Gradient Polarization Coupling via Configurational Entropy Engineering for Giant Energy Storage Performance

ABSTRACT

Multilayer ceramic capacitors (MLCCs) have become the core materials in advanced electronics and power equipment thanks to the excellent functional characteristics, including energy storage, filtering, and coupling. However, the next‐generation electronic devices place higher demands on the energy storage performance for MLCCs. This study demonstrates that the directional regulation of gradient polarization coupling (GPC) constitutes an effective approach to achieving a giant energy storage density. With the guidance of theoretical predictions, we propose a high configurational entropy (HCE) strategy in NaNbO₃‐based (NN) multilayer ceramic capacitors to constructing the alternating multipolar nanodomains. Alternately distributed weakly polar and strongly polar domains with embedding nonpolar nanoclusters possess the effective gradient coupling of polarization. Polymorphic polarization coupling realizes the dynamic orientation of local nanoclusters to drive the orientation of the overall electric dipoles, which could reduce hysteresis loss while maintaining high polarization strength. As a consequence, the NN‐20H MLCCs achieve a recoverable energy storage density of 20.4 J/cm³ and an ultrahigh breakdown strength of 1680 kV/cm, which demonstrates great advancement in reported lead‐free ceramic capacitors. This work illustrates the GPC strategy to advance novel insights for next‐generation MLCCs with high energy storage performance.

This study demonstrates that the directional regulation of gradient polarization coupling (GPC) constitutes an effective approach to achieving a giant energy storage density. With the guidance of theoretical predictions, we propose a high configurational entropy (HCE) strategy in NaNbO₃‐based (NN) multilayer ceramic capacitors to constructing the alternating multipolar nanodomains. Alternately distributed weakly polar and strongly polar domains with embedding nonpolar nanoclusters possess the effective gradient coupling of polarization.

1. Introduction

With the development of the energy and information industries, advanced electronic power devices are imposing more stringent requirements on multilayer ceramic capacitors (MLCCs) [1, 2, 3]. Dielectric ceramic capacitors, owing to their high capacitance values, volumetric efficiency, superior power density, and exceptional reliability, play an irreplaceable role in pulse power systems, new energy vehicles, and renewable energy storage applications [4, 5, 6]. Currently, commercial ferroelectric ceramics are predominantly Pb‐based and BaTiO₃‐based (BT) materials [7, 8]. However, the environmental hazards of Pb‐based materials conflict with the global demand for the next‐generation eco‐friendly materials [2]. Additionally, BT‐based materials are confronted with high dielectric loss at high frequencies, ferroelectric deactivation caused via low Curie temperatures, and the drawbacks of high‐temperature synthesis processes [2, 9]. Consequently, the development of performance for new‐generation lead‐free ferroelectric materials has become an urgent priority.

Conventional ferroelectric ceramics face limitations in meeting the requirements of next‐generation high‐energy‐density devices due to low energy storage density (<10 J/cm³) and efficiency (η, <80%) [10, 11]. The energy storage density could be calculated by the following equation (The integral area is shown in Figure S1): $W_{tot}={\sum }_0^{P_{max}}Edp$, $W_{rec}={\sum }_{P_r}^{P_{max}}Edp$, where W_tot, W_rec represent the total energy density and recoverable energy density, respectively [6, 9]. E, P_max, and P_r are the electric field, saturation polarization, and remanent polarization correspondingly. Among lead‐free ferroelectric candidates, NaNbO₃ (NN) ceramics have attracted significant attention thanks to their tunable multiphase structures and wide bandgap (∼3.4 eV) [12, 13]. The energy storage properties of NN‐based ceramics are intrinsically linked to the complex phase transition and ferroelectric domain characteristics [12].

Simultaneously enhancing all energy storage performance metrics for NN‐based ceramics currently remains difficult. Generally, NN‐based ceramics exhibit significant near‐antiferroelectric properties due to the antiparallel arrangement of dipoles [13]. The antiferroelectric‐ferroelectric phase transition features a low energy barrier, which results in ferroelectric hysteresis, severely limiting energy storage performance [3]. Simultaneously, long‐range ferroelectric domain structure orientation leads to significant hysteresis loss and susceptibility to breakdown. To break through this limitation, various methods such as nanostructured domain engineering, high‐entropy design, and local structure modification have been adopted to enhance the energy storage performance of perovskite ceramics [14]. Overcoming the disruption of the inherent characteristics of long‐range ferroelectric domains and regulating the size, configuration, and dynamic properties of polar nanoregions (PNRs), the relaxor characteristics have been significantly improved [15, 16]. Nevertheless, domain structures with varying sizes and dynamic characteristics lead to distinct coupling properties, which necessitate trade‐offs in energy storage performance among polarization strength, hysteresis loss, and breakdown field [17, 18, 19].

