect-related inhomogeneities, degrade local structural and electrical robustness and blur the\nparaelectric dilution effect. As a result, the x = 0.3 composition is identified as the optimal point that provides a balanced\ncombination of robust local structural stability, dense crystalline microstructure, and high voltage endurance, thereby\nstabilizing the superrelaxor state with the best overall energy-storage performance.\nRevision: SI, Page 16, a new figure, Supplementary Figure 15, has been added.\nSupplementary Figure 15. SEM image of x = 0.35 ceramic.\nRevision: SI, Page 14, a new figure, Supplementary Figure 13, has been added.\nSupplementary Figure 13. Leakage current density as a function of electric field for x = 0, 0.30, and 0.35 ceramics.\n8\n13. Fig. 2e. How is Burns temperature (T ) extracted? Please provide a plot of these fittings.\nB\nAll the dielectric data presented in this work are from temperatures lower than T , but T is only meaningful if\nB B\nextracted from the high-temperature side. See, for example, [Bokov, A. A., and Z-G. Ye. \"Recent progress in relaxor\nferroelectrics with perovskite structure.\" Journal of Materials Science 41, 31 (2006)].\nResponse: Thank you very much for this important comment and for pointing us to the relevant literature. In the original\nversion, the Burns temperature (T ) was indeed determined in a somewhat simplified way, by using the derivative of\nB\nthe dielectric constant with respect to temperature in the dielectric-temperature spectra. As the reviewer correctly notes,\nthis approach does not rigorously follow the standard definition of T in relaxor ferroelectrics, which should be based\nB\non linear Curie-Weiss fitting in inverse permittivity 1/ε vs T plot at high temperature. The corresponding fitting plots\nr\nand results are now provided in the newly added Supplementary Figure 7, wherein the T values in the article have been\nB\nupdated. We also note that, for the x = 0 ceramic, an evident thermally activated defect-related peak appears on the high-\ntemperature side of the dielectric spectra, which obscures the fitting for T . However, this, in turn, supports our\nB\nconclusion that appropriate content of BaHfO helps suppress defect activity and stabilize the relaxor behavior.\nSupplementary Figure 7. Temperature-dependent 1/ε and Curie-Weiss fitting results at 1 MHz for (a) x = 0.1, (b) 0.2,\nr\n(c) 0.3, and (d) 0.35 ceramics, in which the additional dielectric peak induced by thermal defect activation near the T\nm\ntemperature interferes with the fitting for x = 0.\n14. Figs. 3c4 and 3d4. Can the authors provide an estimate of local polarization (in μC/cm2) based on the local atomic\ndisplacement? This value defines the maximum polarization that can be achieved in this system via polarization rotation\nunder electric field.\nResponse: Thank you very much for this valuable suggestion. We have quantitatively evaluated the local polarization\nusing the Born effective charge method accordingly, which yields an average polarization of 22.5 μC/cm2, agreeing\nwell with the spontaneous polarization estimated from the unipolar P-E loop (Figure 4a). Consequently, we have added\nthis value and corresponding discussion to the revised manuscript at the location indicated below.\nRevision: MS, Page 9, Lines 226-230, a sentence has been amended.\nThis polar displacement is higher than that of the previously reported superparaelectric ceramics20 and corresponds\nto an average polarization of 22.5 μC/cm2 using the Born effective charge method, agreeing well with the spontaneous\n9\npolarization estimated from the unipolar P-E loop (Figure 4a).\n15. Fig. 4g. What is the connection between bandgap and breakdown field? If the logic is “large bandgap -> low leakage\ncurrent -> high breakdown field”, please show a comparison of the leakage current (I-V curve) in each case. In fact,\nbandgap would be a good indicator of leakage only if the conductivity is determined by intrinsic excitations. In\nperovskite oxides, however, the case of intrinsic excitation is relatively rare, and in most cases the leakage is determined\nby extrinsic factors such as doping or trap states.