Article https://doi.org/10.1038/s41467-023-41494-1 Broad-high operating temperature range and enhanced energy storage performances in lead-free ferroelectrics Weichen Zhao 1, Diming Xu 1 , Da Li 1, Max Avdeev 2, Hongmei Jing3, MengkangXu4, YanGuo1, Dier Shi5, Tao Zhou6,Wenfeng Liu7, DongWang 8 & Di Zhou 1 The immense potential of lead-free dielectric capacitors in advanced electro- nic components and cutting-edge pulsed power systems has driven enormous investigations and evolutions heretofore. One of the significant challenges in lead-free dielectric ceramics for energy-storage applications is to optimize their comprehensive characteristics synergistically. Herein, guided by phase- field simulations along with rational composition-structure design, we con- ceive and fabricate lead-free Bi0.5Na0.5TiO3-Bi0.5K0.5TiO3-Sr(Sc0.5Nb0.5)O3 ternary solid-solution ceramics to establish an equitable system considering energy-storage performance, working temperature performance, and struc- tural evolution. A giant Wrec of 9.22 J cm −3 and an ultra-high ƞ ~ 96.3% are rea- lized in the BNKT-20SSN ceramic by the adopted repeated rolling processing method. The state-of-the-art temperature (Wrec ≈ 8.46 ±0.35 J cm−3, ƞ ≈ 96.4 ± 1.4%, 25–160 °C) and frequency stability performances at 500 kV cm−1 are simultaneously achieved. This work demonstrates remarkable advances in the overall energy storage performance of lead-free bulk ceramics and inspires further attempts to achieve high-temperature energy storage properties. With the continuous growth of the world population and the devel- opment of the global economy and society, worldwide energy demand keeps increasing at an alarming rate. Due to the desperate issues, it is vital to exploit a variety of clean and sustainable energy sources1–4. Comparedwith various current energy storage and conversiondevices (e.g., lithium-ion batteries, supercapacitors, solid oxide fuel cells), electrostatic capacitors made of dielectric materials have attracted ever-increasing attention up till nowowing to their benefits in terms of swift charging-discharging rates, ultrahigh power density, excellent thermal stability, and prolonged storage lifespan5–8. Nonetheless, the comparatively low recoverable energy storage density (Wrec) of cur- rent dielectric ceramic capacitors had significantly hindered their practical utilizations in sophisticated electronic components and forefront pulsed power systems. Accordingly, substantial efforts have been undertaken to synergistically boost the comprehensive energy storage characteristics of dielectric materials, especially lead-free Received: 15 March 2023 Accepted: 6 September 2023 Check for updates 1Electronic Materials Research Laboratory & Multifunctional Materials and Structures, Key Laboratory of the Ministry of Education & International Center for Dielectric Research, School of Electronic Science and Engineering, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, China. 2Australian Nuclear Science and Technology Organization, Lucas Heights 2234 NSW, Australia. 3School of Physics and Information Technology, Shaanxi Normal University, 710062 Xi’an, Shaanxi, China. 4State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, China. 5Department of Chemistry, Zhejiang University, 310027 Hangzhou, Zhejiang, China. 6School of Electronic and Information Engineering, HangzhouDianzi University, 310018Hangzhou, Zhejiang,China. 7StateKey Laboratory of Electrical Insulation and Power Equipment, Xi’an JiaotongUniversity, 710049 Xi’an, Shaanxi, China. 8Frontier Institute of Science and Technology and State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, China. e-mail: diming.xu@xjtu.edu.cn; wang_dong1223@mail.xjtu.edu.cn; zhoudi1220@gmail.com Nature Communications | (2023) 14:5725 1 12 34 56 78 9 0 () :,; 12 34 56 78 9 0 () :,; http://orcid.org/0009-0002-8538-0032 http://orcid.org/0009-0002-8538-0032 http://orcid.org/0009-0002-8538-0032 http://orcid.org/0009-0002-8538-0032 http://orcid.org/0009-0002-8538-0032 http://orcid.org/0000-0002-7320-0009 http://orcid.org/0000-0002-7320-0009 http://orcid.org/0000-0002-7320-0009 http://orcid.org/0000-0002-7320-0009 http://orcid.org/0000-0002-7320-0009 http://orcid.org/0009-0004-3566-9174 http://orcid.org/0009-0004-3566-9174 http://orcid.org/0009-0004-3566-9174 http://orcid.org/0009-0004-3566-9174 http://orcid.org/0009-0004-3566-9174 http://orcid.org/0000-0003-2366-5809 http://orcid.org/0000-0003-2366-5809 http://orcid.org/0000-0003-2366-5809 http://orcid.org/0000-0003-2366-5809 http://orcid.org/0000-0003-2366-5809 http://orcid.org/0000-0001-6009-166X http://orcid.org/0000-0001-6009-166X http://orcid.org/0000-0001-6009-166X http://orcid.org/0000-0001-6009-166X http://orcid.org/0000-0001-6009-166X http://orcid.org/0000-0001-7411-4658 http://orcid.org/0000-0001-7411-4658 http://orcid.org/0000-0001-7411-4658 http://orcid.org/0000-0001-7411-4658 http://orcid.org/0000-0001-7411-4658 http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41494-1&domain=pdf http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41494-1&domain=pdf http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41494-1&domain=pdf http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41494-1&domain=pdf mailto:diming.xu@xjtu.edu.cn mailto:wang_dong1223@mail.xjtu.edu.cn mailto:zhoudi1220@gmail.com materials, to fulfill the pressing demands of electronic devices for integration, miniaturization, and environmental friendliness9–13. Currently, common-utilized dielectric capacitors developed for energy storage include thin films, polymer-based thick films, and ceramic materials1,10,13–19. Among the candidate dielectric materials, bulk ceramics usually have low dielectric losses, high-temperature stability, and excellent fatigue resistance, enabling them to be more suitable for applications in various operational situations, such as aerospace, hybrid electrical vehicles, and electromagnetic pulse sys- tems. Lead-free ceramics with relaxation properties for energy storage applications, for instance, BaTiO3 (BT) 20–22, K0.5Na0.5NbO3 (KNN) 5,23,24, NaNbO3 (NN)11,25,26, Bi0.5K0.5TiO3 (BKT)8,27, and Bi0.5Na0.5TiO3 (BNT)17,28–30-based ceramics, have been extensively investigated in past few years. BNT-based materials exhibit intrinsic large saturation polarization (Pmax) and are attributed to hybridization between Bi 6 s and O 2p orbitals31, which surpasses commonly used