Giant electrostrain coefficient under low driving electric field in sodium potassium niobate piezoelectric ceramics with symmetrical bipolar strain

Domain: physics
Published: 2025-11-26
Editorial outcome: major_revision

Abstract
Currently, achieving highly symmetrical bipolar strain and high electrostrain under low driving electric field remains challenging in piezoelectric materials.
The designed potassium sodium niobate-based ceramics exhibit highly symmetrical bipolar strain and ultra high electrostrain coefficient (~2000 pm/V) under a low driving electric field of 8.4 kV/cm through A-site defect engineering and charge compensation. The highly symmetrical bipolar strain is related strongly to the lowly aligned defect dipoles by partially substituting A-site (Na+/K+) ions with Mn2+. The eye-catching performance is ascribed to the unique microstructure of atomic-scale polar nanoregions embedded in nanodomains (~34 nm) by tuning Na+/K+ ions deficiency and coexistence of multiple phases. Phase-field simulations reveal that flattened energy barrier and multiphase nanodomains interplay to boost electrostrain at low driving fields. This work provides an innovative way of designing lead-free piezoelectric materials with highly symmetrical bipolar strain and giant electrostrain coefficient at low driving electric field, promising for high-precision actuators applications.

Introduction
Piezoelectric actuators are widely used in various fields that require high precision and fast response, such as precise optical instruments, microelectromechanical systems, and robotics, etc.1,2. The miniaturization and integration of electronic components have increased the performance requirements for piezoelectric actuators, particularly the need for a large electrostrain coefficient (d*33) under a low driving electric field (ED)3,4 (d*33 = S/E, S is electrostrain at E, E refers to the electric field under the high d*33) and high precision with low displacement accumulated error (DAE) during the application process5. DAE can be mitigated by constructing stable defect dipoles, which facilitate the design of high symmetrical bipolar strain5–8. As a core element for piezoelectric actuators, the piezoelectric material with large d*33, low ED, and highly symmetrical bipolar strain is urgently expected.

To achieve a large electrostrain coefficient, extensive research efforts have been devoted in recent decades. However, the manufacturing and applications of lead-based materials have been limited due to the raised concerns from the health and environmental issues9,10. Therefore, lead-free piezoelectric material systems have garnered significant attention. Among the lead-free piezoelectric systems, the (Na1/2Bi1/2)TiO3 ceramics exhibited highly asymmetrical bipolar strain and large d*33 ~1500 pm/V at fairly high ED of 100 kV/cm11. However, the high ED may restrict its commercial applications due to reasons such as non-linearity and potential electrical breakdown3. In 2022, Huangfu et al. proposed an innovative strategy that is the synergistic effects (Fig. 1a1) of defects engineering and domains engineering, enabling (K,Na)NbO3-based ceramics to achieve excellent d*33 (2100 pm/V) at ED (50 kV/cm), which has reignited researchers’ attention to (K,Na)NbO3-based systems12. Subsequently, based on this strategy, Li/Sr-doped (K,Na)NbO3 ceramics with a high d*33 (~3080 pm/V) at 50 kV/cm13 and (K0.48Na0.52)0.99NbO2.995 ceramics with a giant d*33 (~3500 pm/V) at 20 kV/cm14 are obtained, attributed to the interaction between the nano-domains and highly aligned defect dipoles (V0Na=K - V''O). Nano-domains constructed by multiphase coexistence can effectively decrease the energy barrier15. However, the introduction of V0Na=K - V''O, the energy profile in these nano-domains promotes defect dipoles alignment along the external electric fields, resulting in the global system falling into a deep potential well. Consequently, a significantly asymmetric Landau energy profile with slightly high energy barrier is formed as depicted in Fig. 1a2, resulting in asymmetric large bipolar strain and a slightly high ED as shown in Fig. 1a312,13. Thus, a unique microstructure is urgently designed to significantly flatten and symmetrize the Landau free energy plot, which dramatically increases electrostrain under low ED and improve symmetry of bipolar strain.

A flattening of the Landau free energy plot can decrease the energy barrier and lead to the system anomalously soft, i.e., a small external electric field can result in comparatively large piezoelectric response16. Nano-size domains formed in ceramic can effectively reduce the energy barrier during polarization switching17. However, it is difficult to further flatten and symmetrize the Landau free energy plot solely by reducing the domain size via establishing multiphase coexistence. Since polar nanoregions (PNRs) embedded in the nano-domains matrix are considered to act as accelerators during domain switching, flatten the Landau energy profile and then benefit the electrostrain and decrease ED18–23. We consider that constructing smaller-scale PNRs would significantly increase the interfacial energy, thereby further flattening of Landau energy profile, ultimately achieving significantly improved piezoelectric performance and reduced ED19. It can be designed that the scale of PNRs is further reduced by constructing a higher level of local structural heterogeneity (LSH), which can be achieved by the ions (such as Mn2+ ions, 1.27 Å: 12 coordination number) with smaller ionic radius occupying A-site of perovskite structure11,20,24–26, as shown in Fig. 1b1. Additionally, Mn2+ ions diffusion path increases due to the introduction of a reducing atmosphere during sintering and more spaces in the A-site of the (K,Na)NbO3 lattice formed by K/Na ions deficiency, which promotes more Mn2+ ions to entry into A-site to form more atomic-scale PNRs (Fig. 1b1). Besides, the incorporation of Mn2+ ions into the A-site (K/Na) vacancies leads to the defects Mn'Na=K with positive charge, which inhibits the formation of oxygen vacancies27,28. A decrease of V0Na=K - V''O concentration results in low defect dipoles alignment along the external electric fields, decreasing the potential well. Thus, Landau free energy plots are symmetrized, thereby enhancing the bipolar strain symmetry15. Finally, we believe that low defect dipoles alignment and a unique microstructure that is atomic-scale PNRs embedded in the nano-domains will make a great contribution to induce flattened and symmetrized Landau free energy plot (Fig. 1b2) and then increase electrostrain, decrease ED and improve symmetry of bipolar strain (Fig. 1b3).

Herein, we provide a readily applicable A-site defect engineering strategy to achieve ultra-high d*33 up to 2000 pm/V under a low driving electric field of 8.4 kV/cm, associated with highly symmetrical bipolar strain (β=15.08% at 40 kV/cm). Our work provides an innovative way of designing new high-performance lead-free piezoelectric ceramics that are promising for high-precision piezoelectric actuator applications.

Results
Electrostrain and temperature stability
Figure S1 in Supplementary Information shows the microstructure of (KN)xNT-BZ+MnO ceramics. All compositions exhibit closely compacted grains with a slight increase in size by K/Na deficiency, revealing high quality, which is also confirmed by the high density of over 95% in Table S1. Figure 2a presents the bipolar strain of all ceramics. The maximum strain (Smax) obviously increases with the decrease of K/Na content and reaches a maximum value of 0.41% at x=0.98, while it decreases with further reduction of K/Na content. Interestingly, all samples exhibit relatively symmetrical bipolar strain curves, demonstrating small variation for Smax in the first and second quadrants. This good symmetry is further improved by reducing K/Na content, as quantitatively revealed by the decreasing β from 37.87% to 10.96% (Fig. S2). This good symmetry of the bipolar strain can also be reflected by the relatively symmetrical P-E loops without obvious translational shift, as shown in Fig. S3. Of particular importance is that the Ei decreases obviously from ~0.72 kV/cm to ~0.06 kV/cm with decreasing K/Na content (Fig. S4), which is much smaller in comparison with other systems that can generate giant asymmetrical bipolar strain15,29–31.