\nResponse: Thank you very much for the helpful comments and we totally agree with the reviewer’s opinion. Firstly,\nwe have added the leakage current density-electric field curves of x = 0, 0.30, and 0.35 ceramics, as shown in the newly\nadded Supplementary Fig. 13. It can be noted that the leakage current density of the x = 0.3 composition is reduced by\napproximately three orders of magnitude compared with x = 0 and 0.35 ceramics, indicating that its larger bandgap\nsignificantly hinders electron transitions from the valence band to the conduction band. Secondly, since the leakage\ncurrent and voltage endurance are also associated with the extrinsic factor (charged defects and trapping states),\nwe have combined the leakage analysis with impedance spectroscopy. the x = 0.3 ceramic exhibits the highest bulk\nresistivity and the largest thermal activation energy for charge transport among the three compositions, indicating that\ndefect-mediated conduction (e.g., via vacancies or trap states) is strongly suppressed at this composition. As a\ncomparison, x = 0.35 ceramic exhibits relatively high leakage behavior and low breakdown strength, which is consistent\nwith its small bandgap, activation energy, and faded energy-storage performance. Therefore, we have added discussions\nin the revised manuscript.\nRevision: SI, Page 14, a new figure, Supplementary Figure 13, has been added.\nSupplementary Figure 13. Leakage current density as a function of electric field for x = 0, 0.30, and 0.35 ceramics.\nRevision: MS, Page 12, Lines 295-298, a new discussion has been added.\nThe larger E in the x = 0.3 composition significantly hinders electron transitions from the valence band to the\ng\nconduction band, thereby reducing the leakage current density by approximately three orders of magnitude relative to x\n= 0 and promoting the high breakdown field observed in the x = 0.3 ceramic (Supplementary Figure 13).\nRevision: MS, Page 12, Lines 306-309, a new discussion has been added.\nan increased density of carrier blocking interfaces due to grain refinement, and strong binding/trapping of charged\nelectrons and vacancies upon the introduction of BaHfO .\n3\n11\n------------------------------------------------------------------------\nReport of Reviewer 2\n------------------------------------------------------------------------\nRecommendation: Major revisions.\nComments:\nThis report outlines a strategy to simultaneously achieve an exceptional comprehensive energy storage performance,\nW of 16.2 J/cm3 and η of 92% at a high E of 68 kV/mm, by actively constructing a super-relaxor critical state—a\nrec b\nphase boundary between relaxor and super-paraelectric phases—through targeted compositional tuning and polarization\nconfiguration control. The approach incorporates both phase-field simulations and first-principle calculations to explore\nthe influence of BaHfO integration into the Sr Bi Na TiO relaxor matrix. The study presents promising result\n3 0.5 0.25 0.25 3\nand could make a significant contribution to the ceramic community if further questions are clarified and refined as\nfollows.\nWe sincerely thank the reviewer for finding our work interesting and for providing precious comments and\nsuggestions to help us greatly improve it.\n1. In the first paragraph of the Results and Discussion, the authors stated that the addition of larger substituent ions,\nsuch as Ba2+ and Hf4+ can expand the volume of the Sr Bi Na TiO unit cell, and the increased lattice dimension\n0.5 0.25 0.25 3\ncan provide greater spatial freedom for polarization enhancement. This description is a problematic assumption without\nclear evidence. Instead, the composition-driven enhancement induced by the strongly isotropic polar disorder via the\nBaHfO doping should be the main reason for providing greater spatial freedom for the polarization enhancement, rather\n3\nthan the increased lattice dimension. The authors should give more evidences to support this conclusion.\nResponse: Thank you very much for this important comment. We agree that our original statement, which linked\npolarization enhancement primarily to an “increased lattice dimension”, was oversimplified and not sufficiently justified.