Ultrahigh energy storage density and efficiency in AgNbO₃-based ceramics by percolating interaction between antipolar regions and defect pairs

Abstract

A critical challenge for the application of lead-free antiferroelectrics in energy storage systems is their poor thermal stability and low efficiency when the superior energy storage density is attained, primarily due to the inherent first-order nature and narrow temperature window of antiferroelectric-to-ferroelectric transitions. Here, we elucidate a unique percolating interaction between antipolar regions in antiferroelectrics and engineered defect pairs using density functional theory and phase field calculations. Strategic distribution of the strongly coupled Li-Ta pairs in AgNbO₃ fosters a percolating interaction that facilitates antipolar rotations, enabling a pronounced polarization change with minimal hysteresis. Guided by theoretical calculations, a large recoverable energy storage density of 12.8 J/cm³, with a high efficiency of 90%, is achieved at room temperature in Ag_0.95Li_0.05Nb_0.35Ta_0.65O₃ ceramics. Moreover, the superior energy storage performance can remain stable within a wide temperature range from −70 to 170 °C, which paves the way for application in advanced energy capacitors.

A percolating interaction between antipolar regions and engineered defect pairs facilitates antipolar rotations, enabling superior energy storage performance in AgNbO₃-based ceramics.

Introduction

The rapid development of advanced pulse power systems and microelectronic devices, e.g., hybrid electric vehicles and miniaturized pulsed energy generators, drives a significant demand for high-performance energy-storage dielectric capacitors that exhibit both large energy storage density and efficiency¹. To date, although most dielectrics can exhibit inherently fast charge-discharge rates and ultrahigh power density, it remains difficult to simultaneously achieve significant enhancements in both energy storage density and efficiency. This challenge is particularly evident as the energy storage density of dielectrics is still much inferior to that of electrochemical batteries, which is regarded as a key and long-standing bottleneck for energy storage dielectrics^2–4.

The widely used estimation equation for recoverable energy storage density of dielectrics, i.e., $U_{\mathrm{e}}=-{\int }_{P_{\max }}^{P_{\mathrm{r}}}EdP$, clearly suggests that antiferroelectrics hold significant prospective for substantial U_e due to the large polarization change (ΔP) by the field-induced phase transition from antiferroelectric (AFE) state displaying low remnant polarization (P_r) to resultant ferroelectric (FE) state exhibiting large maximum polarization (P_max)^5–8. Therefore, antiferroelectric systems are more conducive to achieve larger energy storage density than representative relaxor ferroelectric and superparaelectric systems if the driving field is set to the same as the threshold of AFE-FE transition⁸. The traditional antiferroelectrics for promising U_e are lead-based PbXO₃ (X = Hf, Zr, etc.) systems. But the growing significant environmental and human health concerns associated with the use of Pb-based materials have driven significant efforts to develop high-performance lead-free AFEs for energy storage applications^9,10.

Over the past few decades, AgNbO₃ (AN)-based system has been regarded as one most promising lead-free antiferroelectric systems for energy storage capacitors. These systems can exhibit a large field-induced maximum polarization and achieve a relatively low remnant polarization after the removal of the electric field to zero. It is further understood that pure AgNbO₃ shows an antiferroelectric-dominated ferrielectric phase near room temperature, owing to the low energy difference between antiferroelectric Pbcm and ferrielectric Pmc2₁ phases^10,11. Li doping transforms the antiferroelectric-dominated ferrielectric phase in AgNbO₃ into a ferroelectric R3c phase^12,13. In practice, by introducing dopants such as La, Bi, Nd, and Na to replace Ag at the A-site, the tolerance factor of AgNbO₃-based systems will be reduced^14–16. The enhanced stability of the antiferroelectric phase facilitates the boosts of the U_e up to ~8 J/cm³. But low efficiency (η) calculated by U_e/(U_e + U_loss), still remains lower than 80% due to the large electric hysteresis (ΔE) of antiferroelectric-ferroelectric transitions^17–19, where the energy loss U_loss is simulated by the enclosed area of polarization–electric (P–E) field loops. The low η (i.e., the high loss) can generate excess heat, posing additional risks of material and device failure¹⁰. The design of relaxor antiferroelectrics via random chemical heterogeneity represents a viable strategy for enhancing η by suppressing the AFE-FE phase transition and stabilizing antiferroelectric nanodomains^20–23. Combining relaxor antiferroelectric design with tolerance factor manipulation enhances the η of AgNbO₃-based ceramics while maintaining relatively high U_e. Representative examples include AgNbO₃-AgTaO₃ ceramics (U_e of 6 J/cm³ and η of 90%)²⁴, (Ag, Na, La)NbO₃ ceramics (U_e of 11.4 J/cm³ and η of 80%)²⁵, and (Ag, La)(Nb, Ta)O₃ ceramics (U_e of 8.6 J/cm³ and η of 85%)²⁶. However, the further optimization of energy storage efficiency by a stronger frustration of the AFE-FE phase transition leads to a sharp decrease in P_max. Enhancing the recoverable energy storage density (U_e) necessitates increasing the applied electric field. Notably, over-elevating the applied electric field would generate an increase of conductive leakage current, easily leading to the occurrence of dielectric breakdown and degrading the device lifetime, especially with varying temperatures^1,27. To date, achieving high η (>85%) in the AgNbO₃-based ceramics is always accompanied by relatively low U_e (<9 J/cm³). It is also noteworthy that the high U_e of most reported lead-free antiferroelectric ceramics just appears within the temperature range from room temperature to 150 °C²⁸, not covering the lower temperatures to expand the usability in the extreme climate conditions.