To get the electrostrain, unipolar strain curves of x=0.98 ceramics are measured at different applied electric fields and 1Hz, as depicted in Fig. 2b. The strain obviously increases with the enhancement of the applied electric field, reaching a maximum value up to 0.47% at 50 kV/cm. Furthermore, the maximum strain also exhibits strongly compositional dependent behavior, which increases first and then decreases with the decrease of K/Na content, for example, from 0.23% at x=1, to 0.47% at x=0.98 and 0.40% at x=0.97 (Fig. S5). As for each independent component, the as-calculated d*33 increases first and then decreases with increasing applied electric field, reaching a maximum value at ED, as shown in Fig. 2c. It should be noticed that the x=0.98 ceramic demonstrates ultra-high d*33 over 2000 pm/V at a considerably low ED of 8.4 kV/cm. In comparison with the state-of-the-art piezoelectric bulks, the (KN)xNT-BZ+MnO ceramics showcase more outstanding electrostrain coefficient, as displayed in Fig. 2d. It is worth noting that the unipolar strain hysteresis of x=0.98 ceramic is only 26.35% at ED and 14.33% at 20 kV/cm (Tables S2 and S3 and Fig. S6), which is significantly reduced than those of commercially used PZT-5H ceramics (~23% at 20 kV)12, demonstrating better reversibility.

The temperature stability is also a very important merit for piezoelectric actuators in practical applications. Figure 2e gives the temperature dependence of unipolar strain and the corresponding d*33 of x=0.98 ceramic at its ED of 8.4 kV/cm. The unipolar strain increases from ~0.169% (~2000 pm/V) to a maximum value of ~0.226% (~2690 pm/V) at 100 °C, and then decreases to ~0.152% (~1809 pm/V) at 160 °C, demonstrating that the x=0.98 ceramics possess a high temperature stability (T*90=160 °C). Of particular importance is that, in comparison with the state-of-the-art piezoelectric bulks32–39, the x=0.98 ceramic not only demonstrates superior d*33, but also exhibits larger T*90 with better temperature stability. Besides, a good fatigue unipolar strain of the x=0.98 ceramics, at which only degrades 7.9% after 106 cycles under unipolar ED=8.4 kV/cm (Fig. S7). These distinguished merits make it great potential for piezoelectric micro-actuators applications.

Discussion
Microstructure
The design of A-site ions deficiency should cause an increase in oxygen vacancy according to Eq. (1). However, it is surprising that the concentration of oxygen vacancies decreases continuously with reducing K/Na content, e.g. from 24.66% for x=1 to 15.67% for x=0.97, as depicted in the refinement of O1s curves of X-ray photoelectron spectroscopy in Fig. S8 and the results presented in Fig. 3a. In addition, the refinement of O1s curves of X-ray photoelectron spectroscopy in ceramics sintered in air (Fig. S8) shows the concentration of oxygen vacancies increases continuously from 22.31 to 31.55%. According to Figs. S8 and S9, this may be ascribed to the Mn2+ ions partially substituting for A-site ions (K+ and Na+), as hinted in Eqs. (2) and (3).

To determine the valence state of the Mn element, Mn 2p curves of X-ray photoelectron spectroscopy for (KN)xNT-BZ+MnO ceramics are measured and refined, as shown in Fig. S10. The majority of Mn2+ (75–90%) with minor Mn4+ (10–25%) is determined in all samples sintered in reducing atmosphere, as shown in Fig. 3b. Interestingly, the amount of Mn2+ ions increases from 76.68% for x=0 to 89.94% for x=0.97 with more serious K/Na deficiency. However, the amount of Mn4+ ions in ceramics sintered in air increases from 27.14 to 36.87% in Fig. S11, which means more Mn4+ ions enter the B-site and then increase oxygen vacancy concentration. It indicates that the reducing atmosphere hinders the oxidation of Mn2+ ions that prefer to locate at the B-site, which, on the contrary, promotes more Mn2+ ions to occupy the A-site space left by the K/Na deficiency. A higher K/Na content produces more A-site vacancies (V0Na=K), which also leads to more Mn2+ ions locating at V0Na=K and the formation of Mn'Na=K defects to keep valence balance. This is also the reason for the lower concentration of oxygen vacancy for the compositions with a high level of K/Na deficiency.

2Na + 2K + 2O* -> K2O + Na2O + 2V''Na + 2V''K + 2V0o (1)

2MnO -> K2O + 2Mn'K + O2 + 2e' + Oo (2)

2MnO -> Na2O + 2Mn'Na + O2 + 2e' + Oo (3)

The change of various defects when increasing the K/Na deficiency certainly will lead to the increase of Mn'Na=K - V0Na=K defect dipoles and decrease of V0Na=K - V''o defect dipoles in (KN)xNT-BZ+MnO ceramics. Theoretically, the highly stable Mn'Na=K - V0Na=K defect dipoles make a very low contribution to Ei due to their high migration activation energy40. On the contrary, the V0Na=K - V''o defect dipoles are more easily reoriented along the spontaneous polarization direction to form P and consequently lead to Ei, as a result of oxygen vacancy motion15,41. In the newly designed compositions, the Mn2+ ions will lead to the decreasing concentration of oxygen vacancy to keep charge balance, which remarkably hinders the formation of highly oriented V0Na=K - V''o defect dipoles, thus resulting in smaller Ei. In this case, the Landau free energy plot is more symmetrical due to the lack of contribution from V0Na=K - V''o defect dipoles, which improves the symmetry of electrostrain.

Theoretically, a system with a single phase typically has a higher energy barrier for polarization switching. Since the reversibility of the rhombohedral (R)-monoclinic (M) phase transition in R-orthorhombic (O) phase coexistence tends to optimize the path of polarization rotation and result in nano-domains, which lead to the Landau energy profile more shallower and flatter in comparison with other phases19,42,43. As a result, an R-O phase boundary in KNN-based ceramics is designed via K/Na ions deficiency, which may be easier to induce nano-domains and then flatten the Landau free energy profile. The XRD patterns and the corresponding Rietveld-refinement plots of (KN)xNT-BZ+MnO ceramics are shown in Fig. S12. After Rietveld refinement, it is found that all ceramics can be well-fitted by two mixed phases, namely, a dominant R phase (space group R3m) and a small amount of O phase (space group Amm2), as shown in Fig. 3c. Interestingly, the fraction of R phase decreases from 95.25 to 84.77% with decreasing K/Na content, whereas the mount of O phase increases from 4.75 to 15.23%. This indicates that an R-rich multiple-phase boundary is successfully constructed through A-site deficiency engineering.

