Introduction

Antiferroelectrics (AFEs), in which the spontaneous polarization dipoles are aligned in opposite directions in adjacent sublattices, can switch to parallel direction under electric field, and return to their original after field removal, leading to double polarization–electric field (P–E) hysteresis loop and sprout-shaped strain-electric field (S–E) curve1,2. The unique characteristics make them promising candidate in a wide range of applications including high-energy-storage capacitors3,4,5,6, electrocaloric solid-cooling7,8 and high-strain actuators or transducers9. The prerequisite of the unique macroscopic physical characteristics is a reversible phase transformation between antiferroelectric (AFE) and ferroelectric (FE) phases induced by external stimuli such as electric field, mechanical force, and temperature. The most researched antiferroelectric PbZrO3 (PZ) was reported by Sawaguchi et al. in 19511. Since then, hundreds of AFEs have been discovered over the past 70 years, among which PZ remains the prototype for studying the antiferroelectric underlying structure while PZ-based AFE material exhibits the most attracting physical properties. Lead-free AFE materials are promising alternatives to PZ-based system from the viewpoint of enriching AFE types, improving physical properties, and addressing environmental concerns. Only a limited number of lead-free AFEs have been reported so far, among which the AgNbO3 (AN) and NaNbO3 (NN) are considered the most important representatives, where AgNbO3 has made exciting breakthroughs showing reversible AFE–FE phase transition and improved energy-storage density5,10,11. Typical double hysteresis loop featuring antiferroelectricity, however, has been barely observed in NN, where a classical FE-like P–E loop was often reported, even though it has been suggested to be an AFE based on crystal structure. Great efforts have been made to achieve a well-defined double P–E loop in NN, through a series of approaches including chemical composition modification12,13,24. The distinct octahedron rotations result in a quadrupling and doubling of the unit cell size along the b axis for P and Q polymorphs, respectively, as identified in the superlattice reflections at n/4 for P and n/2 for Q in Supplementary Fig. 1. The rotations of P and Q polymorphs are associated with the B-site cation shift, which can be revealed by the displacement derivatives derived from geometric phase analysis (GPA) of the corresponding atomic resolution STEM images25. The P phase exhibits characteristic AFE order with antiparallel atomic shift along [100]p with a periodicity of 4ap (Fig. 1g), while the Q phase exhibits uniform displacement spanning over 10ap indicating the long-range FE order (Fig. 1h).

Fig. 1: Structure and DFT calculations of NN.
figure 1

a Rietveld-refinement plot and the refined results of SXRD. Schematic crystal structures of the (b) P phase and c Q phase. d BF STEM image taken from [101]p zone axis, showing the same tilt mode of P and Q phases. e BF STEM image taken from [010]p zone axis showing P phase structure. f BF STEM image taken from [010]p zone axis showing Q phase structure. The annular dark field (ADF) images and structural schematics are overlaid in (d), (e), and (f), respectively. g ADF STEM image taken from [100]p zone axis showing P phase structure. h ADF STEM image taken from [100]p zone axis showing Q phase structure. The corresponding GPA shear strain (\(\frac{\partial {u}_{y}}{\partial x}\)) of the ADF STEM images is also overlaid in (g) and (h), respectively. The sign change of shear strain indicates the reversal of polarization. i DFT calculations of free energy as a function of ξ. Based on the continuous parameter ξ, the linear interpolation of atomic positions and lattice parameters was adopted to construct a series of intermediate structures, from P or Q phase (ξ = 0) to the corresponding high symmetry structure (ξ = 1, space group Pm-3m, No. 221). The parameter ξ reflects the rotation distortion of the structure, i.e., there is no distortion at ξ = 1, while distortion becomes stronger with smaller ξ and even stronger with ξ < 0.

