A novel lead‐free relaxor with endotaxial nanostructures for capacitive energy storage

Dielectric capacitors with a fast charging/discharging rate, high power density, and long‐term stability are essential components in modern electrical devices. However, miniaturizing and integrating capacitors face a persistent challenge in improving their energy density (Wrec) to satisfy the specifications of advanced electronic systems and applications. In this work, leveraging phase‐field simulations, we judiciously designed a novel lead‐free relaxor ferroelectric material for enhanced energy storage performance, featuring flexible distributed weakly polar endotaxial nanostructures (ENs) embedded within a strongly polar fluctuation matrix. The matrix contributes to substantially enhanced polarization under an external electric field, and the randomly dispersed ENs effectively optimize breakdown phase proportion and provide a strong restoring force, which are advantageous in bolstering breakdown strength and minimizing hysteresis. Remarkably, this relaxor ferroelectric system incorporating ENs achieves an exceptionally high Wrec value of 10.3 J/cm3, accompanied by a large energy storage efficiency (η) of 85.4%. This work introduces a promising avenue for designing new relaxor materials capable of capacitive energy storage with exceptional performance characteristics.

2][3] However, their progress toward miniaturization, lightweight construction, and integration is hindered by the low energy density of dielectric capacitors, especially when compared to batteries and supercapacitors.Efforts have been focused on increasing the energy density of dielectric capacitors to meet the demands of modern electronic systems and applications.
6][7] Achieving a large polarization difference (∆P = P max -P r ) under high electric field conditions contributes to materials with high-energy storage density.Additionally, a smaller polarization hysteresis (manifesting as high-energy storage efficiency η) helps reduce heat generation and ensures normal operation under high electric field conditions. 8,9elaxor ferroelectric materials, with their unique domain structures and characteristics, exhibit exceptional electrical properties for energy storage applications.The inhomogeneity at the nanoscale or the presence of polar nanoregions (PNRs) is believed to be the origin of their remarkable electrical properties. 10,11Creating local polymorphism that includes localized long-range correlated polar regions and weakly coupled short-range PNRs is a widely accepted approach to achieving significant polarization differences under high electric fields. 12Long-range correlated polar regions act as nucleation sites for relaxorferroelectric phase transitions, promoting the nucleation and expansion of ferroelectric domains and resulting in high macroscopic polarization. 13Meanwhile, decreasing domain size and inter-domain coupling in these materials reduce the energy barrier for domain switching, lowering hysteresis and enhancing energy storage characteristics. 14arious strategies, such as domain engineering, 15 superparaelectric state, 14 defect manipulation, [16][17][18] supercritical behavior, 19 and high-entropy design, 20 have been proposed, to modulate the states of PNRs and optimize energy storage properties.Despite the implementation of the progress, it remains notable that a significant enhancement of energy storage performance is yet to be observed in a multitude of relaxor ferroelectrics.To achieve a large polarization difference and maximize the electric field strength to its fullest potential, the pursuit of a novel design strategy becomes imperative.In recent years, heterogeneous materials with endotaxial nanostructures (ENs) have significantly enhanced a wide array of functionalities, including thermoelectric, 21 plastic, 22 and electromechanical 23 performances.It is worth mentioning that Liu et al. recently achieved a significant improvement in the electromechanical properties of lead-based relaxors by constructing ENs. 23This approach has the potential for widespread application in relaxors to enhance their local structure-sensitive functionalities, such as piezoelectric and energy storage performances.Nonetheless, to date, based on our current understanding, there is still a lack of theoretical guidance for the rational design of EN morphologies aimed at dramatically enhancing dielectric energy storage.This impedes the experimental explo-ration and initiation of such heterostructures in lead-free relaxors.
In this work, guided by phase-field simulations, we achieved ENs by modifying the local structural heterogeneity in Bi 0.5 Na 0.5 TiO 3 -based relaxor ferroelectrics with concomitantly modulated rhombohedra and tetragonal nanoregions.We uncovered that the incorporation of heterostructures, characterized by ENs within the relaxor matrix (Figure 1A), can serve as a bridge for synergistically modulating domain configuration and breakdown phase proportion.Introducing such heterostructures decreases domain size by adjusting the depolarization electrical energy, which promotes the alignment of PNRs and enables their rapid recovery after the removal of the electric field, leading to improved energy storage performance (high ∆P and large η, as reflected in Figures 1B 1 -B 3 and S1).The mechanisms underlying the enhancements in polarization difference and energy storage efficiency have been validated through experiments using scanning transmission electron microscopy (STEM) and piezoresponse force microscopy (PFM).In addition, a pronounced enhancement in breakdown strength is observed due to the reduced breakdown proportion and the increased prevalence of highly insulating grain boundaries/interfaces, as shown in Figure 1C.As expected, this novel type of heterogenous lead-free relaxors [(1x)Bi 0.47 Na 0.47 Ba 0.06 TiO 3 -xSr(Mg 1/3 Ta 2/3 )O 3 ] amalgamates the complementary advantages of various regions, overcoming the challenge posed by the inverse correlation between ∆P and E b , and achieves an excellent W rec of 10.3 J/cm 3 and decent η of 85.4%.These findings shed light on a promising pathway for the design and development of novel lead-free relaxors incorporating ENs, offering comprehensive energy storage performance.

