Superior energy storage performance via engineering crossover region with competing orders in high-entropy multilayer capacitors

Domain: physics
Published: 2026-02-11
Editorial outcome: minor_revision

Abstract
As promising candidates for next-generation energy storage devices in electrical and electronic systems, lead-free multilayer ceramic capacitors face increasingly high performance requirements. To counteract the usual trade-off between energy storage density and efficiency, we here propose a high-entropy design that directly harnesses diverse oxide symmetries to targetedly engineer competing orders and tune the composition into the crossover region between relaxor ferroelectric and superparaelectric states. Atomic-scale structural analysis reveals high-entropy ceramic develops pronounced local polarization fluctuation and dispersed oxygen octahedral rotations, which enhance relaxor behavior and reduce switching barrier. Consequently, superior recoverable energy density of 20.64 J cm-3 and high efficiency of 94.2% are obtained in our designed high-entropy Bi0.5Na0.5TiO3-based multilayer ceramic capacitors, along with excellent thermal/anti-fatigue stability and charge-discharge capabilities. This work provides a transferable strategy to engineer competing orders in lead-free dielectric materials and successfully achieves high-entropy multilayer ceramic capacitors with superior energy storage performance.

Introduction
With the continuous booming of high-power electronics in recent years, lead-free energy-storage dielectric has garnered increasing research attention towards green power devices. Eco-friendly dielectric ceramics with fast discharge speed and performance stability, in comparison to supercapacitors, flywheels and batteries, exhibit huge advantages in energy storage applications1–3. Driven by the demands for high power density and extended cycling lifespan in advanced electronics systems, lead-free multilayer ceramic capacitors (MLCCs) have gained much research interest4–6. In general, the total energy density (W), the recoverable energy density (Wrec) and energy efficiency (η) of a dielectric can be calculated according to the equations: W = ∫ P dE, Wrec = ∫ P dE, η = Wrec/W × 100%, where E, Pmax and Pr are the electric field, maximum polarization and remanent polarization, respectively7,8. Therefore, simultaneously achieving large Pmax, low hysteresis loss and high breakdown electric field (Eb) is highly desired to realize high energy storage performance (ESP). In the past decade, various lead-free matrix materials have been explored to suit the needs of MLCCs, including BaTiO3 (BT)4, NaNbO3 (NN)5, AgNbO3 (AN)9, BiFeO3 (BF)10, Bi0.5Na0.5TiO3 (BNT)11. Manufacturing textured ceramics and weakening polarization-strain coupling are regarded as useful approaches to enhance the performance of MLCCs6,12. For instance, textured ceramic was a proposed solution to enhance the breakdown strength of MLCCs by lowering the strains, but the low energy efficiency (η~80%) did not own practical worth. Besides, Wrec of 14.6 J cm-3 and η of 93% were achieved in MLCCs with ultraweak polarization-strain coupling. One of the main issues for energy storage performance in MLCCs is finding the best balance between energy density (Wrec over 20 J cm-3) and efficiency (η over 90%), as optimizing one parameter is typically achieved at the expense of sacrificing the other. This issue significantly hinders MLCCs development towards real applications for energy storage, restricting their potential for miniaturization and integration in next-generation device systems.

The energy storage performance of MLCCs is highly dependent on dielectric types with distinct polarization behavior. The polarization response in classical ferroelectrics is closely associated with the long-range-order polarization configuration, which typically results in large hysteresis loss and unsatisfactory ESP13–15. Hence, relaxor ferroelectrics have been developed to realize high ESP via domain engineering. In relaxors, long-range ferroelectric order is broken and replaced by an amount of scattered polar nanoregions (PNRs), which suppress long-range dipole ordering under high electric field, resulting in field-insensitive dielectric constants and delayed polarization saturation16–18. Meanwhile, PNRs lower the domain-switching barrier and minimize hysteresis loss from a thermodynamic perspective19,20. Therefore, employing sophisticated strategies to transform ferroelectric domains into highly dynamic PNRs is widely regarded as key to simultaneously achieving high Wrec and η.

High-entropy strategy is recently emerging as a delicate approach for realizing relaxor ferroelectric that affords excellent compositional flexibility for improving energy storage performance owing to its unique effects21–24. Configurational entropy (Sconfig) is defined as Sconfig = R[∑ yi ln yi + ∑ yj ln yj], where R, N(M) and yi(j) are the ideal gas constant, atomic species and contents at the equivalent positions, respectively25. In most studies, high-entropy design is achieved by the incorporation of diverse cations into equivalent sites, facilitating the formation of a single perovskite structure within a stabilized lattice framework as Sconfig increases26–28. In general, mixing size- and charge-mismatched cations tends to generate heterogeneous nanoscale phases whose formation is difficult to control precisely, so that identifying useful compositions often relies on extensive trial-and-error. Moreover, this approach also tends to promote the excessive formation of weakly polar phases. As a result, superparaelectric or paraelectric states appear at room temperature, accompanied by a dramatic decrease in dielectric constant (εr)29,30. However, low εr usually corresponds to small polarization saturation and thus relatively low ESP under practical operating fields. It is therefore highly desirable to develop novel high-entropy design strategies that can induce heterogeneous nanoscale phases while maintaining a high εr.

We proposed a high-entropy design strategy that engineers competing ferroic orders to achieve high energy storage performance in BNT-based MLCCs. Guided by phase-field simulation, we proportionally introduced various oxides with different symmetry, including BaTiO3 (tetragonal phase, T)31, CaTiO3 (cubic phase, C), SrTiO3 (C), AgNbO3 (orthorhombic phase, O)32 and KNbO3 (O)33, into a high spontaneous-polarization BNT (rhombohedral phase, R) matrix for tuning Sconfig (Fig. S1) of (Bi0.5Na0.5)(1-x)(Sr0.2Ca0.2Ba0.2K0.2Ag0.2)xTiO3. Introducing distinct oxide components into the same lattice targetedly gives rise to locally competing polar states. Consequently, it could lead to pronounced structural distortion and heterogeneity (Fig. 1a, b), thereby possibly enabling the formation of a crossover region between relaxor ferroelectric and superparaelectric states. This strategy is expected to concurrently enhance relaxor behavior and maintain large Pmax in lead-free high-entropy MLCCs and therefore serves as an effective approach to simultaneously realize large Wrec and high η.

Results
Phase-field simulation of competing orders with high-entropy design
Herein, we employed phase-field simulation based on oxide-symmetry considerations to rationalize our compositional design and visualize the competing process of different polar orders17,29,34. To directly visualize the designed competing ferroic orders, we simulated the evolution of domains in both two- and three-dimensional space as a function of Sconfig. Distinct phase states and domain structures emerge upon the incorporation of various oxides with different phases into the matrix as displayed in Fig. 1c and Fig. S2. The distribution of simulated polarization vectors becomes gradually random with the increase of Sconfig, generating diverse polar regions. Based on the result of the competition among ferroic orders of R/T/O/C phases represented by different vectors and colorful regions, the long-range order of the host phase is totally broken and transforms to nanoregions. Therefore, the high-entropy model manifests a heightened level of disorder. As the insets of Fig. 1d, e show, the evolution of the polar structure under an electric field reveals that the high-entropy model is much easier to revert to their initial state and maintains fast domain-switching speed with small hysteresis. In addition, corresponding simulated P-E loops are elucidated with increasing entropy (Fig. S3), revealing a remarkable transition from classic ferroelectric to relaxor ferroelectric and eventually to linear dielectric response. It also demonstrates that minimal Pr and high breakdown strength can be obtained as entropy increases (Fig. 1f). Besides, based on the simulated P-E loops, the Wrec and η are calculated in Fig. 1g as dependence on Sconfig. It shows the η gradually raises with increasing entropy while the highest Wrec is achieved at Sconfig of 2.17R, beyond which Wrec begins to decline as the polarization response becomes weak and linear (Fig. S3). Meanwhile, the 2.17R model exhibits negligible variation in simulated P-E loops across a practical operating temperature range from −50 to 150 oC, demonstrating excellent thermal stability for application (Fig. S4). Therefore, these results highlight that optimizing Sconfig within an appropriate window is critical for forming competing orders and achieving superior energy storage performance.