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Previous experimental and theoretical investigations demonstrated the octahedral rotation with the associated cation displacements plays a critical role in stabilizing an AFE structure26,27. X-ray/neutron-diffraction on NN showed that the volume fraction of P phase increases with increasing temperature, accompanied by a decreasing amount of Q phase20. It is of particular importance that both average cations off-center displacements and oxygen octahedral tilting angles decrease in P phase with increasing temperature, which shows a contrary trend in the Q phase (Supplementary Fig. 2)20. It should be noted that in addition to the temperature associated phase transition, the same phenomenon (decrease of octahedral tilting angle) was also observed in modified AN with improved AFE stability5,28. To understand the structural distortion for the stability of P and Q phases in NN, density functional theory (DFT) calculations were performed based on method of intermediate configurations from ref. 29. Figure 1i presents how the free energy (△E is the free energy difference between P and Q phases) varies as the lattice structure deviates from P(Q) phase. The P phase has slightly higher total energy than Q phase (△E = 0.86 meV/f.u.), being consistent with the previous report17. As the rotation distortion of P phase becomes smaller (larger ξ), the energy curve of P phase intersects with Q phase whose rotation distortion becomes larger (smaller −ξ). This suggests that the P phase can be more stable than Q phase if the former becomes less distorted while the latter more distorted, for example, the scenario at elevated temperature, as reported in previous work20. It shows that the reverse rotation distortion change tunes the stability competition of P and Q phases and leads to Q-to-P phase transition, while the same rotation distortion change does not, as the red Q phase curve is always below P phase curve with the same distortion change, as shown in Fig. 1i. This also suggests that reducing the rotation distortion may be beneficial to stabilize the P phase, while increasing the rotation distortion of the co-existing Q phase by other approaches, for example, do** method in this work, will also stabilize the P phase, that said, facilitating the Q-to-P phase transition.

To experimentally verify the feasibility and effectiveness of our proposed idea, a new material system with composition of (1-x-y)NaNbO3-xAgNbO3-yCaHfO3:1.5 mol% MnO2 (NN-100xAN-100yCH) was designed and prepared. According to previous experiments on NN, the addition of a component with smaller Goldschmidt tolerance factor (t) can stabilize the AFE P phase12,13,14,17. Therefore, the addition of CaHfO3 with a lower t (CH: 0.9182; NN: 0.9671) is considered to be an effective approach to reduce the oxygen octahedral tilt30. The AN is also used to stabilize AFE phase in NN due to its lower electronegativity difference (1.675, versus 2.175 for NN). In addition, the MnO2 is used as a sintering aid to improve the sintering ability and reduce the defects and leakage current31. Herein, we mainly focus on NN, NN-20AN, NN-5CH, NN-5CH-20AN to investigate the structure evolution and the corresponding AFE properties. SXRD and STEM revealed that the addition of AN and/or CH can significantly reduce the oxygen octahedral tilting angles, as well as cation displacements. Of particular importance is that typical AFE features, well-defined double P–E loops and sprout-shaped S–E curves, were successfully achieved in NN-5CH-20AN.

Results

Structure of NN-100xAN-100yCH ceramics

To understand the structure evolution after AN/CH modification, we investigated the XRD of the NN-100xAN-100yCH ceramics. It is found that the addition of a certain amount of AN or CH can make NN maintain an orthorhombic AFE P structure, while a large amount of CH (>7 mol%) will lead to an orthorhombic AFE R phase (Space group Pnma) (Supplementary Fig. 3)14,17. The Rietveld refinements of high-energy SXRD for NN-5CH and NN-20AN-5CH are well-fitted to the P phase without detectable Q phase (Fig. 2a), indicating that the CH or AN/CH can effectively eliminate Q phase. On the basis of Rietveld-refinement results in Supplementary Table 1, we make a comparative study of the [BO6] octahedral tilt and the cation off-centering displacements among NN, NN-5CH and NN-20AN-5CH, as shown in Fig. 2b, c, respectively. The [BO6] octahedral tilting angles Θ about a axis and Φ about b axis (Schematics of Θ and Φ are presented in Supplementary Fig. 4) are 10.13° and 7.24° for NN, which significantly decrease to 8.95° and 6.12° for NN-5CH, and the addition of AN further enhances this trend. This is believed to be a result of the synergistic effect of the lower tolerance factor of CH and the stronger covalent bond characteristic of Ag–O bond in AN. Due to a coupling effect, the change of octahedral rotation also leads to the change of cation off-centering displacements. The NN-5CH and NN-20AN-5CH exhibits obviously reduced displacements of A1 and A2-site cations compared to those of NN (Schematics of A1, A2 and B-site cations are also shown in Supplementary Fig. 4). Even though the displacement change of B-site ions is not as obvious as that of A-site ions, a decrease still can be observed for the modified compositions. The addition of AN in NN-5CH slightly increases cation displacements, which may be associated with the higher polarizability of Ag+ compared to Na+. The reduced octahedral tilting angles and cation displacements are believed to benefit the stabilization of AFE structure.

Fig. 2: SXRD, dielectric properties and temperature dependent XRD.
figure 2

a Retrieved refinement plots of SXRD for NN-5CH and NN-20AN-5CH. A comparison study of (b) the [BO6] octahedral tilting angles Θ and Φ, and (c) the displacement of A1, A2, and B-site cations for NN, NN-5CH and NN-20AN-5CH ceramics derived from the Rietveld refinement of SXRD. Temperature dependence of (d) dielectric permittivity and loss, and (e) XRD for NN-20AN-5CH ceramic.