To overcome these limitations, we propose a gradient polarization coupling (GPC) that is constructed by alternating weakly polar and strongly polar nanodomains with embedding nonpolar nanoclusters via high configurational entropy regulation to enhance the energy storage performance of ceramics. Under an applied electric field, the non‐polar nanocluster structures achieve rapid response first, driving gradient coupling between the weakly polar and strongly polar nanodomains for the electric field, which allows for the simultaneous achievement of high polarization characteristics and low hysteresis loss. Meanwhile, when the free energy of the system modulated by HCE becomes flattened, a polymorphic relaxor phase (PRP) with O‐T‐C phases could get constructed [20]. This PRP structure simultaneously incorporates the strong polarity of the O‐phase and the high‐speed dynamic response of the T/C‐phase [21]. Following the theoretical guidance, a series of Na_(1−0.5x)Bi_0.5x(Nb_(1−x)Fe_0.2xZr_0.2xTi_0.2xHf_0.2xTa_0.2x)O₃ (x = 0, 0.10, 0.15, 0.20, 0.25, 0.30) (abbreviated as NN‐xH, x = 0, 0.10,0.15,0.20,0.25,0.30) ceramics are prepared by the tape‐casting method. Combining the effects of ionic valence and radius (Figure S2) on lattice stability, equimolar HCE components, including Fe³⁺, Zr⁴⁺, Ti⁴⁺, Hf⁴⁺, and Ta⁵⁺ with high solid solubility in NN‐based ceramics, are employed in modulating free energy and conformational entropy. In consequence, the GPC is successfully achieved via the HCE strategy in NN‐20H ceramics. Simultaneously, the local strong stress field and polarization disturbance induced by the HCE effect introduce a rearrangement of polarized configurations, forming intertwined slush domains. Encouragingly, the energy storage properties of the HCE‐modulated ceramics have improved significantly. In particular, an outstanding performance of W_rec∼12.7 J/cm³ with an excellent η∼85.4% are achieved in NN‐20H ceramics. By the tape‐casting process and screen‐printing technique, the NN‐20H‐MLCCs prototype devices are prepared. Consequently, an ultra‐high W_rec∼20.4 J/cm³ at an electric field of 1680 kV/cm get successfully achieved in MLCCs. The prepared MLCCs have significant advantages over recently reported lead‐free ceramics. The achievement of the GPC strategy modulated via HCE in presenting ultrahigh energy storage density provides a new path for further development of MLCCs energy storage performance.

2. Results and Discussion

The configurational entropy of NN‐xH ceramics could be defined as $-R\left({\left(\sum _{i=1}^N{x}_i\ln x_i\right)}_{\mathrm{cation}-\mathrm{site}}+{\left(\sum _{j=1}^M{x}_j\ln x_j\right)}_{\mathrm{anion}-\mathrm{site}}\right)$, where R, N/M, and x_i/x_j denote the ideal gas constant, atomic species, and contents at the cation/anion sites, correspondingly [22, 23, 24]. The configurational entropy of NN‐xH ceramics is shown in Figure S3. The pure NN ceramic is defined as a configurational entropy = 0. While the HCE component exhibits a configurational entropy of −2.3R. As the content of the HCE component increases, the absolute value of configurational entropy gradually rises from 0 to 1.52R. Phase field simulations are employed in predicting the evolution of the polarization configuration and phase structure of NN‐xH ceramics with the HCE strategy. Considering factors such as valence balance, bandgap width, ionic solid solubility, and the lattice mismatch [5, 25], Bi_0.5Na_0.5(Fe_0.2Ti_0.2Zr_0.2Hf_0.2Ta_0.2)O₃ is selected for the object phase to add in NN ceramics. The evolution of polarization configuration with the electric field is shown in Figure 1a. In theoretical predictions from phase‐field simulations, the pure NN ceramics show a large range of long‐range ferroelectric domains. After applying the electric field, the dipole starts to orientate in the direction of the electric field. The dipoles remain consistently oriented over a large range after withdrawal of the electric field, which leads to pure NN exhibiting large remanent polarization and hysteresis [4, 26]. As the entropy of the ceramic configuration increases, the long‐range ordered ferroelectric state is broken in the presence of a strong random field, accompanied by refined domain sizes. Fast polarization response could be achieved through the refined ferroelectric domains. The evolution of the polarization configuration under the corresponding electric field is shown in Figure 1c. In the x = 0.2 component, there are strong‐polar domains and weak‐polar domains with embedded nonpolar nanoclusters simultaneously. As the electric field increases, nonpolar nanoclusters achieve rapid coupling with the electric field. Subsequently, weakly polar nanodomains initiated rapid responses, driving the coupling of alternately arranged strongly polar nanodomains with the electric field. These theoretically validate the reliability of the GPC strategy. With the further introduction of the HCE component, the strong polarity diminishes, accompanied by the ultrafast hysteresis response and low polarization.