Figure 3d, e presents the TEM images of (KN)xNT-BZ+MnO ceramics with representative compositions of x=1 and 0.98. Typical stripe-like domains are clearly observed in both compositions, but with a remarkable decrease in width from 160 nm to 34 nm. The formation of nano-domains is mainly associated with the following two reasons. (1) The instability of multiphase with optimal phase ratios decreases polarization anisotropy so which reduces the domain size19,44. (2) The A-site point defects cause a stronger random field and then result in a higher level of LSH to make additionally interfacial energies (such as electrostatic and elastic energies associated with the heterogeneous interfaces), which results in nano-domains. These nano-domains will be more susceptible to reorientation when subjected to an electric field, which plays a crucial role in achieving a high d*33 under low ED45,46.

To further investigate the intrinsic mechanism of domain response, aberration-corrected STEM is employed to perform atomic mapping of domains (Red box) (Fig. 3d, e) along the [001] zone axis. The polar vectors of the ceramics are quantitatively calculated based on the relative displacements of the Nb5+ cations concerning the center of the nearest A-site cations. Figure 3f, g respectively shows the statistical polar vector angles image in x=1 and x=0.98 ceramics. When x=1, the vast majority of polar vectors share a common polarization direction along the [111] axis, signifying the predominant existence of the R phase. In contrast, polar vectors are observed in all directions for x=0.98 ceramic, indicating a significant anisotropy of the ferroelectric polarization. Meanwhile, polarity vectors with opposite directions in local structure and atomic scale PNRs (Blue box) are also observed in x=0.98 ceramic. This unique microstructure (Fig. S13) can also be found in other locations of the TEM (x=0.98) sample. This means the A-site defect engineering indeed induces a higher level of LSH and results in the formation of many atomic-scale PNRs embedding in the nano-domains, which is verified by the enhancement of dielectric dispersion (Figs. S4 and S15).

Figure 3h presents a systematic statistical analysis of the polar vector angles and their proportions in x=1 and x=0.98 ceramics. It is worth noting that the x=1 ceramic exhibits a very concentrated polar vector distribution with the majority of polar vectors (~54.25%) locating at low polar vector angles (0–20°), while the percentage of high-angle polar vectors (>80°) is <8%, in consistence with the high percentage of R phase. On the contrary, the x=0.98 ceramic displays a highly diffused polar vector with a wide angle (φ) distributed from 0° to 180°. We consider that the polarization vectors of a large number of atomic-scale PNRs deviate from their original <111> directions of R phase and randomly distribute in all directions, because a higher level of LSH results in the enhancement of the random field to disrupt the long-range order of the submicron domains18,47. The diffused polarization vectors distribution at wide angles from 0° to 180° in x=0.98 ceramic illustrates polarization switching path is more diverse, which promotes energy barrier of polarization switching to decrease. Thus, both intrinsic and extrinsic contributions to piezoelectricity can be enhanced due to easier polarization rotation and domain switching under an electric field48,49.

The LSH can also be revealed by the fluctuation of lattice strain (εxx). Figure 3i, j present the strain map on experimental HAADF STEM images for x=1 and 0.98 ceramics. The εxx of x=1 maintains a small variation in the range of ±0.005, whereas the εxx fluctuation is much larger with a value up to ±0.06 for x=0.98, demonstrating more noticeable strain heterogeneity among the B-site cations after A-site engineering. Furthermore, more nanoscale regions with larger εxx fluctuation are also observed in x=0.98 ceramic, as shown in Fig. 3j. There should be a significant lattice mismatch between these nanoscale regions due to the introduction of various defects, resulting in larger lattice strain in x=0.98 ceramic. This is also strong evidence of the high level of LSH.

Figure 4a, b displays vertical piezoresponse force microscopy (PFM) images of x=1 and x=0.98 ceramics. Before measurement, a very high positive DC voltage (30 V) was first applied to the tip during scanning of a 2×2 μm2 area, to enable complete polarization reorientation. Subsequently, a negative DC voltage with various magnitudes was applied to the tip during scanning of a 0.5×0.5 μm2 area to investigate the reversibility of the poled domains. A high voltage as high as 6 V is required to completely induce a reversal of domains in x=1 ceramic, where the square exhibits inverse phase contrast compared to the surrounding part. Interestingly, the domains begin to switch at a very small voltage of 1 V and complete under 2 V in x=0.98 ceramic, which is much lower than that observed in x=1 ceramic. This indicates a considerably stronger domain switching response for the x=0.98 ceramic, due to its lower energy barrier attributed to the unique nano-domains embedded by smaller PNRs50. These atomic-scale PNRs induced by A-site defects (Mn'Na=K and V0Na=K) are embedded in nano-domains and then result in more easily domain switching as accelerators24,51. According to the Rayleigh analysis (in Fig. S17), the ceramic (x=0.98) has significantly higher values of piezoelectric Rayleigh coefficient (α=11×10−16 m2/V2) than that α (3.2×10−16 m2/V2) of ceramic (x=1), also confirming that extrinsic contribution from these unique nano-domains response under small external electric field is enhanced significantly via the design of A-site deficiency. These are also the reason that accounts for the much lower driving electric field and the highest electrostrain coefficient (d*33) (shown in Fig. S17) in x=0.98 ceramic.

To uncover the origin of the large electrostrain in (KN)xNT–BZ+MnO ceramics at low electric fields, we combined Landau thermodynamics with phase-field simulations. An eighth-order Landau potential was fitted to dielectric-temperature spectra, yielding 3D free-energy surfaces at 300 K for x=1 and x=0.98 (Fig. 4c, d). Both compositions exhibit an R-phase ground state (O and T tetragonal phases metastable), yet the R→O and R→T barriers are lower for x=0.98 (Fig. 4e, f). The asymmetric profile at x=1 stems from a defect-dipole induced bias field (0.7 kV cm⁻¹), whereas the nearly symmetric curve at x=0.98 reflects the small experimental bias field (0.15 kV cm⁻¹). Phase-field simulations based on the fitted potential reveal that increased Mn doping enhances local random electric fields, transforming the domain structure from monolithic R domains (x=1) to nanoscale multiphase coexistence (x=0.98) with markedly reduced domain size (Fig. S18). The bipolar strain loop calculated from the phase-field simulation. Loops show a pronounced electrostrain of 0.35% for x=0.98. With unchanged electrostrictive coefficients, the enhanced d*33 correlates directly with (1) flattened free-energy barriers and (2) the multiphase nanodomain state. The reduced barriers enable R→T transitions at lower fields, and the larger c/a ratio of the T phase yields greater strain. Moreover, the multiphase configuration coupled with local random fields promotes reversible domain reconfiguration upon field removal. Thermodynamic and phase-field analyses thus demonstrate that flattening of the energy landscape and multiphase nanodomains collectively drive the high electrostrain in x=0.98 under modest electric fields.

