High-entropy driven electronic and microstructural synergy for superior capacitive energy storage in lead-free ceramics

High-entropy driven electronic and microstructural synergy for superior capacitive energy storage in lead-free ceramics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article High-entropy driven electronic and microstructural synergy for superior capacitive energy storage in lead-free ceramics Peng Li, Yunting Li, Haihua Huang, Hairui Bai, Fei Xu, Jigong Hao, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7666264/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Dielectric capacitors, characterized by their high power density and ultrafast charge/discharge capabilities, are pivotal components in modern pulsed power and renewable energy systems. However, the widespread adoption of ferroelectric ceramics is inherently hampered by the antagonistic relationship between polarization ( P ) and breakdown strength ( E b ), further compounded by significant polarization hysteresis and losses, which collectively obstruct the simultaneous realization of high recoverable energy density ( W rec ) and efficiency ( η ). Herein, we transcend this fundamental limitation via a novel high-entropy engineering strategy in (Bi, Na)TiO 3 -based ceramics. The designed materials achieve an exceptional W rec of 11.1 J/cm 3 and a remarkably high η of ~ 89.1%. This breakthrough is attributed to a synergistic interplay of mechanisms orchestrated by the high-entropy design: (i) a reduction in electronic band curvature that increases the charge carrier effective mass, thereby suppressing mobility and electrical conductivity; (ii) the emergence of self-assembled core-shell microstructures that effectively impede electrical treeing propagation through interfacial stress buffering and field homogenization; and (iii) the stabilization of nanoscale rhombohedral-orthorhombic-tetragonal-cubic (R-O-T-C) multiphase coexistence, which enhances dipole reorientability and disrupts long-range ferroelectric order. The confluence of these effects culminates in a significantly enhanced E b while maximizing the polarization disparity (Δ P = P max ​ - P r ). This study establishes high-entropy engineering as a transformative paradigm for designing advanced lead-free dielectric capacitors with superior energy storage performance. Physical sciences/Materials science/Structural materials/Ceramics Physical sciences/Energy science and technology/Energy storage High-entropy ceramics Core-shell structure Band flattening Polar nanoregions Energy storage Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Dielectric capacitors stand at the forefront of power electronics innovation, enabling key applications ranging from pulsed power systems to grid-scale energy storage by virtue of their ultrafast charge/discharge kinetics, unparalleled power density, and robust thermal stability 1 – 4 . As these technologies evolve toward higher efficiency and miniaturization, dielectric ceramics, which store energy through ionic displacement polarization under high electric fields, offer distinct advantages including sub-microsecond response times and minimal Joule heating, inherent to their physical polarization mechanism 5 , 6 . Nonetheless, this potential remains fundamentally constrained by an intrinsic inverse correlation between maximum polarization ( P max ) and dielectric breakdown strength ( E b ​), exacerbated by substantial polarization hysteresis and losses. These limitations are quantitatively captured by the figures of merit for energy storage: the recoverable energy density ( \(\:{\text{W}}_{\text{rec}}\text{}\text{=}\text{}{\int\:}_{{\text{P}}_{\text{r}}}^{{\text{P}}_{\text{m}}}\text{E}\text{}\text{dP}\) ) and efficiency ( \(\:\eta\text{}\text{=}\text{}{\text{W}}_{\text{rec}}\text{/}{\text{W}}_{\text{total}}\) ), where P r , E and W total denote the remnant polarization, applied electric field, and total energy storage density (Fig. S1 a). Achieving high values for both parameters concurrently has remained a persistent challenge 7 , 8 . To navigate this performance trade-off, research efforts have pursued several distinct pathways. Domain and phase engineering strategies aim to enhance relaxor behavior, effectively suppressing P r ​ 9–12 . Grain orientation control has been employed to substantially improve E b , and thus the energy storage density by mitigating electric-field-induced strain 13 . More recently, high-entropy design, achieved by incorporating multiple principal elements into cationic sites to induce severe lattice distortion and chemical disorder, has emerged as a promising avenue. This approach reduces domain size and polarization switching hysteresis​ while concurrently boosting E b​ 14–18 . Seminal studies have demonstrated that energy storage properties can exceed 10 J/cm 3 and 90% efficiency in high-entropy stabilized systems based on (Bi, Na)TiO 3 (BNT) 19 , 20 , BaTiO 3 (BT) 21 , and (K, Na)NbO 3 (KNN) 22 , 23 . Notably, an ultrahigh energy density of 182 J/cm 3 with 78% efficiency was reported in high-entropy Bi 2 Ti 2 O 7 -based films 24 . Parallel strategies exploit core-shell architectures to decouple the enhancement of Δ P and E b ​, as evidenced in BNT-based ( W rec ~ 5.07 J/cm 3 , η = 85.17%) 25 , BT-based ( W rec ​= 7.6 J/cm 3 , η = 84%) 26 , and NaNbO 3 (NN)-based ceramics ( W rec = 7.72 J/cm 3 , η = 83.78%) 27 . Despite these advances, two critical challenges impede further progress. First, current strategies often operate in isolation; the potential synergies between high-entropy modifications and core-shell structuring remain largely unexplored. Second, electronic band structure engineering, a crucial lever for regulating charge carrier mobility and thereby E b , is yet to be comprehensively investigated in BNT-based systems. In this work, we bridge these gaps through a unified approach that concurrently modulates the electronic and microstructural landscapes. By introducing a suite of heterovalent cations at the A- and B-sites in the (1- x )(Bi 0.34 Na 0.3 Sr 0.28 La 0.04 )TiO 3 - x Ba(Mg 1/3 Ta 2/3 )O 3 (abbreviated as BNSLT- x BMT) system, our high-entropy engineering strategy delivers a tripartite synergy: (ⅰ) flattening of conduction band curvature to suppress charge carrier mobility, (ⅱ) instigation of self-assembled core-shell grains that homogenize local electric fields and hinder breakdown propagation, and (ⅲ) stabilization of a nanoscale R-O-T-C multiphase coexistence that enhances polarizability and dipole reconfigurability under high fields. This concerted manipulation culminates in an ultra-high W rec of 11.1 J/cm 3 with an η of 89.1% at x = 0.10 (configurational entropy S config = 1.8 R ), representing a tenfold enhancement over conventional BNT. Our findings establish coupled electronic-microstructural tailoring as a transformative paradigm for overcoming the polarization-breakdown compromise in next-generation dielectric capacitors. Results and discussion Composition-driven structural evolution The configuration entropy ( S config ) defined as \(\:{\text{S}}_{\text{config}}\text{}\text{= -}\text{R}\text{[}{\left(\sum\:_{\text{i}\text{=1}}^{\text{N}}{\text{x}}_{\text{i}}\text{ln}{\text{x}}_{\text{i}}\right)}_{\text{cation-site}}\text{+}{\text{(}\sum\:_{\text{j}\text{=1}}^{\text{M}}{\text{x}}_{\text{j}}\text{ln}{\text{x}}_{\text{j}}\text{)}}_{\text{anion-site}}\text{]}\) , where R , N ( M ) and x i ( x j ) denote the ideal gas constant, atomic species and contents at the equivalent cation or anion sites, respectively, has been proposed to quantify the compositional inhomogeneity. The S config progressively increases from 0.69 R (low-entropy) for the virgin BNT to greater than 1.5 R (high-entropy) for the BNSLT- x BMT ceramics with x = 0.06–0.15, as displayed in Fig. S1 b. The high-entropy-induced multinuclear-type core-shell structure (see Fig. 1 a, b and Fig. S3a, b), and onion-like core-shell structure (see Fig. 1 c, d) can be readily observed in both bright-field and high-angle annular dark-field (HAADF) STEM images of x = 0.10 ceramics. As demonstrated in Fig. 1 e, energy-dispersive X-ray spectroscopy (EDS) line profile traversing the core-shell structure (along the green arrow in Fig. 1 a) delineates a pronounced enrichment of Sr within the core, concomitant with a depletion of Bi and Na. This chemical partitioning is visually confirmed by EDS elemental mapping (Fig. 1 f), which clearly depicts Sr segregation in the core. Consistent results obtained from multiple core-shell structured ceramics (Fig. S2b, c, and Fig. S3c, d) affirm Sr enrichment in the core. To decipher the formation mechanism of the core-shell structure, we constructed the probable migration pathway during crystallization for doping elements (Sr, La, Ba, Ta, Mg) within the BNT matrix lattice, as schematically shown in Fig. 1 g, and computed the diffusion energy barriers for the pertinent elements using first-principles calculation (Fig. 1 h, i). The results unequivocally demonstrate that Sr possesses the highest diffusion energy barrier among the doping cations. This implies a pronounced tendency for Sr to be trapped and accumulate in the core region during sintering, with a markedly lower propensity for outward diffusion, thereby providing the primary thermodynamic driving force for the development of the core-shell heterogeneity. The disparity in cationic mobility is thus identified as the intrinsic origin of the observed core-shell microstructure in high-entropy ceramics. Additionally, a series of well-defined core-shell interfaces (Fig. 1 j, Fig. S2d and Fig. S3e) without dislocation contrast could be observed in the x = 0.10 ceramics, which is beneficial to enhance the E b . The high-magnification morphological images (Fig. 1 k) and the inverse Fourier transform (IFFT) images of lattice fringes (Fig. 1 l, Fig. S3f, Fig. S4) of the core and shell regions reveal the ubiquitous presence of nano-scaled polar nanoregions (PNRs) within the matrix, suggesting strong relaxor characteristic induced by the high-entropy design, which facilitates a significant polarization disparity Δ P . In addition, as the entropy value increases, the grain sizes of the samples (Fig. S5) generally exhibit a decreasing trend, which increases the density of barriers to electrical breakdown. The phase evolution was further probed by XRD (Fig. S6) and temperature-dependent dielectric spectroscopy (Fig. S7a-f). With increasing BMT content (and thus S config ), a clear transition from a classical ferroelectric to a pseudocubic relaxor phase is observed 28 , 29 . The dielectric relaxor behavior is quantitatively assessed using the modified Curie-Weiss law (Fig. S7g). The diffuseness coefficients ( γ ) monotonically increase from 1.76 for virgin BNT (low entropy) to 1.96 for x = 0.15 composition (high entropy), confirming a significantly enhanced relaxor characteristic. This is rationalized by the high-entropy-induced cation disorder, which strengthens random fields, breaks long-range ferroelectric order, and promotes the formation of highly dynamic PNRs. Selected-area electron diffraction (SAED) patterns (Fig. S8b, c) from the shell and core regions exhibit no superlattice reflections, consistent with an average pseudocubic structure. However, careful analysis of SAED pattern (Fig. S8d) spanning the core-shell interface reveals a slight splitting of diffraction spots corresponding the same crystallographic planes, attributed to lattice strain and distortion arising from the core-shell compositional heterogeneity. Energy storage performance The unipolar polarization-electric field ( P - E ) hysteresis loops for BNT and the BNSLT- x BMT series, measured at their respective breakdown fields, are given in Fig. 2 a. The corresponding energy storage properties, W rec and η , are summarized in Fig. 2 b. The low-entropy BNT ceramic exhibits a fat P - E loop with a large P r and a low E b , characteristic of strong ferroelectricity, resulting in poor energy storage performance. As the entropy increases, the loops become progressively slimmer, indicative of enhanced relaxor behavior. The optimum composition, x = 0.10 ( S config = 1.8 R ), achieves an ultrahigh W rec of 11.1 J/cm 3 and an outstanding η of 89.1% at 860 kV/cm. The statistical breakdown strength, a critical parameter, was rigorously evaluated using the two-parameter Weibull distribution: X i = ln( E i ), Y i = ln(ln(1/(1- P i ))), where P i = i /( n + 1), E i is the breakdown strength of each tested sample in ascending order, P i is the cumulative probability of dielectric breakdown, n represents the total number of tested samples 30 , 31 . All samples exhibit high Weibull moduli ( β > 12), attesting to the high reliability of the data, as shown in Fig. 2 c. The inset in Fig. 2 c reveals a dramatic enhancement in E b with increasing entropy: from 269 kV/cm for BNT (low entropy) to 358 kV/cm for x = 0 (medium entropy), and ultimately to 863 kV/cm for x = 0.10 composition (high entropy). This substantial improvement is a cornerstone of the superior performance. Figure 2 d and 2 e detail the electric field-dependent energy storage behavior of the x = 0.10 ceramics. The P - E