FIGURE 1.

Phase‐field simulation of HCE strategy; (a) Variation of polarization configuration with electric field for NN‐xH ceramics; (b) Fitted P‐E loops at the same electric field; (c) P‐E loop of NN‐20H ceramic during the electric field loading and unloading process; (d) Potential barrier energy in NN‐xH ceramics for polarization oriented.

The P‐E loops corresponding to the phase field simulation under the same electric field are calculated as shown in Figure 1b. The pure NN exhibits large polarization hysteresis and low energy storage efficiency. With the introduction of HCE components, the P‐E loops significantly illustrate reduced hysteresis and saturation polarization. The P‐E loops are linear for absolute values of configurational entropy greater than 1.52R. Figure 1d shows the distribution of barrier energy levels for polarization‐oriented after HCE regulation. There are large energy level barrier differences in the pure NN components, which lead to difficulties for the strong‐polar nano domains to achieve rapid polarization orientation in response to the electric field. As the increasing conformational entropy, the energy barrier of the polarization orientation tends to flatten, which provides thermodynamic conditions for the GPC in the NN‐xH ceramics. A continuity distribution of polymorphic nanodomains is successfully achieved in the NN‐20H ceramics, which simultaneously offers high saturation polarization, efficiency, and breakdown electric field. The free energy of the system further gets flatten as the absolute value of the configurational entropy reaches 1.52R (Figure S3). NN‐30H ceramics present nearly linear P‐E hysteresis lines.

Guided by the phase field simulation of HCE‐modulation strategy to improve the energy storage performance, a series of NN‐xH ceramics (x = 0, 10, 15, 20, 25, 30) regulated via HCE strategy are prepared. To confirm the valence state of Fe in the ceramics, we supplemented the X‐ray photoelectron spectroscopy (XPS) of the NN‐xH ceramics and performed peak fitting on Figure S4. Due to the low proportion of Fe atoms in the ceramics, only the NN‐30H ceramics could stably produce detectable Fe atom spectra. The ceramics mainly contain Fe^{3 +}, accompanied by a small amount of Fe^{2 +}. Since the proportion of Fe^{2 +} is very low, it has a minimal impact on the overall valence stability of the ceramics. To explain the microscopic origin of GPC in NN‐xH ceramics, we performed spherical aberration‐corrected electron microscopy for NN‐20H ceramics. The atomic arrangement of NN‐20H ceramics is observed via utilizing a high‐angle annular dark field transmission electron microscope [27, 28] (HAADF‐STEM), and a variety of polarization configurations are analyzed in terms of the cation vector motions, as shown in Figure 2a. The arrows indicate the atomic displacement vectors corresponding to the direction of spontaneous polarization, encompassing both direction and magnitude, quantified as the deviation of A (B) site atoms relative to the center of their four nearest B (A) site neighbors [3, 29]. Based on the direction of spontaneous polarization of the O(R)‐T‐C phase (As shown in Figure 2d), polarization vectors are fitted to verify the phase structure of NN‐20H ceramics. The existence of A/B sites for the perovskite structure is indicated in Figure 2d. Figure 2a reveals that the phase structure composition of NN‐20H ceramic consists of alternating O phase and T phase, accompanied by a small amount of distorted C phase structure. The polarization configuration mainly exhibits O and T phase structures with 45° or 135° polarization orientations, intertwined with 90° polarization orientations for the T phase. In addition, low‐polarity nanodomain clusters appear diffusely to further reduce the orientation barrier. This intertwined domain structure resembles a slush‐like state. The high entropy engineered NN‐based ceramic exhibits a polymorphic nanodomain structure where strongly polar nanodomains and weakly polar nanodomains interweave. This effectively disperses and suppresses the formation of current pathways. When a strong external electric field is applied, it becomes difficult for charges to form continuous paths that would lead to short‐circuit breakdown. Additionally, the polar nanoregions structure can simultaneously achieve high saturation polarization and high breakdown electric field. Furthermore, due to the variations in size, orientation, and stability of the different polar nanoregions, the PNRs structure exhibits a diffuse phase transition and delayed polarization saturation. Moreover, this locally polymorphic domain structure holds small domain wall energies. Preferential orientation of nonpolar regions surrounding the cubic (C) phase drives the sequential coupling of alternating weakly and strongly polar nanodomains to the electric field, which provides a dynamic basis for gradient polarization coupling (GPC).