Under the guidance of phase-field simulation, we prepared a series of (Bi0.5Na0.5)(1-x)(Sr0.2Ca0.2Ba0.2K0.2Ag0.2)xTiO3 (BNT-CE, x=0.02/0.85R, 0.1/1.27R, 0.2/1.65R, 0.3/1.94R, 0.4/2.17R, 0.5/2.34R). BNT-CE ceramics exhibit a pure perovskite structure with diffraction peaks regularly shifting towards low angle as Sconfig increases, indicative of lattice expansion (Fig. S5)35,36. However, for samples with entropy higher than 2.17R, Sr/Ca-rich secondary phase emerges, indicating that the solid solution limitation is reached37. Meanwhile, Rietveld refinements (Fig. S6) indicate that raising Sconfig reduces the R polar fraction, weakening the overall polarity of the BNT-CE ceramics. As revealed by Raman spectra (Fig. S7), the peak ν2 representing the A-site vibration mode exhibits a redshift and reduced intensity with the increase of entropy, indicating enhanced random fields arising from A-site chemical complexity. The B-O (200-400 cm−1) modes gradually broaden while BO6-related modes (450-800 cm−1) become narrower and more intense with the increase of Sconfig, which means short-range chemical disorder and dispersed octahedra distribution38–40. In order to evaluate the overall ESP, unipolar P-E loops of BNT-CE ceramics were measured at their characteristic Eb (Fig. 2a). Consistent with the simulation results, the transition from classical ferroelectric to relaxor ferroelectric is observed with increasing Sconfig, characterized by delayed polarization saturation. Pr is abruptly decreased from 44.7 to 1.1 μC cm−2 while Pmax exhibits only a slight reduction from 60.9 to 60.5 μC cm-2. Such negligible Pr and large Pmax in high-entropy ceramic contribute to the improved ESP. Consequently, the 2.17R ceramic realizes high Wrec of 10.51 J cm−3 and high η of 88.2%, which are over 7- and 4-fold higher than those of the low-entropy 0.85R ceramic (Fig. 2b), respectively. In Fig. S8, the statistical Eb of BNT-CE ceramics were calculated by Weibull distribution fitting based on ten samples, with a good reliability supported by all the slopes β higher than 1041. The result shows that the Eb increases steadily from 243 kV cm-1 to 535 kV cm-1 with the increase of entropy. The average grain size of the BNT-CE ceramics decreases markedly from 1.42 μm to 0.63 μm with increasing Sconfig while the relative density of all samples increases only slightly from 96.8% to 97.4% (Fig. S9), owing to enhanced lattice strain energy and reduced driving force for grain coarsening42. Refined and dense microstructure helps to depress leakage current (Fig. S10), which induces enhanced barriers in carrier transport and diminishes the conduction loss at high electric field, thus substantially improving Eb21. To clarify the evolution of Eb in BNT-CE ceramics, we carried out finite-element simulations based on the SEM images (Fig. S9) to visualize the electric-field distribution and the propagation of electrical trees at 400 kV cm−1, as shown in Fig. 2c43. The higher grain-boundary density in 2.17R ceramic provides more blocking and dissipation sites, which slows the propagation of electrical trees and therefore contributes to the decrease of leakage current and the higher breakdown strength.

The temperature-dependent dielectric properties of BNT-CE ceramics were then measured to evaluate their relaxor behavior (Fig. 2e and Fig. S11). A shoulder-like flat peak emerges as Sconfig reaches 1.65R and subsequently disappears for Sconfig higher than 1.65R, accompanied by a shift of the Curie temperature (Tm) towards lower temperature, which facilitates the coexistence of multiple phases and promotes domain switching44,45. Notably, by tuning Sconfig, the 2.17R ceramic is placed in the crossover region between relaxor ferroelectric and superparaelectric states with a high dielectric constant (~1800) at room temperature, rather than falling into a superparaelectric state with low εr as in many reported high-entropy systems27,29,46. In this crossover region, highly dynamic polar nanoregions and strong competition among ferroic orders allow a large polarization with a small remanent polarization and a high breakdown field7,47. Meanwhile, 2.17R ceramic exhibits excellent temperature coefficient of εr (within ±15%) in −30 to 125 oC (Fig. S12), which meets the Y7R capacitor standard for application. Illustrated by the simulated domain evolution results of 2.17R model during a wide temperature span of −100 to 300 oC (Fig. 2f), the fraction of C phase (gray region) gradually increases with rising temperature, while the polarization configuration under maximum electric field keeps unvaried across all temperatures. To further elucidate the variation of relaxor behavior, the diffuseness coefficient γ is calculated by the modified Curie-Weiss equation: 1/εr − 1/εm = (T − Tm)γ/C48. The γ increases from 1.03 to 1.91 as Sconfig increases (Fig. S13), supporting the enhanced relaxor behavior in 2.17R high-entropy ceramic17. The dynamic domain responses of the 0.85R and 2.17R ceramics were also measured by piezo-response force microscopy (PFM) to monitor the evolution of ferroelectric domains (Fig. S14). With increasing entropy, the switched domains induced by a 20V electric field fade more rapidly and are more readily reverted to their initial configuration upon field removal, indicating shorter relaxation time and low hysteresis loss in 2.17R high-entropy ceramic46,49. In addition, we calculated the distribution of the unit cell c/a ratio to clarify the structural origin of this crossover and the enhanced breakdown strength through HAADF-STEM analysis (Fig. 2g, h). The average c/a ratio significantly decreases from 1.027 for the 0.85R ceramic to 1.009 for the 2.17R ceramic, as shown in Fig. 2i, which indicates weak long-range ferroelectric anisotropy and polarization-strain coupling in the 2.17R ceramic50. The reduced average c/a helps to diminish local field amplification and thermal loss under high electric field, which is beneficial for improving breakdown strength39. Moreover, the 2.17R ceramic exhibits a dispersed distribution of c/a ratio, in contrast to the more clustered distribution observed in the 0.85R ceramic, with the standard deviation increasing from 0.04 (0.85R) to 0.06 (2.17R) as entropy rises, which indicates stronger spatial heterogeneity of lattice distortion.

Local structural evolution of entropy-driven ceramics
As revealed in phase-field simulations, competing orders generated by chaotic chemical environments and distorted local structures serve as the structural foundation for achieving high energy storage performance. Thus, the evolutions of polarization configuration in both high-entropy and low-entropy ceramics were systematically investigated to elucidate the underlying polarization response mechanism through high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). The atomic-resolution images of the 0.85R (Fig. 3a) and 2.17R (Fig. 3b) ceramics along [001] are marked by colorful vectors, which represent the polarization angle of the B-site cations relative to the lattice centers of the four nearest neighboring A-site cations8. The 0.85R ceramic exhibits pronounced polarization displacement (Fig. 3c) and large domain sizes, with the R phase as the dominant phase. With increasing Sconfig, the notable reduction of R/O phase, combined with the existing tiny amount of T phase and increased fraction of C phase induce the competition of diverse ferroic orders within local regions. Compared to the low-entropy ceramic, the remarkable distinction in polarization orientation of high-entropy ceramic reflects substantial structural distortion and diverse heterogeneous polarization configuration, wherein strongly polar phases are intricately embedded within a weakly polar cubic matrix. Figure 3c stresses a contrast in the displacement distribution that the average displacement of ~9.4 pm in the 2.17R ceramic is much smaller than that of ~18.4 pm in the 0.85R ceramic. This trend is consistent with the grain-size evolution (Fig. S9), where smaller grains are expected to confine the polarization correlation length and suppresses domain coalescence51. This reduced polarization displacement promotes complex interactions among randomly distributed ions and competing ferroic orders, giving rise to highly dynamic polar nanoregions with weak domain coupling22,49,52. Therefore, tuning configurational entropy to induce local compositional inhomogeneity provides an effective way to regulate the formation of competing orders and to modulate the associated structural distortions. To comprehensively clarify structural features in local polar fluctuations of BNT-CE ceramic, we discerned the local E-field distribution by differential phase contrast (DPC) analysis12. The DPC-STEM (Fig. 3d) image of the 2.17R ceramic shows rapidly varying hues in the local electric-field distribution, with color indicating the field direction and brightness representing its magnitude. The pronounced fluctuations in both color and brightness highlight the polar heterogeneity of the local fields. Three representative types of E-field distribution are observed, as displayed in Fig. 3e, which can be associated with polar regions (region 1), disordered polar nanoregions (region 2) and weakly polar matrix (region 3), respectively. These distinct E-field distributions reflect the presence of different local polar states within the crossover region. It directly visualizes the coexisting polar states that arise from competing ferroic orders in the high-entropy ceramic, which is favorable for achieving high saturation polarization and low polarization hysteresis.