\nIn the revised manuscript, we have therefore removed this wording and now emphasize that the key factor is a\ncomposition-driven enhancement of local polar disorder and off-center displacements induced by BaHfO doping, rather\n3\nthan a simple lattice expansion. To support this conclusion, we have analyzed relaxed supercells representative of the x\n= 0 and 0.3 compositions and evaluated the polar configurations. It can be noted that enhanced lattice and octahedral\ndistortion in x = 0.3 composition compared with x = 0, which brings a more isotropic distribution of local polar vectors\nand larger polar magnitudes of them, as denoted by the direction and magnitude of polar vectors overlaid on the atoms\nin the right panel of Figure 1a. In this case, the rotation of the spontaneous polarization with diverse orientations to align\nwith the external electric field promotes the large polarization, indicating the composition-driven enhancement induced\nby the strongly isotropic polar disorder. Therefore, we have added the calculated results and discussions in the revised\nmanuscript to support our conclusion.\nRevision: MS, Page 4, Lines 104-114, a discussion has been added.\nIn the SBNT–xBH system, the introduction of BaHfO will induce composition-driven local structural distortion and\n3\nstrongly isotropic polar disorder. Density-functional-theory calculations on relaxed supercells for x = 0 and 0.3 system\nreveal enhanced lattice and octahedral distortion in the BaHfO -modified composition, accompanied by a more isotropic\n3\ndistribution and larger magnitudes of local polar vectors with average polarization of 27 μC/cm2, as illustrated by the\n12\npolarization arrows overlaid on the atomic models in Fig. 1a. Under an applied electric field, the rotation and alignment\nof these diverse local polarizations give rise to a large microscopic polarization response while avoiding strong long-\nrange coupling, consistent with the superrelaxor critical state and the coexistence of high recoverable energy density\nand high efficiency in the SBNT–0.3BH ceramic.\n2. The temperature-dependent dielectric permittivity curves (Fig. 2d), Raman scattering spectra (Fig. S6, Supplementary\nInformation) and P−E loops (Fig. 2f), as well as the high-temperature impedance response (Fig. 4e) show different\ntrends for x = 0.35 composition. The authors should describe their correlations and give explanation for the observed\nchange in trend. Also, the authors should show the reliability of experimental data.\nResponse: Thank you very much for the comments. We fully share the reviewer’s concern and have carefully verified\nthe behavior of the x = 0.35 composition by remeasuring the temperature-dependent dielectric permittivity, Raman\nspectra, P–E loops, and high-temperature impedance on 2–3 different pellets and multiple heating–cooling cycles before\nwe preparing the manuscript, all showing good reproducibility. To support this trend and its reliability, we also\nperformed additional structural and electrical characterizations. As shown in the newly added Supplementary Figure 15,\nthe x = 0.35 ceramic exhibits coarser and more heterogeneous grains than x = 0.3, indicating increased microstructural\ninhomogeneity. The Raman spectra, which are highly sensitive to local atomic vibrations, bonding topology, and\ncrystallinity, display weaker and significantly broadened peaks for x = 0.35, even though the long-range perovskite\nphase remains pure in the XRD patterns. In addition, the x = 0.35 composition shows a slightly smaller bandgap, a\nmarkedly higher leakage current density (as confirmed by the newly added leakage current density curve,\nSupplementary Figure S13), and a lower thermal activation energy for ion/defect migration compared with x = 0.3.\nThese results suggest that further increasing the BaHfO content pushes the system beyond the optimal solid-solution\n3\nwindow, where effects such as enhanced ionic-size mismatch, possible defect configurations, and incomplete reaction\nmay begin to degrade the local structure and electrical robustness, thereby blurring the paraelectric contribution from\nBaHfO phase. Importantly, these observations further identify x = 0.3 ceramic as the optimal composition,\n3\nproviding a balanced combination of robust local structural stability, dense crystalline microstructure, and high voltage\nendurance, and thus realizing the superrelaxor state with superior energy-storage performance. Therefore, we have added\ndiscussions based on these experimental findings in the revised manuscript.