FIGURE 2.

HAADF‐STEM of NN‐20H ceramics. (a) Polarization vector distribution of random zone in NN‐20H ceramic for [001] axis; (b) The relative ratio of interionic spacing at B site; (c) a/c ratio; (d) A/B sites and space arrangement; (e) Radar chart of displacement and angle; (f) Angle and displacement distribution of polarization vector extraction for [001] axis; (g) Displacement distribution mapping of polarization; (h) Element distribution mapping of NN‐20H ceramics in HAADF‐STEM for [110] axis.

Figure 2b shows the interionic distances of adjacent B‐site ions. Regulation via HCE exacerbates the random ionic displacement in perovskites, which disrupts the original long‐range ferroelectric domains in NN ceramics and favors the formation of slush domains. Figure 2c corresponds to the lattice constant ratio (a/c) of NN‐20H ceramics, where a distinct lattice torsion is observed. This is attributed to the significant oxygen octahedral distortion induced by the incorporation of HCE components. Figure 2e,f shows the displacements and angles of the polarization vectors extracted from HAADF‐STEM images. The distance from the central position represents the displacement of spontaneous polarization. It can be seen that the polarization directions are concentrated at 45°/135° and 90°, indicating that the strongly and weakly polar nanodomains associated with the tetragonal (T) and orthorhombic (O) phases, respectively, are dominant. Only a small amount of nonpolar nanoclusters with polarization directions of 0°/180° are present. Figure 2g presents the mapping image of polarization displacement. A nanodomain structure with alternating strongly and weakly polar regions can be directly observed therefrom, with a small number of nonpolar nanoclusters embedded in it, which provides direct evidence for the mechanism of gradient polarization coupling (GPC). Figure S5e,f shows the angular and distance distributions of polarization vectors along the [110] direction for NN‐30H ceramics. It can be observed that the polarization clusters exhibit a slush‐like interwoven distribution. These slush domains further compress the size of PNRs, enhancing the reversible polarization strength. Meanwhile, the highly dynamic characteristics ensure extremely low hysteresis loss, which significantly enhances the relaxor behavior of the ceramics.

The atomic‐scale elemental distribution of NN‐20H, characterized by HAADF‐STEM, is presented in Figure 2h. There is obvious compositional agglomeration or elemental segregation observed, which verifies the structural stability of the perovskite phase. Different from other perovskite ceramics (e.g., BT, BNT, and BF), NN‐based ceramics exhibit a rhombohedral to orthorhombic phase transition temperature below 173 K (−100°C), which prevents the formation of rhombohedral (N) phase structures at room temperature or higher. Due to the distinct polarization projection directions along the [110] axis between the rhombohedral (N) and orthorhombic (O) phases, we provide the HAADF‐STEM images of NN‐20H ceramics for [110] axis (as shown in Figure S5a,b). The polarization projection directions of the O/T/C phases are labeled in Figure S5c accordingly. As shown in Figure S5d, the projection direction of O/T spontaneous polarization can be determined. It is evident that the NN‐20H ceramic exhibits a predominant distribution of tetragonal (T) phase and distorted orthorhombic (O) phase structures along the [110] axis, accompanied by a minor presence of non‐polar or weakly polar cubic phase. In contrast, no long‐range ordered polarization distribution of the rhombohedral (N) phase is observed along the [110] axis. These findings conclusively demonstrate the absence of the N‐phase structure in NN‐20H ceramics.