Recently, it has been revealed that the percolating electric field formed by incorporating dopants with different radius and valence into ABO₃ ferroelectric matrix, can break the long-range-ordered transitions to nano-sized glassy transitions displaying low hysteresis^29,30. Additionally, the interaction of the local percolating field will increase the driving electric field for the maximum polarization outputs near ferroelectric transitions^30–34. Thus, it can be anticipated that the proper designed percolating field into AgNbO₃ systems could not only decrease the scale of AFE-FE phase transition regions for low P–E field hysteresis (low ΔE, i.e., high energy storage efficiency), but also hinder the electrical domain wall motion to ascend the amplitudes of forward switching field (E_AFE-FE) and backward switching field (E_FE-AFE), which is beneficial for larger energy storage density. As shown in Supplementary Fig. 1, the evolution of the Landau free energy profile clearly illustrates the principle for the changes in E_AFE-FE, E_FE-AFE, and ΔE (E_AFE-FE−E_FE-AFE) with increasing the designed local field. Thus, this designed approach enables simultaneous enhancements in both U_e and η. Moreover, the optimization of nano-sized domain structures and the strong percolating interaction energy in AgNbO₃ could increase the thermal stability of electric domain configurations, which is important for optimizing the temperature stability of superior energy storage density and efficiency.

Motivated by this analysis, our multi-scale calculation reveals that the coordinated effect of Li⁺ and Ta⁵⁺ cations with adjacent oxygen octahedrons in AgNbO₃ superlattice structures can lead to the percolating dipole interaction field in the antiferroelectric matrix for the simultaneous decrease of ΔE and increase of E_AFE-FE due to the special rotated antipolar alignment, meanwhile remaining large polarization in the saturation state. Consequently, a remarkable U_e of 12.8 J/cm³ with a high η of 90% is achieved at room temperature in Ag_0.95Li_0.05Nb_0.35Ta_0.65O₃ (ANLi-65Ta) ceramics. Intriguingly, the superior energy storage performance of ANLi-65Ta ceramics maintains the stability within the temperature range from −70 to 170 °C. To our best knowledge, this performance with remarkable thermal stability exceeds that of the most reported lead-free bulk ceramics, overcoming the long-standing bottleneck in lead-free energy storage dielectrics.

Results

Atomic-scale design of Li-Ta pairs within the antipolar regions of AgNbO₃

In the antiferroelectric state of AgNbO₃, the characteristic alignments are evidenced by the two adjacent antiparallel polar states, i.e., antipolar region^22,23. Under an adequate electric field, the antipolar alignment can be reoriented into the same direction, corresponding to the field-induced ferroelectric state. The polar state is used to describe each polarization variant within the lattice. Here, 2×2×1 supercell structures of the antiferroelectric phase (Pbcm) in AgNbO₃ were built by using density functional theory (DFT) calculations. The representative positions of Li⁺ and Ta⁵⁺ cations within the AgNbO₃ unit cell structure are illustrated in Fig. 1a, where different cations and anions are marked by spheres with distinct colors. Figure 1b shows the projection of the lattice structure in the y–z plane for AN, AN-Li, and ANLi-Ta, where AN-Li and ANLi-Ta represent Li⁺ cation-doped AgNbO₃ superlattice and the composition with incorporation of Ta⁵⁺ cation into the AN-Li superlattice, respectively. The antipolar alignments in pure AgNbO₃, as indicated in the upper and lower dashed blue rectangles, are determined by the displacement of Nb⁵⁺ cations in NbO₆ octahedral units. The potential substitution sites for Li⁺ cations in AgNbO₃ supercell structure can be classified into two types: Li1, located within the polarization region, and Li2, situated at the antiferroelectric boundary region, as indicated by the dashed yellow and black rectangles in Fig. 1b, respectively. Supplementary Fig. 2a–c reveals that when Li⁺ cations are placed at the low-energy polarization region (Site of Li1) rather than the high-energy boundary (Site of Li2), a larger additional position shift of Nb along the y-axis can be achieved, resulting in a larger local polarization. Such a localized mechanism is consistent with the previous experimental observations, which revealed that Li dopants can thermodynamically stabilize the R3c ferroelectric phases of AgNbO₃ due to the A-site and B-site coordinating displacements, especially when the substitution level of Li for Ag reaches ≥5%^12,35–37. In addition, the substitution of Li⁺ cations for Ag⁺ cations causes the decreased lattice parameters because of the smaller ionic radii (1.17 Å CN = 12) of Li⁺ cation than that (1.48 Å CN = 12) of Ag⁺ cation³⁵. Additionally, the substitution of Ta for Nb results in stronger ionic bonding and compresses oxygen octahedrons⁹.

Fig. 1. Atomic-scale mechanism for percolating interaction between antipolar regions and Li-Ta pairs.

a The schematic AgNbO₃ (AN) perovskite structure where Li⁺ cation substitutes Ag⁺ cation at A-site and Ta⁵⁺ cation replaces Nb⁵⁺ cation at B-site. b Stable superlattice structures and associated polarization distributions of the AN, AN-Li, and ANLi-Ta after complete relaxation, where P₁ represents the induced extra polarization by Li dopants, indicating the induced ferroelectric (FE) state. c The polarization distributions in ANLi-Ta superlattice show that the formation of strongly coupled Li-Ta pairs could rotate the antipolar states, resulting in the transformation from the normal antipolar state of the antiferroelectric (AFE) system represented by antiparallelly arranged blue lines to the rotated antipolar state (i.e., rotated antiferroelectric state, RAFE) represented by colored lines with various degrees of rotation.