\nRevision: MS, Pages 12-13, Lines 309-322, a discussion has been added.\nWe note that the x = 0.35 composition exhibits a distinct deviation from the trend in dielectric response, electric\nproperty, and structural evolution established from x = 0 to 0.3. Compared with SBNT–0.3BH, the x = 0.35 ceramic\nshows clear signatures of microstructural (e.g., coarser and more heterogeneous grains, broadened and weakened Raman\npeak) and electrical degradation (e.g., a reduced bandgap, noticeably higher leakage, and lower thermal activation\nenergy for ion/defect migration). These complementary observations indicate that further increasing the BaHfO content\n3\npushes the system beyond the optimal solid-solution window, where the possible reasons, including enhanced ionic-\nsize mismatch and defect-related inhomogeneities, degrade local structural and electrical robustness and blur the\nparaelectric dilution effect. As a result, the x = 0.3 composition is identified as the optimal point that provides a balanced\ncombination of robust local structural stability, dense crystalline microstructure, and high voltage endurance, thereby\nstabilizing the superrelaxor state with the best overall energy-storage performance.\ns\nSupplementary Figure S15. SEM image of x = 0.35 ceramic.\nRevision: SI, Page 14, a new figure, Supplementary Figure 13, has been added.\nSupplementary Figure S13. Leakage current density as a function of electric field for x = 0, 0.30, and 0.35 ceramics.\n3. To understand the relationship between the dielectric properties and phase structures in SBNT−xBH ceramics, please\nprovide the complete XRD refinement analyses for all compositions. Moreover, specifically explain the roles of the\ncubic and tetragonal structures play in enhancing the energy storage characteristics, particularly in relation to the\nemergence of the super-paraelectric/super-relaxor state.\nResponse: Thank you very much for this helpful suggestion. In the revised manuscript, we have performed full XRD\nRietveld refinements for all SBNT-xBH compositions; the results are presented in the revised Supplementary Fig. S3,\nwith R < 10% for all cases, confirming the reliability of the refinements. The analysis shows a coexistence of tetragonal\nwp\n(polar) and cubic (non-polar) perovskite phases, with the tetragonal fraction decreasing and the cubic fraction increasing\nas x increases from 0 to 0.30. The polar tetragonal phase provides large local polarization, whereas the non-polar cubic\nphase corresponds to BaTiO incorporation. This, together with composition-induced local distortion and random fields,\n3\nweakens long-range dipole correlation and enhances local polar fluctuations. At the optimal composition x = 0.3, this\nbalance between polar tetragonal and non-polar cubic fractions stabilizes a room-temperature superrelaxor state with a\n14\nflattened dielectric response and highly recoverable polarization, which underpins the superior energy-storage\nperformance. Therefore, we have also added a discussion in the revised manuscript to clear the structure-property\nrelationship.\nRevision: MS, Page 6, Lines 140-145, a discussion has been added.\nRietveld refinements (Supplementary Figure S3) reveal coexisting tetragonal polar and cubic non-polar phases in all\nSBNT–xBH ceramics. With increasing BaHfO content from = 0 to 0.30, the tetragonal fraction decreases while the\n3\ncubic fraction increases, indicating a composition-driven phase evolution from a tetragonal-dominated polar state\n𝑥\ntoward a mixed tetragonal/cubic state.\nRevision: MS, Page 6, Lines 154-150, a discussion has been added.\nThis dielectric behavior is consistent with the phase evolution revealed by XRD refinement. As the cubic fraction\nincreases from x = 0 to 0.3, T shifts toward room temperature, the ε-T curve becomes progressively flatter, and the\nm\nstrength of relaxor behavior is enhanced (Fig. 2d). At the optimal composition x = 0.30, a balanced polar and nonpolar\nphase coexistence, together with composition-induced local distortion and random fields, stabilizes a room-temperature\nsuperrelaxor state.