loops remain extremely slim with near-zero P r across a wide field range (100–860 kV/cm) due to strong relaxor characteristic 32 . Both P max and Δ P increase linearly with the applied field without showing signs of saturation, while η remains consistently high (> 89.1%), underscoring the material’s capability to withstand ultrahigh fields with minimal energy loss 33 – 35 . A radar chart (Fig. 2 f) provides a holistic comparison of the key performance metrics ( W rec , η , E b , P max , Δ P ) for the low- (BNT), medium- ( x = 0), and high-entropy ( x = 0.10) ceramics, vividly illustrating the comprehensive superiority of the high-entropy design. Quantitatively, the x = 0.10 ceramics exhibits a 231%, 853%, and 46% improvement in E b , W rec , and η , respectively, compared to BNT, and a 146%, 177%, and 10% improvement compared to the x = 0 medium-entropy ceramics (Fig. 2 g). The overall energy storage performance (Fig. 2 h and Table S1 ) surpasses that of most recently reported lead-free ceramic systems, positioning our high-entropy ceramic at the forefront of dielectric energy storage research. Structural origins of the superior energy storage performance To unravel the atomic-scale structural origins of the superior energy storage performance, we conducted atomic-resolution HAADF-STEM to analyze the polarization configurations within the PNRs of the x = 0.10 ceramic. HAADF-STEM images of both core and shell regions along [001] c (Fig. S9) reveal polarization vectors (yellow arrows) from the central B-site to the corner A-site cations. Two-dimensional Gaussian fitting confirms the presence of a tetragonal (T) phase, while regions with near-zero polarization amplitude are identified as cubic (C). However, the [001] c projection cannot distinguish between rhombohedral (R) and orthorhombic (O) phases due to their similar projections. To resolve this, we performed polarization vector mapping of both core and shell regions along the [011] c zone axis, as shown in Fig. 3 a, b. This orientation allows clear differentiation: polarization vectors along [111] c signify the R phase, while those along [110] c indicate the O phase. The locally magnified polarization vector images of the sample core along the [011] c and [001] c directions are displayed in Fig. 3 c. Moreover, Fig. S10 presents polarization vector images without atoms for both the core and shell regions along [001] c and [011] c . These analyses unambiguously identifies that the coexistence of R, O, and T phases in the matrix C phase occurs locally within nano-regions in both the core and shell of the x = 0.10 ceramic. The nanoscale phase heterogeneity is a hallmark of the high-entropy composition, creating intense random fields that effectively disrupt long-range ferroelectric order and are paramount for the enhanced relaxor behavior. We further performed a statistical analysis of the polarization vector deviation angles (Fig. 3 d, e) and magnitudes (Fig. 3 f, g) in both core and shell regions. The broad distribution of polarization angles reflects enhanced polarization anisotropy and disorder, implying a more flexible polarization response to external electric fields, which facilitates the reduction of P r . Concurrently, the fluctuation in polarization magnitude indicates a reduction in local polarization strength, further reinforcing the relaxor characteristic. This non-uniform distribution of PNRs, with variations in both direction and magnitude, signifies the presence of strong random fields, which are conducive to high energy storage efficiency 36 , 37 . The dynamic nature of these PNRs was probed by piezoresponse force microscopy (PFM) (Fig. S11). The written domains under poling voltages were found to be metastable, relaxing back to their initial state shortly after the electric field was removed. This observed reversibility and low coercivity confirm the high dynamics of the PNRs, which require a lower energy barrier for reorientation. This characteristic is crucial for achieving a large P max under high fields while maintaining a low P r , as it delays polarization saturation and enhances W rec . Electronic structure and carrier confinement First-principles density functional theory (DFT) calculations were employed to decipher the electronic structure evolution 38 – 40 . Models for BNT, Sr/La-doped BNT ( x = 0), and the high-entropy system ( x = 0.10) were constructed, as shown in Fig. 4 a-c. The partial density of states (PDOS) for BNT (Fig. 4 d) shows the valence band maximum (VBM) is dominated by O-2p orbitals, while the conduction band minimum (CBM) is primarily composed of Ti-3d orbitals. Doping with Sr, La, Ba, Ta, and Mg (Fig. 4 e, f) introduces states deep within the valence and conduction bands but induces negligible change to the band gap ( E g ), consistent with our experimental UV-Vis results (Fig. S12). The critical effect of high-entropy doping is manifested in the band structure (Fig. 4 g-i). Compared to virgin BNT, the high-entropy system exhibits significantly flattened bands, particularly near the CBM, due to the [SrO], [LaO], [MgO] local distortion weakens the interatomic interaction. This reduced band curvature \(\:\:\left(\frac{{d}^{\text{2}}\text{E}\text{(}\text{k}\text{)}}{{\text{dk}}^{\text{2}}}\right)\) directly implies an increase in the effective mass of charge carriers ( m * ) according to the relation: \(\:\frac{1}{{m}^{\text{*}}}\) = \(\:\frac{1}{{\hslash\:}^{2}}\:\) · \(\:\frac{{d}^{\text{2}}\text{E}\text{(}\text{k}\text{)}}{{\text{dk}}^{\text{2}}}\) . A large m * leads to reduced carrier mobility ( σ ) based on \(\:\text{σ}\text{}\text{=}\text{}\frac{\text{n}{\text{e}}^{\text{2}}\text{τ}}{{\text{m}}^{\text{*}}}\) . Hall effect measurements (Fig. 4 j-m) provide experimental validation. All compositions exhibit n-type conduction. With increasing entropy, the electrical resistivity rises markedly (Fig. 4 k), while both the carrier concentration and mobility decrease substantially (Fig. 4 l, m). This excellent agreement between theory and experiment robustly demonstrates a carrier confinement effect induced by high-entropy engineering. This flattened bands (increased m * ) and the compositional disorder act in concert to severely impede charge transport, suppressing leakage current and enhancing the insulating strength. This novel electronic structure manipulation strategy is a key contributor to the ultrahigh E b and superior W rec in this work. Role of core-shell structure in breakdown strength Finite element simulations were conducted to visualize the role of core-shell microstructure in the dielectric breakdown process. Three models designed based on SEM and TEM results were compared: BNT (low entropy, large grains), x = 0.10 without a core-shell structure (high entropy, fine grains), and x = 0.10 with a core-shell structure (high entropy, fine grains), as depicted in Fig. 5 a-c. The simulations reveal that the electric field is highly concentrated at grain boundaries due to their lower dielectric constant compared to the grain interiors 41 , 42 . Under a simulated field of 380 kV/cm, breakdown paths readily propagate across the entire BNT sample (Fig. 5a1-a3). Grain refinement in the high-entropy sample without a core-shell structure hinders this propagation, confining the breakdown to about half the sample length (Fig. 5b1-b3). The introduction of the core-shell structure (Fig. 5c1-c6) has a profound effect: it effectively shields and homogenizes the electric field at the grain boundaries and core-shell interfaces, preventing dangerous local field concentrations. As shown in Fig. S13, the reduced grain size combined with the formation of the core-shell structure leads to a more uniform polarization distribution. Consequently, even under a much higher simulated field of 680 kV/cm, the breakdown progression in the core-shell sample is significantly retarded compared to the others, as display in Fig. 5a4-a6 and 5b4-b6. The core-shell interface acts as a barrier, deflecting and pinning the electrical treeing channels. This, combined with the reduced grain size and increased electrical resistivity synergistically contribute to the dramatically improved E b and the associated W rec . Charge/discharge performance and temperature stability For practical applications, superior discharge capability and thermal reliability are imperative. Figure 6 a shows the overdamped discharge current curves of the x = 0.10 ceramics under varied electric fields. The corresponding discharged energy density ( W d ), calculated by \(\:{\text{W}}_{\text{d}}\text{=}\text{R}\int\:\frac{{\text{I}}^{\text{2}}\left(\text{t}\right)\text{dt}}{\text{V}}\text{}\) (where the load resistance R = 187 Ω, V is the sample volume, I is the current, and t is time) 43 , is presented in Fig. 6 b. The W d value increases steadily with the applied field. Most notably, an ultra-short discharge time ( t 0.9 , time to release 90% of the stored energy) of merely 26.6 ns is achieved, indicating an ultra-fast discharge rate, which can be attributed to the highly dynamic nature of the PNRs enabling ultrafast polarization reversal. The underdamped discharge current waveforms are shown in Fig. 6 c. The calculated current density ( C D = I max / S , where S is the electrode area, I max denotes the maximum current) and power density ( P D = E ⋅ I max /(2 S )) reach impressive values of 1515.2 A/cm 2 and 280.3 MW/cm 3 , respectively, at 370 kV/cm (Fig. 6 d). These outstanding metrics underscore the potential of this material for high-power applications. It is worth noting that the W rec and W d exhibit minimal variation with fluctuations of less than 7.9% and 9.4%, respectively, over the temperature range of 25–125 o C, suggesting excellent thermal stability, as shown in Fig. S14a-d. The robust stability originates from the high-entropy-stabilized phase structure and relatively smooth dielectric content with elevated temperature 44 , as evidenced by in-situ temperature-dependent XRD patterns (Fig. S15) and ε r - T curves (Fig. S7e), ensuring reliable operation under varying environmental conditions. Conclusions In summary, we have demonstrated a high-entropy strategy that synergistically engineers the electronic and microstructural properties of (Bi, Na)TiO 3 ​-based ceramics to achieve unparalleled energy storage performance. The incorporation of multiple principal elements simultaneously: (ⅰ) flattens the electronic band structure, suppressing carriers mobility and conductivity; (ⅱ) drives the self-assembly of core-shell microstructure, which homogenize local electric fields and effectively impede the propagation of breakdown paths; (ⅲ) stabilizes a nanoscale coexistence of R-O-T-C phases, creating intense random fields that disrupt long-range ferroelectric order, enhance dipole reconfigurability, and yield slimmer hysteresis loops with large Δ P . This tripartite synergy successfully decouples the traditional trade-off between polarization and breakdown strength. The resultant lead-free ceramic achieves a superior W rec of 11.1 J/cm 3 with a high η of 89.1%, exceptional W d of 280.3 MW/cm 3 , and an ultrafast discharge speed ( t 0.9 ~ 26.6 ns), alongside excellent temperature stability. Our work establishes coupled electronic-microstructural engineering via high-entropy design as a transformative and universal paradigm for developing next-generation dielectric capacitors for advanced energy storage applications. Methods Ceramics preparation Polycrystalline samples of BNT and (1- x )(Bi 0.34 Na 0.3 Sr 0.28 La 0.04 )TiO 3 - x Ba(Mg 1/3 Ta 2/3 )O 3 (BNSLT- x BMT, x = 0, 0.06, 0.08, 0.10, 0.15) series were synthesized via a conventional solid-state reaction route. High-purity powders of Na 2 CO 3 (99.8%), Bi 2 O 3 (99%), TiO 2 (99.9%), SrCO 3 (99.95%), La 2 O 3 (99.9%), BaCO 3 (99.99%), MgO (99.99%) and Ta 2 O 5 (99.5%) were pre-dried and subsequently weighed according to stoichiometric ratios. The powders were mixed by planetary ball milling in ethanol for 24 h. After drying, the mixtures were calcined at 850 o C for 3 h in air and then milled again under identical conditions to ensure homogeneity. Polyvinyl alcohol (PVA) binder was added to the resulting powders, which were then granulated and sieved. The granules were uniaxially pressed into pellets with a diameter of 10 mm. After binder burnout at 600 o C, the pellets were sintered at temperatures between 1100 and 1150 o C for 2 h to obtain dense ceramics. Structural characterization Crystal structure and phase purity were examined using X-ray diffractometer (XRD; TD-3700, Dandong Tongda Technology Co. Ltd., China) with Cu Kα radiation. Microstructure analysis was performed using a field-emission scanning electron microscope (FE-SEM; Merlin Compact, Zeiss, Germany). Grain size statistics were derived from SEM images using Nano Measure software. The core-shell microstructure, elemental mapping, and domain morphology were observed using a transmission electron microscope (TEM; FEI Talos F200X, America) equipped with an energy-dispersive X-ray spectroscopy (EDS) system. Atomic-scale polarization mapping was carried out using a dual spherical- aberration corrected scanning transmission electron microscopy (STEM; Spectra 300, Thermo Fisher Scientific) at 300 kV. Atomic column positions were determined via two-dimensional Gaussian fitting, and polarization vectors were extracted using custom MATLAB scripts. Domain dynamics were investigated using piezoelectric force microscopy (PFM; MFP-3D, Asylum Research, USA). Optical band gaps ( E g ) were determined from UV-Vis absorption spectra. Electrical performance measurement For ferroelectric measurements, ceramics were polished to 30–40 µm thickness and coated with gold electrodes 0.5 mm in diameter. Polarization-electric field ( P - E ) hysteresis loops were measured using a ferroelectric test system (RT1-Premier II, Radiant Technologies Inc., USA) to evaluate the energy storage performance. Temperature- and frequency-dependent permittivity was acquired using an inductance-capacitance-resistance (LCR) meter (E4980A, Agilent, USA) accompanied with a temperature control system. Charge-discharge performance was evaluated using a dedicated tester (CFD-003, Tongguo Technology, China) based on a RC circuit. Hall effect measurements were performed in a Physical Property Measurement System (PPMS-9, Quantum Design) using a Keithley 2400 SourceMeter and 2182A Nanovoltmeter. DFT calculations First-principles calculations based on density functional theory (DFT) were performed using the Vienna Ab initio Simulation Package (VASP) with the projector augmented-wave (PAW) method. The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) was employed for the exchange-correlation functional. A plane-wave cutoff energy of 520 eV was chosen for the geometry optimization and electronic structure calculations. The Brillouin zone was sampled with Γ-centered k-point meshes of 5×5×1 for structural optimization and 9×9×1 for electronic structure calculations. All atomic positions were optimized until Hellmann-Feynman forces were less than 0.01 eV/Å. The energy and electronic convergence criteria were set to 10 − 5 eV and 10 − 6 eV per atom, respectively. Diffusion energy barrier was calculated using the climbing-image nudged elastic band (CI-NEB) method. Finite element simulations Finite element simulations of electric field distribution and breakdown propagation were performed using models constructed from SEM and TEM images. Three configurations were considered: (A) low-entropy large-grained BNT, (B) high-entropy fine-grained ceramic without core-shell structure, and (C) high-entropy fine-grained ceramic with core-shell structure. Each model was discretized into a 2D grid of 170×238 points over an area of 2.5×3.5 µm 2 . The evolution probability of breakdown channels was modeled using a modified fractal dielectric breakdown model: $$\:p\left({i}^{{\prime\:}},{j}^{{\prime\:}}-i,j\right)=\frac{{({\varPhi\:}_{{i}^{{\prime\:}},{j}^{{\prime\:}}}-{\varPhi\:}_{i,j}-{\varPhi\:}_{0})}^{\eta\:}}{\varSigma\:{({\varPhi\:}_{{i}^{{\prime\:}},{j}^{{\prime\:}}}-{\varPhi\:}_{i,j}-{\varPhi\:}_{0})}^{\eta\:}}+{({\varPhi\:}_{{i}^{{\prime\:}},{j}^{{\prime\:}}}-{\varPhi\:}_{{i}^{{\prime\:}{\prime\:}},{j}^{{\prime\:}{\prime\:}}}-{\varPhi\:}_{0})}^{\eta\:}-loss$$ where \(\:{\varPhi\:}_{0}\) denotes the threshold potential, \(\:{\varPhi\:}_{i,j}\) is the potential at the discharged point, \(\:{\varPhi\:}_{{i}^{{\prime\:}},{j}^{{\prime\:}}}\) , and \(\:{\varPhi\:}_{{i}^{{\prime\:}{\prime\:}},{j}^{{\prime\:}{\prime\:}}}\) are potentials at candidate and linked points, respectively, η is the fractal dimension, and loss represents tip energy loss during electrical tree propagation. Declarations Data availability All data necessary to support the conclusions of this study are included in the paper and its Supporting Information files. Any additional datasets generated and/or analyzed during the current study are available from the corresponding author upon justified request. Competing interests The authors declare no competing interests. Author contributions Y.T.L., P.L. and Z.X.C. conceived and designed the research. Y.T.L. led the sample fabrication, energy storage and dielectric measurements, structural and stability characterization, and data processing, with assistance from F.X., J.G.H., P.F., J.D., Z.B.P., W.F.B. and W.L. H.H.H and Z.X.C. carried out the DFT calculations. H.R.B. performed finite element simulations in consultation with P.L. The manuscript was drafted by Y.T.L. and revised critically by P.L., W.L., J.W.Z. and Z.X.C. All authors contributed to data analysis, discussion, and final approval of the manuscript. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 52102132, 12204215, and 52402264), the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2025MS695, and ZR2024ME201), and the Shandong Higher Education Institutions Youth Innovation Team Project (Grant No. 2024KJH145). References Qi H et al (2019) Ultrahigh energy-storage density in NaNbO 3 -based lead-free relaxor antiferroelectric ceramics with nanoscale domains. Adv Funct Mater 29:1903877 Wang G et al (2019) Ultrahigh energy storage density lead-free multilayers by controlled electrical homogeneity. Energy Environ Sci 12:582–588 Yan F et al (2022) Boosting energy storage performance of lead-free ceramics via layered structure optimization strategy. Small 18:2202575 Zhu L et al (2023) Heterovalent-doping-enabled atom-displacement fluctuation leads to ultrahigh energy-storage density in AgNbO 3 -based multilayer capacitors. Nat Commun 14:1166 Wang G et al (2021) Electroceramics for high-energy density capacitors: current status and future perspectives. Che Rev 121:6124–6172 Yang L et al (2019) Perovskite lead-free dielectrics for energy storage applications. Prog Mater Sci 102:72–108 Che Z et al (2022) Phase structure and defect engineering in (Bi 0.5 Na 0.5 )TiO 3 -based relaxor antiferroelectrics toward excellent energy storage performance. Nano Energy 100:107484 Gao P et al (2019) New antiferroelectric perovskite system with ultrahigh energy-storage performance at low electric field. Chem Mater 31:979–990 Li P et al (2025) Nano-domain configuration boosting energy storage capacity of NaNbO 3 -based relaxor ferroelectrics. J Power Sources 653:237756 Pan H et al (2019) Ultrahigh-energy density lead-free dielectric films via polymorphic nanodomain design. Science 365:578–582 Xi J et al (2024) Compromise boosted high capacitive energy storage in lead-free (Bi 0.5 Na 0.5 )TiO 3 -based relaxor ferroelectrics by phase structure modulation and defect engineering. Chem Eng J 502:157986 Zhou X et al (2019) Superior thermal stability of high energy density and power density in domain-engineered Bi 0.5 Na 0.5 TiO 3 -NaTaO 3 relaxor ferroelectrics. ACS Appl Mater Interfaces 11:43107–43115 Li J et al (2020) Grain-orientation-engineered multilayer ceramic capacitors for energy storage applications. Nat Mater 19:999–1005 Chen L et al (2022) Giant energy-storage density with ultrahigh efficiency in lead-free relaxors via high-entropy design. Nat Commun 13:3089 Chen L et al (2023) Large energy capacitive high-entropy lead-free ferroelectrics. Nano-micro Lett 15:65 Ge G et al (2022) Tunable domain switching features of incommensurate antiferroelectric ceramics realizing excellent energy storage properties. Adv Mater 34:2201333 Kong X et al (2025) High-entropy engineered BaTiO 3 -based ceramic capacitors with greatly enhanced high-temperature energy storage performance. Nat Commun 16:885 Wei T et al (2025) High-entropy assisted capacitive energy storage in relaxor ferroelectrics by chemical short-range order. Nat Commun 16:807 Li D et al (2025) Atomic-scale high‐entropy design for superior capacitive energy storage performance in lead‐free ceramics. Adv Mater 37:2409639 Wei T et al (2025) High-entropy assisted capacitive energy storage in relaxor ferroelectrics by chemical short-range order. Nat Commun 16:807 Zhang M et al (2024) Ultrahigh energy storage in high-entropy ceramic capacitors with polymorphic relaxor phase. Science 384:185–189 Li D et al (2025) Atomic-Scale High‐entropy design for superior capacitive energy storage performance in lead‐free ceramics. Adv Mater 2409639 Chen L et al (2022) Giant energy-storage density with ultrahigh efficiency in lead-free relaxors via high-entropy design. Nat Commun 13:3089 Yang B et al (2022) High-entropy enhanced capacitive energy storage. Nat Mater 21:1074–1080 Xue G et al (2023) Core-shell structure and domain engineering in Bi 0.5 Na 0.5 TiO 3 -based ceramics with enhanced dielectric and energy storage performance. J Materiomics 9:855–866 Yang S et al (2025) Lead-free BaTiO 3 -based composite ceramics with ultra-high energy storage performance via synergistic modulation of polarization and breakdown strength. J power sources 632:236399 Dong X et al (2022) (1- x )[0.90NN-0.10Bi(Mg 2/3 Nb 1/3 )O 3 ]- x (Bi 0.5 Na 0.5 ) 0.7 Sr 0.3 TiO 3 ceramics with core-shell structures: a pathway for simultaneously achieving high polarization and breakdown strength. Nano Energy 101:107577 Li F et al (2018) Local structural heterogeneity and electromechanical responses of ferroelectrics: learning from relaxor ferroelectrics. Adv Funct Mater 28:1801504 Dai Z et al (2021) Improved energy storage density and efficiency of (1 – x )Ba 0.85 Ca 0.15 Zr 0.1 Ti 0.9 O 3 -xBiMg 2/3 Nb 1/3 O 3 lead-free ceramics. Chem Eng J 410:128341 Chen L et al (2022) Local diverse polarization optimized comprehensive energy-storage performance in lead‐free superparaelectrics. Adv Mater 34:2205787 Zhu Y et al (2022) High conduction band inorganic layers for distinct enhancement of electrical energy storage in polymer nanocomposites. Nano-Micro Lett 14:151 Yang B et al (2023) Engineering relaxors by entropy for high energy storage performance. Nat Energy 8:956–964 Bi W et al (2023) Comprehensive energy-storage performance enhancement in relaxor anti-ferroelectrics via strengthening local polarization. Chem Eng J 478:147383 Pu Y et al (2019) Enhancing the energy storage properties of Ca 0.5 Sr 0.5 TiO 3 -based lead-free linear dielectric ceramics with excellent stability through regulating grain boundary defects. J Mater Chem C 7:14384–14393 Wang W et al (2019) Enhanced energy storage properties of lead-free (Ca 0.5 Sr 0.5 ) 1-1.5 x La x TiO 3 linear dielectric ceramics within a wide temperature range. Ceram Int 45:14684–14690 Wang W et al (2022) Enhancement of energy storage performance in lead-free barium titanate-based relaxor ferroelectrics through a synergistic two-step strategy design. Chem Eng J 434:134678 Wang W et al (2023) Enhanced energy storage properties in lead-free (Na 0.5 Bi 0.5 ) 0.7 Sr 0.3 TiO 3 -based relaxor ferroelectric ceramics through a cooperative optimization strategy. ACS Appl Mater Interfaces 15:6990–7001 Shah SZA et al (2023) A DFT computational design and exploration of direct band gap silver-thallium double perovskites. Mater Sci Eng B 298:116846 Rana MZ et al (2023) Structurlectronic, optical and thermodynamic properties of AlAuO 2 and AlAu 094 Fe 006 O 2 compounds scrutinized by density functional theory (DFT). Heliyon 9, e21405 Geng W et al (2013) Influence of interface structure on the properties of ZnO/graphene composites: a theoretical study by density functional theory calculations. J Phys Chem C 117:10536–10544 Zhou Z et al (2025) Ultrahigh capacitive energy storage of BiFeO 3 -based ceramics through multi-oriented nanodomain construction. Nat Commun 16:2075 Yan F et al (2022) Composition and structure optimized BiFeO 3 -SrTiO 3 lead‐free ceramics with ultrahigh energy storage performance. Small 18:2106515 Wang W et al (2023) Enhancing energy storage performance in Na 0.5 Bi 0.5 TiO 3 -based lead-free relaxor ferroelectric ceramics along a stepwise optimization route. J Mater Chem A 11:2641–2651 Shi W et al (2024) Moderate Fields, Maximum potential: achieving high records with temperature-stable energy storage in lead-free BNT-based ceramics. Nano-micro Lett 16:91 Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformation.docx High-entropy driven electronic and microstructural synergy for superior capacitive energy storage in lead-free ceramics Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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\u003c/strong\u003eand \u003cstrong\u003ed\u003c/strong\u003eHAADF\u003cstrong\u003e \u003c/strong\u003eSTEM images of an onion-like core-shell grain. \u003cstrong\u003ee\u003c/strong\u003e EDS line scan profile (along the green arrow in \u003cstrong\u003ea\u003c/strong\u003e) across a core-shell interface. \u003cstrong\u003ef\u003c/strong\u003e Corresponding EDS elemental mapping. \u003cstrong\u003eg\u003c/strong\u003e Schematic illustration of the proposed atomic migration pathways for dopant cations within the BNT lattice. \u003cstrong\u003eh\u003c/strong\u003e Relative diffusion energy dependence of diffusion coordinates for dopant elements replacing Na/Bi or Ti elements in the BNT lattice. \u003cstrong\u003ei\u003c/strong\u003eCalculated diffusion energy barriers of various dopant cations (Marks “A” and “B” correspond the substitution of La/Ba/Sr in the Na-site and Bi-site, respectively; while mark “C” corresponds the substitution of Ta/Mg in the Ti-site). \u003cstrong\u003ej\u003c/strong\u003e High-resolution TEM lattice fringe image acquired across a core-shell interface (green box area in \u003cstrong\u003ec\u003c/strong\u003e). \u003cstrong\u003ek\u003c/strong\u003e High-resolution TEM image of the shell region. \u003cstrong\u003el\u003c/strong\u003e Inverse Fast Fourier Transform (IFFT) image of the lattice fringe in \u003cstrong\u003ej\u003c/strong\u003e.