RESULTS AND DISCUSSION
The inherent microstructural configuration of a material fundamentally governs its performance characteristics.To verify the presence of ENs, the microstructure of the polished surface for SMT3 ceramics with the highest W rec is carried out using backscattered electron imaging.As reflected in Figure S2a, a distinct core-shell hierarchical structure is detected in SMT3 ceramics, but not in the pristine BNT (the inset of Figure S2a).The existence of the heterogeneous structure can also be further confirmed by dielectric properties.Figure S2b-e provides the temperature-dependent dielectric constants (ε r ) of samples with various SMT dopant concentrations.Within the examined temperature range, all samples display a distinctive "double-peak" feature in their ε r (T) curves, characterized by two dielectric anomaly peaks located near T m in the low-temperature region and T m1 in the hightemperature region.These features are consistent with those reported for BNT-based ceramics. 24,25Over time, various viewpoints have emerged regarding the unique dielectric response in BNT ceramics.The currently prevailing view holds that the two distinct dielectric responses arise from the thermal evolution and mutual transformation of two different types of PNRs during the temperature increase process. 26As increasing SMT content, the T m values of samples monotonically decrease from 75.8 • C to  27 Herein, we introduce a parameter ΔT relaxor , defined as the difference between T m (200 kHz) and T m (1 kHz), which represents the degree of diffusion and compositional inhomogeneity, to quantify the behavior described above. 28With increasing SMT content, the ΔT relaxor values of the samples show an increasing trend (Figure S2f), ultimately reaching saturation in SMT3 samples with a value of ∼20.4 • C, indicating a considerable degree of heterogeneity. 29Therefore, subsequent investigations will primarily focus on SMT3 ceramics.
Local heterogeneity within multiple grains is distinctly visualized at the mesoscale by transmission electron microscopy (TEM) (inset of Figure 2A).Figure S3 provides an enlarged image focused on individual grains, along with the corresponding energy-dispersive X-ray spectroscopy (EDS).Interestingly, unlike the local heterostructures (comprising a ferroelectric core and a non-ferroelectric shell) typically reported in most BNT-based ceramics, 30 SMT3 ceramics with ENs exhibit no distinct domain configurations, instead presenting only alternating bright and dark patterns, which is primarily attributed to the segregation of local elements. 23Integrating the evidence from EDS analysis, the existence of the Sr 2+ -enriched phase is corroborated within the ENs.Research indicates that Sr 2+ doping can significantly reduce the phase transition temperature of BNT 31 ; thus, the EN regions primarily exhibit a weakly polar state.
To gain insight into the polarization configuration of SMT3 ceramics and the underlying mechanisms influencing its correlated energy storage properties, atomic-scale investigations are conducted using spherical aberrationcorrected STEM.Atomically resolved high-angle annular dark-field (HAADF) images for BNT (Figure S4a) and SMT3 (Figures 2A,B and S4b) ceramics along the [100] are carried out and quantitatively analyzed.Based on the intensity of each atomic column, the positions of the A-site and B-site atomics are accurately fitted with a 2D Gaussian peak.Figures 2C,D and S4c,d provide the polarization vectors on the atomic scale for various local regions, wherein these vectors are delineated as the deviation of a B-site atom relative to the center of its four nearest neighboring A-site atoms.For the no-EN region in SMT3 ceramics, that is, the smooth matrix, PNRs (rhombohedral R + tetragonal T) of approximately 1-3 nm are clearly observed, indicating that the introduction of SMT effectively enhances the local random field and thus disrupts the domain configurations of BNT ceramics.This is consistent with the domain evolution characteristics, as demonstrated in Figures S4e,f (from dense domain boundary state [BNT] to highly relaxed state [SMT3]).Interestingly, these polar clusters are not isolated by non-polar matrix, rather than connected by detectable transition states (Figure 2E).Owing to the requirements of lattice symmetry, the polarization direction of traditional T and R phases can only be triggered in specific orientation. 32During the polarization rotation, it will undergo multiple potential polarization orientation, colloquially referred to as transitional states.The polarization orientation in such transitional states is not limited by the highly symmetrical crystal orientation of the R or T phases, showing a wide range of transitional orientation.For polarization intensity, both R/T polarization and transitional state polarization vector have a relatively large polarization strength, 33 which are easily disturbed by electric fields and can trigger substantial responses under weak electric fields.It is worth mentioning that the local polarization magnitude in specific regions is about 59.0 pm, with an average displacement magnitude of 17.4 pm, which is significantly larger than those reported for the BNT-BT and BNT-ST systems. 34As a result, under the stimulation of a weak external electric field, SMT3 ceramics are prone to polarization switching, which can easily induce a high polarization at room temperature, reduce losses, and improve the thermal breakdown strength.