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The additions of CH and AN also change the temperature-induced phase transition behavior in NN, as depicted in the temperature-dependent dielectric spectra of NN-100xAN-100yCH ceramics (Supplementary Fig. 5, 6), revealing an altered physical nature. In particular, two dielectric anomalies are observed in NN-20AN-5CH over measuring temperature range (Fig. 2d), with a shoulder peak locating around 167 °C (marked as T2) and the other one locating around 203 °C (marked as T3). To reveal the phase structure evolution sequence of NN-20AN-5CH, temperature-dependent XRD was measured and given in Fig. 2e. The XRD is found to be in good agreement with AFE P phase over a large temperature range from -100 to ~170 °C, AFE R phase around 170–250 °C, and paraelectric (PE) S phase (Space group Pbnm) over 250 °C, based on the Rietveld refinements (Supplementary Fig.7). The temperature dependences of the lattice parameters and cell volume further confirm the phase transition. Therefore, it can be deduced the T2 is associated with AFE P to AFE R phase transition, while T3 is assigned to be AFE R to PE S phase transition temperature, even though with small variation in temperature with XRD analysis.

Reversibility between AFE and FE phases

Reversibility of the electric field-induced AFE–FE phase transition is essential for an AFE material9. To evaluate the reversible behavior of the newly designed compositions, we measured the first and second cycles of the P–E loops and I–E curves by using NN, NN-20AN, NN-5CH, and NN-20AN-5CH as representatives, as shown in Fig. 3. A slowly increasing polarization at low electric field is observed in virgin NN ceramic, exhibiting a sudden improvement when the electric field increases to a critical value (Fig. 3a) accompanied by a current peak (marked as EAF) in the I–E curve (Fig. 3b). The sudden change in polarization and current is associated with the AFE to FE phase transition. However, a large remnant polarization remains when the electric field reduces to zero, due to the irreversible FE to AFE phase transition. The typical square shaped P–E loop and two-peak I–E curve in the second cycle confirm a FE nature for the high electric-field-treated sample, in accordance with those generally observed in NN ceramic reported earlier32. After partially substituting Na+ with Ag+, the first positive half cycle of P–E loop is similar to that of virgin NN, while the first negative half cycle and second cycle of the loops exhibit pinched shape, as shown in Fig. 3c. Meanwhile, the first positive half cycle of I–E curve exhibits one current peak similar to that of virgin NN, while two peaks are observed in the negative half part (Fig. 3d). It should be noted that four peaks are observed in the second cycle of I–E curve. However, in contrast to the classical I–E curve in an AFE material, where two peaks appear at increasing electric field and the other two upon withdrawal, all these four peaks appear upon increasing electric field. The peaks appearing at higher electric field are associated with the AFE–FE phase transition, analogous to that usually observed in an AFE material. The other two peaks appearing at lower electric field, however, may be caused by the induced FE phase back-switching to AFE phase (to differ them from the so-called reversible FE–AFE phase transition, we define this critical electric field as E1 and −E1). Due to the irreversibility of FE–AFE phase transition in NN-20AN, the induced FE phase cannot spontaneously reverse to the AFE state, thus a backward electric field is required to overcome the energy barrier. Of particular importance is that the double P–E loops and four-peak I–E curves are observed for both NN-5CH and NN-20AN-5CH, which almost overlap on first and second cycles, as shown in Fig. 3e-h, demonstrating typical AFE characteristics and good reversibility of AFE–FE phase transitions. The reversibility of the induced FE phase can also be reflected by the piezoelectric coefficient (d33), with values around 35 and 10 pC N-1 in poled NN and NN-20AN respectively (Fig. 3i), clearly demonstrate the irreversible field-induced FE phase in these compositions33. In contrast, nearly zero d33 is observed for both NN-5CH and NN-20AN-5CH, revealing the field-induced FE phase switches back to AFE state upon field removal9,34. Interestingly, the NN-20AN-5CH exhibits the least sensitive εr under electric field, where the εr–E curves almost overlap before and after field application (Supplementary Fig. 8), indicating the highest stability of its AFE phase.

Fig. 3: The reversible behavior of the newly designed NN-based ceramics.
figure 3

The first and second circles of P–E loops and I–E curves for (a) and (b) NN; (c) and (d) NN-20AN; (e) and (f) NN-5CH; (g, h) NN-20AN-5CH. i The piezoelectric coefficient d33 for the poled samples. The Raman spectra under various conditions of virgin state, electric field on and off states for (j) NN and (k) NN-20AN-5CH. The electric fields applied are 150 and 300 kV cm-1 for NN and NN-20AN-5CH respectively, to ensure the field-induced AFE–FE phase transition.

