Impact of stress-induced precipitate variant selection on anisotropic electrical properties of piezoceramics

Domain: earth_science
Published: 2024-11-28
Editorial outcome: major_revision

Abstract
Precipitation hardening has been recently validated as a new mechanism for domain wall pinning and mechanical loss reduction in piezoelectrics. While anisometric precipitates have high pinning strengths, there is limited knowledge about the electrical anisotropy of the precipitation-hardened piezoceramics. In the present work, we successfully orient the precipitates in Li0.18Na0.82NbO3 piezoceramics by applying a uniaxial stress during the aging and studied its electrical anisotropy. Predicted by mechanical simulation and verified by transmission electron microscopy, it is demonstrated that the precipitate variant with its long axis perpendicular to the applied stress is energetically favored. The electrical anisotropy of the stress-assisted aged Li0.18Na0.82NbO3 is studied by applying electrical fields parallel or perpendicular to the stress axis. The domain wall contribution to permittivity is found to vary by more than a factor of two depending on orientation. In addition, the domain walls are more difficult to be activated by increasing the temperature when the electric field is perpendicular to the stress axis. Our work highlights the precipitate variant selection induced by stress-assisted aging and the related electrical anisotropy in piezoceramics. This technique enables the precipitate orientation in piezoceramics and the utilization of its anisotropy, providing fundamental insight into precipitate-domain-wall interactions and setting the ground for leveraging precipitation hardening effect in piezoceramics.

Introduction
Piezoelectric hardening stands as a pivotal strategy aimed at mitigating the mechanical loss in piezoelectric materials during their application. The strategy is particularly crucial for piezoelectric devices operating in close proximity to their resonance frequency, e.g., ultrasonic sensors, motors, and imaging devices1,2. Recently, investigations of cutting-edge two-dimensional infrared imaging equipment have been made pioneering work by Hu et al.3, where the pressing challenge of piezoelectric hardening in such necessitates prompt attention and resolution. The principal objective of piezoelectric hardening is to suppress domain wall (DW) motion, which constitutes the primary source of mechanical loss and self-heating in these devices4,5.

For decades, the prevailing method for hardening piezoelectric materials has been chemical doping, which is extensively adopted in both the commercial and academic spheres6–8. However, the hardening efficacy of chemical doping diminishes at elevated vibration velocities or temperatures due to disruptions in the internal bias field established by mobile oxygen vacancies9, which serve to stabilize the domain structure10–12. These drawbacks of traditional hardening limit the use of hard piezoelectrics in high-power applications, where mechanical loss increases significantly with rising vibration velocity. In response to this limitation, hardening through a composite approach was proposed as an alternative strategy, capitalizing on the superior stability of secondary phases and their ability to effectively pin DWs via mechanical stress at phase interfaces13–15.

A classical hardening technique in metals, precipitation hardening, which introduces precipitates through a thermal treatment of supersaturated alloys16, was recently successfully implemented in Ba0.7Ca0.3TiO3 (BCT) and Li0.18Na0.82NbO3 (LNN) piezoceramics17,18. By establishing a proper aging scheme, precipitates with dimensions of several hundred nanometers were introduced into grains of the abovementioned piezoceramics. The intragranular precipitates directly interact with DWs and result in a more pronounced pinning effect, as compared to secondary phases located at grain boundaries. In situ, high-energy X-ray diffraction (XRD) further confirmed the suppression of DW motion in the presence of precipitates19.

In the case of anisometric precipitates, which were previously observed in LNN piezoceramics17,20, it is intuitively expected that the pinning effect on DWs varies in accordance to the relationship between the applied excitation (electric field or stress) and orientations of the precipitate. The related phenomenon of anisotropy in mechanical properties has been studied in precipitation-hardened metals21–23, underscoring its distinct influences on impeding different slip and twinning modes. Analogously, electrical properties in piezoceramics with precipitates should also exhibit anisotropic characteristics, stemming from two potential sources. One source arises from the crystal orientation: intrinsic electrical parameters, such as the piezoelectric coefficient and permittivity, manifest as tensors with distinct coefficients, thereby producing divergent electrical responses when an electric field is applied along different crystallographic directions24. Milestone advancements have been achieved by Wang et al. in delving into the electrical characteristics25. However, this effect can be largely neglected in non-textured polycrystalline materials where random grain orientation eliminates the anisotropy. The other source of anisotropy is the precipitate orientation, which can persist even in polycrystalline materials when a preferred precipitate orientation exists in the materials. The studies on precipitate-related anisotropy in ceramics, especially on electrical properties, are in its infancy. Similar to single crystals, achieving such anisotropy in polycrystalline materials can give rise to an enhancement in property if used in the proper direction. For example, if the pinning effect from precipitates on DWs is maximized in a certain direction, the mechanical quality factor could be significantly enhanced when applying an electric field in that direction. Hence, it is of great fundamental significance to investigate the anisotropy in precipitation-hardened piezoceramics as a cornerstone for functional anisotropy enticed by a prior application of a separated deviatoric field.

Investigating such precipitate-related macroscopic anisotropy necessitates the sophisticated alignment of precipitate particles at the microscopical level. It has been reported that applying a uniaxial stress during aging can lead to a shape change (“rafting”) or a preferred orientation (“variant selection”) of precipitates in various metallic alloys26,27. For instance, in Ni-based alloys, the application of tensile and compressive stress along [001] direction leads to the formation of plate-like and parallelepiped precipitates, respectively27–30. The effect of uniaxial stress during aging on precipitate morphology has been attributed to elastic effects (e.g., changes in elastic modulus, misfit strain, elastic free energy)26,29–31 and dislocation generation during creep27,28. Stress-driven variant selection of precipitates has also been observed in other alloy systems, e.g., Ti32, Al33, and Ni31 alloys. Song et al. investigated the effect of a uniaxial stress on different aging stages in a Ni–Mo–Cr–W alloy: the precipitates are globular at the early stage (nucleation) where the surface energy weighs in heavily, while during the coarsening stage, the volume energy leads to variant selection to reduce the strain energy of the system31. Through a simulation study, Shi et al. revealed that the variant selection in a Ti alloy is influenced by a competition between externally applied stress and internal stress arising from the precipitation reaction itself32. However, the effect of uniaxial stress on precipitate formation in ceramics has remained unexplored. Even for the well-studied commercial system of magnesia-partially stabilized zirconia (Mg-PSZ), where interfacial strain and morphology of precipitates have been dealt with in great detail34, experimental endeavors of stress-assisted aging appear missing. Prior research in LNN has revealed that plate-like precipitates exhibit coherence with the matrix lattice along the {110}PC habit plane (the subscript “PC” means the hkl indexes are based on the pseudo-cubic coordinate system with the lattice parameter of ~3.9 Å)17,20. The smallest misfit strain of 0.84% is observed along the habit plane between the matrix phase (NaNbO3-rich solid solution, NNss) and precipitate phase (LiNbO3-rich solid solution, LNss). Notably, the NNss exhibits a cubic structure at the aging temperature, thus the possibility of a precipitate habiting on any one of {110}PC is the same, leading to six variants of the precipitates. However, when a uniaxial mechanical stress is applied, the misfit strain between the matrix phase and precipitate phase changes anisotropically. This suggests that certain precipitate variants with minimal overall misfit strain are favored energetically, and their selection leads to a degree of precipitate alignment when uniaxial mechanical stress is applied.