In summary, ultra-high electrostrain coefficient (d*33 ~2000 pm/V) at a low driving electric field of 8.4 kV/cm and high symmetry bipolar strain curves (15.08% at 40 kV/cm) were achieved in (KN)0.98NT-BZ+MnO lead-free ceramics by synergy effect from A-site defect engineering and charge compensation. Furthermore, the (KN)0.98NT-BZ+MnO ceramics also possessed good temperature stability (T*90 ~160 °C) and relatively low unipolar strain hysteresis (26.35%) under 8.4 kV/cm. The partial Mn2+ ions as donor dopants in A-site of KNN perovskite form point defects (Mn'Na=K) and reduce V''o concentration, which weakens the contribution from V0Na=K - V''o and then improves bipolar strain symmetry. The coexistence of R/O multiple phases induces nano-domains that help to flatten the Landau energy profile to a certain degree in x=0.98 ceramic. The atomic-scale PNRs induced by point defects (V0Na=K, Mn'Na=K) embedding in nano-domains further flatten the Landau energy profile by increasing interfacial energies. The flattened and symmetrized Landau free energy plot and multiphase nanodomains results in ultra-high electrostrain, low ED and highly symmetrical bipolar strain in (KN)0.98NT-BZ+MnO ceramics.

Methods
Sample preparation
The KNN-based ceramics with composition of 0.94(K0.48Na0.52)xNb0.96Ta0.04O3-0.06BaZrO3+0.08MnO (abbreviated as (KN)xNT-BZ+8MnO, x is 1, 0.99, 0.98, and 0.97) were prepared through a conventional solid-state method in a reducing atmosphere. 3 mol% ZrO2 was added to each sample to improve the anti-reduction property. Analytically pure raw materials, including BaCO3, Nb2O5, Na2CO3, K2CO3, ZrO2, MnO, and Ta2O5, were weighed according to the stoichiometric formula and then mixed via planetary ball-milling with zirconia balls in ethanol for 24 h. The ball-milled flurries were dried at 70 °C through rotary evaporation and subsequently were calcined at 850 °C for 2 h in air. The calcined powders were ball-milled again and mixed with a PVB binder before being compacted into pellets under uniaxial pressure in a stainless-steel die. The green pellets were 8 mm in diameter and 0.4 mm in thickness. The green pellets were first heated to 600 °C for 2 h in air to remove the binder, followed by sintering at ~1120 °C for 2 h in a reducing atmosphere consisting of H2 and N2 (H2/N2 ~0.6%) to hinder the oxidation of Mn2+ ions during high-temperature sintering. The as-sintered samples were then cooled to ~850 °C and held for 9~10 h in high-purity nitrogen before being naturally cooled. For comparison, part of the green pellets were sintered at ~1120 °C for 2 h in air. All sintered ceramics were ~6.8 mm in diameter and ~0.4 mm in thickness.

Structure characterization
Phase purity and crystal structure 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 microstructure was observed by using a scanning electron microscope (SEM, FE-SEM Sigma 300, ZEISS Corp., Germany). Gold electrodes were sputtered on the samples using ion sputtering equipment (SBC-12, KYKY Technology Corp., Beijing, China). The amount and valence of Mn and O ions were obtained using an X-ray photoelectron microprobe (ESCALAB 250Xi, Thermo Fisher, Britain) equipped with a standard monochromatic AlKa excitation source (hυ=1361 eV). The piezoelectric response was characterized using an atomic force microscope (AFM, MFP-3D, Asylum Research, USA) with a functionality of a piezoresponse force microscope (PFM) for the local poling experiments and switching spectroscopy. A negative DC voltage large enough (30 V) to induce complete polarization orientation was first applied to the tip during the scanning of a 2×2 μm2 area. Then, a positive DC voltage with different values, depending on the composition, was applied to the tip during the scanning of a 0.5×0.5 μm2 area. Microstructure observation by transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM). Samples for electron microscopy were prepared by an FEI Helios NanoLab focused ion beam (FIB). Domain morphology was observed using a TEM (Talos F200X G2, FEI, America) operated at 200 kV equipped with a charge-coupled device camera. Aberration-corrected scanning transmission electron microscope was performed on a probe corrected FEI Spectra 300/TEM (Thermo Fisher Scientific, Eindhoven, Netherlands) equipped with a Schottky field-emission gun and operated at an accelerating voltage of 300 kV. The beam current was 40 pA and had a convergence semi-angle of 17.8 mrad. The STEM images were collected by a high-angle annular dark-field detector with inner- and outer-collection semi-angles of 73 and 200 mrad, respectively. The image analysis and quantification were conducted using custom MATLAB scripts. The polar vectors were calculated by the projected B-site (of high contrast) cation displacement from the center of the nearest four A-site (of low contrast) cations. The position of cations was specified by 2D Gaussian fitting on HAADF-STEM images using the Atomap module. The polar vector map was visualized by the Temul toolkits. For each atomic column (A or B site) found in the STEM images, we recorded its coordinates, intensity, and polar vector for further analyses, including drawing the intensity map, polar vector map, and polar vector angle map.

Measurement of piezoelectric properties
After confirming the sample condition, poling of the samples was conducted in a silicone oil bath under T=80 °C and a DC electric field of 30 kV/cm for 30 min. The poled sample is left at room temperature for one week for aging. The bipolar/unipolar electric-field-induced strain curves including temperature dependence of the strain curves under 1 Hz in the temperature range from 25 to 220 °C and polarization-electric field (P-E) loops were measured under 1 Hz using a TF ANALYZER 3000 ferroelectric measuring system (AixACCT Systems GmbH, Aachen, Germany). The unipolar fatigue cycles at room temperature were carried out using 50 Hz, ED unipolar triangular waves, and then tested at 1 Hz and ED.