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7666264/v1/d6f5c3724e8de7654891a377.jpeg"},{"id":92061421,"identity":"727b45ea-c186-42f6-9550-4725147ce92b","added_by":"auto","created_at":"2025-09-24 08:18:08","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1413139,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEnergy storage performance. a\u003c/strong\u003e Unipolar \u003cem\u003eP \u003c/em\u003e- \u003cem\u003eE\u003c/em\u003e hysteresis loops measured at the respective \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e and 10 Hz for BNT and BNSLT-xBMT ceramics. \u003cstrong\u003eb\u003c/strong\u003e \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e and \u003cem\u003eη\u003c/em\u003e of BNT and BNSLT-xBMT ceramics at their critical electric fields. \u003cstrong\u003ec\u003c/strong\u003e Weibull distribution of the breakdown strength (\u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e). Inset: the theoretical \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e values derived from the Weibull distribution. \u003cstrong\u003ed\u003c/strong\u003e Unipolar \u003cem\u003eP \u003c/em\u003e- \u003cem\u003eE\u003c/em\u003e loops of the optimal \u003cem\u003ex\u003c/em\u003e = 0.10 composition under various electric fields. \u003cstrong\u003ee\u003c/strong\u003e \u003cem\u003eW\u003c/em\u003e\u003csub\u003etot\u003c/sub\u003e,\u003cem\u003e W\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e and \u003cem\u003eη\u003c/em\u003e as a function of applied electric field for the \u003cem\u003ex\u003c/em\u003e = 0.10 ceramic. Inset: \u003cem\u003eP\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e and \u003cem\u003eP\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e versus electric field. \u003cstrong\u003ef\u003c/strong\u003e Radar chart comparing key performance metrics (\u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e,\u003cem\u003e E\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, \u003cem\u003eη\u003c/em\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e, Δ\u003cem\u003eP\u003c/em\u003e) for BNT, \u003cem\u003ex\u003c/em\u003e = 0, and \u003cem\u003ex\u003c/em\u003e = 0.10 ceramics. \u003cstrong\u003eg\u003c/strong\u003e Quantitative comparison of the percentage improvement in \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e, and \u003cem\u003eη\u003c/em\u003e for the \u003cem\u003ex\u003c/em\u003e = 0.10 ceramic relative to BNT and the \u003cem\u003ex\u003c/em\u003e = 0 ceramic. \u003cstrong\u003eh\u003c/strong\u003e Comparison of \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e and \u003cem\u003eη \u003c/em\u003efor the \u003cem\u003ex\u003c/em\u003e = 0.10 high-entropy ceramic with other recently reported lead-free bulk ceramics (see Supplementary Table S1 for data sources).\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7666264/v1/ec6f28fd99b0375e04301648.jpeg"},{"id":92062639,"identity":"6426c919-6e70-4c3a-9b11-a4d328448a2d","added_by":"auto","created_at":"2025-09-24 08:26:08","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1348650,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAtomic-scale polarization mapping and analysis of polar nanoregions (PNRs) in the high-entropy BNSLT-0.10BMT ceramic. \u003c/strong\u003eAtomic-resolution HAADF-STEM images with overlaid polarization vectors (yellow arrows) for the core \u003cstrong\u003ea\u003c/strong\u003e and shell \u003cstrong\u003eb\u003c/strong\u003e regions viewed along the [011]\u003csub\u003ec\u003c/sub\u003e zone axis.\u003cstrong\u003e c \u003c/strong\u003eLocally magnified polarization vector maps from the core region along both [011]\u003csub\u003ec\u003c/sub\u003e and [001]\u003csub\u003ec\u003c/sub\u003e projections. Spatial distribution \u003cstrong\u003ed\u003c/strong\u003e and corresponding statistical histogram \u003cstrong\u003ee\u003c/strong\u003e of polarization deviation angles in the core and shell regions along [011]\u003csub\u003ec\u003c/sub\u003e. Spatial distribution \u003cstrong\u003ef\u003c/strong\u003e and statistical histogram \u003cstrong\u003eg\u003c/strong\u003e of polarization magnitudes in the core and shell regions along [011]\u003csub\u003ec\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7666264/v1/daf2c476db308bc63e051df1.jpeg"},{"id":92062636,"identity":"47941ba2-f327-4b09-8b05-0c75a9c35996","added_by":"auto","created_at":"2025-09-24 08:26:08","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1562476,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFirst-principles calculations and experimental validation of electronic structure evolution. \u003c/strong\u003eComputational supercell models for \u003cstrong\u003ea\u003c/strong\u003e BNT, \u003cstrong\u003eb\u003c/strong\u003e Sr/La-doped BNT (\u003cem\u003ex\u003c/em\u003e = 0), and \u003cstrong\u003ec\u003c/strong\u003e the high-entropy system (\u003cem\u003ex\u003c/em\u003e = 0.10). \u003cstrong\u003ed-f \u003c/strong\u003eCalculated PDOS for the models in \u003cstrong\u003ea-c\u003c/strong\u003e, respectively. \u003cstrong\u003eg-i\u003c/strong\u003e Calculated electronic band structures for the models in \u003cstrong\u003ea-c\u003c/strong\u003e, respectively. \u003cstrong\u003ej \u003c/strong\u003eMeasured Hall resistance as a function of magnetic field for BNT, \u003cem\u003ex\u003c/em\u003e = 0, and \u003cem\u003ex\u003c/em\u003e= 0.10 ceramics. Experimental comparisons of \u003cstrong\u003ek\u003c/strong\u003e electrical resistivity, \u003cstrong\u003ei\u003c/strong\u003ecarrier concentration, and \u003cstrong\u003em\u003c/strong\u003e carrier mobility of BNT, \u003cem\u003ex\u003c/em\u003e = 0, and \u003cem\u003ex\u003c/em\u003e= 0.10 ceramics.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7666264/v1/a81a9a2da073eeec7341fc81.jpeg"},{"id":92061422,"identity":"beb698a0-8cc6-46da-946a-e390a796f10f","added_by":"auto","created_at":"2025-09-24 08:18:08","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1561213,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFinite element simulations of dielectric breakdown propagation.\u003c/strong\u003e Electric field distribution and simulated breakdown path propagation for three models: \u003cstrong\u003ea \u003c/strong\u003eModel A (low entropy: BNT, large grains); \u003cstrong\u003eb\u003c/strong\u003e Model B (high entropy: \u003cem\u003ex\u003c/em\u003e= 0.10 composition, fine grains, without core-shell structure); \u003cstrong\u003ec\u003c/strong\u003e Model C (high entropy: \u003cem\u003ex\u003c/em\u003e = 0.10 composition, fine grains, with core-shell structure). Simulations under 380 kV/cm (a1-a3, b1-b3, c1-c3) and 680 kV/cm (a4-a6, b4-b6, c4-c6).\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7666264/v1/64eed09142960a4c891e277e.jpeg"},{"id":92062888,"identity":"cd38168b-90d9-47c6-b872-44223b029216","added_by":"auto","created_at":"2025-09-24 08:34:10","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":581430,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCharge-discharge performance of the high-entropy BNSLT-0.10BMT ceramics. a \u003c/strong\u003eOverdamped discharge current waveforms under different electric fields. \u003cstrong\u003eb\u003c/strong\u003e Calculated discharge energy density (\u003cem\u003eW\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e) from the date in \u003cstrong\u003ea\u003c/strong\u003e. \u003cstrong\u003ec\u003c/strong\u003e Underdamped discharge current waveforms. \u003cstrong\u003ed\u003c/strong\u003e Maximum current density (\u003cem\u003eC\u003c/em\u003e\u003csub\u003eD\u003c/sub\u003e ) and power density (\u003cem\u003eP\u003c/em\u003e\u003csub\u003eD\u003c/sub\u003e) calculated from the underdamped discharge tests.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7666264/v1/04b4c9f641e4472df8d62105.jpeg"},{"id":106401700,"identity":"3c3286a5-1f4c-4516-a3b9-fb1ba1ad7e52","added_by":"auto","created_at":"2026-04-08 09:09:12","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10412471,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7666264/v1/569703ba-76ac-422b-bfac-67364ecbc5f6.pdf"},{"id":92062643,"identity":"7add2832-c112-4f26-bd7e-ba264d109fe6","added_by":"auto","created_at":"2025-09-24 08:26:08","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":15884477,"visible":true,"origin":"","legend":"High-entropy driven electronic and microstructural synergy for superior capacitive energy storage in lead-free ceramics","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-7666264/v1/fa2b2fe337450077b95e871d.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"High-entropy driven electronic and microstructural synergy for superior capacitive energy storage in lead-free ceramics","fulltext":[{"header":"Introduction","content":"\u003cp\u003eDielectric capacitors stand at the forefront of power electronics innovation, enabling key applications ranging from pulsed power systems to grid-scale energy storage by virtue of their ultrafast charge/discharge kinetics, unparalleled power density, and robust thermal stability\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. As these technologies evolve toward higher efficiency and miniaturization, dielectric ceramics, which store energy through ionic displacement polarization under high electric fields, offer distinct advantages including sub-microsecond response times and minimal Joule heating, inherent to their physical polarization mechanism\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Nonetheless, this potential remains fundamentally constrained by an intrinsic inverse correlation between maximum polarization (\u003cem\u003eP\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e) and dielectric breakdown strength (\u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e​), exacerbated by substantial polarization hysteresis and losses. These limitations are quantitatively captured by the figures of merit for energy storage: the recoverable energy density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{W}}_{\\text{rec}}\\text{}\\text{=}\\text{}{\\int\\:}_{{\\text{P}}_{\\text{r}}}^{{\\text{P}}_{\\text{m}}}\\text{E}\\text{}\\text{dP}\\)\u003c/span\u003e\u003c/span\u003e) and efficiency (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\eta\\text{}\\text{=}\\text{}{\\text{W}}_{\\text{rec}}\\text{/}{\\text{W}}_{\\text{total}}\\)\u003c/span\u003e\u003c/span\u003e), where \u003cem\u003eP\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e and \u003cem\u003eW\u003c/em\u003e\u003csub\u003etotal\u003c/sub\u003e denote the remnant polarization, applied electric field, and total energy storage density (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003ea). Achieving high values for both parameters concurrently has remained a persistent challenge\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eTo navigate this performance trade-off, research efforts have pursued several distinct pathways. Domain and phase engineering strategies aim to enhance relaxor behavior, effectively suppressing \u003cem\u003eP\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e​\u003csup\u003e9\u0026ndash;12\u003c/sup\u003e. Grain orientation control has been employed to substantially improve \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, and thus the energy storage density by mitigating electric-field-induced strain\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. More recently, high-entropy design, achieved by incorporating multiple principal elements into cationic sites to induce severe lattice distortion and chemical disorder, has emerged as a promising avenue. This approach reduces domain size and polarization switching hysteresis​ while concurrently boosting \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb​\u003c/sub\u003e\u003csup\u003e14\u0026ndash;18\u003c/sup\u003e. Seminal studies have demonstrated that energy storage properties can exceed 10 J/cm\u003csup\u003e3\u003c/sup\u003e and 90% efficiency in high-entropy stabilized systems based on (Bi, Na)TiO\u003csub\u003e3\u003c/sub\u003e (BNT)\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, BaTiO\u003csub\u003e3\u003c/sub\u003e (BT)\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e, and (K, Na)NbO\u003csub\u003e3\u003c/sub\u003e (KNN)\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Notably, an ultrahigh energy density of 182 J/cm\u003csup\u003e3\u003c/sup\u003e with 78% efficiency was reported in high-entropy Bi\u003csub\u003e2\u003c/sub\u003eTi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e7\u003c/sub\u003e-based films\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Parallel strategies exploit core-shell architectures to decouple the enhancement of Δ\u003cem\u003eP\u003c/em\u003e and \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e​, as evidenced in BNT-based (\u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e ~ 5.07 J/cm\u003csup\u003e3\u003c/sup\u003e, \u003cem\u003eη\u003c/em\u003e\u0026thinsp;=\u0026thinsp;85.17%)\u003csup\u003e25\u003c/sup\u003e, BT-based (\u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e ​= 7.6 J/cm\u003csup\u003e3\u003c/sup\u003e, \u003cem\u003eη\u003c/em\u003e\u0026thinsp;=\u0026thinsp;84%) \u003csup\u003e26\u003c/sup\u003e, and NaNbO\u003csub\u003e3\u003c/sub\u003e (NN)-based ceramics (\u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e = 7.72 J/cm\u003csup\u003e3\u003c/sup\u003e, \u003cem\u003eη\u003c/em\u003e\u0026thinsp;=\u0026thinsp;83.78%)\u003csup\u003e27\u003c/sup\u003e. Despite these advances, two critical challenges impede further progress. First, current strategies often operate in isolation; the potential synergies between high-entropy modifications and core-shell structuring remain largely unexplored. Second, electronic band structure engineering, a crucial lever for regulating charge carrier mobility and thereby \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, is yet to be comprehensively investigated in BNT-based systems.