We also utilized integrated differential phase contrast (iDPC) to particularly capture the otherwise imperceptible light O atoms, in order to directly analyze the rotation behavior of BO653. The O atoms can be discernible in the iDPC images because this technique offers high sensitivity to light elements, and the relatively small contrast difference with neighboring cations enhances their visibility54. Figure S15 gives the high-resolution iDPC image of 2.17R high-entropy ceramic along [001] direction and illustrates the atom occupancy of the A/B site and O position. The squares with various colors in Fig. 3f denote different BO6 rotation behaviors, revealing irregular alternations between clockwise and anticlockwise orientation. As seen in Fig. 3g, O atoms within the same horizontal layer display varying displacement amplitudes, accompanying by noticeable differences in adjacent O-O distance. Then, the O-O distances (Fig. S16) extracted from the iDPC image are statistically analyzed, which demonstrates that most O atoms deviate from their average positions. This reflects a random and diffuse distribution of oxygen displacements. Quantitatively, octahedral rotation angles range from −4.3 to +4.3 o, indicating relatively small rotation with a non-collective distribution. The statistical histogram in Fig. 3h presents a normal distribution of the octahedra, further confirming the dispersed and random nature of octahedral rotations in high-entropy ceramic. This heterogeneity of octahedral rotation caused by competing orders locally disrupts long-range symmetry and shifts the positive/negative charge center, generating spatially dispersed local dipoles and reduced switching barriers55. Such a configuration delays polarization saturation and facilitates reversible domain switching, thereby sustaining a large Pmax. Furthermore, local distortions of the oxygen octahedra will consume a portion of the electrical energy required for establishing relatively large domains under an applied field23, thus impeding domain growth and delaying saturation polarization. The structural variations by increasing Sconfig promote the formation of a weakly polar region, thereby lowering the energy barrier for reorienting the polarization configuration. Thus, the designed competing orders induced by high-entropy strategy modulate oxygen octahedral rotations, which delays polarization saturation and enhances breakdown strength, thereby maintaining a large Pmax while reducing Pr and enhancing ESP.

Energy Storage Performance of high-entropy MLCCs
To validate the efficacy of the entropy-induced strategy for actual pulse power application, we further fabricated 1210-type MLCCs comprising four active ceramic layers, based on the optimal composition of Sconfig = 2.17R. Figure 4a, b and Fig. S17 present the SEM image and energy-dispersive X-ray spectroscopy (EDS) element mapping of the high-entropy multilayer capacitor, which shows a uniform thickness of ~5.5 μm in the dielectric layer and 1.5 μm in the electrode layer, respectively. Both dielectric layers and electrode layers exhibit a dense microstructure, and the elements in each layer are uniformly distributed. The selected area electron diffraction (SAED) was conducted in the interface region between the two layers (Fig. 4(c-c1)), which exhibits a well-defined and sharp boundary. No obvious element diffusion can be found between the dielectric layer and the electrode layer according to the result of linear scanning (Fig. S18), and both regions exhibit sharp diffraction spots (Fig. 4(d-d2)). The inset of Fig. 4e and Fig. S19 show the unipolar P-E loops of high-entropy MLCCs as a function of E field. High Wrec ~20.64 J cm−3 and η ~94.2% are achieved in high-entropy MLCCs at a high Eb of 1472 kV cm−1. As Fig. 4f reveals, our work represents superior energy storage performance compared to other MLCCs in recent reports. To quantitatively evaluate the trade-off between Wrec and η, we used a figure of merit UF = Wrec/(1-η) to reflect the overall energy storage performance2, as shown in Fig. S20. UF of our work reaches a high value of 355.7 owing to the combined high Wrec and η. Hence, these results demonstrate the effectiveness of regulating competing orders via a high-entropy strategy in realizing superior energy-storage-performance MLCCs.

From a practical application viewpoint, we also evaluated the thermal stability and cycle reliability of the high-entropy MLCCs. In Fig. 4g and Fig. S21, we tested the temperature stability of energy storage performance at the electric field of 900 kV cm−1 in the range from 20 to 140 oC, which shows a high Wrec of ~12.21 J cm–3 and η of over 93.3%, respectively, and displays a slight degradation below 5% for both Wrec and η. Besides, the anti-fatigue reliability tests were conducted to further assess the practical application. As shown in Fig. 4h, the MLCCs survive after 107 cycles with only below 2% attenuation, keeping a Wrec of ~12.15 J cm−3 and η of over 96.2%. In addition, as a key parameter, the charge-discharge performance of high-entropy MLCCs was measured at different electric field. Figure 4i and Fig. S22 illustrate the overdamped discharge curves of the high-entropy MLCCs within the field range of 200 kV cm−1 to 900 kV cm−1, where MLCCs achieve a large discharge energy density (Wdis) of 10.92 J cm−3 with a fast t0.9dis ~0.81 μs (the time to release 90% of Wdis). Meanwhile, high-entropy MLCCs exhibit high current density (CD) of 424 A cm−2 and large power density (PD) of 191 MW cm−3 (Fig. S23). The charge-discharge performance exceeds that of most reported MLCCs, as shown in Fig. S24. The excellent temperature, fatigue stability and charge-discharge property fully show wide application scenarios and huge application potential for the next-generation MLCC devices.

Methods
Phase-field simulation and finite-element simulation
The total free energy of the high-entropy BNT-based system can be expressed as the sum of the following contributions56,57: F = ∫flandau dV + ∫fgrad dV + ∫felas dV + ∫felec dV. The Landau free energy f can be presented as function of P as: f = α1(P12 + P22 + P32) + α11(P14 + P24 + P34) + α12(P12P22 + P22P32 + P12P32) + α111(P16 + P26 + P36) + α112(P14(P22 + P32) + P24(P32 + P12) + P41(P32 + P22) + P21P42 + P22P43 + P21P43) + α113(P12P22P32), where α is the Landau coefficients. fgrad is the gradient energy, representing the domain boundary energy, which can be defined as: fgrad = 1/2 Gij (∂iPj)2, where G is the gradient energy coefficient. The long-range elastic interactions energy felas, including strain-gradient and external-stress fields, is expressed as: felas = 1/2 Cijkl (εij − ε0ij)(εkl − ε0kl) + Ce0ijkl (εij − ε0ij)(εkl − ε0kl), where C is the elastic stiffness tensor, εij, ε0ij and e0ij are the total strain. felec = −1/2 E depol P − 1/2 Eext P, where E represents the inhomogeneous electric field caused by dipole-dipole interactions, Edepol is the depolarization field. P is the average polarization. The temporal evolution of the polarization field can be calculated by solving the time-dependent Ginzburg-Landau (TDGL) equation: dPi(x,t)/dt = −M δF/δPi(X,t), where M is the kinetic coefficient related to the domain mobility, t is time, and i denotes polarization variants. Phase-field simulations were performed in a three-dimensional grid of size 64×64×64 and in the length scale l0 (the numerical grid size) of ~2.0 nm with periodic boundary conditions. The probability of the electrical tree channels is defined using the following equation: p(i0,j0→i,j) = P(@i,j − @i0,j0)m + (@i0,j0 − @i00,j00)m − loss, where @i,j, @i0,j0 and @i00,j00 represent the electrical potential of the discharged point, probable point, and linked point, respectively. @ is the threshold electrical potential of the ceramic for the grain and grain boundary. Loss and m denote the evolution loss of the tip electrical tree channels and the fractal dimension, respectively.

Ceramic preparation
A conventional solid sintering was used to prepare (Bi0.5Na0.5)(1-x)(Sr0.2Ca0.2Ba0.2K0.2Ag0.2)xTiO3 (x=0.02, 0.1, 0.2, 0.3, 0.4, 0.5). The raw powders of Bi2O3 (99.99%), Na2CO3 (99.8%), BaCO3 (99.95%), SrCO3 (99.99%), CaCO3 (99.99%), Ag2O (99.7%), K2CO3 (99%), TiO2 (99.9%), Nb2O5 (99.99%) were mixed and milled for 4 hours by using ZrO2 balls in ethanol. Subsequently, the dried powder was then calcined in an alumina crucible at 850 oC for 2 h. Powders were milled again using smaller size ZrO2 balls, and 0.3 wt.% MnCO3 was added as the sintering aid. Then, the calcined powders were mixed with 6 wt.% polyvinyl alcohol. The green pellet was first burnout binder at 600 oC for 2 h and finally sintered at 1120-1180 oC for 2 h in an oxygen atmosphere.