To investigate the microscopic constructure of the NN‐xH ceramics, the transmission electron microscope (TEM) of NN‐10H and NN‐20H ceramics is shown in Figure 3a. Selected area electron diffraction TEM (SAED‐TEM) is used to observe the diffraction patterns of ceramic crystals. Large‐sized vertically oriented ferroelectric domain structures are present in the NN‐10H ceramics. In addition, superlattice diffraction spots at 1/2 (eoo) and 1/4 (100) crystal planes are observed in the <001>_c axial direction (e and o are Miller indices, with e and o representing odd and even numbers, respectively), which confirms that the phase structure of the NN‐10H ceramics is composed of orthorhombic phases of Pbma and P2₁ma [23]. For NN‐20H ceramics, intertwined nanoscale striped domains are observed to hold a wide presentation in the ceramics. High resolution TEM (HR‐TEM) and the diffractograms turned Fourier transformed (Figure S6) are tested at the nanodomain locations as exhibited in Figure 3b (corresponding to Figure 2a). There are 1/6(100) superlattice diffraction spots in NN‐20H ceramics, which proved the presence of the orthorhombic Pbmn space group. Some diffraction spots combine to form ray‐like patterns in Figure 3b, which is attributed to severe lattice distortion caused by the HCE effect. Meanwhile, no superlattice diffraction spots exist in the other region, which illustrates the modulation of the highly symmetric T/C phase in the NN‐20H ceramics. These provide evidence for the PPR in NN‐20H ceramics. The above results corroborate those obtained by HADDFSTEM. In addition, elemental mapping is performed of the selected area (marked as Figure S7). All elements exhibit homogeneous distribution within the tested region, confirming excellent solid solubility and homogeneity.

FIGURE 3.

Structural Characterization of NN‐xH ceramics; (a) SAED TEM and diffraction of NN‐10H ceramics; (b) SAED TEM and diffraction of NN‐20H ceramics; (c) XRD of NN‐xH ceramics; (d) Raman shift of NN‐xH ceramics; (e) In situ electric field XRD; (f) In situ temperature Raman shift spectroscopy.

The XRD of NN‐xH ceramics is shown in Figure 3c. The structure of the ceramics is characterized by the presence of a single perovskite phase, without any secondary phase. The pure NN‐based ceramics exhibit multiple diffraction peaks in 30°–60°of 2θ splitting, which is consistent with the typical structural features of the orthorhombic P phase [4]. The splitting peaks gradually disappear as the HCE components increase, indicating the disappearance of the strongly polar orthorhombic phase. Correspondingly, the weakly polar orthorhombic phase and low‐polarity T/C phase structures appear. Figure 3d demonstrates the Raman spectra of NN‐xH ceramics. The vibrational modes below 200 cm⁻¹ correspond to the vibrations of the A‐site cations in the chalcogenide lattice. Vibrational modes in the wave number range 200–400 cm⁻¹ correlate with the vibrations of the B─O bonds. At high frequencies of 400–700 cm⁻¹ corresponds to the vibrations of BO₆ octahedra [27, 28]. Figure S8 displays the deconvolution (peak‐fitting) of the Raman spectrum based on the Raman shift. Pure NN ceramics present multiple peaks of Raman shift up to 200 cm⁻¹, which is related to the reverse parallelism of the P‐phase structure. The tetragonal phase is primarily characterized by three deconvoluted peaks in the 200 to 400 cm^{− 1} range and a single peak in the 400 to 700 cm^{− 1} range. In contrast, the appearance of multiple fitted peaks in the 400 to 700 cm^{− 1} region of the Raman spectrum is mainly associated with the oxygen octahedral distortion in the orthorhombic phase. Starting from NN‐15H ceramics, the merging of all split peaks indicates the disappearance of the metastable P phase, which is consistent with the structure of XRD. In addition, the gradual broadening and smoothing of the v₅+v₁ half‐peak width represent the enhancement of the ceramic relaxor properties. The above results indicate that the HCE strategy can significantly improve the relaxor properties of ceramics and regulate lattice polarity.