Since the existence of ENs is key to obtaining low hysteresis and high ∆P, it is necessary to reveal the intrinsic nature of those regions.Figure 2D provides the distribution of atomic polarization vectors in the corresponding region.And the corresponding magnitude and angle of each vector are shown in Figure 2F.It can be clearly observed that the polarization magnitudes of EN region are relatively uniform, and these values (18.0 pm) lie within the range of polarization fluctuations (maximum: 59.0 pm, minimum: 0.9 pm) in the matrix, which is mainly caused by the minor enrichment of polar Ba and Ti elements at the A-and Bsites.However, the obvious Sr 2+ segregation makes them highly ionic and incapable of being polarized. 30Therefore, even under high electric fields, these EN regions can still maintain a weak polar state, providing strong restoring forces to return to the non-polarized state, thus eliminating hysteresis once the electric field is removed.This is different from the weakly polar states in the matrix, which can easily reorient under high fields and maintain a stable polarization even after the field is removed, resulting in a modest hysteresis.It should be noted that, owing to the presence of numerous weakly polar ENs, the lattice distortion inside these regions is less affected by domain walls, which reasonably explains why it is difficult to identify the characteristic peak splitting in long-range XRD characterizations (Figures S5a,b).In addition, from a thermodynamic standpoint, the random distribution of ENs in the whole matrix helps to make up for the strong polar fluctuations in the matrix and build an evenly distributed polarization configuration, so that the free energy in each direction has little difference; that is, the barrier of free energy curve is relatively smooth in this system.Therefore, the designed heterogeneous system facilitates the triggering of high polarization differences and low hysteresis under a weak electric field.
Essentially, the energy storage of relaxor ferroelectrics is closely correlated with the polarization, and from a microscopic view, the local polar relaxor units regulate the polarization level.Herein, we employ PFM to investigate local domain configurations and their dynamic behaviors under an electric field (Figures 3A 1 -A 3 and S6).As depicted in Figures 3A 1 and S6a 1 -a 3 , a composition-driven dynamic domain evolution can be observed, that is, from large-size nanodomain configuration (BNT) to a refined nanodomain (BNT-BT) and even to fuzzy domain signals with no obvious domain configuration (SMT3).Note that the TEM characterization also reveals that BNT displays dense nanodomains (Figure S4e), whereas absent in SMT3 (Figure S4f).The declined domain size indicates the enhanced relaxor characteristics which should be a critical factor for diminished remanent polarization and improved energy storage.Moreover, the dynamic domain behaviors are investigated via a local poling experiment (Figures 3A 2 and S6b). 35Compared with BNT and BNT-BT ceramics, SMT3 possesses a lower density and intensity of domain switching, due to the higher activation energy (E a : ∼0.12 eV, Figure S7 and Table S1) of dynamic ergodic polar entities. 36This is attributed to domain evolution, and line scan profiles (Figures 3A 3 ) further unravel the highly dynamic polar regions and strong reversibility of SMT3 (the switching domains of BNT and BNT-BT ceramics exhibited negligible fluctuations after 10 min.In contrast, the majority of switching domains in SMT3 ceramics to revert to their initial state).Although STEM and Vertical piezoelectric force microscopy (VPFM) have successfully detected small-size nanodomains at the nanoscale, almost few visualized dynamic domain patterns with local polymorphic nanodomain configurations have been reported.Herein, the switching spectroscopy PFM (SS-PFM) is employed 37 to characterize local polymorphic switching behavior of domains.As depicted in the schematic diagram of Figure 3B 1 , the amplitude (or phase)-voltage butterfly (or hysteresis) loops (Figure S8) of SMT3 ceramics are collected in mapping mode over a 450 × 450 nm 2 area consisting of 8 × 8 grid of points.Based on the collected amplitude heatmaps (Figure 3B 2 ,B 3 ), two unique polarization regions, that is, the weak polar and strong polar fluctuation regions, can be identified, conforming to the STEM results.And the lower hysteresis of weakly polar EN regions (inner region of Figure 3B 3 ) reveals its significant intrinsic relaxor behavior.Moreover, it is noteworthy that the local coercive bias V c values (Figure S9) corresponding to both regions are relatively smaller than those of typical ferroelectrics, which is beneficial for polarization switching. 37he existence of distinctive heterogeneous structures not only contributes to improving ∆P but also plays a significant role in enhancing E b .To evaluate the E b of the ceramics, the intrinsic electrical response, for example, relaxor activation energy E rel , and extrinsic micronano structures, for example, average grain size and ENs, are scrutinized.As depicted in Figure S10a, all the asprepared samples presented a single semicircle on the complex impedance spectra, indicating only the bulk response.Therefore, to estimate the resistance activation energy (E rel ) of the system, an equivalent circuit (RQC) is employed to fit the impedance data.The fitting parameters are provided in Table S2.Further analysis indicates that judicious tuning of SMT assists in enhancing E rel (Figure S10b).A high E rel indicates that the transport of oxygen vacancies requires overcoming a relatively high potential barrier, which will limit the transport of carriers, thereby reducing the possibility of breakdown in samples.From the perspective of micro-nanostructures, considering the slight differences in grain size (Figure S10c-f), the improved electrical properties can be primarily attributed to the contributions from the rational ENs by component manipulation.Interfaces (Figure S4b) constructed between the ENs and the matrix, resulting from lattice mismatch triggered by the introduction of multiple atoms, induce surrounding atoms to deviate from their ideal lattice positions.This alteration is thought to exacerbate the possibility of collisions between electrons and lattice ions, leading to local potential fluctuations, thereby increasing displacement and electron scattering, culminat-ing in a reduction of conductivity. 