lead-free relaxor ferroelectric (RFE) counterparts. In light of this, BNT-based systems have received substantial attention in the field of energy storage and have been recognized as one of the most prospective eco-friendly materials for advanced pulsed power applications4,28,32. Typical BNT- based binary or ternary solid solutions have been widely studied recently, including BNT-BT, BNT-NN, BNT-SrTiO3 (BNT-ST), and BNT- BT-NN, etc33–36. In addition, Che et al. constructed a BNT-Ag(Nb0.5Ta0.5) O3 (ANT) ceramic combined with defect engineering and realized a high Wrec of 6.6 J cm−3 at 510 kV cm−1, albeit less success in energy efficiency (ƞ less than 75%)37. Thus, there is still a manifest challenge in obtaining ultrahigh energy storage density while maintaining high efficiency over a broad operating temperature in BNT-based ceramics. Herein, we rationally design an effective strategy tomaintain high energy storage performance upon a wide working temperature range guided by the phase-field method. Specifically, the manipulations of polymorphic polar nanoregions (PNRs) by constructingmorphotropic phase boundary (MPB) in Bi0.5Na0.5TiO3-Bi0.5K0.5TiO3 (BNKT) binary system and incorporated Sr(Sc0.5Nb0.5)O3 (SSN) allow us to establish an equitable system considering energy storage performance, working temperature performance, and structural evolution. A giganticWrec of 9.22 J cm−3, and significantly enhanced energy efficiency ƞ of 96.3% at an external electric field of 535 kV cm−1 are realized in the BNKT-20SSN ceramic by the adopted repeated rolling processing (RRP) method. Encouragingly, apart from the ultrahigh Wrec and exceptional energy efficiency ƞ mentioned above, remarkable temperature-insensitive performance (Wrec ≈ 8.46 ±0.35 J cm−3, Δƞ/ƞ ≤ 2%, 25–160 °C) and a slight fluctuation in frequency stability (Wrec ≈ 8.63 ±0.18 J cm−3, Δƞ/ƞ < 3%, 1–100Hz) at 500 kV cm−1 are accomplished in the BNKT- 20SSN ceramic (RRP). Simultaneously, further relationships among structural construction, energy storage performance, and working temperature performance are studied in-depth to elucidate the structure-performance connection upon temperature influence. Results Phase-field simulations of the structure construction process The phase-field method is a powerful computational method to man- ifest the spatiotemporal evolution of microstructures and the related physical properties. The method is extensively and popularly utilized in dielectric materials, especially energy storage-related dielectric materials, to simulate the processes in terms of grain growth, solidi- fication, thin-film deposition, crack propagation, and breakdown5,38,39. Here, we take Bi0.5Na0.5TiO3-Bi0.5K0.5TiO3 (BNT-BKT) binary system at the morphotropic phase boundary (MPB) as the initial phase and Sr(Sc0.5Nb0.5)O3 (SSN) as the guest phase to perform a two- dimensional phase-field simulation. The physical parameters and cal- culation parameters were set based on the 0.92BNT-0.18BKT (BNKT) system where rich polymorphic polar nanoregions (PNRs) could be observed over the coexistences of the rhombohedral (R3c) phase and the tetragonal (P4bm) phase. The phase-field simulation results of the phase distribution as a function of the SSN phase fraction (see Fig. 1a) show that the R phase dominates in the BNKT end, albeit considerable T phase and local polar inhomogeneity exist. We employed a color scheme using RGB colors alongside vectors todepict different polarizationorientations in thefive left columns (vector contours). The colors visually distinguish ferro- electric domains characterized by distinct polar directions. However, distinguishingbetweendifferentR values proved challenging due to the presence of eight <111> directions. To address this issue, in the right- most column (symmetry contours), we incorporated a color bar to depict the phase contour. It is essential to note that the organization of the color correspondence between these two types of plots is unrelated and follows different schemes. With the increase in the fraction of the guest SSN phase, the fraction of the T phase dramatically increases and the phase fraction reverses at around x=0.3. Subsequently, the polar- ization distribution of the external electric field as a function of the SSN fraction was calculated, as also shown in Fig. 1a. Obviously, the long- range ferroelectric (FE) order of the host phase could be disrupted, and more abundant nanodomains are produced when x increases, permit- ting the material to have the relaxor behavior40. The polarization directions are more disordered with less guest phase in the initial state, but it is harder to polarize fully. When the external electric field is applied and removed, the polarization exhibits a similar arranging behavior and restores its original state at the end, proving the process is reversible. We finally selected the BNKT-20SSN (x =0.2) phase as the target composition, notwithstanding BNKT-30SSN (x =0.3) presents a larger polarization response because the BNKT-20SSN phase displays a relatively reasonable structural construction and a considerable polar order–disorder arrangement as a relaxor ferroelectric. The initial state polarization distribution of the BNKT-20SSN phase to temperature, see Fig. 1b, strongly indicates that temperature is irrelevant to the con- structed structure and could less infect the local energy barrier. The calculated polarization response to an external electric field (along the [100] axis) of the BNKT-20SSN (x =0.2) phase is displayed in Fig. 1c. The calculated P–E loop illustrates the polar structure evolution (O1–P1–N–P2–O2) responding quickly to an external electric field; the polarization distributions are close between O1 and O2 strongly prove the PNRs are reversible, resulting in a low remanent polarization (Pr). Energy storage performance, stability, and charge/discharge properties for practical application Based on the phase-field simulation results above, we selected BNKT- 20SSN as the target material for further study. Calcined BNKT-20SSN powders were used as the initial materials for preparing ceramic tapes by repeated rolling processing (RRP), which was employed to generate a dense structure with minimal porosity during sintering, enhancing the breakdown strength (Eb). As expected, the average grain size of the BNKT-20SSN ceramic (RRP) with compact microstructure is sub- stantially finer than that of