In the formation of precipitates in solids, three types of free energy changes compete: the energy reduction by replacing the matrix phase with the precipitate phase, the energy increase from the interfacial energy, and the misfit strain energy35. The driving force for the precipitation is the energy reduction, whereas the factors leading to energy increase represent barriers to precipitate nucleation. Together, the net energy change dictates the thermodynamics for precipitation process. Lowering the aging temperature elevates the chemical driving force35 but slows down the diffusion kinetics for precipitate growth. Therefore, static aging by tuning temperature alone may not be capable of achieving desired precipitate distribution and size within a practically feasible period36. Alternatively, one can envision lowering the nucleation barrier by applying a stress field to reduce the misfit strain energy, which effectively facilitates the precipitation nucleation without compromising on diffusion kinetics.

In this work, we aged sintered LNN piezoceramics under a constant uniaxial stress to introduce preferred orientations for precipitates. Initially, a mechanical simulation was performed to examine the energy difference between two precipitates oriented parallel and perpendicular to the stress direction, which substantiated the existence of preferred precipitate orientation in stress-assisted aged samples. Subsequently, cylindrical stress-assisted aged LNN samples were cut with varied orientations of their electroding faces, either parallel or perpendicular to the prior applied stress direction. Transmission electron microscopy (TEM) was performed to further evidence the variant selection in stress-assisted aged LNN by examining the relationship between precipitate orientation and applied stress. Electrical investigations, i.e., small-signal Rayleigh measurement and large-signal polarization hysteresis measurement, were conducted to quantify the DW pinning effect when the electric field is parallel or perpendicular to the stress direction. Our study has successfully achieved variant selection of precipitates in ceramic materials and sheds light on the electrical anisotropy in the precipitated LNN piezoceramics. These results provide a fundamental guide and pave the way for enhancing the electromechanical properties of precipitation-hardened piezoceramics.

Results
Precipitate alignment introduced by applying mechanical stress during aging
Here we address the challenge of aligning precipitates designed by applying a compressive uniaxial stress during the aging process. Quenched single-phase LNN piezoceramics were stress-assisted aged using a setup schematically depicted in Fig. 1a (see “Methods” section and Section 1 in the Supplementary Information). The samples which were aged with the maximum stress of 150 MPa and 350 MPa are denoted by “150 MPa-aged sample” and “350 MPa-aged sample”, respectively. For reference, samples aged with the same temperature but without stress (“stress-free aged sample”) were prepared. To examine the electrical anisotropy, all the samples were cut in horizontal and vertical directions (hereafter denoted as “horizontal cut” and “vertical cut”, respectively) to have the applied electric field either parallel or perpendicular to the stress direction, as depicted in Fig. 1b.

From a mechanical perspective, an applied stress can lead to an anisotropic change in the effective misfit strain between precipitate and matrix. For the LNN precipitation system, the matrix NNss phase is stiffer than the precipitate LNss phase, i.e., NNss has larger elastic constants37,38, and the lattice parameter of the precipitate phase LNss is smaller than that of the matrix phase NNss, indicating a negative misfit strain with respect to the matrix. Hence, a compressive stress will compact the LNss lattice more in the stress direction than the NNss lattice, leading to an increased effective misfit strain in the stress direction. As a result, precipitates with their long axis parallel/close to the stress direction are energetically disadvantaged. The possibilities of finding different precipitate variants are depicted in Fig. 1c, d, which are denoted by P1, P2, …, P6. According to the inference above, it can be hypothesized that P1 should be the smallest in the case of <110>PC oriented grains, since its corresponding precipitate variant has its largest interface parallel to the stress direction, where the effective misfit is increased most by the mechanical stress thus it is least energetically favored.

Simulation results
To verify the above mentioned hypothesis and examine the relationship between the system’s mechanical energy, precipitate orientation, and precipitate size, the overall mechanical energies (sum of elastic, interface energy, and the potential of the external force) of two-dimensional matrix-precipitate systems were calculated as a function of precipitate size. Similar simulation has been performed to study stresses associated with the tetragonal precipitates and the tetragonal to monoclinic transformation in MgO-PSZ39,40. The stress-free model is depicted in Fig. 2a, while the models with mechanical stress are schematically depicted in Fig. 2b, c (the explanation of the symbols used in Fig. 2a–c can be found in the “Methods” section). The ellipse represents the cross-section of the plate-like precipitate, where the long axis corresponds to the length direction and the short axis corresponds to the thickness direction. Compared to the stress-free model, the two models with stress are rotated by 45° to have the long axis of a precipitate parallel and perpendicular to the applied stress (corresponding to the P1 and P2 cases in Fig. 1c), representing the two extreme conditions.