\u003c/p\u003e\u003cp\u003eIn this work, we bridge these gaps through a unified approach that concurrently modulates the electronic and microstructural landscapes. By introducing a suite of heterovalent cations at the A- and B-sites in the (1-\u003cem\u003ex\u003c/em\u003e)(Bi\u003csub\u003e0.34\u003c/sub\u003eNa\u003csub\u003e0.3\u003c/sub\u003eSr\u003csub\u003e0.28\u003c/sub\u003eLa\u003csub\u003e0.04\u003c/sub\u003e)TiO\u003csub\u003e3\u003c/sub\u003e-\u003cem\u003ex\u003c/em\u003eBa(Mg\u003csub\u003e1/3\u003c/sub\u003eTa\u003csub\u003e2/3\u003c/sub\u003e)O\u003csub\u003e3\u003c/sub\u003e (abbreviated as BNSLT-\u003cem\u003ex\u003c/em\u003eBMT) system, our high-entropy engineering strategy delivers a tripartite synergy: (ⅰ) flattening of conduction band curvature to suppress charge carrier mobility, (ⅱ) instigation of self-assembled core-shell grains that homogenize local electric fields and hinder breakdown propagation, and (ⅲ) stabilization of a nanoscale R-O-T-C multiphase coexistence that enhances polarizability and dipole reconfigurability under high fields. This concerted manipulation culminates in an ultra-high \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e of 11.1 J/cm\u003csup\u003e3\u003c/sup\u003e with an \u003cem\u003eη\u003c/em\u003e of 89.1% at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 (configurational entropy \u003cem\u003eS\u003c/em\u003e\u003csub\u003econfig\u003c/sub\u003e = 1.8\u003cem\u003eR\u003c/em\u003e), representing a tenfold enhancement over conventional BNT. Our findings establish coupled electronic-microstructural tailoring as a transformative paradigm for overcoming the polarization-breakdown compromise in next-generation dielectric capacitors.\u003c/p\u003e"},{"header":"Results and discussion","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eComposition-driven structural evolution\u003c/h2\u003e\u003cp\u003eThe configuration entropy (\u003cem\u003eS\u003c/em\u003e\u003csub\u003econfig\u003c/sub\u003e) defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{S}}_{\\text{config}}\\text{}\\text{= -}\\text{R}\\text{[}{\\left(\\sum\\:_{\\text{i}\\text{=1}}^{\\text{N}}{\\text{x}}_{\\text{i}}\\text{ln}{\\text{x}}_{\\text{i}}\\right)}_{\\text{cation-site}}\\text{+}{\\text{(}\\sum\\:_{\\text{j}\\text{=1}}^{\\text{M}}{\\text{x}}_{\\text{j}}\\text{ln}{\\text{x}}_{\\text{j}}\\text{)}}_{\\text{anion-site}}\\text{]}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003eR\u003c/em\u003e, \u003cem\u003eN\u003c/em\u003e(\u003cem\u003eM\u003c/em\u003e) and \u003cem\u003ex\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003ej\u003c/sub\u003e) denote the ideal gas constant, atomic species and contents at the equivalent cation or anion sites, respectively, has been proposed to quantify the compositional inhomogeneity. The \u003cem\u003eS\u003c/em\u003e\u003csub\u003econfig\u003c/sub\u003e progressively increases from 0.69\u003cem\u003eR\u003c/em\u003e (low-entropy) for the virgin BNT to greater than 1.5\u003cem\u003eR\u003c/em\u003e (high-entropy) for the BNSLT-\u003cem\u003ex\u003c/em\u003eBMT ceramics with \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.06\u0026ndash;0.15, as displayed in Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003eb. The high-entropy-induced multinuclear-type core-shell structure (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea, b and Fig. S3a, b), and onion-like core-shell structure (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec, d) can be readily observed in both bright-field and high-angle annular dark-field (HAADF) STEM images of \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 ceramics. As demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee, energy-dispersive X-ray spectroscopy (EDS) line profile traversing the core-shell structure (along the green arrow in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea) delineates a pronounced enrichment of Sr within the core, concomitant with a depletion of Bi and Na. This chemical partitioning is visually confirmed by EDS elemental mapping (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef), which clearly depicts Sr segregation in the core. Consistent results obtained from multiple core-shell structured ceramics (Fig. S2b, c, and Fig. S3c, d) affirm Sr enrichment in the core. To decipher the formation mechanism of the core-shell structure, we constructed the probable migration pathway during crystallization for doping elements (Sr, La, Ba, Ta, Mg) within the BNT matrix lattice, as schematically shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eg, and computed the diffusion energy barriers for the pertinent elements using first-principles calculation (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eh, i). The results unequivocally demonstrate that Sr possesses the highest diffusion energy barrier among the doping cations. This implies a pronounced tendency for Sr to be trapped and accumulate in the core region during sintering, with a markedly lower propensity for outward diffusion, thereby providing the primary thermodynamic driving force for the development of the core-shell heterogeneity. The disparity in cationic mobility is thus identified as the intrinsic origin of the observed core-shell microstructure in high-entropy ceramics. Additionally, a series of well-defined core-shell interfaces (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ej, Fig. S2d and Fig. S3e) without dislocation contrast could be observed in the \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 ceramics, which is beneficial to enhance the \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e. The high-magnification morphological images (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ek) and the inverse Fourier transform (IFFT) images of lattice fringes (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003el, Fig. S3f, Fig. S4) of the core and shell regions reveal the ubiquitous presence of nano-scaled polar nanoregions (PNRs) within the matrix, suggesting strong relaxor characteristic induced by the high-entropy design, which facilitates a significant polarization disparity Δ\u003cem\u003eP\u003c/em\u003e. In addition, as the entropy value increases, the grain sizes of the samples (Fig. S5) generally exhibit a decreasing trend, which increases the density of barriers to electrical breakdown.\u003c/p\u003e\u003cp\u003eThe phase evolution was further probed by XRD (Fig. S6) and temperature-dependent dielectric spectroscopy (Fig. S7a-f). With increasing BMT content (and thus \u003cem\u003eS\u003c/em\u003e\u003csub\u003econfig\u003c/sub\u003e), a clear transition from a classical ferroelectric to a pseudocubic relaxor phase is observed\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. The dielectric relaxor behavior is quantitatively assessed using the modified Curie-Weiss law (Fig. S7g). The diffuseness coefficients (\u003cem\u003eγ\u003c/em\u003e) monotonically increase from 1.76 for virgin BNT (low entropy) to 1.96 for \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.15 composition (high entropy), confirming a significantly enhanced relaxor characteristic. This is rationalized by the high-entropy-induced cation disorder, which strengthens random fields, breaks long-range ferroelectric order, and promotes the formation of highly dynamic PNRs. Selected-area electron diffraction (SAED) patterns (Fig. S8b, c) from the shell and core regions exhibit no superlattice reflections, consistent with an average pseudocubic structure. However, careful analysis of SAED pattern (Fig. S8d) spanning the core-shell interface reveals a slight splitting of diffraction spots corresponding the same crystallographic planes, attributed to lattice strain and distortion arising from the core-shell compositional heterogeneity.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eEnergy storage performance\u003c/h3\u003e\n\u003cp\u003eThe unipolar polarization-electric field (\u003cem\u003eP\u003c/em\u003e-\u003cem\u003eE\u003c/em\u003e) hysteresis loops for BNT and the BNSLT-\u003cem\u003ex\u003c/em\u003eBMT series, measured at their respective breakdown fields, are given in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea. The corresponding energy storage properties, \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e and \u003cem\u003eη\u003c/em\u003e, are summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb. The low-entropy BNT ceramic exhibits a fat \u003cem\u003eP\u003c/em\u003e - \u003cem\u003eE\u003c/em\u003e loop with a large \u003cem\u003eP\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e and a low \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, characteristic of strong ferroelectricity, resulting in poor energy storage performance. As the entropy increases, the loops become progressively slimmer, indicative of enhanced relaxor behavior. The optimum composition, \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 (\u003cem\u003eS\u003c/em\u003e\u003csub\u003econfig\u003c/sub\u003e = 1.8\u003cem\u003eR\u003c/em\u003e), achieves an ultrahigh \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e of 11.1 J/cm\u003csup\u003e3\u003c/sup\u003e and an outstanding \u003cem\u003eη\u003c/em\u003e of 89.1% at 860 kV/cm. The statistical breakdown strength, a critical parameter, was rigorously evaluated using the two-parameter Weibull distribution: \u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e = ln(\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e), \u003cem\u003eY\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e = ln(ln(1/(1-\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e))), where \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e = \u003cem\u003ei\u003c/em\u003e/(\u003cem\u003en\u003c/em\u003e\u0026thinsp;+\u0026thinsp;1), \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the breakdown strength of each tested sample in ascending order, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the cumulative probability of dielectric breakdown, \u003cem\u003en\u003c/em\u003e represents the total number of tested samples\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. All samples exhibit high Weibull moduli (\u003cem\u003eβ\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;12), attesting to the high reliability of the data, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec. The inset in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec reveals a dramatic enhancement in E\u003csub\u003eb\u003c/sub\u003e with increasing entropy: from 269 kV/cm for BNT (low entropy) to 358 kV/cm for \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0 (medium entropy), and ultimately to 863 kV/cm for \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 composition (high entropy). This substantial improvement is a cornerstone of the superior performance. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee detail the electric field-dependent energy storage behavior of the \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 ceramics. The \u003cem\u003eP\u003c/em\u003e - \u003cem\u003eE\u003c/em\u003e loops remain extremely slim with near-zero \u003cem\u003eP\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e across a wide field range (100\u0026ndash;860 kV/cm) due to strong relaxor characteristic\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Both \u003cem\u003eP\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e and Δ\u003cem\u003eP\u003c/em\u003e increase linearly with the applied field without showing signs of saturation, while \u003cem\u003eη\u003c/em\u003e remains consistently high (\u0026gt;\u0026thinsp;89.1%), underscoring the material\u0026rsquo;s capability to withstand ultrahigh fields with minimal energy loss\u003csup\u003e\u003cspan additionalcitationids=\"CR34\" citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. A radar chart (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ef) provides a holistic comparison of the key performance metrics (\u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e, \u003cem\u003eη\u003c/em\u003e, \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e, Δ\u003cem\u003eP\u003c/em\u003e) for the low- (BNT), medium- (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0), and high-entropy (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10) ceramics, vividly illustrating the comprehensive superiority of the high-entropy design. Quantitatively, the \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 ceramics exhibits a 231%, 853%, and 46% improvement in \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e, and \u003cem\u003eη\u003c/em\u003e, respectively, compared to BNT, and a 146%, 177%, and 10% improvement compared to the \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0 medium-entropy ceramics (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eg). The overall energy storage performance (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh and Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e) surpasses that of most recently reported lead-free ceramic systems, positioning our high-entropy ceramic at the forefront of dielectric energy storage research.