MLCC preparation
BNT-based high-entropy powder (x=0.4/2.17R) was utilized in the fabrication of 1210-type MLCCs via tape casting with an MTI MSK-AFA-II system. A 70Ag/30Pd electrode was printed via a DEK 247 screen printer. The stacked layers were then subjected to hot-pressing at 80 oC for 20 min. The resulted MLCCs were sintered at 1080 oC for 2 h in an oxygen atmosphere.

Structure characterizations
Powder X-ray diffraction patterns were collected using a powder X-ray diffractometer (XRD, Rigaku, D/max-2550V) with Cu Kα radiation (λ=1.5406 Å). Raman spectra were obtained with a Raman spectrometer (Renishaw, inVia). Field-emission scanning electron microscopy (FE-SEM, Hitachi, S-4800, Tokyo, Japan) was used to examine the microstructures and density of the ceramics. Apparent density of all ceramic samples was measured by the vacuum-saturated Archimedes method. The theoretical density was determined from the unit-cell parameters obtained by Rietveld refinement of the diffraction peaks. The relative density is the ratio of the apparent density and the theoretical density. The STEM and DPC/iDPC tests were carried out on a 300 kV Thermofisher Spectra 300 electron microscope equipped with double aberration correctors. During the process of testing, the probe convergence angle was 18 mrad, and the collection angle was 50-200 mrad to obtain the HAADF images. For determining the B-site cation displacement vectors and rotation of BO6 octahedra, the noise in the obtained HAADF-STEM and DPC/iDPC images was reduced by Gaussian blur of Velox (Thermofisher) software with sigma of 1.0-1.8. The projected atom positions of A sites, B sites, and O were determined via OpenCV using the Python software, thus, the projected B-site cation displacement was deduced as a vector between each B-site cation and the center of mass of its four nearest corner A-site cations. The rotation of BO6 octahedra was deduced as an angle from the minimum inscribed square of each B-site cation and its four nearest O ions with [001] direction.