To systematically investigate the site-dependent energy of Ta substitution in the AN-Li superlattice, the possible substitution sites can be classified into 16 distinct types, based on the symmetry relation and the distance from the Li doping site (see Supplementary Fig. 2d). Supplementary Fig. 2e and Table 1 display the relative energies of the Ta doping sites (taking the lowest-energy Site3 as zero) and their position differences (i.e., the atomic displacement of B-site cations) along the z-direction. As shown in Supplementary Fig. 2e, Ta⁵⁺ cations preferentially substitute for Nb⁵⁺ cations at sites with lower relative energy. In such cases, the resulting atomic displacement remains minimal, leading to only a slight rotation of the antiparallel polarization. However, with increasing Ta concentration, a growing fraction of Ta⁵⁺ cations randomly incorporates into sites adjacent to Li-doped sites, such as Sites 1, 2, 5, 6, and 10. These proximal substitutions correspond to a notable increase in relative energy, which reflects the enhanced local coupling between Li⁺ and Ta⁵⁺ cations. These strongly coupled Li-Ta configurations are conceptualized as defect pairs. Consequently, the atomic displacement along the z-axis is substantially enlarged, inducing a pronounced rotation of the antiparallel polarization, as depicted in Fig. 1c. The rotation of polarization for antipolar regions is calculated and illustrated in Supplementary Fig. 3. With increasing Ta concentration, the enhanced interaction between strongly coupled Li-Ta pairs and antipolar regions will redistribute the local polarization and lead to the formation of high-percentage rotated antipolar regions (see Fig.1c), referred to as the rotated antiferroelectric (RAFE) state, eventually forming a percolating network that partitions the long-range-order antiferroelectric states into coexisting nano-sized antipolar and polar regions.

Predicted energy storage properties of RAFE sate by phase field simulations

To reveal the influence of percolating interaction between antipolar regions and defect pairs on theoretical U_e and η potentials, a phase-field model has been developed for the ANLi-xTa system before carrying out experiments for cost-effectiveness, where ANLi-xTa represents the detailed composition with the introduction of Ta into Li-doped AgNbO₃, and x is the atomic percent of Ta. The detailed energy descriptions and thermodynamic parameters used in the simulations are given in the Methods section, where dipole interaction energy between antipolar regions in AgNbO₃ and strongly coupled Li-Ta pairs governs the formation and growth of the rotated antipolar regions (see Supplementary Fig. 4). Only strongly coupled Li-Ta pairs with adequate dipole interaction energy can generate and expand the RAFE state. Notably, unlike previously reported relaxor antiferroelectrics^24,38, the incorporation of strongly coupled Li-Ta pairs can greatly hinder the decrease of local polarization magnitude in the AgNbO₃ system (see Supplementary Fig. 2c). Additionally, with increasing Ta concentration, a high interaction field between strongly coupled Li-Ta pairs with neighboring antipolar regions will lead to the enhanced stability of the antiferroelectric state. It will ascend the switching field for AFE-FE transitions as expected, resulting in a possible boost of U_e in ANLi-xTa antiferroelectrics. Owing to the fact that pure AgNbO₃ ceramic possesses a breakdown strength (E_b) of ~180 kV/cm (see Supplementary Fig. 5) and the corresponding calculated strain is ~0.25% in our established phase-field modeling. Leveraging this correlation, a rational assumption for our designed systems is made that the E_b for each ANLi-xTa composition is determined by the electric field at which the system reaches the same critical strain of 0.25%^39–41, while the detailed methodology for determining E_b is included in the Supplementary Information.

Figure 2a shows that the pure AgNbO₃ exhibits an antiferroelectric-dominated state characterized by nearly zero remnant polarization and long-range-order antiferroelectric domain configurations in the micro scale, consistent with the reported¹⁰. Upon the introduction of Li, the ferroelectric states emerge, resulting in the appearance of “butterfly” strain–electric (S–E) field curve and a classic P–E field loop of ferroelectrics under the E_b. With further increasing Ta concentration to gradually occupy the proximity position of Li, more rotated antipolar regions are produced as expected especially as the Ta concentration rises from approximately 45% to 65% and the associate S–E/P–E loop of each composition under applying the field along [100] as shown in Fig. 2b, c becomes significantly slimmer due to the miniaturized antipolar and polar regions and the decreased ΔE for AFE-FE transition. With increasing Ta content, the long-range-order antiferroelectric and ferroelectric domains have been progressively partitioned into the ferroelectric and antiferroelectric nanodomains. Concurrently, the formation of rotated antipolar regions with strong local dipole fields stabilizes ferroelectric and antiferroelectric nanodomains and hints at the domain wall motion. This structural evolution strongly delays the field-induced antiferroelectric-ferroelectric transition, resulting in low polarization under low electric fields. However, a sufficiently increased electric field eventually triggers the AFE-FE transition, leading to a substantial rise in polarization. As a result, the P_max at field application direction [100] increases from 0.34 to 0.45 C/m² under the respective E_b. The corresponding field-induced phase evolution is presented in Supplementary Fig. 6. For the composition with the highest proportion of RAFE state, the most antiferroelectric and ferroelectric nanoregions gradually transform into the RAFE state when the E_b field is applied. Figure 2d provides schematic representations of characteristic polarization vector mapping for ferroelectric, RAFE, and antiferroelectric states, illustrating that the RAFE state exhibits more disordered polarization directions, in contrast to the parallelly ordered polarization arrangement of the ferroelectric state and the completely antiparallel arrangement of the antiferroelectric state. Figure 2e illustrates that the phase fraction of the RAFE state significantly increases with higher Ta concentrations due to the ascending percolated interaction field. Additionally, it has been revealed that AgTaO₃ may be quantum paraelectric state ($R\overline{3}c$)⁴², rather than an antiferroelectric (Pbcm) state of AgNbO_3. To clarify the microstructural basis of superior AgTaO₃-abundant state (ANLi-65Ta), the formation energy difference between $R\overline{3}c$ and Pbcm phases of different Nb-doped AgTaO₃ compositions at absolute zero (0 K) is calculated, as shown in Supplementary Fig. 7. The calculation results clearly show that the antiferroelectric phase is more stable than quantum paraelectric phase when the atomic percent of Ta falls below 80%, verifying the antiferroelectric feature of ANLi-65Ta.