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\n\u003ch3\u003eStructural origins of the superior energy storage performance\u003c/h3\u003e\n\u003cp\u003eTo unravel the atomic-scale structural origins of the superior energy storage performance, we conducted atomic-resolution HAADF-STEM to analyze the polarization configurations within the PNRs of the \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 ceramic. HAADF-STEM images of both core and shell regions along [001]\u003csub\u003ec\u003c/sub\u003e (Fig. S9) reveal polarization vectors (yellow arrows) from the central B-site to the corner A-site cations. Two-dimensional Gaussian fitting confirms the presence of a tetragonal (T) phase, while regions with near-zero polarization amplitude are identified as cubic (C). However, the [001]\u003csub\u003ec\u003c/sub\u003e projection cannot distinguish between rhombohedral (R) and orthorhombic (O) phases due to their similar projections. To resolve this, we performed polarization vector mapping of both core and shell regions along the [011]\u003csub\u003ec\u003c/sub\u003e zone axis, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, b. This orientation allows clear differentiation: polarization vectors along [111]\u003csub\u003ec\u003c/sub\u003e signify the R phase, while those along [110]\u003csub\u003ec\u003c/sub\u003e indicate the O phase. The locally magnified polarization vector images of the sample core along the [011]\u003csub\u003ec\u003c/sub\u003e and [001]\u003csub\u003ec\u003c/sub\u003e directions are displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec. Moreover, Fig. S10 presents polarization vector images without atoms for both the core and shell regions along [001]\u003csub\u003ec\u003c/sub\u003e and [011]\u003csub\u003ec\u003c/sub\u003e. These analyses unambiguously identifies that the coexistence of R, O, and T phases in the matrix C phase occurs locally within nano-regions in both the core and shell of the \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 ceramic. The nanoscale phase heterogeneity is a hallmark of the high-entropy composition, creating intense random fields that effectively disrupt long-range ferroelectric order and are paramount for the enhanced relaxor behavior. We further performed a statistical analysis of the polarization vector deviation angles (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed, e) and magnitudes (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef, g) in both core and shell regions. The broad distribution of polarization angles reflects enhanced polarization anisotropy and disorder, implying a more flexible polarization response to external electric fields, which facilitates the reduction of \u003cem\u003eP\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e. Concurrently, the fluctuation in polarization magnitude indicates a reduction in local polarization strength, further reinforcing the relaxor characteristic. This non-uniform distribution of PNRs, with variations in both direction and magnitude, signifies the presence of strong random fields, which are conducive to high energy storage efficiency\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. The dynamic nature of these PNRs was probed by piezoresponse force microscopy (PFM) (Fig. S11). The written domains under poling voltages were found to be metastable, relaxing back to their initial state shortly after the electric field was removed. This observed reversibility and low coercivity confirm the high dynamics of the PNRs, which require a lower energy barrier for reorientation. This characteristic is crucial for achieving a large \u003cem\u003eP\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e under high fields while maintaining a low \u003cem\u003eP\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e, as it delays polarization saturation and enhances \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\n\u003ch3\u003eElectronic structure and carrier confinement\u003c/h3\u003e\n\u003cp\u003eFirst-principles density functional theory (DFT) calculations were employed to decipher the electronic structure evolution\u003csup\u003e\u003cspan additionalcitationids=\"CR39\" citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. Models for BNT, Sr/La-doped BNT (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0), and the high-entropy system (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10) were constructed, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea-c. The partial density of states (PDOS) for BNT (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed) shows the valence band maximum (VBM) is dominated by O-2p orbitals, while the conduction band minimum (CBM) is primarily composed of Ti-3d orbitals. Doping with Sr, La, Ba, Ta, and Mg (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee, f) introduces states deep within the valence and conduction bands but induces negligible change to the band gap (\u003cem\u003eE\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e), consistent with our experimental UV-Vis results (Fig. S12). The critical effect of high-entropy doping is manifested in the band structure (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eg-i). Compared to virgin BNT, the high-entropy system exhibits significantly flattened bands, particularly near the CBM, due to the [SrO], [LaO], [MgO] local distortion weakens the interatomic interaction. This reduced band curvature\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\left(\\frac{{d}^{\\text{2}}\\text{E}\\text{(}\\text{k}\\text{)}}{{\\text{dk}}^{\\text{2}}}\\right)\\)\u003c/span\u003e\u003c/span\u003e directly implies an increase in the effective mass of charge carriers (\u003cem\u003em\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e) according to the relation: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{{m}^{\\text{*}}}\\)\u003c/span\u003e\u003c/span\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{{\\hslash\\:}^{2}}\\:\\)\u003c/span\u003e\u003c/span\u003e\u0026middot;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{d}^{\\text{2}}\\text{E}\\text{(}\\text{k}\\text{)}}{{\\text{dk}}^{\\text{2}}}\\)\u003c/span\u003e\u003c/span\u003e. A large \u003cem\u003em\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e leads to reduced carrier mobility (\u003cem\u003eσ\u003c/em\u003e) based on \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026sigma;}\\text{}\\text{=}\\text{}\\frac{\\text{n}{\\text{e}}^{\\text{2}}\\text{\u0026tau;}}{{\\text{m}}^{\\text{*}}}\\)\u003c/span\u003e\u003c/span\u003e. Hall effect measurements (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ej-m) provide experimental validation. All compositions exhibit n-type conduction. With increasing entropy, the electrical resistivity rises markedly (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ek), while both the carrier concentration and mobility decrease substantially (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003el, m). This excellent agreement between theory and experiment robustly demonstrates a carrier confinement effect induced by high-entropy engineering. This flattened bands (increased \u003cem\u003em\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e) and the compositional disorder act in concert to severely impede charge transport, suppressing leakage current and enhancing the insulating strength. This novel electronic structure manipulation strategy is a key contributor to the ultrahigh \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e and superior \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e in this work.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\n\u003ch3\u003eRole of core-shell structure in breakdown strength\u003c/h3\u003e\n\u003cp\u003eFinite element simulations were conducted to visualize the role of core-shell microstructure in the dielectric breakdown process. Three models designed based on SEM and TEM results were compared: BNT (low entropy, large grains), \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 without a core-shell structure (high entropy, fine grains), and \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 with a core-shell structure (high entropy, fine grains), as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea-c. The simulations reveal that the electric field is highly concentrated at grain boundaries due to their lower dielectric constant compared to the grain interiors\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. Under a simulated field of 380 kV/cm, breakdown paths readily propagate across the entire BNT sample (Fig.\u0026nbsp;5a1-a3). Grain refinement in the high-entropy sample without a core-shell structure hinders this propagation, confining the breakdown to about half the sample length (Fig.\u0026nbsp;5b1-b3). The introduction of the core-shell structure (Fig.\u0026nbsp;5c1-c6) has a profound effect: it effectively shields and homogenizes the electric field at the grain boundaries and core-shell interfaces, preventing dangerous local field concentrations. As shown in Fig. S13, the reduced grain size combined with the formation of the core-shell structure leads to a more uniform polarization distribution. Consequently, even under a much higher simulated field of 680 kV/cm, the breakdown progression in the core-shell sample is significantly retarded compared to the others, as display in Fig.\u0026nbsp;5a4-a6 and 5b4-b6. The core-shell interface acts as a barrier, deflecting and pinning the electrical treeing channels. This, combined with the reduced grain size and increased electrical resistivity synergistically contribute to the dramatically improved \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e and the associated \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e\u003cb\u003eCharge/discharge performance and temperature stability\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eFor practical applications, superior discharge capability and thermal reliability are imperative. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea shows the overdamped discharge current curves of the \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10 ceramics under varied electric fields. The corresponding discharged energy density (\u003cem\u003eW\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e), calculated by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{W}}_{\\text{d}}\\text{=}\\text{R}\\int\\:\\frac{{\\text{I}}^{\\text{2}}\\left(\\text{t}\\right)\\text{dt}}{\\text{V}}\\text{}\\)\u003c/span\u003e\u003c/span\u003e(where the load resistance \u003cem\u003eR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;187 Ω, \u003cem\u003eV\u003c/em\u003e is the sample volume, \u003cem\u003eI\u003c/em\u003e is the current, and \u003cem\u003et\u003c/em\u003e is time)\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e, is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb. The \u003cem\u003eW\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e value increases steadily with the applied field. Most notably, an ultra-short discharge time (\u003cem\u003et\u003c/em\u003e\u003csub\u003e0.9\u003c/sub\u003e, time to release 90% of the stored energy) of merely 26.6 ns is achieved, indicating an ultra-fast discharge rate, which can be attributed to the highly dynamic nature of the PNRs enabling ultrafast polarization reversal. The underdamped discharge current waveforms are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec. The calculated current density (\u003cem\u003eC\u003c/em\u003e\u003csub\u003eD\u003c/sub\u003e = \u003cem\u003eI\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e/\u003cem\u003eS\u003c/em\u003e, where \u003cem\u003eS\u003c/em\u003e is the electrode area, \u003cem\u003eI\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e denotes the maximum current) and power density (\u003cem\u003eP\u003c/em\u003e\u003csub\u003eD\u003c/sub\u003e = \u003cem\u003eE\u003c/em\u003e \u0026sdot; \u003cem\u003eI\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e/(2\u003cem\u003eS\u003c/em\u003e)) reach impressive values of 1515.2 A/cm\u003csup\u003e2\u003c/sup\u003e and 280.3 MW/cm\u003csup\u003e3\u003c/sup\u003e, respectively, at 370 kV/cm (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed). These outstanding metrics underscore the potential of this material for high-power applications. It is worth noting that the \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e and \u003cem\u003eW\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e exhibit minimal variation with fluctuations of less than 7.9% and 9.4%, respectively, over the temperature range of 25\u0026ndash;125 \u003csup\u003eo\u003c/sup\u003eC, suggesting excellent thermal stability, as shown in Fig. S14a-d. The robust stability originates from the high-entropy-stabilized phase structure and relatively smooth dielectric content with elevated temperature\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e, as evidenced by in-situ temperature-dependent XRD patterns (Fig. S15) and \u003cem\u003eε\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e-\u003cem\u003eT\u003c/em\u003e curves (Fig. S7e), ensuring reliable operation under varying environmental conditions.