The calculated overall mechanical energies and m values as a function of cross-section area of precipitate without and with applied stress are displayed in Fig. 2d–f. The overall mechanical energies and m values were calculated after a complete relaxation ensuring minimal mechanical energy for each given precipitate volume and each scenario (load case and precipitate orientation), thus only reflecting the final states. The kinetics during the precipitate growth can be described by configurational forces as depicted in Fig. S1. For both cases, the mechanical energy naturally increases with increasing precipitate size, as volume and interfacial area increase. In the stress-free case (σ=0), the energy-size curves for the scenarios where the precipitate long axis is parallel and perpendicular to the stress vector σ coincide, indicating that there is no energy preference for the two precipitate variants (Fig. 2d). With σ=150 and 350 MPa, the mechanical energy of the system with the precipitate long axis perpendicular to σ is lower than that of the system with precipitate long axis parallel to σ, and the difference increases with increasing precipitate size. This indicates that the precipitate variant with its long axis perpendicular to the applied stress is favored energetically, consistent with the hypothesis in Fig. 1d, e. The more significant difference at larger precipitate size implies that the variant selection due to the stress tends to occur during the precipitate growth stage, which is consistent with the observation from Song et al.31. In addition, the precipitate-orientation-related overall mechanical energy difference is more prominent in systems with larger mechanical load.

In general, the absolute value of the aspect ratio |m| increases with increasing precipitate size39,40. This is related to the reduced contribution of the interfacial energy term as compared to the volume term. As discussed in the beginning of this section, the compressive stress in LNN leads to an increased misfit strain in the stress direction, which renders precipitate elongation in this direction less energetically favored. In the case of a precipitate with its long axis parallel to the stress, the applied stress decreases the difference in misfit strain between the precipitate and matrix along the long axis. Hence, the dimensions in the cross-section are more equiaxed and the |m| value is reduced.

Precipitate morphology characterized by TEM
A bright-field TEM image of a [100]PC-oriented grain in stress-free aged LNN (500°C-24h+600°C-6h) from a previous study is featured in Fig. 3a for reference17. Precipitate variants habiting on (011)PC and (01-1)PC can be clearly identified and are labeled as “edge-on precipitate”. In addition, precipitate variants habiting on (110)PC/(1-10)PC (ellipsoids with long axis in [010]PC) and (101)PC/(10-1)PC (ellipsoids with long axis in [001]PC) are detected and labeled as “inclined precipitate”. No variant selection is observed in the stress-free aged LNN. In stress-assisted aged LNN samples, plate-like precipitates approximately measuring 200–400 nm in length and 10–30 nm in thickness can be observed as well, corresponding to the long and short axes of the precipitate cross-section, respectively. However, only the variant habiting on (101)PC can be observed in the stress-assisted aged LNN, where the applied stress is in the [101]PC direction. Note that the long axis of the precipitates is aligned perpendicular to the applied stress, as illustrated in Fig. 3b–d. This relationship between precipitate orientation and the stress direction is validated in other representative TEM images (Figs. S2 and S3). Energy dispersive spectroscopy (EDS) analysis reveals the composition of the precipitates and demonstrates the presence of Nb and O with a notable Na deficiency. In addition, the presence of Li within the precipitates is detected by electron energy loss spectroscopy (EELS), confirming LNss precipitates (Fig. S4). The TEM results indicate that the precipitates oriented with their long axis perpendicular to the stress direction are preferred in the stress-aged LNN samples, as predicted by our mechanical simulation.

Rayleigh measurement
Rayleigh measurement, i.e., the quantification of the real part of relative permittivity εr or piezoelectric coefficient d33 as a function of AC field amplitude, is an effective method to separate the contributions from reversible mechanisms (field-induced lattice strain and reversible DW motion) and irreversible mechanisms (irreversible DW motion)41,42. To investigate the electrical anisotropy of stress-assisted aged LNN piezoceramics, Rayleigh measurements (εr-E curve) were conducted on both cuts. The permittivity close to E=0 V/mm (εinit) is almost solely contributed by the reversible mechanisms and is independent of field amplitude. In comparison, εr − εinit represent the contribution from the irreversible mechanisms and depends on the field amplitude43. Stress-free aged samples were considered as a reference, as depicted in Fig. 4a, where the horizontal cut and vertical cut exhibit no difference in their (εr − εinit)-E curves, characterizing the Rayleigh behavior as isotropic. Differently cut samples in stress-assisted aged samples reveal significant differences in small-scale behavior (Fig. 4b, c, which correspond to 150 MPa-aged sample and 350 MPa-aged sample, respectively). Compared to vertical cut, the (εr − εinit) increases more significantly with electric field in horizontal cut samples. In addition, compared to the stress-free aged and 150 MPa-aged sample, the vertical cut of the 350 MPa-aged samples features the smallest hysteresis in the (εr − εinit)-E curve. The hysteresis is attributed to the depinning of part of DWs from precipitates. The smallest hysteresis in the vertical cut of the 350 MPa-aged sample indicates that the DWs in this sample are barely depinned by increasing the electric field amplitude.

The nonlinear coefficients, α, and the y-axis interceptions of the εr-E curves, εinit, were determined from linear fitting of the εr-E curves (Fig. S5). These two parameters are proportional to the irreversible and reversible contributions to permittivity, respectively, and the ratio α/εinit thus reflects the relative contribution from irreversible DW motion. For the stress-assisted aged samples, the α/εinit values of the vertical cuts are smaller than those of the horizontal cuts, as revealed in Fig. 4d. The difference is more significant in the 350 MPa-aged samples. Compared to the stress-free aged sample, the α/εinit is enhanced in the horizontal cut of stress-assisted aged samples while α/εinit is suppressed in the vertical cut of stress-assisted aged sample.

As predicted by the simulation and evidenced by the TEM characterization, precipitates with their long axes perpendicular to the applied stress carry a reduced penalty in mechanical energy in the stress-assisted aged LNN samples. That means, the precipitates tend to have in-plane orientations in the horizontal cut, while they tend to have out-of-plane orientations in the vertical cut. The Rayleigh results indicate that the stress-induced variant selection of precipitates has an influence on the irreversible DW motion driven by small-signal electric fields. The irreversible DW motion is suppressed to a larger degree when the precipitates are oriented out-of-plane regarding to the electroding faces (vertical cut), while the DWs are less impeded when the precipitates are oriented in-plane (horizontal cut). This difference is more significant in the samples aged with larger stress, where the anisotropic misfit strain changes and the variant selection effect is more prominent.