The Figure S9 exhibits the surface morphology of the NN‐xH ceramic grains. All ceramics show a dense and uniform microstructure without secondary phases. In addition, the average grain size of the ceramics decreases significantly with the increase of the HCE content. The retarded diffusion and pinning effect brought about by high configurational entropy inhibits the growth and diffusion of crystal cells, leading to the decrease in the average grain size. The average grain size decreased significantly from 3.11 to 1.97 µm. The temperature dependence of the dielectric constant for NN‐xH ceramics is shown in Figure S10a–f. A clear dielectric anomaly peak exists in NN and NN‐10H ceramics, which is the phase transition peak from the strong‐polar P phase to the ralexor Pbnm phase. In contrast, the dielectric anomaly peak disappears from NN‐15H to NN‐30H ceramics, which corresponds to the disappearance of the strong‐polar phase in the system. The curve of temperature dependence of dielectric constant becomes flat with the increase of the configurational entropy of the system, indicating the enhanced relaxor behavior of the NN‐xH ceramics. Simultaneously, the disappearance of the dielectric anomaly peak indicates that ceramics are in a polymorphic relaxor phase with respect to O‐T‐C over a large temperature range, which provides further evidence for the formation of PRP.

The in situ electric field XRD pattern of NN‐20H ceramics is exhibited to validate the electric field response pattern of NN‐20H (Figure 3e). The absence of significant change in the peak position with increasing electric field indicates the absence of electric field‐induced phase transition, which is related to the relaxor behavior of the ceramics. In addition, it could be observed in the mapping plot of the peak intensities with respect to the electric field (Figure S11a,b) that an elevation of the lattice polarity is achieved at low electric fields, which indicates the fast response of the NN‐20H ceramics to the electric field. The in situ warming temperature XRD spectra are tested for the NN‐20H ceramics, as displayed in Figure S12a. No significant phase transition is observed within the tested temperature range. A distinct peak shift toward lower angles is detected in the magnified (210) and (211) peaks (as displayed in Figure S12b). Based on the characteristics of PRP, two factors may account for this phenomenon: The first is the thermal expansion of the lattice induced with temperature. In the other factor, it may represent a shift of the orthogonal phase to the T and C phases. Similarly, there is no change for peak shape in the in situ warming Raman spectra (as shown in Figure 3f) [12, 20]. The broadening of v₁+v₅ peaks with increasing temperature is also related to the aforementioned two factors.

To investigate the energy storage performance of NN‐xH ceramics, the P‐E loops are tested as shown in Figures S13 and S14. The P‐E hysteresis loops of NN‐xH ceramics exhibit a distinct morphological evolution under different electric fields. At low electric fields, the hysteresis loops show a nearly linear behavior due to the rapid electric field coupling of nonpolar nanoclusters. With the increase in electric field, the polarization intensity increases significantly, which is attributed to the enhanced polarizability caused by the sequential coupling of weakly and strongly polar nanodomains to the electric field. Such polarization coupling, dependent on the electric field magnitude, verifies the realization of the gradient polarization coupling strategy. The pure NN ceramic is difficult to obtain a high breakdown field strength due to large leakage conductance. The premature failure at a low electric field leads to low saturation polarization. At the same time, the large polarization hysteresis accompanies with the low energy storage efficiency, which makes the pure NN ceramics demonstrate the low energy storage performance. In addition, the P‐E loops in NN‐10H ceramics show a significant bunching behavior (Figure 4a), which may be due to the presence of the P phase with antiparallel structure [19]. Parts of the P phase irreversibly transform into the P₂₁ma phase under the electric field, resulting in a presentation of large orientation hysteresis. The saturation polarization and orientation hysteresis of the NN‐xH ceramics are significantly improved with the increase of HCE components. The P‐E loops of the NN‐20H ceramics become elongated and show significant relaxor behavior, as shown in Figure 4a. At the same time, high η (∼85.1%), large P_max (39.0 µC/cm²), and high breakdown electric field (1060 kV/cm) are achieved (Figure 4e,f), which yields an excellent W_rec of ∼12.7 J/cm³. Similarly, a great W_rec of ∼11.9 J/cm³ along with a high η of ∼89.1% are realized in NN‐25H ceramics. For NN‐30H ceramics, as illustrated in Figure 4e accompanied by the absolute value of the free energy of the system up to 1.52 R, the P‐E loops illustrate an approximate linearity, with a high η∼90.8% is obtained. However, due to the low saturation polarization (∼27.2 µC/cm²), it is difficult to achieve high energy storage performance. Figure 4b demonstrates the P‐E loops of all components under the same electric field of 400 kV/cm. With the increase of the HCE, the NN‐xH ceramics exhibit a reduced P_max and elevated η under the same electric field, which indicates a significant enhancement of the relaxor behavior.

FIGURE 4.