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn summary, we have demonstrated a high-entropy strategy that synergistically engineers the electronic and microstructural properties of (Bi, Na)TiO\u003csub\u003e3\u003c/sub\u003e​-based ceramics to achieve unparalleled energy storage performance. The incorporation of multiple principal elements simultaneously: (ⅰ) flattens the electronic band structure, suppressing carriers mobility and conductivity; (ⅱ) drives the self-assembly of core-shell microstructure, which homogenize local electric fields and effectively impede the propagation of breakdown paths; (ⅲ) stabilizes a nanoscale coexistence of R-O-T-C phases, creating intense random fields that disrupt long-range ferroelectric order, enhance dipole reconfigurability, and yield slimmer hysteresis loops with large Δ\u003cem\u003eP\u003c/em\u003e. This tripartite synergy successfully decouples the traditional trade-off between polarization and breakdown strength. The resultant lead-free ceramic achieves a superior \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e of 11.1 J/cm\u003csup\u003e3\u003c/sup\u003e with a high \u003cem\u003eη\u003c/em\u003e of 89.1%, exceptional \u003cem\u003eW\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e of 280.3 MW/cm\u003csup\u003e3\u003c/sup\u003e, and an ultrafast discharge speed (\u003cem\u003et\u003c/em\u003e\u003csub\u003e0.9\u003c/sub\u003e ~ 26.6 ns), alongside excellent temperature stability. Our work establishes coupled electronic-microstructural engineering via high-entropy design as a transformative and universal paradigm for developing next-generation dielectric capacitors for advanced energy storage applications.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eCeramics preparation\u003c/h2\u003e\u003cp\u003ePolycrystalline samples of BNT and (1-\u003cem\u003ex\u003c/em\u003e)(Bi\u003csub\u003e0.34\u003c/sub\u003eNa\u003csub\u003e0.3\u003c/sub\u003eSr\u003csub\u003e0.28\u003c/sub\u003eLa\u003csub\u003e0.04\u003c/sub\u003e)TiO\u003csub\u003e3\u003c/sub\u003e-\u003cem\u003ex\u003c/em\u003eBa(Mg\u003csub\u003e1/3\u003c/sub\u003eTa\u003csub\u003e2/3\u003c/sub\u003e)O\u003csub\u003e3\u003c/sub\u003e (BNSLT-\u003cem\u003ex\u003c/em\u003eBMT, \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0, 0.06, 0.08, 0.10, 0.15) series were synthesized via a conventional solid-state reaction route. High-purity powders of Na\u003csub\u003e2\u003c/sub\u003eCO\u003csub\u003e3\u003c/sub\u003e (99.8%), Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e (99%), TiO\u003csub\u003e2\u003c/sub\u003e (99.9%), SrCO\u003csub\u003e3\u003c/sub\u003e (99.95%), La\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e (99.9%), BaCO\u003csub\u003e3\u003c/sub\u003e (99.99%), MgO (99.99%) and Ta\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e (99.5%) were pre-dried and subsequently weighed according to stoichiometric ratios. The powders were mixed by planetary ball milling in ethanol for 24 h. After drying, the mixtures were calcined at 850 \u003csup\u003eo\u003c/sup\u003eC for 3 h in air and then milled again under identical conditions to ensure homogeneity. Polyvinyl alcohol (PVA) binder was added to the resulting powders, which were then granulated and sieved. The granules were uniaxially pressed into pellets with a diameter of 10 mm. After binder burnout at 600 \u003csup\u003eo\u003c/sup\u003eC, the pellets were sintered at temperatures between 1100 and 1150 \u003csup\u003eo\u003c/sup\u003eC for 2 h to obtain dense ceramics.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eStructural characterization\u003c/h2\u003e\u003cp\u003eCrystal structure and phase purity were examined using X-ray diffractometer (XRD; TD-3700, Dandong Tongda Technology Co. Ltd., China) with Cu Kα radiation. Microstructure analysis was performed using a field-emission scanning electron microscope (FE-SEM; Merlin Compact, Zeiss, Germany). Grain size statistics were derived from SEM images using Nano Measure software. The core-shell microstructure, elemental mapping, and domain morphology were observed using a transmission electron microscope (TEM; FEI Talos F200X, America) equipped with an energy-dispersive X-ray spectroscopy (EDS) system. Atomic-scale polarization mapping was carried out using a dual spherical- aberration corrected scanning transmission electron microscopy (STEM; Spectra 300, Thermo Fisher Scientific) at 300 kV. Atomic column positions were determined via two-dimensional Gaussian fitting, and polarization vectors were extracted using custom MATLAB scripts. Domain dynamics were investigated using piezoelectric force microscopy (PFM; MFP-3D, Asylum Research, USA). Optical band gaps (\u003cem\u003eE\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e) were determined from UV-Vis absorption spectra.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eElectrical performance measurement\u003c/h2\u003e\u003cp\u003eFor ferroelectric measurements, ceramics were polished to 30\u0026ndash;40 \u0026micro;m thickness and coated with gold electrodes 0.5 mm in diameter. Polarization-electric field (\u003cem\u003eP\u003c/em\u003e - \u003cem\u003eE\u003c/em\u003e) hysteresis loops were measured using a ferroelectric test system (RT1-Premier II, Radiant Technologies Inc., USA) to evaluate the energy storage performance. Temperature- and frequency-dependent permittivity was acquired using an inductance-capacitance-resistance (LCR) meter (E4980A, Agilent, USA) accompanied with a temperature control system. Charge-discharge performance was evaluated using a dedicated tester (CFD-003, Tongguo Technology, China) based on a RC circuit. Hall effect measurements were performed in a Physical Property Measurement System (PPMS-9, Quantum Design) using a Keithley 2400 SourceMeter and 2182A Nanovoltmeter.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003eDFT calculations\u003c/h2\u003e\u003cp\u003eFirst-principles calculations based on density functional theory (DFT) were performed using the Vienna Ab initio Simulation Package (VASP) with the projector augmented-wave (PAW) method. The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) was employed for the exchange-correlation functional. A plane-wave cutoff energy of 520 eV was chosen for the geometry optimization and electronic structure calculations. The Brillouin zone was sampled with Γ-centered k-point meshes of 5\u0026times;5\u0026times;1 for structural optimization and 9\u0026times;9\u0026times;1 for electronic structure calculations. All atomic positions were optimized until Hellmann-Feynman forces were less than 0.01 eV/\u0026Aring;. The energy and electronic convergence criteria were set to 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e eV and 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e eV per atom, respectively. Diffusion energy barrier was calculated using the climbing-image nudged elastic band (CI-NEB) method.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003eFinite element simulations\u003c/h2\u003e\u003cp\u003eFinite element simulations of electric field distribution and breakdown propagation were performed using models constructed from SEM and TEM images. Three configurations were considered: (A) low-entropy large-grained BNT, (B) high-entropy fine-grained ceramic without core-shell structure, and (C) high-entropy fine-grained ceramic with core-shell structure. Each model was discretized into a 2D grid of 170\u0026times;238 points over an area of 2.5\u0026times;3.5 \u0026micro;m\u003csup\u003e2\u003c/sup\u003e. The evolution probability of breakdown channels was modeled using a modified fractal dielectric breakdown model:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:p\\left({i}^{{\\prime\\:}},{j}^{{\\prime\\:}}-i,j\\right)=\\frac{{({\\varPhi\\:}_{{i}^{{\\prime\\:}},{j}^{{\\prime\\:}}}-{\\varPhi\\:}_{i,j}-{\\varPhi\\:}_{0})}^{\\eta\\:}}{\\varSigma\\:{({\\varPhi\\:}_{{i}^{{\\prime\\:}},{j}^{{\\prime\\:}}}-{\\varPhi\\:}_{i,j}-{\\varPhi\\:}_{0})}^{\\eta\\:}}+{({\\varPhi\\:}_{{i}^{{\\prime\\:}},{j}^{{\\prime\\:}}}-{\\varPhi\\:}_{{i}^{{\\prime\\:}{\\prime\\:}},{j}^{{\\prime\\:}{\\prime\\:}}}-{\\varPhi\\:}_{0})}^{\\eta\\:}-loss$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varPhi\\:}_{0}\\)\u003c/span\u003e\u003c/span\u003e denotes the threshold potential, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varPhi\\:}_{i,j}\\)\u003c/span\u003e\u003c/span\u003e is the potential at the discharged point, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varPhi\\:}_{{i}^{{\\prime\\:}},{j}^{{\\prime\\:}}}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varPhi\\:}_{{i}^{{\\prime\\:}{\\prime\\:}},{j}^{{\\prime\\:}{\\prime\\:}}}\\)\u003c/span\u003e\u003c/span\u003e are potentials at candidate and linked points, respectively, \u003cem\u003eη\u003c/em\u003e is the fractal dimension, and loss represents tip energy loss during electrical tree propagation.\u003c/p\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003ch2\u003eData availability\u003c/h2\u003e\u003cp\u003eAll data necessary to support the conclusions of this study are included in the paper and its Supporting Information files. Any additional datasets generated and/or analyzed during the current study are available from the corresponding author upon justified request.\u003c/p\u003e\u003c/div\u003e\u003cp\u003e\u003ch2\u003eCompeting interests\u003c/h2\u003e\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAuthor contributions\u003c/h2\u003e\u003cp\u003eY.T.L., P.L. and Z.X.C. conceived and designed the research. Y.T.L. led the sample fabrication, energy storage and dielectric measurements, structural and stability characterization, and data processing, with assistance from F.X., J.G.H., P.F., J.D., Z.B.P., W.F.B. and W.L. H.H.H and Z.X.C. carried out the DFT calculations. H.R.B. performed finite element simulations in consultation with P.L. The manuscript was drafted by Y.T.L. and revised critically by P.L., W.L., J.W.Z. and Z.X.C. All authors contributed to data analysis, discussion, and final approval of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e\u003cp\u003eThis work was supported by the National Natural Science Foundation of China (Grant Nos. 52102132, 12204215, and 52402264), the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2025MS695, and ZR2024ME201), and the Shandong Higher Education Institutions Youth Innovation Team Project (Grant No. 2024KJH145).