Polarization hysteresis
The pinning effect of DWs by precipitates differs between small- and large-signal electric field, as indicated in a previous study17. Representative room-temperature P–E loops of the 150 MPa-aged and 350 MPa-aged samples with different cuts are featured in Fig. 5a, b. The polarization of all aged samples does not saturate at electric fields below the dielectric breakdown field. Compared to the unaged sample, which exhibit typical ferroelectric P–E loop (Fig. S6), the strong pinning force from the precipitates does not allow the establishment of saturated polarization in the aged samples up to 8 kV/mm, which is consistent with the sample aged stress-free at a similar condition (500°C-24h+600°C-6h) in the previous study17. The P–E loops of the horizontal and vertical cuts behave differently for the stress-assisted aged samples, where the vertical cuts exhibit lower remanent and maximum polarizations, indicating a stronger pinning effect on DWs. Unlike the small-signal property, for which the anisotropy differs distinctly in the 150 MPa-aged and 350 MPa-aged samples, the anisotropy in the large-signal P–E loop due to stress change is very small (Fig. 5e). This phenomenon indicates that the polarization under large-signal electric field is less sensitive to the variant selection of precipitates in LNN. It is worth noting that the stronger DW pinning effect in the vertical cut is consistent with the Rayleigh result, where the irreversible DW contribution is more suppressed in the vertical cut, suggesting that the effect of the stress-induced variant selection on DW pinning has the same trend under small- and large-signal electric fields.

Since a typical ferroelectric P–E loop cannot be observed in the aged LNN at room temperature, thermal activation was contemplated to fully open the P–E loop. The P–E loops of the 150 MPa-aged samples at elevated temperatures are displayed in Fig. 5c, d. Unlike in some other ferroelectrics, in which the maximum polarization decreases with increasing temperature, the LNN samples exhibit the opposite trend. This can be attributed to the prevailing thermal activation of DWs over the spontaneous polarization decrease with increasing temperature. The P–E loops of the horizontal cut are found to open more with increasing temperature, as compared to the vertical cut. The maximum polarization Pm of the horizontal/vertical cut from the 150 MPa-aged sample as a function of temperature is depicted in Fig. 5f, and the normalized Pm is displayed in the inset. The increased Pm with temperature is suggested to relate to the thermally activated DW motion. Thermal activation is more effective in the horizontal cut (Fig. 5f). This mimics the related influence of precipitate orientation with increased electric field (Fig. 4d), where the horizontal cut also reaches higher relative maximum polarization with rising electric field. In contrast, the P–E loops in the vertical cut demonstrate stronger pinning effects as function of temperature (Fig. 5f) as well as electric field (Fig. 4d). This resilience to temperature excursions again demonstrates the strong advantage of precipitation hardening to chemical doping.

In summary, we have synthesized LNN piezoceramics and aged them under a uniaxial stress to introduce precipitates. The significance of this work lies in providing a simple method to introduce electrical anisotropy, which can be utilized to achieve a stronger DW pinning in a certain direction as compared to samples with isotropic electrical properties. The following conclusions can be drawn from this work:
(a) It is predicted by calculation that, for a LNN ceramic with NNss as the matrix and LNss as the precipitate, a uniaxial stress during the aging process can lead to a variant selection of precipitates: precipitates with their long axes perpendicular to the applied stress are energetically favored. The variant selection is attributed to the stiffness contrast between the precipitate and the matrix, which changes the mechanical energy.
(b) Precipitate variant selection has been successfully introduced by a stress-assisted aging of LNN piezoceramics. TEM has verified that the precipitates are oriented with their long axes perpendicular to the stress, which is consistent with the prediction by the theoretical calculation.
(c) The induced variant selection gives rise to an anisotropy in the electrical properties. The DWs in the variant, where the precipitates are mostly oriented out-of-plane, are stronger pinned under both small- and large-signal electric fields. Furthermore, the DWs in this variant are more difficult to be thermally activated, indicating the pinning effect from precipitates is more temperature-stable.

Methods
Sample preparation
The LNN ceramics with a nominal composition of Li0.18Na0.82NbO3 were synthesized by solid-state reaction. The starting powders, Li2CO3 (Alfa Aesar, 99%), Na2CO3 (Alfa Aesar, 99.95%), and Nb2O5 (Alfa Aesar, 99.9%), were weighted stoichiometrically, except that 1% excess Na2CO3 was added to compensate for volatilization during the sintering process. The ball milling and calcination processes were reported elsewhere17. The calcined powders were then compacted into cylinders and subjected to cold isostatic pressing with a pressure of 357 MPa. The dimension of the green samples was ~Φ6 mm × 9 mm. These green samples were sintered at 1300 °C for 2 h with a heating and cooling rate of 4 K/min.

Quenching is necessary for precipitation in LNN ceramics, as revealed by XRD examination of two aged samples, one of which underwent quenching and the other one was furnace-cooled after sintering (Fig. S9). To prevent cracks caused by thermal shock during quenching, the sintered cylindrical samples were lathed and ground to a dimension of ~Φ4 mm × 8 mm44. Then, these samples were reheated to 1300 °C and held for 2 h, followed by air quenching. The cooling rate was carefully controlled (with ~5 min to cool from the maximum temperature to room temperature) to avoid cracks.

Stress-assisted aging was conducted on quenched cylindrical samples using a load frame (Z010, Zwick/Roell, Ulm, Germany) equipped with a furnace. A two-stage aging consisting of the nucleation stage and growth stage for the precipitates was adopted. The sample was preheated to 300 °C, where the precipitate formation is kinetically suppressed. Then, the desired mechanical compressive stress of either 150 or 350 MPa was applied to the sample at a loading rate of 0.4 N/s (0.032 MPa/s). The sample was heated to the nucleation temperature (550 °C) and held for 24 h, and then to the growth temperature (650 °C) and held for another 8 h. After aging, the mechanical stress was released at a rate of 1 N/s, and the temperature was decreased to room temperature with 5 K/min. Each cylindrical sample was cut into 4~5 horizontal cuts and 4~5 vertical cuts. Platinum electrodes were sputtered onto the largest faces of the cut samples, so that the applied electrical field was parallel and perpendicular to the applied stress in the horizontal cut and vertical cut, respectively.