the sample prepared by conventional cold isostatic pressing (Supplementary Fig. 1a, b). Correspondingly, as pre- sented in Supplementary Fig. 2, the theoretical Eb of the BNKT-20SSN ceramic (RRP) evaluated by the Weibull distribution experiments is much higher than that of the cold isostatic pressing sample, and the Weibull modulus β value of 19 (>10) was obtained, indicating the reliability of the breakdown strength34. The magnitude of Eb is an essential factor affecting the energy storage density of dielectric materials. Figure 2a shows the room-temperature P–E hysteresis loops of the BNKT-20SSN ceramic (RRP) measured from 100 kV cm−1 to the critical electric field (535 kV cm−1) at 10Hz. Of particular noteworthy is that the P–E loops show a near-zero Pr and negligible hysteresis during the charging/discharging process, even at a high electric field of 535 kV cm−1. In addition, the I–E curve reveals that the initial broad peak (P1) corresponds to the transformation of PNRs into a highly polarized state, while the subsequent peak (P2) signifies the relaxation of the highly polarized state, see Supplementary Fig. 3. The current value Article https://doi.org/10.1038/s41467-023-41494-1 Nature Communications | (2023) 14:5725 2 remains unchanged from its original value upon unloading the positive field, indicating the absence of an irreversible component in the field- induced phase transitions of BNKT-20SSN ceramic41,42. As can be observed from Supplementary Fig. 4, both the Pmax and ΔP increase rapidly as the electric field rises. However, the Pr value remains almost constant around zero even at the critical electric field, facilitating energy storage efficiency. As a result, a giant Wrec (9.22 J cm −3) and a prominent high-level of η (96.3%) >95% are simultaneously achieved in the BNKT-20SSN ceramic (RRP) under the critical electric field of 535 kV cm−1, which outperform the majority of recently reported lead- free bulk ceramics with admirable energy storage performance, as shown in Supplementary Fig. 5. Moreover, it was commendable that the BNKT-20SSN ceramic (RRP) demonstrates an ultrahigh energy storage performance at relatively high temperatures (~150 °C), sur- passing themajority of lead-free bulk ceramics and even certainMLCCs (Multi-Layer Ceramic Capacitors), see Fig. 2b5,6,8,9,17,20,23,28,29,40,43–53 and Supplementary Table 1. This achievement signifies the substantial potential of BNKT-20SSN ceramic (RRP) as a promising candidate for advanced high-temperature energy storage applications. Apart from the ultrahigh Wrec and η, another crucial criterion to determine the availability of high-power pulsed electronic compo- nents is the charge/discharge performance. The overdamped dis- charge property for the BNKT-20SSN ceramic (RRP) under various applied electric fields was measured at room temperature using a purpose-constructed resistance–inductance–capacitance (RLC) load circuit, and the regular overdamped oscillation waveforms reflect steady discharge behavior, as illustrated in Supplementary Fig. 6. Meanwhile, it can be observed that the discharge current rapidly approaches its peak (Imax = 8.2 A, at 500 kVcm−1) and then tends to diminish swiftly. Moreover, the high discharge energy density (Wd) ~5.2 J cm−3 can be liberated in a short period of time (t0.9, 90% ofWd is released) ~244 ns at 500 kVcm−1 (Fig. 2c). According to the foregoing data, the BNKT-20SSN ceramic (RRP) exhibits excellent charge/dis- charge characteristics, making it a promising candidate for pulsed power applications. To ensure steady functioning in complex settings, ideal frequency reliability, and temperature stability must be guaranteed. The frequency-dependent energy storage property of BNKT-20SSN T=300oC T=200oCT=100oCT=25oC T=400oC T=480oC a c b SymmetryVector x= 0. 00 x= 0. 10 x= 0. 20 x= 0. 30 Loading(E ) Unloading (E ) R R R T R R R T T T T R R R R R T T T T T R TT T R T T T Phase R C T b 0 1 2 3 4 0.1 0.2 0.3 0.4 0.5 0 P (a .u ) E (a.u) O1 O2 P1 P2 N T= 25oC Fig. 1 | The phase-field simulation results of (1-x)BNKT-xSSN. a Calculated microstructural evolutions under given fields with vector contours and phase dis- tributions with symmetry contours. b Magnification into the microstructure evolution of the BNKT-20SSN ceramic at various temperatures. c Calculated P–E hysteresis loop andmicrostructure evolution of the BNKT-20SSN ceramic at 25 °C. Arrows capture the polarization magnitude and orientation. Article https://doi.org/10.1038/s41467-023-41494-1 Nature Communications | (2023) 14:5725 3 ceramic (RRP) was investigated at 500 kV cm−1, as shown in Fig. 2d, all P–E hysteresis loops are slender with practically unchanged Pmax values at various frequencies. The corresponding results are recorded in Supplementary Fig. 7, it can be seen that the BNKT-20SSN ceramic (RRP) exhibits excellent frequency reliability (Wrec ≈ 8.63 ±0.18 J cm−3, ƞ ≈ 94.5%± 2.4%) across the entire frequency range (1–100Hz). Like- wise, Fig. 2e gives the temperature stability of BNKT-20SSN ceramic (RRP) at 500 kV cm−1, with the attainable Pmax value marginally decreasing as the enhancement of the random electric field raises the reaction rate of the PNRs during heating. As expected, this result fits well with the P–E curves derived from phase-field simulations, as pre- sented in Fig. 2f. Simultaneously, the corresponding microstructural evolution in the existence of the external electric field at various temperatures demonstrates that the domain size and polarization strength decrease as temperature increases (Fig. 2f and Supplemen- tary Fig. 8). Of particular significance is that the BNKT-20SSN ceramic (RRP) features not only a wide operating temperature range (25–160 °C) but also an unprecedently high Wrec (≈ 8.46 ±0.35 J cm−3) and ƞ (≈96.4 ± 1.4%) in contrast to certain other cutting-edge lead-free ceramics with excellent temperature stability (Fig. 2g, h)6,8,9,18,34,40,46,47. Furthermore, the comparisons of comprehensive performances (Wtot, Wrec, η, Wd, Wrec ~ 150 °C and η ~ 150 °C) between our study and recently reported lead-free systems are summarized in Fig. 2i5,6,8,40,45,47,54. It is clear that the BNKT-20SSN ceramic (RRP) covers a vast regionof the radardiagram, suggesting thatoverall considerable improvements of energy storage performance, particularly Wrec/η at high temperatures (around 150 °C), and excellent overdamped dis- charge properties can be achieved