Fig. 2. Phase-field calculations are used for determining the energy-storage performance of formed RAFE.

a RAFE design approach by increasing the percolating interaction between defect pairs and antipolar regions, including the associated evolution of FE, RAFE, and AFE distributions. b, c The evolution of calculated strain–electric (S–E) field and polarization–electric (P–E) field loops with varying ANLi-xTa (x = 0, 5, 25, 45, and 65) composition, respectively. d The characteristic features of polar vectors for FE, RAFE, and AFE states. e Phase fraction evolution of different microstructures with changing ANLi-xTa and AN composition. f–h Breakdown strength (E_b), Energy storage efficiency (η), and Recoverable energy storage density (U_e) variations of ANLi-xTa system with increasing Ta concentration.

Figure 2f–h demonstrates that a simultaneous enhancement in E_b, U_e, and η can be achieved by forming more rotated antipolar regions, which is driven by a percolating interaction between strongly coupled Li-Ta pairs and the antipolar regions in the AgNbO₃ antiferroelectric matrix. Notably, the theoretical E_b, η, and U_e are markedly increased from 180 kV/cm, 44.5%, and 1.8 J/cm³ at AgNbO₃ to 820 kV/cm, 96.6%, and 15.7 J/cm³ for ANLi-65Ta, respectively, by inducing the large proportion of RAFE (~90%). The corresponding field-induced strain curves transition from a steep slope to a slanted slope (see Fig. 2b), enhancing the stability of materials and electromechanical breakdown properties⁴⁰. After introducing Li into AgNbO₃ (i.e., ANLi-0Ta), the formation of a long-range-order ferroelectric phase leads to a largely enhanced remnant polarization upon removal of the external electric field, further causing a sharp decrease in both η and U_e compared to the undoped AgNbO₃ system, as shown in Fig. 2g, h. Furthermore, when the temperature increases, long-range-order ferroelectric structures of ANLi-0Ta gradually transform into long-range-order antiferroelectric structures in a narrow temperature window (see Supplementary Fig. 8). With continuously increasing Ta concentration, the rotated antipolar regions gradually restrict the growth and diminishment of antiferroelectric and ferroelectric nanoregions, being able to maintain the characteristic structure across a wide temperature range. It suggests the great potential for increasing the thermal stability of the boosted U_e and η.

Superior energy-storage performance in Li/Ta co-doped AgNbO₃ ceramics

AgNbO₃ ceramics doped with Li and Ta were fabricated according to the composition design in phase field simulation, (Ag_0.95Li_0.05)(Nb_1−x/100Ta_x/100)O₃ (abbreviated as ANLi-xTa) with x values of 0, 5, 25, 45, and 65. The measured mean densities of ANLi-xTa (x = 0, 5, 25, 45, and 65) are 6.52, 6.71, 7.28, 7.78, and 8.03 g/cm³, respectively, by using Archimedes’ method. Figure 3a presents the P–E loops of AN, ANLi-xTa (x = 0, 5, 25, 45, and 65), and AgTaO₃ (AT) ceramics under the respective E_b. Compared to the computational results in the single crystal model, P_max does not exhibit a similar significant enhancement in the experiment of ANLi-xTa polycrystalline ceramics. The P_max slightly increases from 38.25 μC/cm² at ANLi-0Ta to 40.39 μC/cm² at ANLi-65Ta under E_b. Every P–E loop has been measured under E_b three times. The error value for the P_max for all compositions is below ±0.1 μC/cm². Under the same applied electric field, the P_max evidently drops with increasing Ta concentration, as shown in Supplementary Fig. 9. In addition to the miniaturized domains and delayed AFE-FE transition with increasing Ta concentration, the continuous decrease in grain size from 3.92 μm (ANLi-0Ta) to 0.78 μm (ANLi-65Ta), as shown in Supplementary Fig. 10 further restricts polarization enhancement under the same electric field. In ferroelectric/antiferroelectric ceramics, the decreased grain size hinders domain wall motion and domain switching due to the enhanced clamping effects from grain boundaries and the absence of mobile domain wall⁴³. ANLi-5Ta ceramics exhibit typical ferroelectric polarization hysteresis and current–electric field loops (see Supplementary Fig. 11a, b), indicating a predominant ferroelectric structure at room temperature due to the influence of Li on the microstructure of AgNbO₃. In contrast, characteristic double hysteresis loops appear in the composition with x = 25 (see Supplementary Fig. 11c). As shown in Supplementary Fig. 12a, with increasing Ta concentration, the value of room-temperature strain at the same field of 160 kV/cm sharply decreases from ~0.3% of ANLi-5Ta to ~0.02% of ANLi-65Ta. At the same time, the strain hysteresis also sharply decreases, resulting in slimmer strain loops with a slanted slope in ANLi-65Ta ceramics, agreeing well with calculated strain behavior and experimental slimmer P–E loop characteristics. As shown in Supplementary Fig. 12b, c, the forward and backward switching fields for the field-induced antiferroelectric-to-ferroelectric phase transition increase from 110 kV/cm and 16 kV/cm in ANLi-25Ta to 187 kV/cm and 170 kV/cm in ANLi-65Ta, respectively. This increase in the switching fields demonstrates the enhanced stability of the antiferroelectric phase with increasing Ta concentration from ANLi-25Ta to ANLi-65Ta at room temperature, consistent with the tendency of the established Ag(Ta_xNb_1−x)O₃ phase diagram⁴⁴. The lowest ΔE of approximately 17 kV/cm is achieved for ANLi-65Ta due to the influence of RAFE state, in comparison with other representative AN-based systems (see Fig. 3b)^{9,24–26,45,46}. Accordingly, the U_e and η simultaneously increase from 0.2 J/cm³ and 9% for ANLi-0Ta to 12.8 J/cm³ and 90% for ANLi-65Ta (see Supplementary Fig. 13), i.e., ~64 times and ~10 times enhancements in U_e and η respectively, surpassing almost all reported lead-free AgNbO₃ and NaNbO₃ (NN)-based antiferroelectric ceramics, as shown in Fig. 3c^{1,28,38,47–51}. Such enhancement in energy storage performance arises not only from the increased E_b but also from the high polarization, which derives from a delayed field-induced antiferroelectric-to-ferroelectric transition enabled by the percolating interaction between antipolar regions and defect pairs.