Calculation of the system energy under mechanical stress
We proceed by focusing on the mechanical energy and interfacial energy only and compare precipitates only at same volume to be able to neglect the formation enthalpy of the precipitate phase. The models were configured as <110>PC-oriented with the long axis of a precipitate parallel and perpendicular to the applied stress. A Finite Element discretization of the model was solved with the help of the Finite Element library FEniCS45. The parameters and necessary conversions adopted in the simulation are described in the Supplementary Information. Assuming plane strain conditions, an infinite matrix domain M with an elliptical precipitate domain P was considered as the integration volume (see Fig. 2a–c). The stiffness of the precipitate and matrix are denoted by CP and CM, respectively, and the interface energy is modeled by an energy density γ at the precipitate/matrix interface Γ. The smaller lattice of LNss leads to a volume reduction in the region where the precipitate forms, implemented by an eigenstrain field ε046,47. The internal mechanical energy of the system consists of an elastic and interface contribution:
Eint = Eelastic + Einterfacial = ∫P∪M 1/2 (ε − ε0) : C (ε − ε0) dV + ∫Γ γ dS (1)
C(x) = {CP, x ∈ P; CM, x ∈ M} (2)
where ε denotes the elastic strain tensor; C is the locally defined stiffness tensor, which equals to CP and CM when the spatial coordinate x is within the precipitate domain P and matrix domain M, respectively; the colon in the first term denotes the double contraction product between the fourth-order stiffness tensor C and the second-order stiffness tensor ε; dV and dS are the infinitesimal volume and surface element, respectively. The models with mechanical stress are schematically depicted in Fig. 2b, c. Compared to Fig. 2a, the two models are rotated by 45° to have the <110>PC of the NNss parallel to the vertical applied stress. The overall mechanical energy for a system with mechanical stress is:
Etot = Eint + Eext = Eint + ∫∂M t · u dS (3)
where the applied stress vector is denoted by t = [0 −σ]T, and u is the displacement.

For the relationship between overall mechanical energy and precipitate size, the aspect ratio m=(a−b)/(a+b) of the elliptical precipitate was optimized by minimizing the mechanical energy of the system for each given precipitate size, which is represented by the cross-section area A. Thus, the most energetically stable solution is ensured for each precipitate size.

TEM characterization
Structural and chemical investigations of precipitates were performed with scanning transmission electron microscopy (STEM) using probe C corrected Jeol ARM200CF (Jeol Ltd., Tokyo, Japan), equipped with a Jeol Centurio 100 mm2 Silicon Drift Detector (SDD) EDS system and a Gatan Quantum ER Dual EELS system (Gatan, Pleasanton, CA, USA). One horizontal cut and one vertical cut from a 350 MPa-aged sample were prepared for TEM examination. The TEM specimens were prepared by grinding with SiC paper of 1200, 2400, and 4000 grit, followed by polishing with diamond paste containing 3 and 0.25 µm particles to a thickness of ~100 µm. The polished discs were then dimple ground to around 10 µm thickness using a dimpler grinder (Model 656, Gatan, Pleasanton, CA, USA) and further thinned to electron transparency by Ar-ion milling (Gatan PIPS Model 691, New York, NY, USA) at voltages ranging from 3.5 to 2.5 kV until a hole appeared, followed by cleaning at 0.8 kV. The samples were cooled during the Ar-ion milling process. In order to retain information regarding the direction of mechanical load, a horizontal cut was processed as a plane view, while a vertical cut was prepared in the cross-sectional view orientation.