simultaneously in studied samples. Within the measured cycling numbers of 1–104 at 300 kV cm−1, the values of Pmax and Pr maintain stability as well, see Supplementary Fig. 9. In light of this, the BNKT-20SSN ceramic (RRP) outperforms other state-of-the-art lead-free ceramics in terms of overall electrical characteristics, implying a significant potential for practical applica- tion in high-performance pulsed power capacitors. Elucidation of multiphase-nanoregion coexistence and local atomic polar displacement Phase-field method calculation permits an efficient strategy for the subsequent sample preparation and optimization process. As indi- cated by the calculations, rich polymorphic polar nanoregions (PNRs) could be observed in the BNKT-20SSN system with the coexistence of the rhombohedral (R3c) phase and the tetragonal (P4bm) phase. High- resolution neutron powder diffraction (NPD) was then conducted to verify the two-phase coexistence. The Rietveld refinement over the 0 100 200 300 400 500 600 0 10 20 30 40 50 100 kV∙cm-1 150 kV∙cm-1 200 kV∙cm-1 250 kV∙cm-1 300 kV∙cm-1 350 kV∙cm-1 400 kV∙cm-1 450 kV∙cm-1 500 kV∙cm-1 535 kV∙cm-1 RT,@10 Hz Wrec = 9.22 J∙cm-3 �=�96.3% E (kV∙cm-1) P (μ C ∙cm -2 ) 0 100 200 300 400 500 0 10 20 30 40 50 160oC 25oC P (μ C ∙cm -2 ) E= 0 kV ·c m -1 ;T =2 5 o C E = 0 kV ·c m - 1 ;T =1 60 o C E= 0 kV ·c m -1 ; T =2 5 o C E= 0 kV ·c m -1 ;T =1 60 o C 20 40 60 80 100 120 140 160 0 3 6 9 12 15 8 Wrec ƞ Temperature (oC) @ 500 kV∙cm-1 Wrec≈8.46±0.35 J∙cm-3 0 25 50 75 100 95% W re c (J ∙cm -3 ) η � (% ) Δη/η ≤ 2 % 2 4 6 8 17 60 70 80 90 100 50 BKT BNT KNN NN AN BF BT MLCC 45 ) %( η 44 43 28 40 47 23 This Work 5 46 Wrec (J∙cm-3) 9 20 29 17 48 51 52 49 53 6 @~150 oC 16 8 −200 0 200 400 600 800 1000 0 1 2 3 4 5 6 100 kV∙cm-1 Time (ns) 200 kV∙cm-1W di s(J ∙cm -3 ) t0.9 ~ 244 ns 300 kV∙cm-1 400 kV∙cm-1 500 kV∙cm-1 0 10 20 30 40 50 P (μ C ∙cm -2 ) E (kV∙cm-1) @ 500k V∙cm-1 1H z 2H z 5H z 10 Hz 20 Hz 50 Hz 10 0H z 30 Hz 0 10 20 30 40 50 @ 500 kV∙cm-1 P (μ C ∙cm -2 ) 25 o C E (kV∙cm-1) 30 o C 14 0o C 12 0o C 90 o C 70 o C 50 o C 10 0o C 15 0o C 16 0o C 0 50 100 150 200 250 0 2 4 6 8 10 9 40 BNT BKT KNN BF BT AN NN BT-BNT-NN 8 34 46 47 6 Temperature (oC) This Work W re c (J ∙cm -3 ) 18 a d c e f g h b 0 2 4 6 8 10 0 1 2 3 4 5 6 0 3 6 9 0 20 40 60 80 100 0 20 40 60 80 100 0 2 4 6 8 10 BNT-based BKT-based KNN-based BF-based BT-based AN-based NN-based This work Wrec (J∙cm-3) η (%) Wtot (J∙cm-3) Wd (J∙cm-3) Wrec (J∙cm-3) ~150 oC~150 oC η (%) E (kV∙cm-1) i Fig. 2 | The energy storage performance under various conditions and charge/ discharge characteristics of BNKT-20SSN ceramic (RRP). a Room-temperature P–E loopsmeasured till the critical electric field of the BNKT-20SSN ceramic (RRP). b Comparisons of Wrec versus η (~150 °C) between our work with some recently reported lead-free bulk ceramics and certain MLCCs (Multi-Layer Ceramic Capa- citors). c Time dependence of discharge energy density under different electric fields (R = 202Ω). d Frequency-dependent, and e temperature-dependent P–E loops at 500kV cm−1. f Calculated P–E loops and microstructure evolution as a function of E at different temperatures. g Wrec and η as a function of temperature under 500 kV cm−1. h A comparison of energy storage performances across a wide operating temperature range between our study and other reportedbulk ceramics. i Comparisons of comprehensive properties (Wtot, Wrec, η, Wd, Wrec ~150 °C and η ~150 °C) between our study and other representative ceramics with excellent energy storage comprehensive performance. Article https://doi.org/10.1038/s41467-023-41494-1 Nature Communications | (2023) 14:5725 4 NPD pattern gives a successful result, suggested by χ2 of 2.87 and Rwp of 5.12%, and the fitted results of NPD data are presented in Fig. 3a and Supplementary Table 255. Direct R phase and T phase fractions by the refinement are determined to be 10.1(5) wt% and 89.9(5) wt%, respectively, over the whole pattern. The atom fractions were set as constants in the refinement due to the value shifts dramatically in each refinement cycle, indicating that the cations in BNKT-20SSN form an ideal solid solution where Sr2+ and (Sc0.5Nb0.5) 4+ ions may totally dif- fuse into the matrix of the BNKT. Besides, no additional peaks could confirm the existence of a superlattice structure. Unlike the powder X-ray diffraction (PXRD) pattern, the NPD pattern is more sensitive to cations in the structure. TheM-points (two odd numbers and one even number Miller indices), R-points (three odd numbers Miller indices, especially 111), and X-points (one odd number and two even numbers Miller indices) indicate the existenceof in-plane tiltingof theTphase in the structure with the Glazer notion of a0a0c+. Though all three indi- cator points could be observed in the NPD pattern, no peak splitting exists in eitherpoint. Theweak intensities could thus come from the in- plane tilting by the T phase, the local disorder-induced out-of-plane tilting by the cubic (C) phase, and/or cation-ordering over theA/B sites. However, the X-points are often the weakest intensities among the three indicator points, and the observed X-point shows a considerable intensity than the other two, particularly theM-points, suggesting the A-site disordering by the combination of Bi3+, Na+, K+, and Sr2+. Atomic-resolution spherical aberration transmission electron microscopywas used in the scanning transmission electronmicroscopy (STEM) mode along with a high-angle annular dark-field (HAADF) detector in order to analyze the local structure of multiphase- nanoregion coexistence. Precise atom arrangement of the 100/010 plane was captured and fitted by the 2D Gaussian function, see Fig. 3b. The arrangement presents a direct process of the formation of polar- ization, the coexistence of multiphase PNRs, and nanoregion distribu- tion. The 110-plane atom arrangement could hardly distinguish the R andTphases; the 111-plane atomarrangement showsonly theoverlapof A andB sites; the higherMiller indices planes projection images present insufficient resolution hindered by theMoiré fringe formation.With the processing by the 2D Gaussian function, the polarization vector could be straightforwardly described by a vector from the B-site cations center to the A-site cations corner, represented by the yellow arrows in Fig. 3b. The R and T phases could be directly identified by the long magnitude arrows, whereas the C phase shows near-zero polarization. The bond lengths calculated from the B-site cations and the A-site cations alongvertical andhorizontal directions are noted as c anda, and the c/a ratio was then used to distinguish the R phase and the T phase, see Supplementary Fig. 10. Apparently, the captured image presents multiphasePNRswithR andTphases coexisting in theCmatrix. The size of the same polarization direction and magnitude PNRs is ~2 nm. The coexistentmultiphase-nanoregiondestroys the long-range ferroelectric 20 40 60 80 100 120 140 160 0. 