Ferroelectric and dielectric measurements
P-E loops were measured using ceramic samples with an electrode size of 1 mm diameter and a thickness of ~60 μm under an alternating current voltage with a frequency of 10 Hz by using a ferroelectric measuring system (aixACCT TF Analyzer 2000E). A broad frequency dielectric spectrometer (Novocontrol GmbH, Concept 80) was used to measure temperature- and frequency-dependent dielectric properties. Under temperature- and frequency-dependent charge-discharge tests were conducted on a commercial charge-discharge platform (CFD-001, Gogo Instruments Technology, Shanghai, China) using an RLC load circuit under a direct current voltage, operated at a 1 kHz. We calculated charge-discharge properties by employing the following formula: Wdis = ∫ I V0(t)dt, CD = Imax/S and PD = E × Imax/S, where S represents the effective electrode area and V0 is the effective volume of the tested samples.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript titled “Ultrahigh energy storage performance from designed competing orders in high-entropy multilayer capacitors” by Deng et al. explores entropy-induced ferroic behavior and reports the fabrication of high-entropy multilayer ceramic capacitors for energy storage applications. I have the following minor revision suggestions:\n1. In the structural characterization section, the authors mention that Raman spectroscopy data were collected; however, these data are not included in either the main manuscript or the supplementary materials.\n2. As the abstract begins by emphasizing “lead-free” materials, the motivation should be revised to align more clearly with this focus.\n3. The section title “Property Measurement” is somewhat vague. It would be more appropriate to use a specific title such as “Ferroelectric and Dielectric Measurements” or another suitably descriptive heading.\n4. The manuscript should include references for the indexing of XRD peaks.\n5. The term “ultrahigh” in the title is somewhat exaggerated. Consider replacing it with a more suitable alternative, such as “enhanced,” “superior,” or another term that accurately reflects the results.\n6. The parameters W_dis and W_rec are mentioned—please clarify whether these represent different quantities. If they are not distinct, revise the notation or description accordingly.\n7. What is the breakdown strength of the MLCC capacitor?\n8. The summary section should be revised.", "reviewer_2": "The researchers present a thorough study of high-entropy BNT-based multilayer ceramic capacitors (MLCCs), combining phase-field simulation, atomic-scale HAADF-STEM characterization, and device-level testing. The data are of high quality and the conclusions are well supported.\nHowever, the work applies an existing high-entropy design strategy. That is to say introducing multiple ferroic orders and local structural distortions to enhance relaxor behavior and energy-storage performance. This has been reported in recent studies at Nature Communications (Wei et al. in 2025 https://www.nature.com/articles/s41467-025-62335-3 or Chen et al. in 2022 https://www.nature.com/articles/s41467-022-30821-7). As such, the authors should highlight what sets them significantly apart from existing works. While the additional fabrication of MLCCs and fatigue testing adds useful application relevance, it may not, by itself, constitute sufficient conceptual advancement.\nIn addition, while I do not disagree that the increased breakdown field can stem from the increase in entropy, I would be more careful with statements, such as Line 205 – 207: “Therefore, tuning configurational entropy to induce local compositional inhomogeneity effectively regulates the formation of competing orders, thereby tuning the structural distortion and breakdown strength.”. The breakdown field can also depend on the microstructure; therefore, determining the porosity of the sample is necessary.\nFurthermore, the authors highlight the degradation in grain size, which does impact the crystal and domain structure, as well as the breakdown field. As such, I would encourage taking this trend into account when discussing the results.\nOverall, I find the manuscript to be technically strong and of interest to a specialist audience, which is why I would recommend transferring it to a more materials science specialized journal."}, "author_response": "Dear Editors and Reviewers,\nThanks very much for your efficient work and insightful comments on our\nmanuscript (Manuscript No. NCOMMS-25-72903). We have carefully considered to\nyour comments and made the major revisions accordingly. The details are marked red\nin the revised manuscript. Meanwhile, we also responded to the comments point-by-\npoint.\nWith regard to Reviewer 1’s comments\nGeneral Overview\nThe manuscript titled “Ultrahigh energy storage performance from designed\ncompeting orders in high-entropy multilayer capacitors” by Deng et al. explores\nentropy-induced ferroic behavior and reports the fabrication of high-entropy multilayer\nceramic capacitors for energy storage applications. I have the following minor revision\nsuggestions:\nOverall Response:\nWe would like to thank the reviewer for taking the time to assess our manuscript\nand for providing constructive suggestions that greatly improved the revised version of\nour manuscript.\nComment 1: In the structural characterization section, the authors mention that Raman\nspectroscopy data were collected; however, these data are not included in either the\nmain manuscript or the supplementary materials.\nResponse 1:\nThanks for the reviewer’s careful examination. We apologize for this oversight.\nIndeed, we had conducted Raman spectroscopy tests earlier, but we finally omitted it\nfrom the manuscript owing to the limited manuscript length and the extensive\nexperimental data already presented. In light of the reviewer’s comment, we recognized\nthat the Raman spectroscopy allows us to probe the local structure induced by\nconfigurational entropy (S ), which is consistent with the HAADF-STEM/iDPC\nconfig\nresults presented later. We have therefore reinstated the Raman results and integrated\nthe corresponding discussion in the revised manuscript (see Fig. R1, i.e. new Fig S7).\nFig. R1 presents the Raman spectroscopy of the BNT-CE ceramics with different\nS . In general, the peak ν representing A-site vibration mode exhibits a red shift and\nconfig 2\nreduced intensity with the increase of entropy, which means enhanced random fields\narising from A-site chemical complexity. The B-O (200-400 cm-1) modes gradually\nbroaden while BO -related modes (450-800 cm-1) narrows and strengthens in intensity\n6\nwith the increase of S , which means short-range chemical self-averaging of B-O\nconfig\nenvironment and dispersed octahedra distribution.1, 2 Together, these features signify\nsuppressed long-range ferroelectric order, possibly yielding a small hysteresis loss.\nWe believe that the Raman spectroscopy results further support the local\ndistortion of BNT-CE ceramics and the accuracy of our compositional design.\nFig. R1. a Raman spectroscopy of BNT-CE ceramics; b Evolution of v2 peak site with increasing entropy.\nComment 2: As the abstract begins by emphasizing “lead-free” materials, the\nmotivation should be revised to align more clearly with this focus.\nResponse 2:\nThanks for the reviewer’s comment. We have also noticed this issue. Actually,\n“lead-free” dielectrics attract much attention in recent years because of their\nenvironmental friendliness and commercial potential. Therefore, the new high-entropy\nmaterial, as a member of lead-free systems, is proposed in our work, which exhibits\nsuperior energy storage performance apart from the above merits. To clarify this point,\nwe have revised the description (marked in red) in the Abstract “This work provides a\ntransferable strategy to engineer competing orders in lead-free dielectric materials”\nand Introduction “With the continuous booming of high power electronics in recent\nyears, lead-free energy-storage dielectric has garnered increasing research attention\ntowards green power devices.” sections.\nComment 3: The section title “Property Measurement” is somewhat vague. It would be\nmore appropriate to use a specific title such as “Ferroelectric and Dielectric\nMeasurements” or another suitably descriptive heading.\nResponse 3:\nThanks for reviewer’s professional advice. We do agree and now changed the title\nas “Ferroelectric and Dielectric Measurements” in the revised manuscript.\nComment 4: The manuscript should include references for the indexing of XRD peaks.\nResponse 4:\nThanks for the reviewer’s suggestion. The indexing of the XRD main diffraction\nBragg peaks indicated corresponds to that of the usual perovskite structure based\non the BNT matrix system. We have added reference 363 and 374, to support this\nindexation in the revised manuscript. The possible secondary phase in higher-S was\nconfig\nidentified by comparison with the corresponding PDF card (Sr(Ca Nb )O , #17-\n0.33 0.67 3\n0174) and with previously reported literature.4 Accordingly, we have updated the Fig.\nS5 in reversed Supplementary Information.\nComment 5: The term “ultrahigh” in the title is somewhat exaggerated. Consider\nreplacing it with a more suitable alternative, such as “enhanced,” “superior,” or\nanother term that accurately reflects the results.\nResponse 5:\nThanks for the reviewer’s suggestion. After careful consideration, we have\nreplaced “ultrahigh” with “superior” to make the wording more rigorous.\nCorrespondingly, we have updated the relative description in the revised manuscript.\nComment 6: The parameters W_dis and W_rec are mentioned — please clarify whether\nthese represent different quantities. If they are not distinct, revise the notation or\ndescription accordingly.\nResponse 6:\nThanks for the reviewer’s important comment. The W and W represent two\nrec dis\ndistinct parameters in our manuscript. Specifically, W denotes the recoverable\nrec\nenergy storage density obtained from the quasi-static P-E loops, while W refers to the\ndis\ndischarged energy density measured from the dynamic charge-discharge tests.5 These\ntwo parameters differ because they originate from different measurement\nmechanisms and time scales.