Energy storage performance of NN‐20H ceramics. (a) P‐E loops of NN‐xH ceramics; (b) P‐E loops of NN‐xH ceramics at the electric field of 400 kV/cm; (c)Weibull distribution for NN‐xH ceramics; (d) Phase field simulation of grain breakdown under the critical electric field; (e) Nominal electric field with nominal charge density; (f) Radar chart of energy storage performance.

We tested the breakdown resistance characteristics of the ceramics and described them via the Weibull distribution, as shown in Figure 4c. The Weibull distribution is often employed to verify the reliability of critical breakdown electric field data: X_i = ln(E_i ) ,  Y_i =  ln(*ln(1‐p)), $P=\frac{i}{n+l}$, in which E_i represents the critical breakdown electric field [30]. The i and n denote the sample code and the total number of samples, correspondingly. The reliability of the Weibull distribution is demonstrated by the fact that β > 10.0 for all fitting results (Figure 4c) [31]. Furthermore, the consequences of the Weibull distribution reveal that E_b increases substantially from 525.3 to 1057.8 kV/cm, corresponding to the x from 0.10 to 0.20. In addition, the breakdown strength of the ceramics is positively correlated with the grain boundary density. This variation acts as a key external factor to enhance the E_b value by increasing the density of highly resistive grain boundaries, the mechanism of which is based on an exponential decay relationship. Therefore, phase‐field simulations are employed to elucidate grain breakdown under critical electric fields (Figure 4d). One should remark that the total energy, consisting of electrostatic energy, is positively correlated with the local electric field. Because of the low breakdown potential energy barrier, the breakdown of the grains consistently occurs prior to the grain boundaries. When a strong electric field is applied to ceramics, charges accumulate at grain boundaries with high insulation resistance. Upon reaching a critical accumulation level, breakdown initiates at grain boundaries first. Due to the lower insulation characteristics within grains, charges rapidly diffuse through grain interiors. Eventually, when electron beams penetrate the entire ceramic, breakdown occurs accompanied by ferroelectric deactivation. Consequently, NN‐20H ceramics with higher grain boundary density exhibit superior breakdown resistance. Figure S15 shows the variation of nominal electric potential energy for NN and NN‐20H ceramics under the same electric field. In contrast to the rapid breakdown of NN ceramics at the critical electric field, the electric potential energy of NN‐20H ceramics accumulates at grain boundaries. Benefiting from the high insulation characteristics of high‐density grain boundaries, the ceramics possess a higher breakdown energy barrier, which endows them with greater reliability and stability in practical applications. Furthermore, benefiting from lattice distortion effects induced by the HCE strategy, enhanced electron scattering occurs in HCE components, further improving the ceramic's breakdown resistance [5, 24, 25, 26], further validating the reliability of the breakdown strength of NN‐xH ceramics.

The Figure 4f shows the radargram of NN‐xH ceramics relative to energy storage performance. Obviously, NN‐20H ceramics offer the largest radar plot area demonstrates the advancement in energy storage performance. Therefore, we selected NN‐20H ceramics to prepare MLCCs. MLCCs typically consist of dielectric layers, inner electrodes, and outer electrodes. The specific preparation process for MLCCs is illustrated in Figure S16. With the consideration of the sintering temperature for NN‐20H ceramics, the metal Pt is employed as the electrode layer. After co‐firing the ceramic with the inner electrodes, the Ag electrode is coated as the outer electrode. The cross‐section and finished product of prepared NN‐20H‐MLCCs are presented in Figure 5a. The dielectric and electrode layers of MLCCs are closely adhered to each other. The total thickness of the prepared MLCCs is about 0.7 mm, along with a length of 3 mm. The enlarged portion of the local section is shown in Figure S17. The thicknesses of the individual dielectric layer and electrode layer are 12 and 2 µm, respectively. Elemental mapping reveals a clear boundary between the dielectric layer and the electrode layer. To investigate the actual grain size of MLCCs, we polished the samples and performed thermal corrosion. Figure S18a–c presents SEM images after thermal corrosion. Following thermal corrosion, grain regrowth occurred in the MLCCs. This is attributed to the unavoidable partial loss of the electrode layers during polishing. Consequently, grains regrew at the locations of the original electrode layers after thermal corrosion. Benefiting from the high‐energy ball milling and the glass phase present in the electrode paste, the average grain size achieved a significant reduction (∼1.43 µm). Moreover, the electrode maintains a continuous morphology without diffusion after sintering. The unipolar P‐E loops of NN‐20H‐MLCCs are shown in Figure 5b. The hysteresis loop of the ceramic exhibits linear behavior under low electric fields, which is attributed to the rapid polarization orientation of the nonpolar nanoclusters and C phases under low electric fields. As the electric field increases, the highly polar orthorhombic phase gradually reaches saturated polarization. Due to the distinct responses of the polymorphic polar nanodomains to different electric fields, the hysteresis loop fails to maintain a well‐saturated and tightly wrapped shape. Benefiting from the favorable match between NN‐20 ceramics and MLCCs preparation process, the breakdown strength of the NN‐20H‐MLCCs is significantly improved, which leads to a significant enhancement of P_max∼43.8 µC/cm². Therefore, a large W_rec is obtained ∼20.4 J/cm³ (Figure 5c), which illustrates a great advantage in terms of energy storage performance over the current lead‐free energy storage ceramics (Figure 5d) [20, 29, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47]. To verify the reliability of breakdown strength, the Weibull distribution is calculated in Figure 5e. The reliability of the Weibull distribution is demonstrated by the fact that β∼29.3 for the fitting results. The fitted E_b value gets 1603 kV/cm from the Weibull distribution, which is consistent with the test data.