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The good reversibility between the AFE and field-induced FE phases in NN-20AN-5CH can also be corroborated by the in-situ electric field-dependent Raman spectra. At a low electric field, both NN and NN-20AN-5CH maintain characteristics of the AFE P phase (Supplementary Fig. 9). A high electric field above 90 kV cm-1 gradually induces AFE P to FE Q phase transition in NN, while a significantly improved electric field above 200 kV cm-1 is required to induce P-to-Q phase transition in NN-20AN-5CH. It is interesting that the Raman spectra of NN remain almost the same after electric field removal, as shown in Fig. 3j. This reflects that the electric field-induced FE Q phase maintains and cannot switch backward to AFE P phase upon the removal of electric field, showing an irreversible Q-P phase transition behavior. On the contrary, the Raman spectra of NN-20AN-5CH return to almost the same shape as the original state after electric field removal (Fig. 3k), demonstrating good reversibility between P and Q phases.

P–E loops, S–E curves and the possible mechanism

Figure 4a-b display the P–E loops and S–E curves of the four representative compositions, respectively. The pure NN exhibits a square-shaped P–E loop with high remnant polarization and large hysteresis, as well as a butterfly-shaped S–E curve, showing the characteristics of a ferroelectric material. The addition of sole AN or CH in NN can transform the P–E loop into a pinched shape, as observed in NN-20AN and NN-5CH. However, the NN-20AN shows a butterfly-shaped S–E curve, similar to that of pure NN but showing higher strain. In contrast, the NN-5CH shows sprout-shaped S–E curve, in which the strain disappears on the removal of the electric field. The difference in shape may be resulted from the increased FE–AFE reversibility for the CH-modified NN. Of particular importance is that a well-defined double P–E loop with near-zero remnant polarization and significantly reduced hysteresis, accompanying with sprout-shaped S–E curve, can be achieved when adding appropriate CH and AN (such as NN-20AN-5CH), demonstrating typical AFE characteristics.

Fig. 4: The polarization and strain of the newly designed NN-based ceramics.
figure 4

a P–E loops and (b) S–E curves. The inset of a shows magnified scale for NN-20AN-5CH. Compositions dependence of (c) Pm, Pr, Pr/Pm; (d) EAF, EFA; (e) Sm, Sneg, Sneg/Sm, derived from the P–E loops, the I–E curves in Supplementary Figs. 12 and 13, and the S–E curves, respectively. f Electric field dependence of P–E loops for NN-20AN-5CH, the inset gives the Pm as a function of maximum measuring electric fields. g The electronegativity difference and tolerance factor of NN-based12,13,17,46,47,

Fig. 5: Polarization field map**.
figure 5

ADF images for (a) NN and (b) NN-20AN-5CH. B-site displacement map for (c) NN and (d) NN-20AN-5CH. The long white lines in (c) and (d) with antiparallel vectors are guiding line for revealing B-site displacements. e Displacement averaged from (c) and (d), oxygen octahedral tilting angle Θ averaged from Supplementary Fig. 19 for NN and NN-20AN-5CH. f Displacement derivative \(\frac{\partial {u}_{y}}{\partial x}\) from (a) indicating displacement wave of NN using geometric phase analysis (GPA). g Displacement derivative \(\frac{\partial {u}_{y}}{\partial x}\) from (b) indicating displacement wave of NN-20AN-5CH using GPA.

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In summary, based on the structure analysis and DFT calculations, we suggest that reducing oxygen octahedral tilt may benefit the stabilization of AFE P phase in NN ceramics. To validate this concept, a series of lead-free NN-based AFEs were synthesized, among which the NaNbO3-20AgNbO3-5CaHfO3 ceramic exhibits well-defined double P–E loops and sprout-shaped S–E curves. XRD and STEM analysis reveal a reduction in oxygen octahedral distortion angle and ionic displacement, which are associated with the low tolerance factor of CH and small electronegativity difference of AN, accounting for the observed stabilized AFE P phase. This may help guide future material design for the discovery of a large number of lead-free AFEs.

Perspective

This work successfully addresses the long-standing challenge of develo** new lead-free NaNbO3-based AFE ceramics with reversible AFE–FE phase transition. The double P–E loops and sprout-like S–E curves of the newly designed compounds are of critical importance for a variety of applications including high-energy-storage capacitors and high-strain actuators. We also proposed an innovative strategy for designing new lead-free AFEs by reducing the distortion angle of the oxygen octahedra. The concept presented here not only provides a practical way of develo** NN-based AFEs with reversible AFE–FE phase transition, but can also be employed to discover other lead-free AFE systems. It should be pointed out that even though we obtained reversible AFE–FE phase transition in NN, the hysteresis of the P–E loops and S–E curves cannot be completely eliminated. More work should be done to achieve hysteresis-free P–E loops and S–E curves, which is of great importance for practical use of AFEs.