Electrical measurement
The large-signal polarization hysteresis measurements were performed with a modified Sawyer–Tower circuit. Three to four samples of each cut and each aging condition were quantified for statistics and reproducibility. The samples were immersed in silicone oil during the measurement. A triangular electric field with a frequency of 1 Hz and amplitude up to 8 kV/mm was applied. High-temperature polarization hysteresis measurements up to 120 °C were realized by heating the silicone oil, and the electric-field parameters were the same as those used in the room-temperature measurement. Cycling test of P–E loops was performed by applying cycling electric field with a frequency of 1 Hz and amplitude up to 8 kV/mm at room temperature. The permittivity measurement used a commercial lock-in amplifier (Stanford Research System, SR830 DSP), a voltage source meter (also SR830 DSP), and a voltage amplifier (Trek, Model PZD700A M/S). These instruments were paired with a custom-made resistor box, which includes precision resistors that are controlled by selection and connected in series with the sample. The frequency was 1 kHz and the applied electric field increased from 0 to 1000 V/mm and then decreased back. Before the measurement, the samples were poled at 8 kV/mm at 100 °C for 15 min and cooled down to room temperature with the field on.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript titled \"Impact of stress-induced precipitate variant selection on anisotropic electrical properties of piezoceramics\" by Changhao Zhao et al. is a well written description of what appears to be a well thought out experiment that bridges basic science concepts through real-world relevant properties and associated applications. It was pleasure to see classical metallurgy concepts being applied by ceramists to solve difficult problems. Despite the many technical achievements of this study, this cross-field approach and subsequent success is maybe the most noteworthy aspect of the study. I think the findings will be of significance from both a basic science perspective (it doesn't take much to think of other methods or systems in which precipitates can be aligned) or applications in hard piezoelectrics for power electronic applications.The conclusions and claims are well supported by the property measurements and micrographs provided. The experimental method was detailed and I believe adequate for the work to be reproduced. I believe there are several places the manuscript can be improved as detailed here:\nMajor comments:\n1) It would be good if the authors did more to distinguish on the basic science side specifically the delineation of this work for work done previously in this area. It took a dive into the references to have clarity on this.\n2) The manuscript theory and modeling section was underwhelming. Although the FE model was nice, I feel like a lot more could be done on the kinetics side of understanding the precipitation process and thus predicting size and distribution of the 2nd phase. I also felt more could be done on prediction of the expected properties from the resulting microstructure. An in depth theoretical understanding, really Heckmann Diagram/ Crystal Physics approach would greatly strengthen the paper.\n3) The microscopy would be greatly enhanced with the addition of either electron tomography or weak beam dark field characterization of the 2nd phase to verify location and spacing, as opposed to the down zone imaging shown in the manuscript.\nMinor comments:\n1) The statement that \"novel hardening strategy known as precipitation hardening\" is an overstatement. Precipitation Hardening has been in use since the early bronze age and the theory was proposed by Alfred Wilm in Germany in 1906.\n2) The S in \"Cs corrected\" should be a subscript.\n3) Greater details in the sample preparation should be included above \"TEM specimens were prepared by grinding, dimpling and final Ar-ion milling\" This is important to ensure no artifacts are added and alter the micrographic interpretation as result of mechanical deformation during grinding and dimpling or ion beam mixing during PIPS milling.\n4) et al28. should be et al.28.\n5) Stress is shown as a single directional vector in Figure 3, It is a compression experiment and should be shown as much.\n5) The statement \"large-signal property is less sensitive to the variant selection of precipitates\" is vague and broad, thus it should be better clarified.", "reviewer_2": "This manuscript presents an interesting work that the precipitates in Li0.18Na0.82NbO3 (LNN) piezoceramics can be oriented by aging with a uniaxial stress. The electrical anisotropy has also been investigated. The precipitates are oriented with their long axes perpendicular to the stress, which is consistent with the prediction by the theoretical calculation. The domain walls in the variant are strongly pinned under both small- and large-signal electric fields, while the precipitates are mostly oriented out-of-plane.\nIt is an informative work. However, I do not quite see the importance of this work. At least, the importance has not been fully presented. Meanwhile, some results are inadequately discussed. I suggest the authors to consider the following comments.\n(1) Has the endurance of this anisotropy been tested?\n(2) I do not quite understand equation (1). What does the colon mean? How does C^M and C^P enters the equations?\n(3) How can this macroscopic anisotropy be possibly used? The authors may provide some insights.\n(4) Why does the maximum polarization decrease as the stress increases? Why does the maximum polarization increase as the temperature increases, as the polarization tends to be less stable?", "reviewer_3": "This communication reports a technique to utilize the anisotropy of precipitation-hardened LNN piezoceramics via precipitate alignment, which was realized by applying a uniaxial stress during the aging process. The precipitate alignment was predicted by a mechanical simulation and verified by a TEM study. The precipitate-related electrical anisotropy was determined by both small- and large-signal electrical measurements. This technique is of great novelty and well matches the scope of Nature Communications. The manuscript is well organized with theoretical simulation, solid experimental results and in-depth discussions. I suggest to accept the manuscript to be published on Nature Communications after addressing the following comments.\n1. In Figs. 1c and 1d, the authors sorted the order of the possibilities of precipitate variants P1 to P6 in <110>PC-oriented and <100>PC-oriented cells. How was the possibility order derived?\n2. The authors stated that the nucleation energy barriers of precipitates can be decreased by applying stress in the introduction section, which should result in an increased precipitate number density. In Figs. 3a and 3b, the number density of precipitates in the samples aged with and without stress look similar. Please explain possible reasons.\n3. In Figs. 5c-5d, the polarization loops exhibit an enhanced polarization with increasing temperature, while in many papers it was reported that the piezoceramics exhibited opposite trend (KNN-based: 10.1039/C9DT02042J, 10.1007/s10854-019-01654-w; PT-based: 10.1080/21870764.2020.1824317;). Please explain the difference.\n4. The significance of this work can be highlighted by introducing potential applications based on the piezoceramics. However, related theoretical research endeavors have also been undertaken in other materials systems, as exemplified in reference (Science, 373 (6561), 1353-1358 (2021); Nature Communications 4, 2224 (2023); Advanced Materials 34, 2203283, (2022)). These endeavors significantly contribute to enhancing the theoretical depth and rigor of this paper."