\nIn detail, an alternating current (AC) voltage with a frequency of 10 Hz is applied\nin the quasi-static P-E measurement used to measure W , corresponding to a period of\nrec\n~0.1 s. In contrast, the charge-discharge tests to measure W use direct current (DC)\ndis\nand the charge-discharge happen during a short time scale of ~10-5 s, which is much\nfaster than the AC signal for P-E loop measurements. Then, the viscous force,\ngenerating from the motion of the domain wall, plays an important role in the process\nof releasing energy for dielectric ceramic. However, the viscous force is significantly\nhigher when high frequency/DC signal is applied, enlarging the energy loss in the fast\nmotion.6 Therefore, smaller W compared with W is constantly obtained due to the\ndis rec\ninadequate energy release at a higher frequency during fast discharge.\nCurrently, most studies including this work emphasize the parameter W because\nrec\nit reflects the intrinsic, reversible energy that can be recovered from the dielectric,\nindependent of circuit or load effects. In contrast, W is influenced by external losses\ndis\nsuch as resistance and dynamic polarization lag, making it system-dependent and less\ncomparable across literature. Therefore, W serves as the standardized figure of merit\nrec\nfor evaluating the true material potential in dielectric energy-storage research.\nWe have added the detailed difference in test condition to the Ferroelectric and\nDielectric Measurements of revised manuscript.\nComment 7: What is the breakdown strength of the MLCC capacitor?\nResponse 7:\nThanks for the reviewer’s valuable comment. The breakdown strength (the electric\nfield at failure) of the high-entropy MLCC is 1472 kV cm-1, as mentioned in the section\nof “Energy Storage Performance of High-entropy MLCCs”. The unipolar P-E loops\nof high-entropy MLCCs at various electric fields are attached here for your reference\n(Fig. R2). They are also displayed in Fig. S19 of the revised Supplementary information.\nFurthermore, we emphasize that MLCCs generally exhibit much higher breakdown\nstrength than bulk ceramics because their ultrathin dielectric layers shorten the electrical\nconduction path. A shorter path reduces the probability for defects accumulation and\nlocal electric fields build up, according to the Gerson-Marshall relationship7, resulting\nin a higher breakdown strength.\nFig. R2. The unipolar P-E loops of high-entropy MLCCs as a function of E-field.\nComment 8: The summary section should be revised.\nResponse 8:\nThanks for your comment. After revising the manuscript in light of the reviewers’\ninsightful comments, the summary section on page 12 has been revised in the main text\nas follows: “In summary, we demonstrated a high-entropy design that directly harnesses\nthe symmetry of different oxides, together with phase-field simulations, to engineer\ncompeting polar orders and form the crossover region. At the local scale, the\ncompetition among diverse orders yields more dispersed and random polar\nconfiguration with the increase of S . In composition with optimized S value,\nconfig config\ndistinct E-field distributions, oxygen displacements and a dispersed distribution of BO\n6\nrotations are observed, and these features together contribute to broad switching\nbarrier and enhanced relaxor behavior. Ultimately, superior performance of W ~\nrec\n20.64 J cm-3 and η ~ 94.2% is achieved in high-entropy MLCCs, along with excellent\ntemperature and fatigue stability, and a large charge-discharge capacity of W ~ 10.92\ndis\nJ cm-3. Our work provides a predictive and transferable solution to the longstanding\nchallenge of simultaneous improvement of W and η in pulse capacitors and highlights\nrec\na broader technological potential for high-entropy multilayer devices in next-\ngeneration energy-storage applications.”\n”\n.”\nWith regard to Reviewer 2’s comments\nComment 1: The researchers present a thorough study of high-entropy BNT-based\nmultilayer ceramic capacitors (MLCCs), combining phase-field simulation, atomic-\nscale HAADF-STEM characterization, and device-level testing. The data are of high\nquality and the conclusions are well supported. However, the work applies an existing\nhigh-entropy design strategy. That is to say introducing multiple ferroic orders and local\nstructural distortions to enhance relaxor behavior and energy-storage performance.\nThis has been reported in recent studies at Nature Communications (Wei et al. in 2025\nhttps://www.nature.com/articles/s41467-025-62335-3 or Chen et al. in 2022\nhttps://www.nature.com/articles/s41467-022-30821-7). As such, the authors should\nhighlight what sets them significantly apart from existing works. While the additional\nfabrication of MLCCs and fatigue testing adds useful application relevance, it may not,\nby itself, constitute sufficient conceptual advancement.\nResponse 1:\nWe would like to thank the Reviewer 2 for recognizing the high quality and the\nsupported conclusions of our work, as well as the useful application prospect with\nregards on the fabrication and fatigue testing of our MLCC devices. However, the\nReviewer 2 also pointed out that our work appears to apply an existing high-entropy\ndesign strategy, implying a certain similarity to previous studies. We are very grateful\nfor this concern, which help us to further clarify the novelty of our approach and we\nhave highlighted these points and modified the manuscript accordingly as follows.\nDefinitely, high-entropy design has become an increasingly popular strategy in\nenergy-storage dielectrics to induce local structural distortions and enhance relaxor\nbehavior. In summary, as shown in Table R1 and Table R2, configuration entropy plays\nan important impact on dielectric property, polarization response and energy storage\nperformance. Different from the existing high-entropy studies, our work adopts a\nrational design strategy that directly harnesses the symmetry of different oxides to\nconstruct high-entropy system and targetedly construct multiple competing polar\norders, which finally places the optimal composition into the crossover region\nbetween relaxor ferroelectric and superparaelectric state. This strategy delivers\nMLCCs with a large P , a small P and superior energy-storage performance, and is\nmax r\ntherefore well suited for practical applications.\nTo better exhibit the distinction between our work and previous studies, we\nsummarize the key parameters (W , η, Curie Temperature (T ) and dielectric constant\nrec m\nat room temperature ( )) as well as the design principle and mechanism of previous\nhigh-level reports usin\n𝜀\ng𝑅 𝑇high-entropy design, to demonstrate the distinction (please see\nTable R1 and Table R2). To further clarify the novelty and significance of our work,\nwe divide the following discussion into two sections, focusing on material design\nand device-based advances. We have also responded point by point to all the other\npoints that Reviewer 2 raised and have addressed all of them in our revised version. We\nthank Reviewer 2, whose comments and criticisms have helped greatly improve the\nquality and clarity of our work.\nTable R1. Comparison of our work with recent reports of high-entropy strategy in energy storage\nperformance and dielectric property.\nComposition Abbr. W (J cm-3) η (%) T (oC) ε Journal\nrec m RT\n[(K Na ) Li Ba Bi ] Nat Commun\n0.2 0.8 0.8 0.08 0.02 0.1\n(Nb Sc Hf Zr Ta Sb 8L1 10.06 90.8 ~ -15 ~500 (2022)(Cited by\n0.68 0.02 0.08 0.1 0.08 0.\n)O reviewer)\n04 3\n(0.75-x)NaNbO -0.10NaTaO -\n3 3\nNat Commun\n0.15SrTiO - 9L2 13.3 92.4 ~ -200 ~ 1050\n3\n(2025)\nxCa(Hf Zr Sn )O\nx/3 x/3 x/3 3\n(1-\nAdv Funct Mater\nx)(Ag Bi Sr )(Nb Ta 10L3 13.5 81.7 ＜10 ~630\n0.71 0.07 0.04 0.85 0.15\n(2025)\n)O -x(0.85NaNbO -0.15BiFeO )\n3 3 3\n(Bi Na K La Sr )Ti Nb Nat Commun\n0.2 0.2 0.2 0.2 0.2 0.95\n11L4 16.4 90 ~ -53 ~860\nO (2025)\n0.05 3\nNat Commun\n(Sr Ba Pb La Na )Nb O 12L5 11 81.9 ~ -100 ~1100\n0.2 0.2 0.2 0.2 0.2 2 6\n(2024)\nBi Na Ba Nd K Sr1/7Ca 13L6 11.8 86.4 ~ -25 ~770 Energy Storage\n1/7 1/7 1/7 1/7 1/7 1\nTiO Mater (2024)\n/7 3\n(Ba Bi Ca Sm Na Sr\n0.33 0.32 0.11 0.07 0.07 0\n14L7 ~20 97.5 ~62 ~800 Science (2024)\n)(Ti Fe Zr )O\n.1 0.63 0.32 0.05 3\n(1-x)(Ba Ca )TiO - Nat Commun\n0.8 0.2 3\n15L8 10.9 93 ~ -20 ~700\nxBi(Mg Zr )O (2025)\n0.5 0.5 3\n(Ca Sr Ba Mg La Bi Adv Mater\n0.2 0.2 0.2 0.05 0.05 0.15\n16L9 10.1 90 ~10 ~900\nNa )TiO (2025)\n0.15 3\n(Bi Ba Sr Ca Na )(Fe Ti Small\n0.5 0.1 0.1 0.2 0.1 0.5\n17L10 13.3 78 ~200 ~300\nZr Nb )O (2024)\n0.3 0.1 0.1 3\nNat Commun\n0.75Na Bi NbO -\n0.85 0.05 3\n18L11 20.08 95 ~ -30 ~ 1000 (2025) (Cited by\n0.25Li La Ti Ta O\n0.2 0.6 0.75 0.2 3\nreviewer)\n(Bi Na )\n0.5 0.5 (1-\nThis\n(Sr Ca Ba K Ag ) Ti 20.64 94.2 ~ 45 ~1800 This work\nx) 0.2 0.2 0.2 0.2 0.2 x 1-\nwork\nNb O\n0.4x 0.4x 3\nTable R2. Comparison of our work with recent reports of high-entropy strategy in design and main\nmechanism.\nAbbr. Design phases Main Mechanism\nIntroducing numerous ions with R/O/T/C local multiple distortion\nL1\ndifferent feature coexistence (Cited by reviewer)\nIntroducing numerous ions with different Modulating quantum\nL2 R/T coexistence\nfeature paraelectric perovskite\nIntroducing numerous ions with different Inducing the coexistence of\nL3 M/T coexistence\nfeature AFE and PE\nModulating B-site content in A-site high-\nL4 R/O/T/C coexistence Forming smaller PNRs\nentropy ceramic\nInducing strong lattice\nL5 Tuning the number of A-site elements Not mentioned\ndistortion\nSuppressing the interfacial\nL6 Tuning the number of A-site elements R/T/C coexistence\npolarization\nConstructing polymorphic\nL7 Tuning the number of A-site elements R/T coexistence\nrelaxor phase\nAchieving highly stable local\nL8 Varying ion content Not mentioned\nstructures\nL9 Varying ion content R/T/C coexistence Decreasing domain size\nForming R-T multiphase\nL10 Varying ion content R/T coexistence\nnanoclusters\nModulating\nantiferrodistortion\nL11 Varying ion content S/T\nconfigurations (Cited by\nreviewer)\nThis Employing various symmetry phase to Forming competing orders\nR/T/O/C\nwork tune entropy in a crossover region\n1. Materials design: directly harnessing oxide symmetry to targetedly\ndesign competing orders and form the crossover region between\nrelaxor ferroelectric and superparaelectric state\nFrom the design perspective, in all previous reports including the papers cited by\nthe Reviewer 2, the high-entropy system is built up by incorporating and mixing\ndifferent kinds of ions based on their valence/size characteristics to generally obtain\nthe coexistence of diverse polar phase. Although this approach can induce the\ncoexistence of multiple orders, it often produces a large fraction of cubic (C) phases and\ndrives the material into a superparaelectric or even paraelectric state at room\ntemperature (T typically shifts below ~ -30 oC and mostly below -70 oC, as shown in\nm\nTable R1). This adversely results in a dramatic decrease in dielectric constant\n(typically below 1000) with a small polarization saturation, which is fundamental\n𝜀\nlyr\nunfavorable for achieving high energy storage performance. Moreover, ion-based trial\nstrategy is often hard to reproduce in previous high-entropy studies and usually requires\na large amount of trial-and-error work to find useful compositions.