\nRevision: SI, Page 4, a figure, Supplementary Figure 3, has been revised.\nSupplementary Figure 3. (a-e) Room-temperature XRD patterns and Rietveld refinement results of SBNT−xBH (x =\n0, 0.1, 0.2, 0.3, 0.35) ceramics and (f) phase proportions of SBNT and SBNT−0.3BH ceramics obtained by refinement.\n4. Why is the c/a map of SBNT−0.3BH in the Fig. S8 (Supplementary Information) done along the [110] zone axis\npc\nrather than [100] zone axis? Is there any specific consideration?\npc\nResponse: Thank you very much for the comments. While quantitatively analyzing the [110] axial image, we firstly\ncalculated the c/a map based on [110]-zone axis STEM image and provided it in the original version. Following the\n15\nreviewer’s suggestion, we have now additionally constructed a c/a map from a [100] HAADF-STEM image for SBNT-\npc\n0.3BH, as shown in the newly added Supplementary Figure S10. The [100] -based map exhibits a similar c/a\npc\ndistribution to that obtained along [110] zone axis, further confirming the reliability and robustness of our local\npc\ntetragonality analysis.\nRevision: SI, Page 11, a new figure, Supplementary Figure S10, has been added.\nSupplementary Figure 10. c/a map of SBNT−0.3BH in the [110] zone axis.\npc\n5. In the Nyquist plots (Z' vs. -Z'') plots as shown in Fig. 4e and Fig. S10 (Supplementary Information), the same intervals\nof Z' and -Z'' should be applied for semicircle comparison and to estimate the resistances. What type of resistance\ncontributes to the semicircle (for example, grain bulk, grain boundary, or interface between electrode and ceramic)?\nResponse: Thank you very much for this helpful comment and for pointing out the ambiguity. In the revised manuscript,\nwe have replotted the Nyquist diagrams in Fig. 4e and Supplementary Fig. S12 using the same Z′ and −Z″ scales for all\ncompositions at a given temperature, wherein the data of ceramics with low resistance and very small semicircles were\nplotted as inserts in the figures. This allows a direct comparison of the semicircle radii and a more reliable estimation\nof the resistances. As shown in the updated plots, the semicircle radius (and thus the resistance) increases markedly\nfrom x = 0 to 0.3, whereas it decreases again at x = 0.35, consistent with the trend in breakdown strength discussed in\nthe main text. To clarify which resistance contributes to the semicircle, we have performed an equivalent-circuit analysis\nusing a standard model consisting of bulk (grain), grain boundary, and electrode–ceramic interface contributions (newly\nadded insert in Figure 4e). The fitting results indicate that, in our measurement frequency range, the dominant semicircle\nis governed by the combined grain and grain-boundary response, while the electrode–ceramic interface only gives a\nminor low-frequency tail and does not significantly affect the extracted resistance. Moreover, with increasing BaHfO\n3\ncontent from x = 0 to 0.3, both the grain and grain-boundary resistances increase, with the grain-boundary contribution\nbecoming more prominent, which is consistent with grain refinement and the increased density of carrier-blocking\ninterfaces. From x = 0.3 to 0.35, both resistances decrease again, in line with the higher leakage and reduced breakdown\nstrength at x = 0.35. Therefore, we have revised the manuscript and added a discussion on impedance fitting results\naccordingly.\nHigh-temperature impedance spectroscopy shows a pronounced increase in the semicircle radius from x = 0 to 0.3,\nfollowed by a decrease at x = 0.35, indicating the highest resistance at x = 0.3 (Fig. 4e and Supplementary Fig. 12).\nEquivalent-circuit fitting results, by considering the contributions from grain, grain boundary, and electrode-electrolyte\ninterface, show that the semicircle at 650 °C is dominated by the grain and grain-boundary resistances. The maximum\nresistance at x = 0.3, dominated by the grain-boundary blocking effect (Fig. 4e and Supplementary Table S4), is\nconsistent with the highest grain boundary at this composition.\nRevision: SI, Page 13, a new figure, Supplementary Figure 12, has been added.