Fig. 3. Polarization, electrical, and energy storage performance of ANLi-xTa ceramics.

a P–E loops of AN, ANLi-xTa (x = 0, 5, 25, 45, and 65) and AgTaO₃ (AT) ceramics. b Comparison of electric hysteresis (ΔE) of ANLi-65Ta with other representative AN-based ceramics. c Comparison of U_e and η of the highest-proportioned RAFE composition (ANLi-65Ta) with other reported lead-free AN and NaNbO₃ (NN)-based antiferroelectric bulk ceramics. d Weibull distribution analysis for E_b and Weibull modulus (β) of ANLi-xTa and AgTaO₃ ceramics. e Temperature-dependent P–E loops of ANLi-65Ta under 510 kV/cm. f Comparison of U_e and temperature stability (T_span) of ANLi-65Ta with other reported state-of-the-art lead-free bulk ceramics when the electric field and η are set as <510 kV/cm and >85%, respectively.

Figure 3d displays the statistical breakdown strengths of ANLi-xTa and AT ceramics, analyzed using Weibull distribution fitting^17,52, while the detailed methodology is included in the Supplementary Information. It is evident that the actual mean E_b significantly increases from approximately 212 kV/cm for ANLi-5Ta to approximately 760 kV/cm for ANLi-65Ta. This tendency is also consistent with the phase field predictions, providing solid verification for the rationality of E_b definition in phase field simulations. Figure 3e illustrates the temperature-dependent unipolar P–E loops of ANLi-65Ta under an electric field of 510 kV/cm. The U_e exhibits high thermal stability over a 240 °C temperature range, decreasing only from 6.7 J/cm³ at −70 °C to 6.2 J/cm³ at 170 °C. Figure 3f shows that ANLi-65Ta, exhibiting an average U_e of 5.3-6.5 J/cm³ over a temperature range (T_span) of 240–255 °C under electric fields of 450–510 kV/cm (see Supplementary Fig. 14), surpasses that of most reported AN, NaNbO₃, BaTiO₃, K_0.5Na_0.5NbO₃, and Bi_0.5Na_0.5TiO₃-based lead-free bulk ceramics^{24,26–28,48,53–66}. Here, T_span is defined by the temperature range when the U_e is higher than 90% of the maximum under the same electric field.

Microstructural basis for the superior energy-storage properties in ANLi-xTa ceramics

Rietveld refinement results, shown in Fig. 4a and Supplementary Fig. 15, reveal the coexistence of the Pbcm and R3c phases in ANLi-xTa ceramics at room temperature^46,67. The composition-dependent percentages and the fitted lattice parameters of Pbcm (M₂/M₃) and R3c phases are presented in Fig. 4b and Supplementary Table 2, respectively. With increasing Ta concentration, the phase fraction of the Pbcm antiferroelectric phase increases, indicating the enhancement of the switching field of the antiferroelectric-ferroelectric phase transition. In addition, the softening and hardening, appearance, and suppression of Raman-active phonons are sensitive to the nano-structural changes, especially for similar M₂ and M₃ phases^68–70. The corresponding room-temperature Raman results shown in Supplementary Fig. 16, demonstrate that the breathing mode of Ag⁺ near 84 cm⁻¹ is only observed in AgNbO₃ and Ag_0.97Li_0.03Nb_0.97Ta_0.03O₃ (AN-3LT) and not in compositions with higher Li/Ta co-doping. It is related to the happening of phase transition from antiferroelectric-dominated ferrielectric phase to ferroelectric phase near ANLi-5Ta ceramics^13,71. The ν₅ mode exhibits a distinct redshift from approximately 260 cm⁻¹ in both AgNbO₃ and Ag_0.97Li_0.03Nb_0.97Ta_0.03O₃ to 221 cm⁻¹ of ANLi-5Ta. Concurrently, the NbO₆ octahedral vibrational modes shift from 96, 107 cm⁻¹ of AgNbO₃ to 94, 103 cm⁻¹ of ANLi-5Ta. This systematic softening of both the ν₅ and NbO₆ phonon modes reflects progressive changes in the local octahedral structure. In addition, with further increasing Ta concentration, all Raman peaks become weaker and broader, due to the disruption of long-range-order electrical domains and the increased disorder or relaxor feature²⁴. When the Ta content is over 40 mol%, the phase transition from M₂ to M₃ happens, resulting in the blueshift of the ν₁ mode from 569 cm⁻¹ of ANLi-25Ta to 591 cm⁻¹ of ANLi-65Ta.