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eQi H et al (2019) Ultrahigh energy-storage density in NaNbO\u003csub\u003e3\u003c/sub\u003e-based lead-free relaxor antiferroelectric ceramics with nanoscale domains. Adv Funct Mater 29:1903877\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang G et al (2019) Ultrahigh energy storage density lead-free multilayers by controlled electrical homogeneity. Energy Environ Sci 12:582\u0026ndash;588\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYan F et al (2022) Boosting energy storage performance of lead-free ceramics via layered structure optimization strategy. Small 18:2202575\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhu L et al (2023) Heterovalent-doping-enabled atom-displacement fluctuation leads to ultrahigh energy-storage density in AgNbO\u003csub\u003e3\u003c/sub\u003e-based multilayer capacitors. Nat Commun 14:1166\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang G et al (2021) Electroceramics for high-energy density capacitors: current status and future perspectives. Che Rev 121:6124\u0026ndash;6172\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYang L et al (2019) Perovskite lead-free dielectrics for energy storage applications. Prog Mater Sci 102:72\u0026ndash;108\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChe Z et al (2022) Phase structure and defect engineering in (Bi\u003csub\u003e0.5\u003c/sub\u003eNa\u003csub\u003e0.5\u003c/sub\u003e)TiO\u003csub\u003e3\u003c/sub\u003e-based relaxor antiferroelectrics toward excellent energy storage performance. Nano Energy 100:107484\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGao P et al (2019) New antiferroelectric perovskite system with ultrahigh energy-storage performance at low electric field. Chem Mater 31:979\u0026ndash;990\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi P et al (2025) Nano-domain configuration boosting energy storage capacity of NaNbO\u003csub\u003e3\u003c/sub\u003e-based relaxor ferroelectrics. J Power Sources 653:237756\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePan H et al (2019) Ultrahigh-energy density lead-free dielectric films via polymorphic nanodomain design. Science 365:578\u0026ndash;582\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eXi J et al (2024) Compromise boosted high capacitive energy storage in lead-free (Bi\u003csub\u003e0.5\u003c/sub\u003eNa\u003csub\u003e0.5\u003c/sub\u003e)TiO\u003csub\u003e3\u003c/sub\u003e-based relaxor ferroelectrics by phase structure modulation and defect engineering. Chem Eng J 502:157986\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhou X et al (2019) Superior thermal stability of high energy density and power density in domain-engineered Bi\u003csub\u003e0.5\u003c/sub\u003eNa\u003csub\u003e0.5\u003c/sub\u003eTiO\u003csub\u003e3\u003c/sub\u003e-NaTaO\u003csub\u003e3\u003c/sub\u003e relaxor ferroelectrics. ACS Appl Mater Interfaces 11:43107\u0026ndash;43115\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi J et al (2020) Grain-orientation-engineered multilayer ceramic capacitors for energy storage applications. Nat Mater 19:999\u0026ndash;1005\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChen L et al (2022) Giant energy-storage density with ultrahigh efficiency in lead-free relaxors via high-entropy design. Nat Commun 13:3089\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChen L et al (2023) Large energy capacitive high-entropy lead-free ferroelectrics. Nano-micro Lett 15:65\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGe G et al (2022) Tunable domain switching features of incommensurate antiferroelectric ceramics realizing excellent energy storage properties. Adv Mater 34:2201333\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKong X et al (2025) High-entropy engineered BaTiO\u003csub\u003e3\u003c/sub\u003e-based ceramic capacitors with greatly enhanced high-temperature energy storage performance. Nat Commun 16:885\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWei T et al (2025) High-entropy assisted capacitive energy storage in relaxor ferroelectrics by chemical short-range order. Nat Commun 16:807\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi D et al (2025) Atomic-scale high‐entropy design for superior capacitive energy storage performance in lead‐free ceramics. Adv Mater 37:2409639\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWei T et al (2025) High-entropy assisted capacitive energy storage in relaxor ferroelectrics by chemical short-range order. Nat Commun 16:807\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhang M et al (2024) Ultrahigh energy storage in high-entropy ceramic capacitors with polymorphic relaxor phase. Science 384:185\u0026ndash;189\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi D et al (2025) Atomic-Scale High‐entropy design for superior capacitive energy storage performance in lead‐free ceramics. Adv Mater 2409639\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChen L et al (2022) Giant energy-storage density with ultrahigh efficiency in lead-free relaxors via high-entropy design. Nat Commun 13:3089\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYang B et al (2022) High-entropy enhanced capacitive energy storage. Nat Mater 21:1074\u0026ndash;1080\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eXue G et al (2023) Core-shell structure and domain engineering in Bi\u003csub\u003e0.5\u003c/sub\u003eNa\u003csub\u003e0.5\u003c/sub\u003eTiO\u003csub\u003e3\u003c/sub\u003e-based ceramics with enhanced dielectric and energy storage performance. J Materiomics 9:855\u0026ndash;866\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYang S et al (2025) Lead-free BaTiO\u003csub\u003e3\u003c/sub\u003e-based composite ceramics with ultra-high energy storage performance via synergistic modulation of polarization and breakdown strength. J power sources 632:236399\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDong X et al (2022) (1-\u003cem\u003ex\u003c/em\u003e)[0.90NN-0.10Bi(Mg\u003csub\u003e2/3\u003c/sub\u003eNb\u003csub\u003e1/3\u003c/sub\u003e)O\u003csub\u003e3\u003c/sub\u003e]-\u003cem\u003ex\u003c/em\u003e(Bi\u003csub\u003e0.5\u003c/sub\u003eNa\u003csub\u003e0.5\u003c/sub\u003e)\u003csub\u003e0.7\u003c/sub\u003eSr\u003csub\u003e0.3\u003c/sub\u003eTiO\u003csub\u003e3\u003c/sub\u003e ceramics with core-shell structures: a pathway for simultaneously achieving high polarization and breakdown strength. Nano Energy 101:107577\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi F et al (2018) Local structural heterogeneity and electromechanical responses of ferroelectrics: learning from relaxor ferroelectrics. Adv Funct Mater 28:1801504\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDai Z et al (2021) Improved energy storage density and efficiency of (1\u0026thinsp;\u0026ndash; \u003cem\u003ex\u003c/em\u003e)Ba\u003csub\u003e0.85\u003c/sub\u003eCa\u003csub\u003e0.15\u003c/sub\u003eZr\u003csub\u003e0.1\u003c/sub\u003eTi\u003csub\u003e0.9\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e-xBiMg\u003csub\u003e2/3\u003c/sub\u003eNb\u003csub\u003e1/3\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e lead-free ceramics. Chem Eng J 410:128341\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChen L et al (2022) Local diverse polarization optimized comprehensive energy-storage performance in lead‐free superparaelectrics. Adv Mater 34:2205787\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhu Y et al (2022) High conduction band inorganic layers for distinct enhancement of electrical energy storage in polymer nanocomposites. Nano-Micro Lett 14:151\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYang B et al (2023) Engineering relaxors by entropy for high energy storage performance. Nat Energy 8:956\u0026ndash;964\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBi W et al (2023) Comprehensive energy-storage performance enhancement in relaxor anti-ferroelectrics via strengthening local polarization. Chem Eng J 478:147383\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePu Y et al (2019) Enhancing the energy storage properties of Ca\u003csub\u003e0.5\u003c/sub\u003eSr\u003csub\u003e0.5\u003c/sub\u003eTiO\u003csub\u003e3\u003c/sub\u003e-based lead-free linear dielectric ceramics with excellent stability through regulating grain boundary defects. J Mater Chem C 7:14384\u0026ndash;14393\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang W et al (2019) Enhanced energy storage properties of lead-free (Ca\u003csub\u003e0.5\u003c/sub\u003eSr\u003csub\u003e0.5\u003c/sub\u003e)\u003csub\u003e1-1.5\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eLa\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eTiO\u003csub\u003e3\u003c/sub\u003e linear dielectric ceramics within a wide temperature range. Ceram Int 45:14684\u0026ndash;14690\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang W et al (2022) Enhancement of energy storage performance in lead-free barium titanate-based relaxor ferroelectrics through a synergistic two-step strategy design. Chem Eng J 434:134678\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang W et al (2023) Enhanced energy storage properties in lead-free (Na\u003csub\u003e0.5\u003c/sub\u003eBi\u003csub\u003e0.5\u003c/sub\u003e)\u003csub\u003e0.7\u003c/sub\u003eSr\u003csub\u003e0.3\u003c/sub\u003eTiO\u003csub\u003e3\u003c/sub\u003e-based relaxor ferroelectric ceramics through a cooperative optimization strategy. ACS Appl Mater Interfaces 15:6990\u0026ndash;7001\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eShah SZA et al (2023) A DFT computational design and exploration of direct band gap silver-thallium double perovskites. Mater Sci Eng B 298:116846\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRana MZ et al (2023) Structurlectronic, optical and thermodynamic properties of AlAuO\u003csub\u003e2\u003c/sub\u003e and AlAu\u003csub\u003e094\u003c/sub\u003eFe\u003csub\u003e006\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e compounds scrutinized by density functional theory (DFT). \u003cem\u003eHeliyon\u003c/em\u003e 9, e21405\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGeng W et al (2013) Influence of interface structure on the properties of ZnO/graphene composites: a theoretical study by density functional theory calculations. J Phys Chem C 117:10536\u0026ndash;10544\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhou Z et al (2025) Ultrahigh capacitive energy storage of BiFeO\u003csub\u003e3\u003c/sub\u003e-based ceramics through multi-oriented nanodomain construction. Nat Commun 16:2075\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYan F et al (2022) Composition and structure optimized BiFeO\u003csub\u003e3\u003c/sub\u003e-SrTiO\u003csub\u003e3\u003c/sub\u003e lead‐free ceramics with ultrahigh energy storage performance. Small 18:2106515\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang W et al (2023) Enhancing energy storage performance in Na\u003csub\u003e0.5\u003c/sub\u003eBi\u003csub\u003e0.5\u003c/sub\u003eTiO\u003csub\u003e3\u003c/sub\u003e-based lead-free relaxor ferroelectric ceramics along a stepwise optimization route. J Mater Chem A 11:2641\u0026ndash;2651\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eShi W et al (2024) Moderate Fields, Maximum potential: achieving high records with temperature-stable energy storage in lead-free BNT-based ceramics. Nano-micro Lett 16:91\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"High-entropy ceramics, Core-shell structure, Band flattening, Polar nanoregions, Energy storage","lastPublishedDoi":"10.21203/rs.3.rs-7666264/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7666264/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDielectric capacitors, characterized by their high power density and ultrafast charge/discharge capabilities, are pivotal components in modern pulsed power and renewable energy systems. However, the widespread adoption of ferroelectric ceramics is inherently hampered by the antagonistic relationship between polarization (\u003cem\u003eP\u003c/em\u003e) and breakdown strength (\u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e), further compounded by significant polarization hysteresis and losses, which collectively obstruct the simultaneous realization of high recoverable energy density (\u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e) and efficiency (\u003cem\u003eη\u003c/em\u003e). Herein, we transcend this fundamental limitation via a novel high-entropy engineering strategy in (Bi, Na)TiO\u003csub\u003e3\u003c/sub\u003e-based ceramics. The designed materials achieve an exceptional \u003cem\u003eW\u003c/em\u003e\u003csub\u003erec\u003c/sub\u003e of 11.1 J/cm\u003csup\u003e3\u003c/sup\u003e and a remarkably high \u003cem\u003eη\u003c/em\u003e of ~\u0026thinsp;89.1%. This breakthrough is attributed to a synergistic interplay of mechanisms orchestrated by the high-entropy design: (i) a reduction in electronic band curvature that increases the charge carrier effective mass, thereby suppressing mobility and electrical conductivity; (ii) the emergence of self-assembled core-shell microstructures that effectively impede electrical treeing propagation through interfacial stress buffering and field homogenization; and (iii) the stabilization of nanoscale rhombohedral-orthorhombic-tetragonal-cubic (R-O-T-C) multiphase coexistence, which enhances dipole reorientability and disrupts long-range ferroelectric order. The confluence of these effects culminates in a significantly enhanced \u003cem\u003eE\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e while maximizing the polarization disparity (Δ\u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eP\u003c/em\u003e\u003csub\u003emax ​\u003c/sub\u003e- \u003cem\u003eP\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e). This study establishes high-entropy engineering as a transformative paradigm for designing advanced lead-free dielectric capacitors with superior energy storage performance.\u003c/p\u003e","manuscriptTitle":"High-entropy driven electronic and microstructural synergy for superior capacitive energy storage in lead-free ceramics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-24 08:18:03","doi":"10.21203/rs.3.rs-7666264/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3ce69a7f-53e8-4663-8674-f1525ee8e64d","owner":[],"postedDate":"September 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":55161900,"name":"Physical sciences/Materials science/Structural materials/Ceramics"},{"id":55161901,"name":"Physical sciences/Energy science and technology/Energy storage"}],"tags":[],"updatedAt":"2026-03-30T10:01:13+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-24 08:18:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7666264","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7666264","identity":"rs-7666264","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}