Phase-field simulation
The simulation details are provided in the Support materials.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Recently, composition and defect engineering have emerged as efficient strategies to improve the electromechanical properties of lead-free piezoelectric ceramics. For example, a giant piezoelectric coefficient of 3080 pmV⁻¹ has been achieved in Li/Sr‐doped (K0.5Na0.5)NbO3 piezoceramics (10.1002/adfm.202306416). In another paper (10.1126/sciadv.adn2829), the authors introduced A-site and oxygen vacancies to (K 0.48Na0.52)0.99 NbO2.995 ceramics and also achieved sufficiently high electrostrain of 0.7% and an effective piezoelectric coefficient of 3500 pmV ⁻¹, thus outperforming most of the existing lead-free piezoelectric ceramics. There were other reports in which very high electromechanical properties were achieved by, e.g. texturing of lead-free ceramics (10.1002/adfm.202214643). In this context, the paper by Fuzhi Cao et al. does not report anything principally new because the idea of strain improvement via Mn doping has already been published by some authors of this paper (https://doi.org/10.1016/j.jeurceramsoc.2022.10.061). The explanation of the increased strain by flattening the Landau energy density profile through A-site defect engineering has also been reported (10.1016/j.actamat.2022.117750). As such, neither high values of electrostrain and d33, nor their explanation do not warrant rapid publication of these research results in Nature Communications. The results are quite specific and won't attract the interest of the broad community of Nature Communication readers. I would suggest transferring this paper to the Journal of the European Ceramic Society, Sensors&Actuators, or alike. Other less important issues that should be considered by the authors during revision are listed below.\n1. Line 49. You cannot apply the requirement of E<10 kV/cm from MLA to a single-layer ceramic pellet. It is well-known that the breakdown electric field increases with decreasing thickness of the ceramic layer.\n2. Line 50. I do not understand what is “tailing phenomena”. Normally, it is the unipolar strain that matters for the actuator applications. Reversing the polarity of driving voltage would cause significant asymmetry and hysteresis albeit some increase of the maximum strain due to increased domain wall motion contribution.\n3. Line 72. Why does the strain increase with decreasing thickness? It is possible that the pellet bending contributes to this effect? Or it is the effect of increased breakdown field. Please, specify.\n4. Line 75. What important for the actuator application is the maximum strain rather than the effective piezoelectric coefficient which strongly changes with the applied electric field.\n5. Line 80. I do not understand the sentence “…the reversibility of the rhombohedral (R)-monoclinic (M) phase transition in R-orthorhombic (O) phase coexistence…”. What is the “reversibility of coexistence”? In general, such a simple thermodynamic picture can be applied to a single-domain ferroelectric without phase coexistence and domains. This is an oversimplified approach when considering a system with multiple domains and grains having coexisting phases.\n6. Line 87. Why “…boundary is designed in KNN-based ceramics via K/Na ions deficiency, which may be which may be easier to induce nano-domains (Fig.1-b1) and flatten Landau free Energy”. Do you have any experimental confirmation of that? Strong S-E hysteresis suggests that the response is purely ferroelectric without nanodomain contribution.\n7. Lines 167-173. The indicated temperature stability range T90 is misleading because of the non-mononous temperature dependence of the strain. It should be much less (c.a. 80 degrees). Please, revise this part. Also, it is not clear whether the developed strain is stable under repetitive cycling at all temperatures.\n8. Fig.3a. What is the meaning of the percentage of oxygen vacancies? Are these relative concentrations? What are the units?\n9. The introduction of PNRs does not lead to pronounced relaxor properties. The strain vs electric field behavior in x=0.98 composition is not characteristic of the relaxor behavior at all. Why it is so? Normally, the presence of nanodomains leads to reduced hysteresis and quadratic vs. field behavior at high electric fields.\n10. Does the strain asymmetry depend on the prepoling field? Is it improved with continuous driving? Is prepoling is necessary for the achievement of the maximum strain?\n11. Please, show the normal d33 values obtained by the resonance-antiresonance or Berlincourt methods. Are they comparable with the PZT or other reported lead-free compositions?\n12. Fig. 4 with the domain Imaging does not look reliable. Where are the domains (ferroelectric+ PNRS) on the área without the filed application? Why does the poled area look saturated? What are the values of the effective vertical piezoelectric coefficients? Are they in agreement with the bulk data? Black contrast without details could be due to the injected charge and electrostatic contribution. A detailed discussion is needed in this part of the manuscript.\n13. Any results on the repetitive driving under the unipolar/bipolar electric fields? The results might significantly change with only a few cycles and the applications of such ceramics may be problematic.", "reviewer_2": "The manuscript entitled \"Giant piezoelectric strain coefficient under low driving electric field in sodium potassium niobate piezoelectric ceramics with symmetry strain\" by F. Cao et al. addresses the development of KNN-based lead-free piezoelectric ceramics possessing very high piezoelectric strain coefficient d33* for actuator applications.\nThe work is sound and its key result is the reported high piezoelectric strain coefficient d33* (~ 2000 pm/V) measured in a sample of the experimental materials under an applied unipolar electric field cycle with a relatively low amplitude of 8.4 kV/cm. The demonstrated results also include a relatively symmetric shape of the bipolar hysteresis loops obtained for the same materials in both S-E and P-E dependencies, along with a fairly reasonable temperature stability. The authors claim these are the core element and urgently expected characteristics for piezoelectric actuators, while the proposed approaches to design such materials are promising for high-precision piezoelectric actuator applications.\nThe paper is well structured, clearly written, and provides sufficient context to guide readers to the problem, the proposed experimental approaches, and the discussion of the results. The experimental design and obtained data are explicitly presented and support the key achievements reported in the paper. The validity and robustness of the data interpretation seem to be at a high level, although some issues require clarification or revision.\nThe authors' position on the significance of the obtained results, as well as the degree of their novelty, seems to be exaggerated. Accordingly, the main claims made in the abstract, conclusion, and outlook of the paper are disputable and can be subject to objections and reservations.\nSome serious reservations regarding the novelty and significance of the study can be made from both the applied and scientific points of view, as outlined below.\n1. Application. The high value of piezoelectric strain coefficient d33* measured under an applied unipolar electric field of 8.4 kV/cm can be regarded as a necessary but still not sufficient condition for high-performance and high-precision actuator applications.\nThe key characteristics for such applications are shown in Fig. 2 (b), (c), and (e). The main concerns here are the precision and the functional performance. The unipolar S-E loops demonstrate notably nonlinear and hysteretic behavior (Fig. 2b and especially Fig. S6), which limits the maximum achievable strain at higher fields and the functional precision in actuator applications. Thus the reported materials cannot compete on these criteria with other recently introduced lead-free systems, such as BNST ceramics that exhibit higher precision and higher maximal unipolar strain (X. Zhou et al. Nat. Commun., 15, 6625 (2024), doi: 10.1038/s41467-024-51082-6, ref. [not cited]).\nIf the S-E nonlinearity and hysteresis effects are ignored, one can still consider applications requiring only qualitative actuation regardless of the precision. In these cases, the most valuable feature would be the maximum achievable electromechanical strain. In this regard, alternative lead-free ceramics such as recently reported examples of BNT-based (W. Feng et al. Nat Commun. 13, 5086 (2022). doi: 10.1038/s41467-022-32825-9, ref. [5]) and KNSN-based (G. Huangfu et al., Science 378, 1125 (2022), doi:10.1126/science.ade2964, ref. [3], B. Wang et al., Adv. Funct. Mater., 33, 2306416 (2023), doi: 10.1002/adfm.202306416, ref. [6]) have demonstrated better electromechanical performance in terms of maximum electrically induced strain.