Fig. 4. Phase transition behavior and associated microstructure evolution.

a Rietveld refinement results for the X-ray diffraction (XRD) data of ANLi-65Ta ceramics. b Evolution of phase fraction for Pbcm and R3c of ANLi-xTa ceramics at room temperature. c, d Frequency dependence of dielectric permittivity versus temperature curves of ANLi-5Ta and ANLi-65Ta, respectively, upon cooling. e Vogel-Fulcher fitting for the angular frequency dispersion versus the temperature of maximum permittivity (T_m) to obtain the freezing temperature (T_f). f Temperature-composition phase diagram of ANLi-xTa ceramics.

The temperature-dependent dielectric permittivity curves depicted in Fig. 4c, d and Supplementary Fig. 17 reveal the phase transitions of ANLi-xTa ceramics. With increasing Ta concentration, the temperature for phase transitions from AFE M₃ to AFE M₂ and from AFE M₂ to FE R both gradually decreases. Notably, the decrease of M₃-M₂ transition temperature is faster than the M₂-R case. Consequently, the M₃-M₂ and M₂-R phase transition lines converge together near ANLi-65Ta, being inclined to form the antiferroelectric and ferroelectric coexistent region (i.e., M₃-M₂-R) at ANLi-65Ta. In addition, the abrupt changes in dielectric loss curves during temperature variations are closely associated with the phase transitions. For the antiferroelectric (M₂)-ferroelectric (R) phase transition, the dielectric loss peaks systematically shift toward higher temperatures with increasing measurement frequency. For the paraelectric AT ceramics, no dielectric anomaly indicative of a phase transition is observed. As shown in Supplementary Fig. 18, the increase in dielectric permittivity with decreasing frequency at elevated temperatures is attributed to the contribution of leakage current. The frequency dispersion of the M₂ to R and M₃ to R transitions is fitted using the Vogel-Fulcher relation to determine the freezing temperature (T_f)^29,30. As shown in Fig. 4e, with increasing Ta concentration, the freezing temperature (T_f) gradually decreases. Above T_f, it is acknowledged that the polarization shows the ergodic polar dynamics, which has no clear frequency dependence in dielectric results, indicating a much shorter relaxation time and lower activation energy for polarization fluctuation^72,73. In comparison with the T_f (−18.8 °C) of ANLi-45Ta ceramics, the freezing temperature has been much decreased to −121.5 °C of ANLi-65Ta ceramics. In other words, the temperature range for ergodic polarization state has been maintained at a much lower temperature. In addition, as shown in Supplementary Table 3, ANLi-65Ta ceramics exhibit much lower activation energy (E_a) than that of ANLi-25Ta and ANLi-45Ta ceramics. The substantially lower T_f of ANLi-65Ta indicates that its nanodomains remain mobile and ergodic at much lower temperatures⁷², justifying the enhanced dynamics of nanodomains compared to those in ANLi-45Ta. Figure 4f shows the temperature-dependent phase diagram of the ANLi-xTa system established from corresponding dielectric and X-ray diffraction (XRD) results, clearly suggesting that the unfrozen antiferroelectric (M₃ and M₂ with Pbcm symmetry) and ferroelectric coexistent nanostructures can remain stable above the freezing temperature of ANLi-65Ta.

To further investigate the rotation configuration of antipolar structures under different proportions of Li/Ta in AgNbO₃, atomic-scale high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was employed in the ANLi-5Ta and ANLi-65Ta ceramics. Figure 5a shows that the ANLi-5Ta sample generally exhibits a long-range-order antiferroelectric domain pattern with alternating polarization directions every two atomic layers. In comparison, the polarization vectors of ANLi-65Ta, presented in Fig. 5d, are more disordered and deviate from the primary antiferroelectric directions. The polarization angle mapping and corresponding histogram in Fig. 5b, e indicate that both ANLi-5Ta and ANLi-65Ta display a bimodal symmetric angle distribution, reflecting their average antiferroelectric characteristics. Distinct from ANLi-5Ta, the formation of a RAFE state with increased polar rotation in ANLi-65Ta results in a more dispersed angle distribution. Additionally, for ANLi-5Ta, Gaussian fitting of the polarization displacement distribution in Fig. 5c reveals two distinct peaks centered near 4.7 pm and 8.4 pm. This bimodal distribution indicates that the local polarization magnitudes are not random but are concentrated around these two specific values, which are attributed to the formation of the R3c ferroelectric state after Li doping into the AgNbO₃ system. This highlights the prominent ferroelectric-like characteristic of ANLi-5Ta, consistent with the DFT results for AN-Li. With further increasing Ta concentration, Fig. 5f shows that ANLi-65Ta displays only a single peak in its polarization magnitude distribution, suggesting that ANLi-65Ta contains a substantial fraction of RAFE state due to the presence of abundant rotated antipolar regions, smearing the antiferroelectric boundary region. Furthermore, as shown in Supplementary Fig. 19, the polarization angle distribution in Ag(Ta_0.8Nb_0.2)O₃ (ANT80) exhibits a distinct bimodal characteristic, which is a signature of the antiferroelectric state. In contrast, the polarization angles in pure AT ceramics are distributed across the entire range, characteristic of a quantum paraelectric state. These results confirm that the antiferroelectric phase remains stable even at Ta concentrations as high as 80 at.%, thereby corroborating the reliability and accuracy of the DFT calculations.