0 0. 5 1. 0 1. 5 T R Observed Calculated Difference Tetragonal (P4bm) Rhombohedral (R3c) Rwp = 5.12% χ2 = 2.87 λ = 1.622 Å In te ns ity /1 04 2� ��deg.� T phase 89.9(5)% R phase 10.1(5)%NPD data 11 0, M -p oi nt 11 1, R -p oi nt 21 0, X -p oi nt 21 1, M -p oi nt T T R C T T R T TT T T R R TR R R b c d f g e R T a T C R C R Fig. 3 | Crystal structure analysis and local structure analysis of the BNKT- 20SSN. a Constant wavelength neutron powder diffraction refinement result at room temperature. b Atomic-resolution HAADF-STEM polarization vector image along [001] direction. c–e Magnification of the marked areas in (b). f Polarization magnitude mapping, and g polarization angle mapping. Article https://doi.org/10.1038/s41467-023-41494-1 Nature Communications | (2023) 14:5725 5 order and produces abundant small-size PNRs, consistent with those predicted by the phase-field calculation. Moreover, the randomly dis- tributed nanoregions of different polarization directions and magni- tudes could reduce polarization anisotropy. The enhanced polarization magnitude implies that the internal field is strong. The facts stated above could all lead to a more accessible and quicker polarization response to the external electric field, higher energy efficiency, and better energy storage performance. To better understand the polar- izations in the sample, color-filled 2D patterns of summarized polar- ization directions andmagnitudes are plotted in Fig. 3f, g. The patterns are highly corresponding to the phase-field calculation, signifying the reliability and the practical value of the phase-field prediction to design the dielectric materials for energy storage. Composition-driven and temperature-driven features Pure BNT and (1-x)BNKT-xSSN ceramics were prepared to understand composition-driven and temperature-driven energy storage properties further. The powder X-ray diffraction (PXRD) patterns at room tem- perature (Supplementary Fig. 11a) show that all samples exhibit a typical BNT-based perovskite structure without impurities. The Rietveld refinement over PXRDpatterns of each component was then processed by GSAS II software to determine the phases, and the results are dis- played in Fig. 4a–c and Supplementary Fig. 1255. It is widely accepted that the BNT solid solution displays a rhombohedral (R3c) symmetry at room temperature31, consistent with the refinement result. The ratio of the R phase and the T phase gradually decreases with the increase of x, and the pure T phase was determined in the 0.82BNT-0.18BKT at 25SSN ceramic, identical to those from previous studies56–58. Temperature- dependent PXRDpatterns of the BNKT-20SSN in the temperature range of 25–200 °C (Supplementary Fig. 13) indicate no peak splitting or phase change occurs, suggesting good temperature stability. Further- more, all elements exhibit homogeneous distribution characteristics with no segregation inBNKT-20SSNceramic, see Supplementary Fig. 14. The genesis of optimum energy storage properties is intimately connected to the dynamic reaction of domain structures to external electric fields18,28. Here, the dynamic domain response to an applied voltage and the relaxation behaviors of the BNT, BNKT, and BNKT- 20SSN ceramics were characterized by employing piezo-response force microscopy (PFM), as displayed in Fig. 4d–i, the schematics of the applied voltage and region are similar to our previous work (Sup- plementary Fig. 15, 16)40. For the BNT ceramics (Fig. 4d, g), significant phase deviations and amplitude signals were observed even at a lower external voltage (10 V), and the overwhelmingmajority of domains did not flip after a 20min relaxation time, demonstrating a robust FE characteristic with substantial Pmax and Pr. A similar occurrence was also seen in the BNKT ceramic (Fig. 4e, h), albeit the feedback signal (after 20min) of the BNKT ceramic is slightly weaker than that of the BNT at an applied voltage of 10 V. On the contrary, the phase differ- ence and amplitude signals of the BNKT-20SSN ceramic (Fig. 4f, i) are weak in the entire electrical scan zone and become more potent at higher external voltages. After a 20-min relaxation duration, the sig- nals have significantly decreased. The facts mentioned above could all lead to a negligible Pr and hysteresis loss in the BNKT-20SSN ceramic, thus increasing the energy storage efficiency. 20 40 60 80 100 120 9% 91% R T Observed Calculated Difference Rhombohedral (R3c) Tetragonal (P4bm) Rwp = 4.36% χ2 = 1.00 ) .u .a( ytisnetnI 2 � deg. 15V10V 20V 30V 15V10V 20V 30V 15V10V 20V 30V 15V10V 20V 30V 15V10V 20V 30V 15V10V 20V 30V 15V10V 20V 30V 15V10V 20V 30V a b d c e f g 20 mins 20 minsih BNT BNKT-20SSNBNKT 20 mins 20V 30V g 15V10V 20V 30V 15V10V 20V 30V 15V10V 20V 30V 15V10V 20V 30V j k l m -100 -50 0 50 100 -60 -40 -20 0 20 40 60 BNT x= 0 x= 0.05 x= 0.10 x= 0.15 x= 0.20 x =0.25 E (kV∙cm-1) P (μ C ∙cm -2 ) 100 200 300 400 0 1k 2k 3k 4k 5k Temperature (oC) ytivitti mrep cirtceleid evitala R x= 0 x= 0.20 x= 0.10 x= 0.15 x= 0.05 x= 0.25 1kHz 1MHz 4.4 4.8 5.2 5.6 6.0 −3 −2 −1 0 1 �=11.5 BNKT x=0.05 �=11.0 x=0.15 �=13.3 x=0.20 �=17.2 x=0.10 �=10.9 �=16.1 x=0.25 �=10.1 BNT ln (-l n( )1+n(/i-1 )) ln (E) −200 −100 0 100 200 −60 −40 −20 0 20 40 60 x=0 x=0.10 x=0.20 x=0.30 P (μ C ∙cm -2 ) T= 25oC ln (E) 20 40 60 80 100 120 21 % 79 % R T 2θ� deg. Observed Calculated Difference Rhombohedral (R3c) Tetragonal (P4bm) Rwp = 3.94% χ2 = 0.79 ) .u .a( ytisnetnI 20 40 60 80 100 120 R 2 � deg. Rwp = 5.58% χ2 = 1.39 Observed Calculated Difference Rhombohedral (R3c) ) .u .a( ytisnetnI Fig. 4 | Phase analysis, relaxation behavior, dielectric and ferroelectric prop- erties of BNT and (1-x)BNKT-xSSN ceramics, along with their breakdown ana- lysis. The Rietveld refinement of PXRD patterns of a BNT, b BNKT, and c BNKT- 20SSN. Out-of-plane PFM phase images along with amplitude after polarization with