}, "author_response": "Reviewer #1 (Remarks to the Author):\nThe manuscript titled \"Impact of stress-induced precipitate variant selection on\nanisotropic electrical properties of piezoceramics\" by Changhao Zhao et al. is a well\nwritten description of what appears to be a well thought out experiment that bridges\nbasic science concepts through real world relevant properties and associated\napplications. It was pleasure to see classical metallurgy concepts being applied by\nceramists to solve difficult problems. Despite the many technical achievements of this\nstudy, this cross-field approach and subsequent success is maybe the most noteworthy\naspect of the study. I think the findings will be of significance from both a basic science\nperspective (it doesn't take much to think of other methods or systems in which\nprecipitates can be aligned) or applications in hard piezoelectrics for power electronic\napplications. The conclusions and claims are well supported by the property\nmeasurements and micrographs provided. The experimental method was detailed and I\nbelieve adequate for the work to be reproduced. I believe there are several places\nthe manuscript can be improved as detailed here:\nMajor comments:\n1) It would be good if the authors did more to distinguish on the basic science side\nspecifically the delineation of this work for work done previously in this area. It\ntook a dive into the references to have clarity on this.\nResponse: Description of the concept precipitation hardening was added at the\nbeginning in the introduction.\nPage 2, line 28: “A classical hardening technique in metals, precipitation hardening, which\nintroduces precipitates through a thermal treatment of supersaturated alloys1, was recently\nsuccessfully implemented in Ba Ca TiO (BCT) and Li Na NbO (LNN) piezoceramics2,3. By\n0.7 0.3 3 0.18 0.82 3\nestablishing a proper aging scheme, precipitates with dimensions of several hundred nanometers\nwere introduced into grains of the abovementioned piezoceramics. The intragranular precipitates\ndirectly interact with domain walls and result in a more pronounced pinning effect, as compared to\nsecondary phases located at grain boundaries.”\n2) The manuscript theory and modeling section was underwhelming. Although the FE\nmodel was nice, I feel like a lot more could be done on the kinetics side of\nunderstanding the precipitation process and thus predicting size and distribution of\nthe 2nd phase. I also felt more could be done on prediction of the expected\nproperties from the resulting microstructure. An in depth theoretical understanding,\nreally Heckmann Diagram/Crystal Physics approach would greatly strengthen the\npaper.\nResponse: Thanks for your suggestion. As we compared different precipitate shapes\nwith the same volume, only the final state of each volume was modeled based on elastic\nand interface energy, and no diffusion process was modeled. Nevertheless, to visualize\nthe kinetics that determine the final precipitate shape, we introduce the theory of\nconfigurational forces and plot energy gradients for different precipitate shapes.\nThe configurational force vectors on the interface of different precipitate shapes during\nthe optimization process are depicted in Figure R1, provided in the supplemental as S1.\nThe arrows can be interpreted as energy gradients and thus can predict the precipitate\nshape which is more energetically-favorable. It can be seen that the energy gradient is\nreduced by an elongation of the precipitate until the equilibrium configuration is\nreached, where all force vectors are equal.\nFigure R1. Configurational forces on the precipitate interface for (a) initial, (b) intermediate and\n(c) final configuration. The green curves are the outlines of precipitates. The color of arrows\nreflects the amplitude of the configurational force.\nWe pointed out that the calculated overall mechanical energy is for the final state of\neach configuration, and inserted the configurational model part into the section 2 of the\nSI of the manuscript.\nPage 7, line 6: “The overall mechanical energies and m values were calculated after a complete\nrelaxation ensuring minimal mechanical energy for each given precipitate volume and each\nscenario (load case and precipitate orientation), thus only reflecting the final states. The kinetics\nduring the precipitate growth can be described by configurational forces as depicted in Figure S1.”\nUnfortunately, the models used in our manuscript are not suitable to predict\nferroelectric properties. This would require for example a phase field approach, which\nexceeds the scope and intention of this manuscript.\n3) The microscopy would be greatly enhanced with the addition of either electron\ntomography or weak beam dark field characterization of the 2nd phase to verify\nlocation and spacing, as opposed to the down zone imaging shown in the manuscript.\nResponse: As suggested by the reviewer, to characterize the size, shape, and location\nof the LN precipitates in different orientations, we performed \"semi\" electron\ntomography of these precipitates in real space, using an analytical double tilt holder\nwith an approximate tilting range of around 40° in both the x and y directions. The\nanalysis was conducted using a Cs-corrected ARM200CF (JEOL, Tokyo, Japan)\noperated at 200 kV. The TEM sample was prepared as lamellae using a Ga+-source\nfocused ion beam Helios Nanolab 650 HP (Thermo Fisher Scientific, Waltham, MA,\nUSA). The thickness of the lamellae was approximately 80 nm, as measured by EELS.\nFigure R2 (provided in SI as Figure S2) shows a TEM image of NN grain with the\nss\ncorresponding SAED pattern in the [111] zone axis. The LN precipitates, with their\npc ss\nFigure R2. TEM image with corresponding SAED pattern of NN ss grain with LN ss precipitates\nin [111] zone axis. A splitting of (011) spots is due to unit cell mismatch between LN and\npc pc\nNN.\nlong axes oriented perpendicular to the applied stress (indicated by a red arrow), lie on\n(011) planes. This grain was used further for detailed \"semi\" tomography.\npc\nFigure R3a depicts HAADF and corresponding bright-field STEM image of LN\nss\nprecipitates in [111] zone axis, with their long axes perpendicular to the applied stress\npc\n(indicated by red arrows). Note that there is a rotational difference between the TEM\nand STEM image, (compare Figure R2 and Figure R3a). The LN precipitates appear\nss\nto have a plate-like shape with internal pores. Note that pores in precipitates were also\nobserved in TEM samples prepared by conventional method described in the main text,\nalthough they were less pronounced due to the thicker samples in that case.\nTo confirm the shape and size of precipitates, we captured images of the NN\nss\ngrain\nwith LN precipitates at different tilting angles. First, the grain was tilted ~36° in the x\nss\nFigure R3. HAADF and corresponding BF STEM images of LN precipitates, with their long\nss\naxes perpendicular to the applied stress (indicated by red arrows). Tilting angles and directions\nare included. Dark/bright spots within the precipitates in HAADF/BF STEM images\ncorrespondingly indicate pores.\ndirection (Figure R3b). In another set of experiments, the grain was tilted ~ -32° (Figure\nR3c) and ~ 18° (Figure R3d) in the y direction, starting from the [111] zone axis. From\npc\nthe images, it is evident that tilting in the x and y directions does not significantly affect\nthe shape of the precipitates; however, it does influence their thickness (changing by up\nto 20%). This leads us to conclude that the precipitates indeed have a plate-like shape\nand do not exhibit cylindrical symmetry. Results are provided in the supplementary\ninformation (Figures S2 and S3).\nMinor comments:\n1) The statement that \"novel hardening strategy known as precipitation hardening\" is\nan overstatement. Precipitation Hardening has been in use since the early bronze\nage and the theory was proposed by Alfred Wilm in Germany in 1906.\nResponse: This statement was modified as follows:\nPage 2, line 28: “A classical hardening technique in metals, precipitation hardening, which\nintroduces precipitates through a thermal treatment of supersaturated alloys1, was recently\nsuccessfully implemented in Ba Ca TiO (BCT) and Li Na NbO (LNN) piezoceramics2,3.”\n0.7 0.3 3 0.18 0.82 3\n2) The S in \"Cs corrected\" should be a subscript.\nResponse: This mistake was corrected.\n3) Greater details in the sample preparation should be included above \"TEM\nspecimens were prepared by grinding, dimpling and final Ar-ion milling\" This is\nimportant to ensure no artifacts are added and alter the micrographic interpretation\nas result of mechanical deformation during grinding and dimpling or ion beam\nmixing during PIPS milling.\nResponse: As suggested, we expanded and provided a more detailed description of the\nTEM sample preparation in the article.