Fig. 5. Microstructure analysis for RAFE features in ANLi-5Ta and ANLi-65Ta.

a, d Atomic-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) polarization vector images along [110] direction with magnification of the marked images, showing the different distribution of polarization in different atomic layers of antiferroelectric structure. b, e Polarization angle mapping with the related statistical histogram. c, f Polarization magnitude mapping with the related statistical histogram.

In this study, a strategy for achieving large energy storage properties in lead-free antiferroelectrics is developed by combining DFT and phase-field simulations. The multi-scale calculations and accordingly designed experiments illustrate that the increase of percolating interaction between defect pairs and antipolar regions in AgNbO₃-based antiferroelectrics can lead to the formation of substantial rotated antipolar regions from the initial antiferroelectric state. Consequently, a substantial recoverable energy storage density of 12.8 J/cm³ with a high energy storage efficiency of 90% is achieved. In addition, the superior energy storage properties are maintained over a wide temperature range of 240 °C. Such a comprehensive energy storage capability surpasses those of most reported lead-free bulk dielectric ceramics. The design and synthesis of lead-free AgNbO₃-based ceramics guided by the multi-scale calculations would push forward the application process of advanced energy-storage dielectric capacitors in electronic circuits and power systems.

Methods

DFT calculations

Our DFT calculations were conducted by using the Vienna Ab-initio Simulation Package⁷⁴. The spin-polarized Perdew–Burke–Ernzerhof exchange⁷⁵–correlation functional and projector augmented wave method⁷⁶ were adopted with the valence-electron configurations of 4d¹⁰5s¹ for Ag, 4p⁶4d⁴5s¹ for Nb, 2s¹ for Li, 2s²2p⁴ for O, and 5d⁴6s¹ for Ta. The cut-off energy of 400 eV for all calculations. The 2 × 2 × 1 160-atom supercell of the Pbcm phase of AgNbO₃ was adopted. The atomic positions and lattice constants were fully relaxed until the total energy difference, and forces were less than 10⁻⁷ eV and 0.01 eV/Å, respectively. The Monkhorst–Pack k-point mesh of 1 × 1 × 1 was adopted for geometrical optimization calculations for all structures⁷⁷.

Phase field simulation

AgNbO₃-based system is taken as a typical lead-free antiferroelectric system by solving the time-dependent Ginzburg-Landau (TDGL) equation:

$$\frac{\partial P_{\mathrm{i}}\left(x,t\right)}{\partial t}=-L\frac{\delta F}{\delta P_{\mathrm{i}}\left(x,t\right)},\left(i=1,2,3\right)$$ 1

where L is the kinetic coefficient related to the domain mobility, t is time, P_i(x, t) is the polarization and F is the total free energy of the whole system, expressed as following⁷⁸:

$$F=\int \int \int \left(f_{\mathrm{lan}}+f_{\mathrm{grad}}+f_{\mathrm{elas}}+f_{\mathrm{elec}}+f_{\mathrm{localelec}}\right)dV$$ 2

where V is the volume of the system. The landau free energy f_lan can be calculated by

$$\begin{array}{c}{f}_{\mathrm{lan}}=a_1\left(P_1^2+P_2^2+P_3^2\right)+a_{11}\left(P_1^4+P_2^4+P_3^4\right)+a_{12}\left(P_1^2{P}_2^2+P_2^2{P}_3^2+P_1^2{P}_3^2\right)\hfill \\ +a_{112}\left[P_1^4\left(P_2^2+P_3^2\right)+P_2^4\left(P_1^2+P_3^2\right)+P_3^4\left(P_1^2+P_2^2\right)\left)\right)\right]+a_{111}\left(P_1^6+P_2^6+P_3^6\right)\hfill \\ +a_{113}\left(P_1^2{P}_2^2{P}_3^2\right)\hfill \end{array}$$ 3

where a₁, a₁₁, a_12, a₁₁₂, a₁₁₁, and a₁₁₃ are Landau coefficients.

The gradient free energy f_grad representing the energy from polarization inhomogeneity is described as^79,80:

$$f_{grad}={\sum }_i\left\{\begin{array}{c}\alpha \left[{\left(\frac{\partial P_{\mathrm{i}}}{\partial x}\right)}^2+{\left(\frac{\partial P_{\mathrm{i}}}{\partial y}\right)}^2+{\left(\frac{\partial P_{\mathrm{i}}}{\partial z}\right)}^2\right]\hfill \\ +\beta \left[{\left(\frac{{\partial }^2{P}_{\mathrm{i}}}{\partial x^2}\right)}^2+{\left(\frac{{\partial }^2{P}_{\mathrm{i}}}{\partial y^2}\right)}^2+{\left(\frac{{\partial }^2{P}_{\mathrm{i}}}{\partial z^2}\right)}^2\right]\hfill \end{array}\right\},\left(i=1,2,3\right)$$ 4

where α is a negative coefficient representing the stability of AFE phase, β is a positive coefficient representing the stability of FE phase.