\nSupplementary Figure 10. Impedance spectrum of SBNT−xBH dielectric ceramics measured at temperatures of (a) x\n= 500 °C, (b) 560 °C, (c) 600 °C, (d) 650 °C.\nRevision: MS, Page 11, a figure, Figure 4e, has been added.\nFigure 4e. Impedance spectra and fitting results of SBNT−xBH dielectric ceramics at 650 °C, wherein the inset shows\nthe equivalent circuit model used for fitting.\nSupplementary Table S4. Fitting parameters for impedance spectra of SBNT-xBH ceramics measured at 650 °C.\nR C R C R C\n1 1 2 2 3 3\nx\n(Ω cm2) (μF cm-2) (Ω cm2) (μF cm-2) (Ω cm2) (μF cm-2)\n0 59 1.244 × 10-5 75 8.625 × 10-8 10 8.10 × 10-10\n0.1 8562 9.474 × 10-7 3.862 × 104 3.665 × 10-9 253 5.01 × 10-10\n0.2 12670 4.921 × 10-9 8.299 × 104 2.975 × 10-10 956 2.59 × 10-10\n0.3 12030 7.894 × 10-7 1.046 × 105 1.510 × 10-9 563 3.97 × 10-10\n0.35 864 6.255 × 10-10 4174 8.625 × 10-5 60 1.31 × 10-8\n6. Abbreviations should be given with full names or chemical formula while they appear first time in the text, such as\nDFT (density functional theory) and BBT12.\nResponse: Thank you very much for the comments. We have carefully checked all abbreviations throughout the revised\nmanuscript and supplementary information, and we have provided the full names and/or chemical formulae at their first\noccurrence accordingly.\n7. The label ‘Density grain’ in Fig. S7a (Supplementary Information) should be corrected to ‘Dense grain’.\nResponse: Thank you very much for pointing out this typo. We have corrected the label “Density grain” to “Dense\ngrain” in the revised Supplementary Figure 7a (now Supplementary Figure 8a).\nRevision: SI, Page 9, a label in Supplementary Figure 8a, has been revised.\nSupplementary Figure 8. (a) Grain morphology in the TEM image and SAED image of SBNT−0.3BH ceramic.\n18"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have made significant efforts to revise the manuscript and add supporting data. Now I believe the manuscript is in a better form and can be recommended for publication in Nature Communications.", "reviewer_2": "Most of the issues have been resolved in the revised manuscript, making it of better quality. However, there are still a few minor problems in the revised manuscript that need to be modified before the manuscript can be accepted for publication.\nFor example:\n1.The chemical composition labeling in Figure 1b (top and bottom) is incorrect.\n2.The caption in Supplementary Figure 2, “....and (d) SBNT−0.3BH....”, should be “....and (e) SBNT−0.3BH....”\n3.The caption in Supplementary Figure 10, “....in the [110]pc zone axis”, should be “....in the [100]pc zone axis.” Additionally,\nSupplementary Figure 9 and 10 should be merged into one figure for easy reading.\n4.In the Nyquist plot of Supplementary Figure 12, the curve for the composition at x = 0 is missing. Additionally, the same Z' and -Z'' intervals should be applied for semicircular comparison and resistance estimation.\n5.A clear microscale bar should be marked in the SEM image of Supplementary Figure 15."}, "author_response": "Ref. Manuscript ID: NCOMMS-25-69169A\nDear reviewers,\nThe authors sincerely appreciate your time and effort in re-reviewing our manuscript. Your invaluable insights and\nconstructive comments have significantly strengthened the quality, clarity, and rigor of our work. We are particularly\ngrateful for your meticulous evaluation and thoughtful suggestions.\nIn the revised manuscript, we have carefully addressed each comment and implemented corresponding revisions\nthroughout the main text and the Supplementary Information. For ease of reference, all changes have been highlighted\nin yellow. We believe these revisions satisfactorily resolve the concerns raised and further improve the overall\npresentation of the study.\nThank you again for your attention and contributions. We wish you a Merry Christmas and a Happy New Year.\nYours sincerely,\nBing Xie, Tianyu Li, Shujun Zhang\nOn behalf of all authors\n____\nEmail: tianyuli@ustb.edu.cn & s.j.zhang@cityu.edu.hk\nDepartment of Physics & Department of Chemistry\nCity University of Hong Kong\nHong Kong SAR, China\n&\nEmail: xieb@nchu.edu.cn\nSchool of Power and Energy\nNanchang Hangkong University\nNachang 330063, China\n------------------------------------------------------------------------\nReport of Reviewer 1\n------------------------------------------------------------------------\nRecommendation: Acceptance.