\nHowever, in our work, to simultaneously regulate the amount of weakly polar\nphases and modulate the dielectric constant at room temperature ( ), we tune\nthe S\nconfig\nby directly harnessing the multiple oxides with different s\n𝜺\ny𝑹m𝑻metry (C,\ntetragonal (T), orthorhombic (O) and rhombohedral (R) phase) rather than selecting ions\nonly by their valence and electronegativity (Table R2). Demonstrated by phase-field\nsimulation, we strategically introduce various oxides with different symmetry, including\nBaTiO (T), CaTiO (C), SrTiO (C), AgNbO (O) and KNbO (O) into BNT (R) matrix,\n3 3 3 3 3\nto induce the formation of different domains and design diverse competing orders.\nWe\ntargetedly place the optimal composition into the crossover region of relaxor\nferroelectric and superparaelectric states, where the polar state is intrinsically\nunstable and the competition among different polar orders is intensified at room\ntemperature.19 The T\nm\n(Curie temperature) of our optimal composition (2.17R ceramic)\nshifts close to room temperature (T\nm\n~ 42 oC) with high ~ 1800. In other words,\nstrong competition among polar orders persists at r\n𝜀\no𝑅o𝑇m temperature and the\nfeature of BNT is partly remained by keeping a modest fraction of R phases, while\navoiding extensive formation of weakly polar C phase. This combination enables a\nlarge P together with a low P. Therefore, the 2.17R ceramic in our work maintains\nmax r\nexcellent temperature coefficient of permittivity (within ±15%) in -30 to 125 oC (Fig.\nR3, i.e. Fig. S12), meeting the Y7R capacitor standard for further application. Our\nsymmetry-based entropy tuning provides predictive control over competing polar orders\nand dielectric response, and is readily transferable as a general design strategy for other\nhigh-performance lead-free dielectrics.\nFig. R3 Temperature coefficient of ε (1kHz) as a function of temperature for the BNT-CE ceramics.\nOn the other hand, to substantiate our design, we employ advanced characterization\nthat not only reveals the nanoscale electric-field distribution but also provides oxygen-\nresolved evidence of dispersed octahedral rotations, and we directly link these features\nto the energy-storage behavior. We first map the local polar state using HAADF-STEM\nand find a clear entropy-driven evolution from R-dominated configuration at low\nentropy to the coexistence of R, T, O, and C phases at high entropy. Meanwhile, we add\nadditional DPC (differential phase contrast) image to further support the presence of\ncompeting polar orders by observing three representative types (polar regions,\ndisordered polar nanoregions and weakly polar matrix) of electric-field\ndistribution, as shown in Fig. R4 (d-e).20 Furthermore, we offer an early application of\niDPC-STEM that directly captures diffuse oxygen displacements without long-range\ncoherence and quantifies small BO octahedral rotations, which follow an\n6\napproximately normal distribution from about -4.3 to +4.3o. This rotational\nheterogeneity locally disrupts long-range symmetry and shifts the centers of positive\nand negative charge, generating spatially dispersed local dipoles and a broad\ndistribution of local polarization vectors and switching barriers. This oxygen atom\nanalysis not only confirms the entropy-tuned competing orders but also goes beyond\nprevious high entropy studies, which mainly focus on inducing multiple local distortions\nor tuning antiferrodistortive configurations, as summarized in Table R2. These results\nhave been incorporated into the updated Fig. 3 and are summarized in Fig. R4.\nFig. R4 (new Fig. 3) The local structural evolution in BNT-CE ceramics and the BO6 octahedra distortion\nin high-entropy ceramic. Atomic-resolution HAADF-STEM polarization vector image along [001] direction\nof a the 0.85R and b 2.17R ceramics; c Polarization displacement of the 0.85R and 2.17R ceramics; d\nDPC image with diverse characteristics of E-field distribution and e enlarged images of the regions in d; f\niDPC image of A/B sites and oxygen ions along [001] direction of the 2.17R high-entropy ceramic and the\ncolorful squares represent the BO6 with different rotation angle; g The distance and relative position of\nadjacent O atoms of the enclosed region in f; h The statistical result of the rotation angle distribution of\nBO6 octahedral of the 2.17R ceramic.\nIn addition, unlike most previous reports (in Table R1 and Table R2), we\nestablish an optimal S window rather than a monotonic “the-higher-the-better”\nconfig\ntrend, supported by both simulation and experiment (as displayed in Fig. R5). Phase-\nfield simulation shows that once S goes beyond a critical value, the response\nconfig\nbecomes predominantly linear, leading to a dramatic decrease in P and P – P.\nmax max r\nExperimentally, we prepare a series of entropy-driven ceramic (0.85R, 1.27R, 1.65R,\n1.94R, and 2.17R) to validate the design, thereby capturing the continuous transition\nfrom classical ferroelectric to relaxor ferroelectric. But when entropy exceeds a critical\nvalue, XRD reveals minor secondary phase. The resulting dielectric and electrical\nheterogeneity creates interfacial field amplification, thereby lowering E and\nb\ncomplicating reproducible processing.21 The good agreement between simulations\nand experiments allows to identify the same optimal range for entropy and explains\nwhy performance peaks at these entropy values. In detail, one study reported by Chen\net al. compared pure KNN with one KNN-based\n([(K Na ) Li Ba Bi ](Nb Sc Hf Zr Ta Sb )O ) high-entropy\n0.2 0.8 0.8 0.08 0.02 0.1 0.68 0.02 0.08 0.1 0.08 0.04 3\nceramic, and the other work reported by Wei et al. compared two NN-based\n(0.7(0.94NaNbO -0.06BiFeO )-0.3Bi Li TiO and 0.75Na Bi NbO -\n3 3 0.5 0.5 3 0.85 0.05 3\n0.25Li La Ti Ta O ) high-entropy ceramics. Therefore, compared to previous\n0.2 0.6 0.75 0.2 3\nhigh-entropy studies, our strategy is fundamentally different, as we highlight the\nexistence of an optimal S window that maximizes energy storage performance.\nconfig\nFig. R5 a Simulated P-E loops with different Sconfig; b XRD spectrum of BNT-CE ceramics.\nsuperior energy-storage performance\nLowering the cost of the electrode stack and optimizing the manufacture\nprocess. As summarized in Table R3, almost all previously reported MLCCs, especially\nthose based on complex or high-entropy dielectrics, still use Pt internal electrodes. Pt is\nusually chosen because it is chemically inert and shows little interdiffusion with the\ndielectric under typical co firing conditions, so it provides a convenient platform for\nlaboratory scale demonstrations. However, the very high cost of Pt used in commercial\nMLCCs strongly limit the practical relevance of these Pt-based devices. In this work,\nwe replace Pt with 70Ag/30Pd internal electrodes, which are much less costly and\ncompatible with MLCC manufacturing processes. Cross-sectional EDS (please see\nFig. R6 or Fig. S18 in the Supplementary Information) after co-firing shows no\ndetectable Ag migration or reaction products at the dielectric-electrode interfaces,\nindicating that even for a multicomponent high-entropy dielectric the interfaces\nremain sharp and stable without sacrificing performance. These results demonstrate\nthat an industry compatible 70Ag/30Pd electrode stack can replace costly Pt while\nmaintaining stable interfaces, which is essential for the practical deployment of high-\nentropy MLCCs with high energy storage potential.\nTable R3. The electrode types and energy storage performance in different MLCC studies.\nComposition Electrode W η Cite\nrec\n0.5 0.5 3\n2 0.88Bi Na TiO -0.12Ca(Zr Ti )O Pt 13.4 90.2 23\n0.5 0.5 3 0.8 0.2 3\n3 0.94Na Bi TiO -0.06BaTiO Pt 7.8 77 24\n0.5 0.5 3 3\n4 0.2BiFeO -0.8(Ba Sr Ca Bi Na )TiO Pt 12.1 86.1 25\n3 0.2 0.2 0.2 0.2 0.2 3\n5 0.88(Na Bi Sr La )TiO -0.12Bi(Mg Nb )O Pt 15.6 90.2 26\n1/4 1/4 1/8 1/4 3 2/3 1/3 3\n0.99(0.55Bi Na TiO -NaNbO -0.25SrTiO )-\n6 0.5 0.5 3 3 3 Pt 20 86 27\n0.01MnO\n2\n0.05 0.85 0.7 0.3 3\n8 (Bi Na0 )0.65(Sr Bi ) Ti Hf O Pd 14.9 93.4 29\n0.5 .5 0.7 0.2 0.35 0.88 0.12 3\n9 0.6Bi Na TiO -0.4Sr Bi TiO 30Ag/70Pd 8.43 69.2 30\n0.5 0.5 3 0.7 0.2 3\n10 0.48BaTiO -0.4Bi(Mg Hf )O -0.12SrTiO 70Ag/30Pd 5.7 92 31\n3 0.5 0.5 3 3\n0.67NaNbO -0.18(Bi Na )TiO -\n11 3 0.5 0.5 3 70Ag/30Pd 12.65 88.5 32\n0.15Bi(Mg Hf )O\n0.5 0.5 3\nFig. R6 Linear scanning of the interface between the dielectric layer and the electrode layer by using\nEDS measurements.\nHighlighting the power density and discharge energy density for actual\napplication. Power density (P ), extracted from charge-discharge testing, is an intuitive\nD\nmetric for pulse applications, yet it is often omitted in prior reports of MLCCs. We\ntherefore benchmark two device-level parameters: P (~ 191 MW cm-3) and W (10.92\nD dis\nJ cm-3) for comparing with other MLCCs reports. As shown in Fig. R7, our work\ndisplays a superior property with simultaneously achieving large P and high W\nD dis\nfor actual application. We have added corresponding description into main text and\nincluded the comparison in the Supplementary Information (Fig. S24).\nFig. R7 The comparison of PD and Wdis among different MLCCs.\nOur capacitor part of this work is not only a demonstration of design feasibility but\nalso an important extension of our symmetry guided high-entropy design to a realistic\ndevice. The resulting high-entropy MLCCs are not only technically strong in terms of\nW , η, power density and discharge speed, but also show stable performance under\nrec\nthermal and fatigue cycling, demonstrating that our high-entropy design can be\ncompatibly integrated into multilayer capacitor and effectively bridges the gap between\nhigh entropy ceramics and practical MLCC devices.