FIGURE 5.

Energy storage performance of NN‐20H MLCCs; (a) Morphology of the NN‐20H‐MLCCs and cross section; (b) Unipolar P‐E loops for NN‐20H‐MLCCs under different electric fields; (c) Energy storage performance for NN‐20H‐MLCCs; (d) Advanced energy storage performance for NN‐20H‐MLCCs; (e) Weibull distribution; (f) Discharge energy storage performance.

To research the energy storage performance of NN‐20H‐MLCCs in aggressive environments, the P‐E loops in the temperature range from 20°C to 100°C under the electric field of 1000 kV/cm are illustrated in Figure S19a. As the temperature increases, the saturation polarization appears to decrease slightly with an improvement in efficiency, which is due to the thermal relaxation of the dipole caused by the warming up. The variations in W_rec are always less than 5% (Figure S16b), reflecting the excellent temperature stability of NN‐20H‐MLCCs. Meanwhile, the NN‐20H‐MLCCs exhibit cycling stability with 10⁶ cycles. The P_max, W_rec, and η all remain almost constant for 10⁶ cycles, which proves that NN‐20H‐MLCCs boast favorable fatigue resistance (Figure S16c,d). To verify the discharge energy storage performance of NN‐20H‐MLCCs with the overdamping, a 200 Ω resistor is applied, and the discharge current waveform of NN‐20H‐MLCCs is shown in Figure S20. According to this, the discharge energy storage density W_d could be derived from the following equation: $W_d=R\int I{(t)}^{2}dt/V$, in which R stands for the applied resistance of 200 Ω, and I, t denotes the discharge current as well as time, correspondingly [48, 49, 50]. The W_d achieves 8.1 J/cm³ at an electric field of 1000 kV/cm, which is closely in line with the ferroelectric test results (Figure 5f). More importantly, the NN‐20H‐MLCCs exhibit extremely fast discharge rates of t_0.9∼43.9 ns. According to the above results, NN‐20H ceramics demonstrate optimum stability in harsh application conditions and excellent discharge performance.

3. Conclusion

Guided by the theoretical predictions, we propose a gradient polarization coupling (GPC) via HCE modulation that is constructed by alternating weakly polar and strongly polar nanodomains with embedding nonpolar nanoclusters via high configurational entropy regulation to enhance the energy storage performance of ceramics. Under an applied electric field, the non‐polar nanocluster structures achieve rapid response first, driving gradient coupling between the weakly polar and strongly polar nanodomains for the electric field, which allows for the simultaneous achievement of high polarization characteristics and low hysteresis loss. Under the theoretical guidance of phase field simulation, the prepared NN‐xH ceramics exhibit significant improvement in energy storage performance. In particular, the NN‐20H‐MLCCs achieve an ultrahigh recoverable energy storage density of 20.4 J/cm³ and an excellent E_b of 1680 kV/cm with η∼85.0%. The improved ceramics of the GPC strategy via HCE modulation offer significant performance advantages in the current field of lead‐free ceramic capacitors. This provides a new vision for the development of the next generation of MLCCs.

4. Experimental Section

The experimental methods and testing methods are provided in the Supporting Information.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File: smll74369‐sup‐0001‐SuppMat.docx.

Data Availability Statement

The data that supports the findings of this study are available in the supplementary material of this article.