34,38To elucidate the inherent mechanism of enhancing E b in ceramics with ENs, herein, a phase-field breakdown model is employed using COMSOL Multiphysics (for education) to simulate the local electric field distribution and breakdown pathways in ceramics, individually considering scenarios with ENs and without ENs.A detailed model (Figure S11) and computational parameters (Table S3) are provided in the Supporting Information.Based on the preceding STEM analysis, it is assumed that the EN regions are elliptical and are embedded within a matrix consisting of two phases (a strong polar and a weak polar phase), with its polarity intermediate between the two phases.As illustrated in Figure 4A 1 -B 4 , under the influence of an external electric field, the breakdown path of the ceramic initiates and progressively develops from the top.The times taken for complete breakdown in ceramics with and without ENs are 4.90 and 5.10 s, respectively.This suggests that the presence of ENs effectively delays the progression of ceramic breakdown paths.To quantify this behavior, Figure 4C presents the percentage area of the breakdown phase under different external fields.It is evident that under an equivalent applied electric field, the ceramics with ENs exhibit a significantly reduced breakdown phase proportion compared to those without ENs.This further corroborates that the presence of ENs can effectively retard the breakdown of ceramics.
After gaining insights into the polarization configuration and E b , the W rec and η of ceramics under various electric fields are calculated via P-E loops, as illustrated in Figures 5A,B and S12a-f.For BNT and BNT-BT ceramics, a relatively low ∆P (7 and 13.6 μC/cm 2 ) and relatively small E b (120 and 155 kV/cm) resulted in inferior performance (BNT: W rec = 0.23 J/cm 3 , η 5.9%; BNT-BT: W rec = 0.67 J/cm 3 , η = 14.6%).Its performance is chiefly constrained by the strongly correlated polar nanodomain within the grains and the low non-intrinsic E b .With the introduction of SMT, the E b of ceramic first increases and then decreases as the SMT increases.This change is consistent with the two-parameter Weibull distribution function analysis (Figure S13), thereby confirming the reliability of the experimental results.By rational component manipulation, a slim P-E loop with a large P max of 53.1 μC/cm 2 and a suppressed P r of 4.5 μC/cm 2 can be achieved at a high E b of 655 kV/cm in SMT3 ceramics.As expected, an ultrahigh W rec of 10.3 J/cm 3 accompanied by an η of 85.4% is realized.For further comparison, Figure 5C,D provides the W rec and E b or η values of recently reported lead-free relaxors.It is apparent that W rec value in this work exhibits a significant rise when subjected to the same electric field.
Meanwhile, only few selected few materials can simultaneously achieve a high W rec >10.0 J/cm 3 and a substantial η >80.0%.These findings indicate that the design and development of relaxors with ENs hold significant advantages in terms of high-performance energy storage materials.
For practical applications of capacitors, the long-term working stability of energy storage properties are of utmost importance.The W rec and unipolar P-E loop of the SMT3 ceramics between 20 • C and 140 • C are shown in Figure 6A.The results show that SMT3 ceramics display stable W rec , with variations of ≤12.2% across the entire temperature range.This outstanding temperature stability can be primarily attributed to the strong relaxor behavior resulting from the ENs.Additionally, the outstanding insulating characteristics of the ceramics effectively suppress the thermal activation of carriers, thereby minimizing conduction losses at elevated temperatures.Besides thermal stability, SMT3 ceramics with ENs also display excellent frequency stability across a broad operating frequency range of 1-1000 Hz.0][41][42][43][44][45][46] Obviously, the SMT3 ceramics not only possess a high W rec but also exhibit outstanding temperature stability, indicating the potential advantages of lead-free ceramics with ENs in high-temperature applications.In addition to the stability, the pulse charge/discharge is also important for highpower energy storage applications.Figure 6D,E exhibits the discharge energy density (W dis ) curves of SMT3 investigated under room temperature by a resistance-capacitance circuit.The W dis can be determined using the formula:  dis =  ∫ 2  ()∕, where R represents the total load resistor (13.0 kΩ) and V denotes the sample volume.With an increase in electric field from 100 to 590 kV/cm, the W dis reaches its maximum value of 8.62 J/cm 3 , accompanied by a fast discharge time of 0.76 μs, demonstrating the exceptional pulse power performance of SMT3.Compared to the P-E loop measurement, the charge-discharge measurement produces lower energy density, which may be due to the domain clamping effects generated by high frequency and electric field and higher joule heat loss.