The elastic strain energy f_elas can be expressed by $f_{\mathrm{elas}}=\frac{1}{2}{C}_{\mathrm{ijkl}}{e}_{\mathrm{ij}}{e}_{\mathrm{kl}}=\frac{1}{2}{C}_{\mathrm{ijkl}}\left({\epsilon }_{\mathrm{ij}}-{\epsilon }_{\mathrm{ij}}^0\right)\left({\epsilon }_{\mathrm{kl}}-{\epsilon }_{\mathrm{kl}}^0\right)$, where C_ijkl is the elastic stiffness tensor. e_ij, ε_ij, and ε⁰_kl are the elastic strain, total strain, and the spontaneous strain, respectively. The electrostatic energy f_elec can be calculated by $f_{\mathrm{elec}}=-\frac{1}{2}{E}_{\mathrm{i}}{P}_{\mathrm{i}}-E_{\mathrm{i}}\overline{P_{\mathrm{i}}}$, where E_i is the electric field component, including the dipole field, depolarization field, and applied electric field, $\overline{P_{\mathrm{i}}}$ is the average polarization. The local random distribution electric field energy f_localelec related with dopant valence and concentration can be expressed as: $f_{\mathrm{localelec}}=E_{\mathrm{i},\mathrm{localelec}}\overline{P_{\mathrm{i}}}$, where E_i,localelec is the random distribution electric field. Additionally, the normalized nearest neighbor polar directions are averaged to distinguish the regions of AFE, RAFE, and FE. The simulations were carried out in two dimensions with cell sizes 256Δx × 256Δy (Δx and Δy are the number of grid points, which are equal to 2 nm) with periodic boundary conditions.

Sample preparation

(Ag_0.95Li_0.05)(Nb_1−x/100Ta_x/100)O₃ ceramics were fabricated by the solid state reaction method with chemical powders of Ag₂O (99.9%, Alfa Aesar), Li₂CO₃ (99%, Alfa Aesar), Nb₂O₅ (99.9%, Alfa Aesar), and Ta₂O₅ (99.9%, Alfa Aesar). The raw chemical powders were ball-milled in ethanol for 12 h in nylon cans with zirconium dioxide grinding beads using a planetary ball mill with a rotation rate of 700 r/min. Then the mixed powders were dried and calcined at 900 °C for 6 h in an oxygen atmosphere. The calcined materials were ground and then ball-milled again for 12 h. After drying, the powders were pressed into disks with a diameter of 8 mm under 200 MPa via cold isostatic pressing. The sintering was done at 1080 °C for 6 h in an oxygen atmosphere, where the heating and cooling rates are set as 3 and 5 °C/min, respectively. The ceramic samples were thinned and polished using an automatic metallographic grinding and polishing machine (YMPZ-1) at a rotation speed of 500 r/min. Final polishing was performed with an alumina-based slurry for 1 min. Pt electrodes were then deposited on both surfaces via a plasma magnetron sputtering system (VTC-16-D) with a deposition time of 80 s. Then, the ceramic samples were polished to a thickness of ~80 μm for energy-storage measurement. The diameter of silver electrodes is around 1.5 mm.

Characterization

The measurements of breakdown field and all P–E loops were characterized using a Radiant Premier II ferroelectric test station at room temperature, with an applied electric field frequency of 10 Hz. The P–E loops of AN and ANLi-5Ta were measured under Standard bipolar settings, and the P–E loops of ANLi-25Ta, ANLi-45Ta, and ANLi-65Ta were measured under Standard monopolar settings. Room-temperature Raman spectra from 50 to 1000 cm⁻¹ were measured by using a Horiba Alimentation LabRAM spectrometer with a laser wavelength of 532.2 nm. The temperature-dependent dielectric permittivity of ANLi-xTa (x = 5, 25, and 45) and ANLi-65Ta ceramics was measured from 400 to −100 °C with a cooling rate of 3 °C/min under different frequencies of 100 Hz, 1 kHz, 10 kHz, 100 kHz, and 500 kHz by using a dielectric temperature measurement system (CNOGTICAL DMS 1000 with HIOKI3532 LCR meter). XRD measurement was performed at Bruker D8 ADVANCE with the voltage of 40 kV and the current of 30 mA, where the XRD scanning range for samples is set from 20° to 90° with the rate of 1°/min and the step of 0.02°. Atomic HAADF images were obtained by a double spherical aberration (Cs) corrected STEM (Spectra 300, ThermoFisher Scientific) equipped with probe and image correctors and operated at 300 kV. The Weibull distribution fitting was employed to evaluate breakdown strength.

Author contributions

L.Z. and D.W. conceived and designed the experiments. J.G., Z.Z., and Y.R. performed the TEM observations. L.H., Y.L., and C.Z. fabricated the samples and performed the electrical property measurements. L.Z., K.C., and C.B. conducted DFT calculations. L.H., L.Z., and D.W. performed the phase field simulations. S.Z., D.Y.W., S.Y., X.R., and Z.C. revised the manuscript. L.H., L.Z., and D.W. wrote the manuscript and analyzed the data.

Peer review

Peer review information

Nature Communications thanks Chang Won Ahn (eRef), who co-reviewed with Muhammad Sheeraz (ECR), and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data supporting the findings of this study are available within the paper and its Supplementary Information. Relevant additional data can be obtained from the corresponding author upon request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-68297-4.