\nIn conclusion, our work is clearly distinct from the existing high-entropy studies,\nas it constructs high-entropy system by directly harnessing oxide symmetry, targetedly\nintroduces competing orders and then forms crossover region, and combines this with a\ndetailed exploration of electric-field distribution and octahedral distortion. We again\nthank Reviewer 2 for the constructive comments, and we would be grateful for any new\ncomments if some of these points still remain unclear.\nComment 2: In addition, while I do not disagree that the increased breakdown field can\nstem from the increase in entropy, I would be more careful with statements, such as Line\n205 - 207: “Therefore, tuning configurational entropy to induce local compositional\ninhomogeneity effectively regulates the formation of competing orders, thereby tuning\nthe structural distortion and breakdown strength.”. The breakdown field can also\ndepend on the microstructure; therefore, determining the porosity of the sample is\nnecessary.\nResponse 2:\nThanks for the reviewer’s professional insightful comment. We do agree that\nmultiple factors impact the increase in the breakdown field strength, such as grain size\n(Fig. S9), grain boundary, porosity (relative density, see in Fig. S9). In the revised\nmanuscript, we focus on explaining the enhanced breakdown strength in terms of\nmicrostructure and electrical properties, rather than treating S as directly\nconfig\ndetermining the breakdown strength. We now describe entropy tuning as a contributing\nfactor instead of the sole origin of the improved breakdown strength.\nTo better clarify the origin of the improved breakdown strength, and in response to\nthe reviewer’s comment, we have added relative density measurements for the BNT-\nCE ceramics. The relative density serves as an indirect metric of porosity and is\nused to assess the microstructural evolution among the compositions.33 The relative\ndensity ( ) could be calculated by , where is apparent density and\n𝜌𝑎\ni𝜌s 𝑟 t 𝑒 heoretical density. 𝜌𝑟𝑒 = 𝜌𝑡ℎ𝑒𝑜𝑟𝑦 𝜌𝑎\n𝜌𝑡ℎ𝑒𝑜𝑟𝑦\nFig. R8 a-e XRD refinement of BNT-CE ceramics.\nFirst, we determined the theoretical density ( ) for each composition from\nthe unit cell parameters extracted from Rietveld re𝜌fi𝑡nℎe𝑒𝑜m𝑟𝑦ent of the XRD patterns. Fig.\nR8 (Fig. S6 in revised Supplementary Information) shows the refinement process. All\nof the agreement factors R are below 4%, indicating reliable fits. Subsequently, we used\np\nvacuum-saturated Archimedes measurements by using five samples for each\ncomposition to obtain apparent density ( ). The relative density is the ratio of apparent\ndensity and theoretical density. Fig. R\n𝜌\n9𝑎 (f) (see Fig. S9 in revised Supplementary\nInformation) shows that the relative density of the BNT-CE ceramics remains very high\n(96.8% - 97.4%) with only a slight increase along the series. This small change indicates\nthat porosity (relative density) is not the dominant origin of the enhanced breakdown\nstrength.\nInstead, the grains become smaller and more uniformly distributed with the\nincrease of S , significantly decreasing from 1.42 μm to 0.63 μm (Fig. R9 (a)-(e)),\nconfig\nwhich indicates entropy-induced microstructural refinement. This grain refinement\npromotes more complete sintering and a more homogeneous electric field distribution.\nMeanwhile, smaller and more homogeneous grains increase the fraction of grain\nboundary area, where space charge regions and potential barriers hinder long range\ncharge transport and raise the grain boundary resistance. These effects are more likely\nresponsible for the higher breakdown strength.\nFig. R9 (a)-(e) The evolution in grain size and (f) the relative density of BNT-CE ceramics.\nTo clarify the evolution of E in BNT-CE ceramics, we have carried out finite-\nb\nelement simulations based on the SEM image to visualize the electric-field\ndistribution and the propagation of electrical trees under an applied field (Fig. R10,\nseen in Fig. 2(c-d) in revised manuscript).34 The simulation results show that the electric\nfield tends to concentrate near grain boundaries, so the breakdown path is strongly\ncontrolled by the grain-boundary network. Electrical trees first develop inside grains\nunder the external field, but their growth is interrupted or diverted once they encounter\na grain boundary. In the 2.17R ceramic, the higher grain-boundary density provides\nmore blocking and dissipation sites, which slows the propagation of electrical trees\nand therefore contributes to the higher breakdown strength.\nWe have added the discussion and simulation method into page 6 of Phase-field\nsimulation and finite-element simulation, respectively. Here is the revision on page 6,\n“The average grain size of the BNT-CE ceramics decreases markedly from 1.42 μm to\n0.63 μm with increasing S while the relative density of all samples increases only\nconfig\nslightly from 96.8% to 97.4% (Fig. S9), owing to enhanced lattice strain energy and\nreduced driving force for grain coarsening.35 This refined and dense microstructure\nhelps to depress leakage current (Fig. S10), which induces enhanced barriers in carrier\ntransport and diminishes the conduction loss at high electric field, thus substantially\nimproving E .36 To clarify the evolution of E in BNT-CE ceramics, we carried out finite-\nb b\nelement simulations based on the SEM images (Fig. S9) to visualize the electric-field\ndistribution and the propagation of electrical trees under 400 kV cm-1.34 The higher\ngrain-boundary density in 2.17R ceramic provides more blocking and dissipation sites,\nwhich slows the propagation of electrical trees and therefore contributes to the decrease\nof leakage current and the higher breakdown strength.”\nWe have also added the measurement details into the Methods section.\nFig. R10 Real-time breakdown process. The evolution of electric field and the growth of breakdown\npaths at the same electric field of 400 kV cm-1 for a 0.85R ceramic, b 2.17R ceramic.\nComment 3: Furthermore, the authors highlight the degradation in grain size, which\ndoes impact the crystal and domain structure, as well as the breakdown field. As such,\nI would encourage taking this trend into account when discussing the results.\nResponse 3:\nThanks for reviewer’s suggestion. We agree with the Reviewer 2 that the change\nin grain size has an important impact on the crystal structure and the domain\nstructure in addition to its effect on breakdown field. A detailed discussion has been\nprovided in Response 1, and we have revised our manuscript accordingly. In general,\nsmaller grains confine the polarization correlation length and strengthen domain-\nwall pinning at grain boundaries.37 As the grains become smaller, the larger number\nof grain boundaries introduces additional strain and structural disorder, which makes it\nmore difficult for a single long range ferroelectric phase to dominate and instead\npromotes the coexistence of multiple local polar structures. At the same time, the\nreduction in grain size limits the polarization correlation length and confines\nferroelectric domains to nanometer scale regions. The domains become more\nfragmented and their orientations are more random, which reduces long range domain\ncoalescence and internal stress concentration. Such a refined domain configuration is\nmore compatible with the relaxor like state, leading to a lower remanent polarization\nwith slimmer P-E loops. We have added corresponding description (on page 6 and 9)\ninto the revised manuscript in red.\nComment 4: Overall, I find the manuscript to be technically strong and of interest to a\nspecialist audience, which is why I would recommend transferring it to a more materials\nscience specialized journal.\nResponse 4:\nThanks to the reviewer for this positive assessment by recognizing the technical\nstrength of our work. We agree our work will be of interest to a specialist audience,\nwhich is in line with Nature Communications policy as it is written in their aims &\nscope, “Papers published by the journal aim to represent important advances of\nsignificance to specialists within each field”.\nBeyond this, we believe that the breadth of our study also fits the cross\ndisciplinary readership of Nature Communications, as we successfully connect\npredictive simulations with experimental realization and even device application,\ncovering phase field simulations, electric distribution recognition, oxygen-resolved\nimaging and device-scale advancement. More importantly, we directly harness the oxide\nsymmetry to tune configuration entropy to targetedly design competing orders and form\ncrossover region, which is fundamentally distinct from existing high-entropy studies\nthat mainly mix many ions with different size and valence (see Tables R1 and R2).\nEstablishing this crossover region suppresses the formation of excessive C phase\nregions and thus simultaneously realizes high recoverable energy storage density and\nhigh efficiency. Our work provides a predictive strategy for developing high-\nperformance dielectric materials and offers a practical pathway from fundamental\ndesign to real device applications.\nWe again thank the Reviewers for the thoughtful and constructive comments,\nwhich have helped us improve and clarify the novelty of this work clearly. We have\nrevised the manuscript accordingly to make these points more explicit. If there are any\nfurther questions, suggestions, or comments, we would be very grateful to receive them\nand will do our best to address and revise them promptly."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have satisfactorily addressed the concerns raised in my previous review and those of the other reviewers. The revised manuscript shows clear improvements in clarity and scientific rigor, strengthening the presentation and interpretation of the results. I support its progression to the next stage of the publication process in “Nature Communications”.", "reviewer_2": "I would like to thank the authors for going above and beyond to address all of the concerns I raised regarding the original submission. The revised manuscript now makes a strong, compelling case for the uniqueness of the results while substantially enhancing the depth and quality of the scientific discussion. As such, I am pleased to recommend that the current version be published in Nature Communications."}, "author_response": ""}]

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