\nFurthermore, one may concern whether the paper indeed provides «an innovative way of designing new high performance lead-free piezoelectric ceramics that show promise for high-precision piezoelectric actuator applications». Let us consider the concept itself. The shape of the bipolar hysteresis loops shown in Fig. 2a suggests a relatively high impact of electrostriction (manifested by nonlinear S-E) and a relatively low contribution of piezoelectricity (manifesting by low negative strain amplitude in bipolar switching). Along with the reported manifestations of PNR and LSH, these are reasonable indications to presume that these materials may be relaxors. To prove or disprove this presumption, a series of additional experiments on direct piezoelectric properties and relaxor manifestation are needed. In the absence of such experiments, we can draw attention to the fact that the unipolar S-E hysteresis demonstrated in Fig. 2b, is very similar to that measured in the “Relaxor ferroelectric in state 2” as categorized by F. Li et al. in their seminal paper “Local structural inhomogeneity and electromechanical responses of ferroelectrics: A study on relaxor ferroelectrics”, Adv. Funct. Mater. 28, 1801504 (2018), doi: 10.1002/adfm.201801504, ref. [18]. According to this category, «State 2 may exhibit a high apparent d33* (…) at a moderate E-field. However, such an E-field-induced strain behavior is accompanied by large hysteresis and nonlinearity, which are associated with domain wall motion and E-field-induced nonpolar to polar phase transitions occurring simultaneously under an applied electric-field in State 2. Thus, for piezoelectric applications, State 2 relaxor ferroelectrics do not show an obvious advantage over State 3 relaxor ferroelectrics and classical ferroelectrics, due to the large nonlinearity inherently associated with State 2 relaxors; meanwhile, for electrostrictive and capacitor applications, State 1 relaxors show great advantages over State 2, owing to their low hysteresis and losses» (Citation: from Ref. [18], Subsection 3.2.3, Page 8 of 21). If the above quotation from [18] is correct and the proposed method of introducing LSH into KNN-based ceramics results in noticeable frequency dispersion of PNR dynamics, then high-precision applications of such material are unlikely to be feasible.\nBesides, the consideration of the prospects of materials for actuator applications would additionally require consideration of the operating frequency range as well as the stability of the electromechanical properties with respect to the number of operating cycles. Characterization of the dielectric permittivity and losses in the operating frequency and temperature ranges would also be useful.\n2. Extent of novelty with respect to the prospects of application. Most of the material design methods used in the study, such as engineering of defects and local structural inhomogeneity, have already been addressed in numerous previous studies (Refs. [3-12]). For KNN-based ferroelectric ceramics, these methods were implemented and resulted in very large field- induced deformation, albeit with a highly asymmetric bipolar hysteresis loop, ref. [3]. A substantial advance claimed by the authors was the introduction of additional measures to suppress the internal bias, which presumably arose due to the formation of polar defect pairs. This resulted in a significant improvement in the symmetry of the P-E and S-E loops. But what applications can practically benefit from the improved symmetry of the bipolar S-E hysteresis?\n3. Scientific impact. The degree of novelty compared to previous works on the design of lead-free KNN-based piezoelectric materials is centered around the measures taken to suppress the internal bias, presumably arising from the formation of polar defect pairs. For this purpose, the study considers a combination of doping material with Mn together with the use of a reducing atmosphere (N2/H2) during the sintering stage and cooling after sintering and holding in an inert atmosphere (N2). The relationship between all elements of the logically constructed hypothesis requires experimental verification. This is partially accomplished with the presented study of the XPS spectra and the subsequent analysis of the defect states as a function of the change in the ceramic composition. However, the influence of the reducing and inert atmospheres remains unclear. What happens in the case of sintering and cooling in air or only in an inert atmosphere (N2 without H2)? Does this lead to the formation of a secondary phase? Conductivity and/or dielectric losses? A decrease in the electromechanical performance? Since the introduction of reducing atmosphere was one of the key innovative achievements in this study, it would be very useful to obtain more detailed information on its effect on the state and distribution of crystal defects, LSH and PNR formation, and functional properties.\n4. Other issues. The free energy profile simulations shown in Fig. 4(c,d) for x=1 and x=0.98 ceramics are presented as color plots. In both cases, the angular energy gradient appeared to be approximately the same (red to green for the x=1 composition and green to blue for x=0.98). Thus, it seems that the simulations only resulted in a difference in the absolute values of the simulated free energies between the x=1 and x=0.98 compositions, while not resulted in any significant difference in terms of the energy gradient as might be interpreted from Fig. 1(a1-ac). In view of this discrepancy, the supplementary information file does not provide enough simulation details to check the accuracy, consistency and correctness of the simulations. What exactly were the calculation parameters taken different for the x=1 and x=0.98 ceramics and what is their origin? Is it possible to provide more of the original data used in the calculations to highlight the origin of the difference between the free energy profiles for the two different compositions?\nPossible typos:\nP. 10, line 194: «to keep valance balance»: to keep valence balance?\nP. 16, line 292: «Figs. 4(j-k)»: Figs. 4(c,d)?\nP. 19, line 356: «valance»: valence?\nFigs. 4(a,b): scale bar is missing.", "reviewer_3": "This paper presents a technique to enhance the effective piezoelectric strain coefficient at lower driving fields and simultaneously increase the symmetry of strain-field response of KNN-based piezoceramics. The effective d33* reported exceeds that of lead-based and lead-free piezoceramics at similar or reduced driving fields. These properties are said to be achieved due to the flattening of the Landau potential with increasing A-site K/Na deficiency, which results in polar nanoregion formation and reduced domain size. Alongside the improved piezoelectric properties, strain-field asymmetry is reduced due to reduced internal bias fields, temperature stability is enhanced and low strain hysteresis achieved. The improvements in piezoelectric properties through engineering the energy potential landscape have been proposed and used previously, but this specific approach appears to be newly applied to this material system and could be significant for the future development of lead-free piezoelectrics. The conclusions draw strong links between the results and the energy potential flattening, but these are not in themselves novelties developed in this paper but rather a new application of an existing method for engineering high performance piezoceramics. It would be useful for the authors to explain the new contribution of their work to the field in this regard.\nI also suggest the authors address the comments below related to the results and discussion within the paper:\n1. Whilst the reason for the increased piezoelectric properties are explained in relation to the defect chemistry as a function of K/Na deficiency, the paper would benefit from more explanation of the interplay between the PNRs and other observed effects such as the enhanced temperature stability and low strain hysteresis. These seem counter-intuitive when taken together but the origin of improved temperature stability is not discussed in detail.\n2. What is the reason for the sharp decline in piezoelectric properties at higher driving fields (Figure 2d)?\n3. The mechanisms by which the defect engineering leads to PNR formation and increased strain is clearly indicated in the schematic in figure 1, but the improved symmetry is not so clearly shown. There is also a minor inconsistency between the text on line 93 (‘nano-domains matrix’) and the figure (‘ceramic matrix’) in this figure, inconsistent use of capitals and a spelling mistake (‘phaes’) that should be corrected.\n4. A reduction in domain size and polar nanoregions are observed with TEM and STEM, respectively. The method is given for the STEM but not the TEM – this should be added.\n5. A statistical analysis of the polar vector angles is given – is this from a single image per sample? What steps were taken to ensure the STEM and TEM images were representative of the bulk samples?\n6. A phase field model is used to show the energy landscapes for two of the investigated materials but the methodology does not, to me, adequately describe what is shown in Figure 4c and d in the paper. For example, it describes the energy potential in relation to domain walls and a film but the figure shows the polarisation for different compositions as a function of direction. Perhaps I am just misunderstanding what is being shown but this needs more explanation to make it useful and usable for readers of the paper. Figures 4(j-k) are referred to on page 16 but these should be 4c and 4d, so it made me think perhaps something was missing.