Methods

Theoretical calculations

The Vienna ab initio Simulation Package (VASP) was employed to conduct Density functional theory (DFT) calculations40,41. The projector-augmented wave (PAW) method was adopted to describe the ion–electron interaction, while the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional was used to depict the exchange-correlation part of the electron-electron interaction42. A plane wave basis set with a kinetic-energy cutoff of 500 eV was implemented to ensure convergence43, and crystal structures were optimized until energy and force convergence reached a threshold of <10–6 eV and 0.01 eV Å–1, respectively. In addition, sampling of the Brillouin zone was carried out using the Monkhorst-Pack k-point meshes with a reciprocal space resolution of 2π × 0.03 Å–1 for structural optimization44,45.

Fabrication of ceramics

The (1-x-y)NaNbO3-xAgNbO3-yCaHfO3 with 1.5 mol% MnO2 (x = 0.2, y = 0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, abbreviated as NN-20AN-100yCH; y = 0.05, x = 0, 0.1, 0.2, 0.3, 0.4, abbreviated as NN-100xAN-5CH) ceramics were synthesized by a high-temperature solid-state method. The reagents used were high-purity Na2CO3 (99.8 %), Nb2O5 (99.99 %), HfO2 (99.99 %), CaCO3 (99.8 %), Ag2O (99.7 %) and MnO2 (98.8 %). Stoichiometric amounts of reagents were weighted, ball milled, and then calcined at 900-980 oC for 6 h in air or in O2 atmosphere depending on their compositions. The calcined powders were ball milled again with MnO2 addition, dried and hand-pressed into pellets with 7 mm in diameter and 1 mm in thickness. Then, the pellets were cold isostatic pressed again at 250 MPa to further improve their density, followed by sintering at 1190–1320 °C for 5 h in air or in O2 atmosphere. Finally, the as-sintered pellets were polished, coated with silver electrode on both sides, and fired at 600 °C for 30 min.

Characterization of phase structure

Phase purity and crystal structures of the as-prepared samples were characterized by using an X-ray powder diffractometer (XRD, SmartLab-3kW, Rigaku Ltd., Tokyo, Japan) with Cu Kα radiation. The high-quality synchrotron X-ray powder diffraction (SXRD) data was performed at TPS 19 A (Taiwan Photon Source) of the National Synchrotron Radiation Research Center with a calibrated wavelength of 0.77489 Å and the energy of 16 KeV. The Rietveld analysis of the SXRD was performed using GSAS. The microstructure was observed by using a scanning electron microscope (SEM, FE-SEM Sigma 300, ZEISS Corp., German) with energy dispersive spectroscopy (EDS), after polished and thermally etched. Aberration-corrected scanning transmission electron microscope (STEM) was performed on a probe corrected FEI Spectra 300 S/TEM (ThermoFisher Scientific, Eindhoven, Netherlands) equipped with an X-FEG source and operated at an accelerating voltage of 300 kV. A beam current of 50 pA and a semi-angle of convergence of 24.4 mrad was utilized. ADF images were collected with a detector semi-angle range of 72–200 mrad while BF images were collected with a detector outer semi-angle range of 6 mrad. Atom column locations were determined via 2D Gaussian fitting.

Measurement of dielectric and piezoelectric properties

The temperature dependence of dielectric permittivity and loss was measured using a precision impendence analyzer (E4990A, Keysight, Bayan, America) connecting with a temperature control system (DMS-500, Balab, Wuhan, China) in the temperature ranging from −150 to 450 °C at frequencies of 1, 10, and 100 kHz. The variation of dielectric permittivity at virgin and poled state was measured before and after poling the samples over their corresponding AFE–FE phase transition electric field. The piezoelectric coefficient d33 was recorded by using a Piezo-d33 meter (ZJ-3A, Chinese Academic Society, Bei**g, China), after poling the samples over their corresponding AFE–FE phase transition electric field. The electric field dependence of normalized dielectric permittivity (dielectric tunability) was measured using a ferroelectric tester (TF Analyzer 3000, aixACCT, Aachen, Germany) with a maximum bias field of 100 kV cm-1.

Measurement of ferroelectric properties and strain

The polarization vs. electric field hysteresis (P–E) loops, current vs. electric field (I–E) curves and strain vs. electric field (S–E) curves were characterized at 1 Hz using a ferroelectric tester.