\nComments:\nThe authors have made significant efforts to revise the manuscript and add supporting data. Now I believe the\nmanuscript is in a better form and can be recommended for publication in Nature Communications.\nWe sincerely thank the reviewer for this positive assessment and for recognizing the efforts made in revising the\nmanuscript and adding supporting data. We appreciate your recommendation and constructive evaluation,\nwhich have been invaluable in improving the quality of our work.\n2\n------------------------------------------------------------------------\nReport of Reviewer 2\n------------------------------------------------------------------------\nRecommendation: Revision.\nComments:\nMost of the issues have been resolved in the revised manuscript, making it of better quality. However, there are still a\nfew minor problems in the revised manuscript that need to be modified before the manuscript can be accepted for\npublication. For example:\nWe would like to express our sincere gratitude to the reviewer for the careful re-evaluation of our manuscript\nand for the constructive comments, which have been essential in improving the quality of this work. We\nparticularly appreciate the reviewer’s continued time and effort.\n1. The chemical composition labeling in Figure 1b (top and bottom) is incorrect.\nResponse: Thank you very much for bringing this issue to our attention. We are sorry that the labels for x = 0 and x =\n0.3 were reversed. We have corrected the labels in revised Figure 1b accordingly.\n2. The caption in Supplementary Figure 2, “....and (d) SBNT−0.3BH....”, should be “....and (e) SBNT−0.3BH....”\nResponse: Thank you very much for the comments. We have revised the caption of Supplementary Figure 2 from “(d)\nSBNT−0.3BH” to “(e) SBNT−0.3BH” and have confirmed its correctness accordingly.\n3. The caption in Supplementary Figure 10, “....in the [110] zone axis”, should be “....in the [100] zone axis.”\npc pc\nAdditionally, Supplementary Figure 9 and 10 should be merged into one figure for easy reading.\nResponse: Thank you very much for this important suggestion. In the revised manuscript, we have revised the caption\nof Supplementary Figure 10 from “[110] zone axis” to “[100] zone axis” and have also merged Supplementary\npc pc\nFigures 9 and 10 into a single figure (Supplementary Figure 10 now). The numbering of the subsequent supplementary\nfigures has been updated accordingly.\n4. In the Nyquist plot of Supplementary Figure 12, the curve for the composition at x = 0 is missing. Additionally, the\nsame Z' and -Z'' intervals should be applied for semicircular comparison and resistance estimation.\nResponse: Thank you very much for the comments. In fact, the Nyquist plot for the x = 0 composition has been included\nin Supplementary Figure 12 (Supplementary Figure 11 now); however, due to its extremely low resistance, the\ncorresponding semicircle is not visible under the same scale. To clearly present this feature, we have plotted the x = 0\ndata separately as an inset within the same figure. In addition, we have adjusted the Z′ and -Z″ ranges to ensure that\nidentical intervals are applied for all compositions, enabling a consistent semicircular comparison and resistance\nestimation.\nRevision: SI, Page 12, a figure, Supplementary Figure 11, has been revised.\n= 500 °C, (b) 560 °C, (c) 600 °C, (d) 650 °C.\n5. A clear microscale bar should be marked in the SEM image of Supplementary Figure 15.\nResponse: Thank you very much for the helpful suggestion. In the revised manuscript, we have added a clearer and\nmore distinct microscale scale bar to the SEM image in Supplementary Fig. 15 (Supplementary Fig. S14 now) to\nimprove readability.\nRevision: SI, Page 15, a figure, Supplementary Figure S14, has been revised.\nSupplementary Figure S14. SEM image of x = 0.35 ceramic.\n4"}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors have necessary modifications according to the reviewer’s suggestions. I would recommend it for publication in\nits current state."}, "author_response": ""}]

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