different voltages and relaxation durations, d, gBNT, e,h BNKT, and f, i BNKT- 20SSN ceramics. j Temperature and frequency-dependent dielectric spectra. k Unipolar P–E hysteresis loops at 100kV cm−1. l Calculated P–E loops at 25 °C. m Weibull distribution of the breakdown strength on samples. Article https://doi.org/10.1038/s41467-023-41494-1 Nature Communications | (2023) 14:5725 6 In order to further investigate the mechanism of relaxation polarization behavior over a wide range of temperatures, the tem- perature (from room temperature to 400 °C) and frequency (from 1 kHz to 1MHz) dependent dielectric permittivity of pure BNT and (1-x) BNKT-xSSN ceramics were performed and depicted in Fig. 4j and Supplementary Fig. 17. The pure BNT ceramic possesses two typical temperature-dependent dielectric anomalous peaks, labeled as “Ts” (depolarization temperature shoulder) and “Tm” (temperature of the maximum dielectric constant) at low and high temperatures, respectively59–62. At the ambient temperature (Tamb), as displayed in Supplementary Fig. 17a, the pure BNT ceramic exhibits a non-ergodic relaxor state and behaves as a normal ferroelectric with a R3c sym- metry space group31,35,63. Afterward, with the addition of BKT (Sup- plementary Fig. 17b), theBNKTceramicwithR andTphase coexistence at MPB displays amuch higher maximum permittivity value (~ 4600 at 1MHz) than that of the pure BNT ceramic (~2500 at 1MHz). The Tm of the BNKT ceramic shifts to a lower temperature, and a relatively broad permittivity peak can be detected in the MPB composition64. Subse- quently, with increasing the content of SSN, themaximum value of the dielectric permittivity decreases step by step, see Fig. 4j. The two dielectric anomaly humps squint towards lower temperatures, and a gradually broaden temperature plateau of the dielectric constant can be observed. The analysis results of ln(1/ε´−1/εm´) versus ln(T – Tm) for BNT and (1-x)BNKT-xSSN ceramics are presented in Supplementary Fig. 18. It is observed that the calculated values of γ for (1-x)BNKT-xSSN ceramics lie within the range of 1.86−1.99, indicating the pronounced relaxor behavior. Noteworthy, the dielectric relaxor or frequency dis- persion behavior of the BNKT-20SSN ceramic could be noticed around Tamb, which allows for the formation of relaxor ferroelectric (a sig- nificant polar order–disorder arrangement) at room temperature and is beneficial to upgrading the energy storage performances32. The bipolar P–E hysteresis loops of all components mentioned above were performed under 100 kV cm−1 at room temperature, and the results are shown in Fig. 4k. The pure BNT ceramic exhibits a canonical FEbehaviorwith largePmax, Pr, considerable hysteresis, and a fully saturated P–E loop. A lower coercive electric field (Ec) and a slightly improved Pmax were obtained in the BNKT (MPB) ceramic, indicating a softened FE activity. The hysteresis losses decrease dra- matically, accompanied by slimmer P–E loops seen in the SSN- introduced compositions, and are consistent with those calculated from the phase-field simulationmethod (Fig. 4l). To better understand composition-driven breakdown strength, the values of theoretical Eb of all ceramic samples were evaluated by the Weibull distribution experiments, see Fig. 4m. With increasing the SSN concentration, the theoretical Eb values first increased and then decreased, reaching a maximum at the BNKT-20SSN ceramics. To investigate the energy storage performance of the ceramics, the P–E hysteresis loops were performed on a ferroelectric analyzer. As depicted in Supplementary Fig. 19, the room-temperature P–E loops of the BNKT-20SSN ceramic were measured from 100 kV cm−1 to the critical electric field (385 kV cm−1) at 10Hz. As a consequence, a great Wrec of 5.23 J cm−3 along with a high energy efficiency of 90.2% are simultaneously achieved in the BNKT-20SSN ceramic, demonstrating a substantial promotional impact of combinatorial-optimization strategy guided by phase-field simulations on energy storage performance. Discussion The selection of promising dielectric materials to combine is a foun- dational but inevitable procedure in material science. The presented phase-field method assistant strategy could be used to investigate dielectric material with high energy storage performance upon a wide working temperature range5,40. By learning the structural evolution, polarization distribution, and characteristics of PNRs in combinations of BNT-BKT-SSN atmorphotropic phase boundary that affords possibly engineerable ceramic materials from the phase-field calculation simulation strategy, we could initiatively decide and select the optimal composition for further study to achieve the remarkable performances. To state, various combinations in perovskite structure have been considered to acquire substantial polar nanoregions in the structure to enhance energy storage performances. The initial BNT ceramic shows a considerable ferroelectric performance, but the Pr is too large for energy storage applications31,32,37; following the BNKT binary system at the morphotropic phase boundary is an ideal fundament for massive afterward studies56,61. We intentionally choose ionic radius and valence distinguishable cation pairs as guests for targeting a solid solution and thus enable the discovery of diverse ferroelectric/energy storage performances. The phase-field method supports an efficient strategy of rational design of a targeted material with relaxor behavior by implying reduced PNRs, thermal stability, reversible response to the external electric field, high Pmax, and low Pr, all of which could effec- tively optimize the ferroelectric/energy storage performances. The designed BNKT-20SSN ceramic (RRP) shows extraordinary perfor- mances of giantWrec andultrahigh η, unprecedented temperature, and frequency stabilities. Multi-methods analysis describes the occurrence of the performances. The small, uniform, dense grain structures by the RRP process method guarantee the breakdown strength and sub- sequent applications. The coexisting R/T/C multiphase nanoregions confirmed by atomic-scale TEM provide small-scaled PNRs with dif- ferent polarization distributions in both magnitude and orientation, suggesting a relaxor-behavior FE with large Pmax of energy storage density and small Pr of energy loss and allowing the polarization of nanoregions flipping along the same directions with lower