CONCLUSIONS
In summary, this study successfully demonstrates a novel approach for modifying domain configuration through the design of ENs in lead-free relaxor materials, leading to outstanding energy storage performance.With HAADF STEM and SS-PFM analysis, the local polymorphic domain configuration of such relaxor is revealed.The presence of flexible transitional polar states and strengthened random fields, combined with the inherent grain inhomogeneity characterized by the coexistence of weakly polar ENs and regions with strong polar fluctuations, contributes to the significant enhancement of ΔP.The incorporation of ENs with weak polarization effectively reduces the proportion of breakdown phase, thereby triggering a high E b .Specifically, by judiciously adjusting the balance between ΔP and E b , the SMT3 ceramics exhibit a giant W rec of 10.3 J/cm 3 with a large η of 85.4% under 655 kV/cm, along with excellent thermal and frequency stability (variation of W rec < ±12.2% over 20 • C-140 • C, variation of W rec <6.5% in 1-1000 Hz), highlighting their potential for practical applications.Overall, this work demonstrates the feasibility and benefits of constructing unique heterogeneous structures in guiding the discovery and development of various high-performance lead-free relaxor ferroelectric materials.

A C K N O W L E D G M E N T S
This work was supported by the National Key Research and Development Program of China (2022YFB3807402) and the National Science Foundation of China (no.51972215).We would like to thank Hui Wang for her help with the SEM images.