\n7. The intrinsic and extrinsic contributions to piezoelectricity are mentioned but not measured, despite comprehensive field-dependent strain-field measurements. Could the authors comment on how these contributions change as a function of K/Na content in their materials?\n8. The electrical characterisation is clearly presented but there are a couple of minor details missing/inconsistencies in the paper. The frequency at which ferroelectric measurements should be reported in the methods and/or the figures. The strain hysteresis value in the conclusion is quoted as 29.16% but at Ed for x = 0.98, the hysteresis is quoted in Table S2 as 26.35%. The field condition should be stated next to the value quoted in the conclusions.\nThere are also some minor errors between the manuscript and the referenced figures that should be addressed.\n9. A red and blue box are mentioned in reference to Figure S12 but these are not on the figure.\n10. Figure 4(j-k) mentioned but not included.\n11. Figure S12 caption doesn’t seem complete.\n12. Supplemental figures are not referred to in correct order/some not mentioned, e.g. S8 and S10 (should appear on page 10).", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to reviewers\nDear Editor and Reviewers,\nWe gratefully appreciate the editor and all reviewers for their time spend making\npositive and constructive comments. These comments are all valuable and helpful for\nrevising and improving our manuscript entitled “Giant piezoelectric strain coefficient\nunder low driving electric field in sodium potassium niobate piezoelectric ceramics\nwith symmetry strain”(NCOMMS-24-76132), as well as the important guiding\nsignificance to our researches.\nIn the following, we include a point-by-point response to the comments from each\nreviewer. In the revised manuscript, all the changes have been highlighted in blue.\nAttached please find the revised version, which we would like to submit for your kind\nconsideration.\nResponses to reviews\nReviewer # 1: ... [Full text of rebuttal for Round 1] ..."}, {"round": 2, "reviewer_comments": {"reviewer_2": "Dear Editor, Dear Authors,\nWe have carefully read the revised manuscript and the authors' response letter.\nLet us first answer the editor's main question: \"Have our concerns been addressed in the revisions?\" Our answer is no. Most of our concerns have not been sufficiently addressed.\nIn our opinion, the most problematic and questionable thing about this papers is that it first prioritizes the authors' concept and claims, and then chooses the most convenient way to present the experimental results and calculations so that they best match these initial claims and concept. These include the choice of measurement ranges, the choice of presenting results of numerical simulations, the use of simplistic modelling/simulation approach, and the avoidance of considering results that are not well supporting the original claims and concept. Thus, the article still suffers from a lack of sufficient argumentation, internal questioning and critical analysis.\nNext, we retain the previous numbering of our comments.\nComments 1, 2, and 3: We suggested ending the debate, acknowledging the excellent results achieved by the authors, and keeping our criticisms only for recording in the review file, so that readers could see the reviewers’ alternative opinions.\nIn this iteration, we received a large volume of text in response to our comments. We acknowledge the right of authors to respond to any of our comments, but we prefer to leave our opinions, assessments, and criticisms unchanged and to cease further discussion. Especially since this does not lead to any significant improvement of the manuscript, but only to a repetition of previous arguments.\nComment 4. Well done, we appreciate that our comment resulted in a substantial update of the manuscript with new valuable data. However, we believe that Fig. R5 (Piezoelectric coefficient d33 of (KN)xNT-BZ+MnO ceramics) should definitely be illustrated for a wider readership. The fact that “the d33 value is insensitive to compositional changes” is not well consistent with the concept of “free energy profile flattening” proposed and promoted in the paper (see also Comment 6 for details). However, this should not be a reason to discard this illustration. In fact, there is a slight increase in the direct-effect piezoelectric coefficient as the sample composition changes from x=1 to x=0.98 (Fig. R5), which can be in favour of the proposed free energy flattening interpretation, but perhaps to a much lesser extent than was concluded from the measurements of the electric field induced strain (Fig. S16(c,d)). A possible reason for the discrepancy between the values of the piezoelectric coefficients d33* measured in the direct mode (pC/N, Fig. R5) and the conversed mode (pm/V, Fig. S16(c,d)) is that the latter may include a significantly high contribution from electrostriction, which was not addressed at all in the paper.\nComment 5.1. The problem is not in the \"meticulousness\" but in the correct terminology. Unfortunately, the revised version is still unsatisfactory. In the perovskite-like lattices of niobates-tantalates, the K and Na ions cannot be called \"defects\" as stated in lines S186-S187 (Supplementary Information). Mn ions can replace other ions, including K/Na, and thus form so-called \"aliovalent substitutions\", which are classified as defects. They can also occupy A-site vacancies. A-site vacancies are also classified as defects. But in this case, the verb «occupy» does not mean the same as the verb «replace». So please check the wording/terminology carefully.\nComment 5.2. The questions concerned the physical basis of introduction of the concentration of Mn(2+) into the formula for the coefficient a1 as a simple additive correction term, the origin of the obtained value of 50, appearing as the correction factor of this term. We have not received any satisfactory answer. Furthermore, nothing makes this issue clearer for other readers in the revised version. In particular:\n5.2 (a) We have reviewed the referenced article (Science (2019) 365: 578, DOI: 10.1126/science.aaw8109), including its supplementary file, and found no information therein that would support this approach. Furthermore, this paper does not address any BNT-related materials and is not authored by T. Y. Li, C. Liu, P. Shi, et al. The referenced article is authored by H. Pan, F. Li, and Y. Liu and addresses BiFeO3-BaTiO3-SrTiO3 solid-solution films. If the paper has been misquoted, please correct it and cite the correct one, making it visible to all readers, not just reviewers. If the quotation was correct, please give us a more precise reference (with exact page and line numbers).\n5.2 (b) It is not sufficient to simply refer to another paper where \"a similar approach has been carried out in a similar way\" unless the cited paper properly addresses the physical basis of the approach itself. We therefore insist that the physical basis of the approach used in the modelling be clearly expressed and accessible to all readers.\n5.2 (c) It is also not enough to say that \"the value 50 was determined by fitting to experimental observations\". We (and probably many other readers) would like to know more details. How was the fitting processed? What exactly was the main fitting criterion? What exactly were the experimental data used for the fitting? We believe that all this information is critically important and thus should be disclosed to all readers, for example in the Supplementary file.\n5.2 (d) What is the point of the presented numerical simulation? What quantitative increase in d33 does it predict for x=0.98 compared to x=1 with all the numerical parameters used? Does this prediction agree quantitatively with any experimental observations? If the numerical simulation does not predict anything quantitatively, but only qualitatively confirms the initial hypothesis on which it is based, what scientific impact does it bring?\nGiven the above, we would suggest reconsidering the need for numerical modelling, at least in its current form.\nComment 5.2.1. Our comment concerned the discrepancy between the results and the stated calculation formulae. All readers, including reviewers, have the right to check the presented approaches, calculations and results. In this case, we simply took into account formulae (S4) and (S5) and analysed the influence of the introduced additional term “50c”, associated with the concentration of Mn(2+). It is obvious from a trivial analysis that for any non-zero values of Px, Py, Pz, the free energy value increases (and does not decrease) with increasing Mn(2+) concentration c. Next, if this were the only coefficient related to the compositional differences between the two cases illustrated in Fig. 4(c) and Fig. 4(d), then the x=0.98 case shown in Fig. 4(d) should be characterized by higher free energy values compared to the case shown in Fig. 4(c). But we observe the opposite. Now, this discrepancy is explained by specific «normalization process». And we reasonably wonder on why this manipulative normalization was applied at all, why it was applied differently to the cases x=1 and x=0.98, why it was omitted from the description of the calculations in Supplementary Information? In any case, to avoid the discrepancy between the demonstrated results and the stated calculation procedure, all the mathematical manipulations should be transparent for all readers, including those applied differently to different cases. This would avoid illusory impressions, such as, for example, that a change in composition associated with an increase in the Mn(2+) concentration leads to a decrease in the free energy, as could be concluded from the current representation.