energy and higher dynamics. ThePNRsof theBNKTceramicwere confirmedwith a size of ~200nm,and theguest-invitedBNKT-20SSN reduced the size to ~2 nm65. Notably, typical relaxor REs present only minor differences in polarization magnitude but only in orientation, which differs from what we reported here1,66. This phenomenon may be because of the considerable amount of SSN concentration, x = 0.20, and the fact that the A site is composed of 0.42Bi-0.34Na–0.08K–0.16 Sr, introducing considerably strong local heterogeneity and destabilizing the polar- ization ordering. The system retains the original PNRs of BNKT, but the PNRs are reduced and dissociated, forming a local order–disorder coexistence system. The metastable order–disorder system in BNKT- 20SSN presents a lower Pmax than BNKT, but the abundant PNRs pro- mote the performance of energy storage. Moreover, BNKT-20SSN ceramic (RRP) exhibits unprecedented temperature and frequency stabilities where the Wrec and η typically decrease when temperature increases, indicated by the decrease of Pmax and the occurrence of the non-negligible Pr. This case may come from a series of benefits. First, the average structure is stable upon temperature change to 200 °C. Second, the heterogeneity in the metastable order–disorder system may act as a pinning effect and hinder further atom thermal vibration- induced local structure change67,68. Finally, the randomly distributed PNRs also show some order–disorder, inviting a suitable local energy barrier to the external electric field and frequencies, indicated by the flat temperature-dependent dielectric response. In summary, a rational phase-field calculation guided dielectric material designing method is presented to achieve small-scale and stable PNRs with overall well-behaved energy storage performance theoretically and experimentally. The so-calcined BNKT-20SSN guided by calculations with improved RRP techniques shows a Wrec of 9.22 J cm−3 and an ultrahigh ƞ of ~96.3% at large external electric field 535 kV cm−1, accompanied with excellent temperature-insensitive (Wrec ≈ 8.46 ± 0.35 J cm−3, ƞ ≈ 96.4 ± 1.4%, 25–160 °C) and frequency stability (Wrec≈ 8.63 ±0.18 J cm−3, ƞ ≈ 94.5% ± 2.4%, 1–100Hz) at 500 kV cm−1. This research provides a paradigm for the synergistic development of lead-free dielectric materials with enhanced compre- hensive energy storage capacity over a broad operating temperature range to fulfill the pressing demands of modern energy storage components. Article https://doi.org/10.1038/s41467-023-41494-1 Nature Communications | (2023) 14:5725 7 Methods Ceramics preparation The lead-free ceramics with the composition of (1-x) Bi0.5(Na0.82K0.18)0.5TiO3-xSr(Sc0.5Nb0.5)O3 (abbreviated as BNKT-xSSN, where x =0, 0.05, 0.10, 0.15, 0.20, and 0.25) were fabricated via a conventional solid-state reaction method. The pre-dried oxides and carbonate powders of Bi2O3 (≥99.9%), Na2CO3 (≥99.8%), K2CO3 (≥99.5%), TiO2 (≥99.9%), SrCO3 (≥99.5%), Sc2O3 (≥99.9%) and Nb2O5 (≥99.99%) (Aladdin Chemical Reagent Co., Ltd., CN) were used as the starting materials. The raw powders were weighed according to the stoichiometric ratio, and 2 wt.% excess of Bi2O3, Na2CO3, and K2CO3 were added to compensate for the weight loss at high temperatures. The mixtures were planetarily ball-milled for 24 h at 300 rpm with ethanol in nylon jars using Y-stabilized zirconia balls as milling media. After drying, the mixtures were calcined at 800–850 °C for 4 h in an alumina crucible and ball-milled again similarly. After drying and sieving, the powders were uniaxially pressed into pellets at 10MPa in a 12mm diameter stainless steel cylindrical die. Then, the preformed green ceramic sheets were pressed at 300MPa for 3min through cold isostatic pressing. Finally, the samples were sintered at 1140–1200 °C for 4 h with a heating rate of 4 °Cmin−1 in closed alumina crucibles. To minimize the evaporation of the volatile elements Bi, Na, and K, the samples were embedded in powders of the same composition. For the electrical measurements, the silver paste was coated on both surfaces of the sintered samples and fired at 650 °C for 20min to form electrodes. Repeated rolling processing The green ceramic tapes with BNKT-20SSN composition were pre- pared by a repeated rolling processing (RRP) method, in which the pre-sintered powders were used as raw materials. After sieving, the calcined powders of BNKT-20SSN were thoroughly mixed with poly- vinyl alcohol (PVA). The extrusion force generated by the two tightly contiguous rollers could greatly improve the density of the green ceramic tape and also help to form a dense structure during sintering with minimal porosity, resulting in a significant increase in Eb. And then, the ceramic tapes prepared by RRP were punched into disks with a diameter of 12mm and then calcined at 650 °C for 2 h to burn out the PVA. Subsequently, the greendiskswere embedded in the pre- sintered powders of the same composition and sintered at 1070–1140 °C for 2 h using a double crucible method, so that the volatilization of Bi, Na, and K elements during high-temperature sin- tering could be suppressed. Structural characterization The phase purity and crystalline structure were characterized at an X-ray diffractometer (SmartLab-3 kW, Rigaku, Tokyo, Japan) with Cu Kα radiation. Neutron diffraction patterns were collected on the high- resolution powder diffractometer ECHIDNA at ANSTO over the angu- lar range 8 ≤ 2θ/° ≤ 160, using a step size Δ2θ = 0.05° and a wavelength of 1.622Å at room temperature. TheRietveld refinements onPXRDand NPDwere analyzed using the programGSAS II55. Themicrostructure of the ceramics was observed by field-emission scanning electron microscopy (FE-SEM, FEI Quanta 250 FEG, Hillsboro, Oregon, USA). The Nano Measurer software was used to calculate the average grain size of the samples based on the SEM images. The HAADF atomic-scale images were acquired using an atomic-resolution STEM (aberration- corrected Titan Themis G2microscope) and processed by 2DGaussian fitting in MATLAB scripts to evaluate the polarization vector, magni- tude, and angle maps. Dielectric measurements For the dielectric measurements, the silver paste was coated on both surfaces of the sintered samples and fired at 650 °C for 20min to form electrodes. Temperature and frequency-dependent dielectric permittivity and tanδ were tested by an accurate inductor– capacitance–resistance (LCR) meter (E4980A, Agilent, USA) with a 3 °Cmin−1 heating rate. Ferroelectric measurements The room-temperature P–E loops with a triangle signal of 10Hz and temperature and frequency-dependent P–E loops weremeasured on a ferroelectric analyzer (aix ACCT, TFAnalyzer 2000,Aachen,Germany). For the P–E loops measurements, the sintered disks were polished to ≈35μm and then sputtered with gold electrodes on both surfaces. Pulsed charge–discharge test The change–discharge properties of ceramics with a thickness of ≈50μm were investigated via a specially designed resistance, induc- tance, and capacitance (RLC) load circuit. Dielectric breakdown test The breakdown performances were measured via a ferroelectric ana- lyzer (aix ACCT, TF Analyzer 2000, Aachen, Germany). The statistical Eb properties for perovskite structure ceramics are generally estimated by Weibull distribution equations: Xi = ln(Ei), Yi = ln(ln(1/(1-Pi))), Pi = i/ (n + 1), where Ei is the experimental breakdown strength of each sam- ple in ascending order, Pi is the cumulative probability of dielectric breakdown, n represents the total number of samples for ceramics. The Weibull distribution modulus, which can estimate the value of Eb, was represented by the slope of the fitting line. PFM characterization The surface morphology, dynamic response, and relaxation behavior of the domains under external voltages were investigated by piezo- electric force microscopy (PFM, MFP-3D, Asylum Research, USA). The surfaces of each ceramic specimen used for PFM measurement were finely polished with polycrystalline diamond polishing paste. Phase-field simulations Phase-field simulations have been employed to investigate a single crystal undergoing the Cubic (C) to Tetragonal (T) to Rhombohedral (R) ferroelectric transition. This study encompasses varying defect doping concentrations in the range of x =0 to 0.30, denoted as BNKT- xSSN. The comprehensive evaluation of the ferroelectric system’s total free energy is expressed as follows: F = Z V f bulk + f grad + f couple � � dV + Z V f elas + f elec � � dV ð1Þ where fbulk represents the bulk free energy density, f bulk =α1 P2 1 +P 2 2 +P 2 3 � � � α11 P2 1 +P 2 2 +P 2 3 � �2 +α12 P2 1P 2 2 +P 2 2P 2 3 +P 2 1P 2 3 � � +α112 P4 1 P 2 2 +P 4 2P 2 3 +P 4 1 P 2 3 + P 2 1P 4 2 +P 2 2P 4 3 +P 2 1P 4 3 � � +α113 P2 1P 2 2P 2 3 � � +α111ðP2 1 +P 2 2 + P 2 3Þ 3 ð2Þ where αij represents the coefficient, the value of which is contingent upon both concentration c and the temperature T. fgrad represents the gradient energy density. f gradient = 1 2 G11½ P1,1 � �2 + P1,2 � �2 + P1,3 � �2 + P2,1 � �2 + P2,2 � �2 + P2,3 � �2 + ðP3,1Þ2 + ðP3,2Þ2 + ðP3,3Þ2� ð3Þ where G11 signifies the coefficient for gradient energy, while fcouple pertains to the dipole effect induced by doping. Article https://doi.org/10.1038/s41467-023-41494-1 Nature Communications | (2023) 14:5725 8 f couple = � R d3x P i = 1,2,3PiðxÞ � φlocðxÞ, where φlocðxÞ is the dipolar field generated through doping, expected to exhibit a random dis- tribution and remain unchanged during the cooling process. felas cor- responds to the energy density associated with long-range elastic interactions, and felec pertains to the energy density attributed to electrostatic interactions. f elas = 1 2 cijkleijekl = 1 2 cijklðεij � ε0ij Þðεkl � ε0klÞ, where cijkl denotes the elastic constant tensor, εij signifies the total strain, and ε0kl represents the electrostrictive stress-free strain, i.e., ε0kl = QijklPkPl. felec = fdipole + fdepola + fappl, where fdipole is the dipole- dipole interactions arising from polarization, fdepola, represents the depolarization energy density, and fappl, denoting the energy density resulting from an applied electric field. 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Author contributions The work was conceived and designed by W.C.Z., D.Z., and W.C.Z. fabri- cated the samples, tested the energy storage, dielectric, structure, sta- bility, and other properties, and processed related data, assisted by D.Z., D.X., andD.L. TheSEM imageswerefilmedandprocessedbyG.Y. andT. Z. The HAADF-STEM images were filmed and processed by H.M.J. and D.X. The PFM images were filmed and processed by M.K.X. and W.F.L. The neutron diffraction data were processed and analyzed by D.X. and M.A. Temperature-dependentXRDdatawereprocessedandanalyzedbyD.E.S. The manuscript was drafted by W.C.Z. and revised by D.Z. and D.X. The phase-field simulations were performed by D.W. and discussed with D.Z. and W.C.Z. All authors participated in the data analysis and discussions. Competing interests The authors declare no competing interests. Article https://doi.org/10.1038/s41467-023-41494-1 Nature Communications | (2023) 14:5725 10 Additional information Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41467-023-41494-1. Correspondence and requests for materials should be addressed to Diming Xu, Dong Wang or Di Zhou. Peer review information Nature Communications thanks Xin Chen, HaixueYan and theother anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available. Reprints and permissions information is available at http://www.nature.com/reprints Publisher’s note Springer Nature remains neutral with regard to jur- isdictional claims in published maps and institutional affiliations. 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To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/. © The Author(s) 2023 Article https://doi.org/10.1038/s41467-023-41494-1 Nature Communications | (2023) 14:5725 11 https://doi.org/10.1038/s41467-023-41494-1 http://www.nature.com/reprints http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/ Broad-high operating temperature range and enhanced energy storage performances in lead-free ferroelectrics Results Phase-field simulations of the structure construction process Energy storage performance, stability, and charge/discharge properties for practical application Elucidation of multiphase-nanoregion coexistence and local atomic polar displacement Composition-driven and temperature-driven features Discussion Methods Ceramics preparation Repeated rolling processing Structural characterization Dielectric measurements Ferroelectric measurements Pulsed charge–discharge test Dielectric breakdown test PFM characterization Phase-field simulations Data availability References Acknowledgements Author contributions Competing interests Additional information