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors declare no conflict of interest.

F I G U R E 1
Design of new relaxors with enhanced energy performance via the design of endotaxial nanostructures (ENs).(A) Schematic diagram of the microstructure of a material with ENs.Phase-field simulated for relaxors with ENs and no-ENs: (B 1 and B 2 ) the associated evolution of polar structures at various external electric fields; (B 3 ) the P-E loops under a given field of E 0 ; (C) the local electric field distribution and breakdown pathways at the same time.The EN regions are marked by black circles.

14. 8 •
C (Figure S2b-e), accompanied by the broadening and weakening of the dielectric peak.The broadening of the dielectric peak is generally considered to be caused by compositional inhomogeneity, which provokes local deviations in lattice distortions, thereby triggering an anomalous dielectric response in this region.Decreasing T m and weakening dielectric peak values indicate that the introduction of SMT contributes to the enhancement of local random fields within the BNT ceramic crystals, thereby causing the decoupling of local long-range coherence, and leading to different degrees of heterogeneity.

F I G U R E 2
Microstructure of SMT3 ceramics at various scales.(A and B) High-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images recorded along the [100] c at various regions, (C and D) the corresponding atomic displacement vector mapping, and (e and f) the corresponding magnitude and angle of each vector.The inset of (A) displays the bright-field transmission electron microscopy (TEM) micrograph for the SMT3 ceramic.

F I G U R E 3
Probing the local polarization response by VPFM and switching spectroscopy piezoresponse force microscopy (SS-PFM).(A 1 ) VPFM-amplitude images of BNT, BNT-BT, and SMT3 ceramics with a scanning area of 3.0 × 3.0 μm 2 .(A 2 ) Corresponding the phase images after litho process as a function of relaxation time (0 and 10 min).(A 3 ) Phase line scan profile corresponding to the white dashed line.(B 1 ) Schematics of SS-PFM mapping of 8 × 8 grid of points over a 0.45 × 0.45 nm 2 region.(B 2 ) Amplitude heatmaps and (B 3 ) representative amplitude and phase images for the measurement of SS-PFM loops.

F I G U R E 4
Simulated local electric field distribution and breakdown pathways at various moments of ceramics with (A 1 -A 3 ) no-endotaxial nanostructures (no-ENs) and (B 1 -B 4 ) ENs. (C) The nominal applied electric field versus nominal breakdown phase area fraction of ceramics with no-ENs and ENs.

F
I G U R E 5 (A) Unipolar P-E loops of SMT3 ceramics under different electric fields.(B) The W rec , W total , and η as a function of electric fields for SMT3 ceramics.(C and D) Comparison of the energy storage performance of SMT3 ceramics with representative lead-free ceramics.F I G U R E 6 (A) Unipolar P-E loops of SMT3 ceramics under different temperatures and corresponding W rec .(B) Unipolar P-E loops of SMT3 ceramics under different frequencies and corresponding W rec .(C) Comparison of the W rec of SMT3 ceramics and other recently reported representative ceramics over a wide range of operating temperatures.(D and E) Discharge properties for SMT3 ceramics at various electric fields.