\nAlternatively, more fairly and preferably, the correct results of the free energy calculations in SI units could be demonstrated in all panels of Fig. 4 (c-f).\nComment 5.2.2. Here, we pointed another discrepancy found between the 3D and 2D representations of the same results, as plotted in Fig. 4(c,d) and Fig.4(d.e). Both illustrations represent the calculated values of free energy in arbitrary units, though the ranges differ in the 3D and 2D representations of the same calculations. Now, this discrepancy is explained by specific «subtraction» of «the the global minima dimensionless Landau energy», as described by equation (R1) g=g-g_min for «a more intuitive representation». Despite we do not really see why and how this simple operation does stimulate «an intuitive representation», we would keep suggesting to mention this additional subtraction in the publication text, just to avoid misunderstanding. Besides, P0 appearing on the horizontal axes in Fig. 4d and Fig. 4e should be also introduced somewhere. We also barely understand its meaning and necessity, since the horizontal axes Px and Px/Po, as well as their ranges are nearly identical in the 3D and 2D representations, only the units differ. Finally, we shall also address here an issue of different groups of points A, B, C and D, E, F. Is there any reason these groups of points should be different in 3D and 2D representations? If the 3D images would be rotated and faced with Px-Pz plane to the reader, it would not be necessary to introduce new points, right?\nComment 5.3. It is still incorrect there. Please check again. Supplementary Information, Line 186: T is not Curie temperature. The Curie temperature is 657 K, as mentioned in the reply to this comment. What value was set for T? 298K? Please also specify it for readers.\nComment 5.5. The new coefficients added (for the elastic and gradient components of the free energy) do not match the notations and formulations of Eqs. (S6) and (S7) Their source is also not indicated in the revised version. We queried these coefficients to make clear and sure that they are not related to any parameters that differentiate between the x=1 and x=0.98 samples (e.g. Mn(2+) concentration). If so, we assume that they were not used in the calculations, since the elastic and gradient components of the free energy seem to be equal additive terms in this simulation and thus do not affect the energy gradient (flattening).\nComment 6. Our initial comment addressed the serious concerns raised above (see Comments 4, 5.2, 5.2b, 5.2c and 5.2d) that the provided free energy flattening simulation is credible, valid and correctly interpreted. We are also concerned that further dissemination of such modeling approaches and their interpretation may be misleading and constitute questionable practice by providing an opportunity for other authors to cite such work in order to view and interpret scientific issues in such a simplistic and unjustifiable way.\nIndeed, the paper claims “a strategy to significantly flatten and symmetrize the Landau energy density profile in potassium sodium niobate (KNN) ceramics via A-site defect engineering and charge compensation” (lines 27–29). Next, in the experimental part, it is clearly shown that the variation of compositions and well-chosen parameters of solid-state synthesis in reduced atmosphere resulted in ceramics with a set of advanced electromechanical properties, the interpretation of which can be supported by the experimentally confirmed differences in phase-, defect- and micro/nano-structure, as perfectly demonstrated in Fig.3. The interpretation of the origin of the observed/achieved phenomena is the most crucial and controversial in this paper. In our opinion, the least obvious points in the manuscript are the origin and impact of the free energy profile flattening, as well as its relation to Mn(2+) ions or any other multiple effects exhibited in Fig. 3. The reasons are as follows.\n1) The increase in electrically induced strain in such systems is not necessarily a primary result of piezoelectricity itself, but can also be affected by electrostriction, especially in relaxors. In our first review comments we drew attention to the fact that the functional response of the system presented in the manuscript resembles that measured in the “Relaxor ferroelectric in state 2” as classified by F. Li et al. in Adv. Funct. Mater. 28, 1801504 (2018).\n2) Now we would also like to draw attention to the fact that the measured direct piezoelectric coefficient d33* (pC/N) (Fig. R5, see also comment 4) does not show such a strong dependence on the composition change as the measured converse-effect coefficient d33* (pm/V), which is seemingly affected by electrostriction.\nThus, the origin of the high electric field induced strain appears to be not fully investigated and understood. This should not be a problem, although the interpretation of the results should be more cautious. Regarding the unclear connection of the claimed free energy flattening with the Mn(2+) ion concentration, we would also like to draw attention to several contradictions: First, the dependency of free energy profile on the ceramic’s composition is not necessarily related only to the Mn(2+) concentration and not necessarily as straightforward as the linear dependence of the additive term to the coefficient a1. Second, if this were the case, then the free energy flattening induced through the additive term to the a1 coefficient, i.e. as a shift towards the paraelectric phase transition, should normally affect the temperature stability of the functional response.\nGiven the above, we would recommend avoiding all interpretations that suffer from insufficient physical basis and lack of experimental evidence and replacing them with a more thorough discussion that will reduce the level of confidence in uncertain points.\nComment 7. Minor issue: Lines 318-319: The indexing of panels with two- and three-dimensional representations is mixed up. Please check.", "reviewer_3": "The authors have now satisfactorily answered my question about the novel aspects of this work. I am not wholly convinced by the model presented alongside the rigorous experimental characterization to explain these effects as it seems to me that the parameters are adjusted to fit the experiments, rather than mechanistically predicting the observed behaviour. However, they do qualitatively explain the authors' proposed model of the approach taken to engineer the piezoelectric properties and so, given that the peer review process is open, I do not take too much issue with these results being presented as there is plenty of discussion that will enable readers to draw their own conclusions on this aspect of the work. Overall, this is a very good paper that has been improved by the additional data included and I am therefore happy to recommend it is accepted for publication at this time.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to reviewers\nDear Editor and Reviewers,\nWe gratefully appreciate the editor and all reviewers for their time making positive\nand constructive comments. These comments are all valuable and helpful for revising\nand improving our manuscript entitled “Giant piezoelectric strain coefficient under\nlow driving electric field in sodium potassium niobate piezoelectric ceramics with\nsymmetrical bipolar strain” and the important guiding significance to our research.\nIn the following, we include a point-by-point response to the comments from each\nreviewer. In the revised manuscript, all the changes have been highlighted in blue.\nAttached please find the revised version, which we would like to submit for your kind\nconsideration. ... [Full text of rebuttal for Round 2] ..."}, {"round": 3, "reviewer_comments": {"reviewer_2": "Dear Editor, Dear Authors!\nWe highly appreciate your patience and interest in our comments and are confident that the work done makes the paper more interesting, consistent and meaningful.\nAt this stage, we would propose to the editor to accept this manuscript for publication. We believe that the authors have made significant progress since the original version. As for our initial critical comments, as well as those of other reviewers, they will also be available to readers in the transparent peer review file.\nWith kind regards and best wishes for your further studies,\nMaxim Morozov, ITMO University, mimax@itmo.ru\nMariia Mikhailova, Tel Aviv University, mikhailova@mail.tau.ac.il", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to reviewers\nDear Editor and Reviewers,\nWe gratefully appreciate the editor and all reviewers for their time making positive\nand constructive comments. These comments are all valuable and helpful for revising\nand improving our manuscript entitled “Giant electrostrain coefficient under low\ndriving electric field in sodium potassium niobate piezoelectric ceramics with\nsymmetrical bipolar strain” and the important guiding significance to our research.\nIn the following, we include a point-by-point response to the comments from each\nreviewer. ... [Full text of rebuttal for Round 3] ..."}]

Decision letter