\nPage 16, line 12: “The TEM specimens were prepared by grinding with SiC paper of 1200, 2400,\nand 4000 grit, followed by polishing with diamond paste containing 3 µm and 0.25 µm particles to\na thickness of approximately 100 µm. The polished discs were then dimple ground to around 10 µm\nthickness using a dimpler grinder (Model 656, Gatan, Pleasanton, CA, USA) and further thinned to\nelectron transparency by Ar-ion milling (Gatan PIPS Model 691, New York, NY, USA) at voltages\nranging from 3.5 to 2.5 kV until a hole appeared, followed by cleaning at 0.8 kV. The samples were\ncooled during the Ar-ion milling process.”\nWe would like to add that, for tomography analyses, we prepared a new TEM sample\nin lamellae form using a Ga+-source focused ion beam (FEI Nanolab Helios 650-FIB,\nWaltham, MA, USA) at 30kV, 16 kV and for final cleaning at 5kV and then 2kV.\nDespite the different preparation methods, we did not observe any artifacts in the TEM\nsamples that could be attributed to the preparation process.\n4) et al 28. should be et al.28.\nResponse: Corrected.\n5) Stress is shown as a single directional vector in Figure 3, It is a compression\nexperiment and should be shown as much.\nResponse: The single arrow was replaced by a pair of arrows in opposite directions.\n6) The statement \"large-signal property is less sensitive to the variant selection of\nprecipitates\" is vague and broad, thus it should be better clarified.\nResponse: It was replaced with:\nPage 12, line 1: “This phenomenon indicates that the polarization under large-signal electric field\nis less sensitive to the variant selection of precipitates in LNN.”\nReviewer #2 (Remarks to the Author):\nThis manuscript presents an interesting work that the precipitates in Li Na NbO\n0.18 0.82 3\n(LNN) piezoceramics can be oriented by aging with a uniaxial stress. The electrical\nanisotropy has also been investigated. The precipitates are oriented with their long axes\nperpendicular to the stress, which is consistent with the prediction by the theoretical\ncalculation. The domain walls in the variant are strongly pinned under both small- and\nlarge-signal electric fields, while the precipitates are mostly oriented out-of-plane.\nIt is an informative work. However, I do not quite see the importance of this work. At\nleast, the importance has not been fully presented. Meanwhile, some results are\ninadequately discussed. I suggest the authors to consider the following comments.\n(1) Has the endurance of this anisotropy been tested?\nResponse: We did a cycling P-E measurement of the sample aged under 150 MPa with\nthe condition of 550 °C-24 h + 650 °C-4 h. It can be seen from Figure R4 that the P-E\nloops remain basically unchanged and the electrical anisotropy is also valid after the\ncycling test. We stated in our manuscript that the electrical anisotropy arises from the\nprecipitate alignment, which occurs at temperature of 550−650 °C. At room\ntemperature, the atomic diffusion is too slow to cause any change to precipitates.\nTherefore, we believe that the electrical anisotropy is stable over a long period. We\ninserted Figure R4 into the SI as Figure S8, and added some text in the methods section\nto describe the cycling measurement:\nPage 16, line 27: “Cycling test of P-E loops was performed by applying cycling electric field with\na frequency of 1 Hz and amplitude up to 8 kV/mm at room temperature.”\n(2) I do not quite understand equation (1). What does the colon mean? How does C^M\nand C^P enters the equations?\nResponse: The colon in equation (1) denotes the double contraction product between\nthe fourth-order stiffness tensor C and the second-order stiffness tensor ε. As the\nstiffness is locally defined, we introduce a proper mathematical definition of C as a\nfunction of the spatial coordinate x, which defines as below:\nC ( x ) =\n C\nC\nP\nM\n, x\n, x\n\n\nM\nP\nFigure R4. Cycling test of stress-aged LNN piezoceramics (aging condition: 150 MPa, 550 °C-\n24 h + 650 °C-4 h).\nThe above equation and descriptions were added in the main text:\nPage 15, line 18: “where 𝜺 denotes the elastic strain tensor; C is the locally defined stiffness tensor,\nwhich equals to CP and CM when the spatial coordinate x is within the precipitate domain P and\nmatrix domain M, respectively; the colon in the first term denotes the double contraction product\nbetween the fourth-order stiffness tensor C and the second-order stiffness tensor ”\n(3) How can this macroscopic anisotropy be possibly used? The authors may provide\nsome insights.\nResponse: Property anisotropy exists in single crystals. However, due to the random\ngrain orientation in polycrystalline materials, properties are averaged and are inferior\nto the best property in single crystals (of course, in specific direction). The significance\nof this work is that it provides an opportunity to introduce electrical anisotropy into\npolycrystalline materials, and can lead to better electromechanical property if it is used\nin a certain direction. To be specific, we found that the precipitates have better pinning\neffect on domain walls when the applied electric field is perpendicular to the stress axis\nthan in other directions or the case without precipitate alignment. Thus, we suggest that\nif we design a piezoelectric device with the applied electric field in the optimal direction,\na lower mechanical loss and a higher mechanical quality factor could be expected.\nWe added several sentences to point out the potential use of the stress-aged\npiezoceramics and emphasize the significance of this work:\nPage 3, line 20: “Similar to single crystals, achieving such anisotropy in polycrystalline materials\ncan give rise to an enhancement in property if used in proper direction. For example, if the pinning\neffect from precipitates on DWs is maximized in certain direction, the mechanical quality factor\ncould be significantly enhanced when applying electric field in that direction.”\nPage 13, line 20: “The significance of this work lies in providing a simple method to introduce\nelectrical anisotropy, which can be utilized to achieve a stronger DW pinning in a certain direction\nas compared to samples with isotropic electrical properties.”\n(4) Why does the maximum polarization decrease as the stress increases? Why does\nthe maximum polarization increase as the temperature increases, as the polarization\ntends to be less stable?\nResponse: As we mentioned in the introduction (page 4, line 29: Alternatively, one can\nenvision lowering the nucleation barrier by applying a stress to reduce the misfit strain\nenergy, which effectively facilitates the precipitation nucleation without compromising\non diffusion kinetics), the mechanical stress may act as an additional driving force for\nthe precipitation. Thus, the reduced maximum polarization could be attributed to the\nlarger precipitation driving force, which leads to a higher density of precipitates and\nconsequently to stronger pinning of domain walls.\nRegarding your second question, we would like to state that there are two competing\nmechanisms when temperature is increasing: a) the domain walls are thermally\nactivated thus contribute more to polarization (in detail, this will depend on the\nfrequency of monitoring the P vs. E curve, if the curve is evaluated in quasi-static\nmanner, then the polarization would only depend on con-cubic distortion and grain\norientations), and b) the spontaneous polarization decreases since the temperature is\napproaching its Curie point. It is true that in some ferroelectrics, in which the lattice\nresponse dominates, the maximum polarization decreases with increasing temperature.\nHowever, the domain wall activation dominates in the LNN system, thus the maximum\npolarization increases with temperature even for samples without precipitates (Figure\nR5).\nFigure R5. Temperature-dependent polarization hysteresis loop of LNN18 without precipitates.\nSome sentences were inserted into the text to explain this to the reader:\nPage 13, line 3: “Unlike in some other ferroelectrics, in which the maximum polarization decreases\nwith increasing temperature, the LNN samples exhibit the opposite trend. This can be attributed to\nthe prevailing thermal activation of DWs over the spontaneous polarization decrease with\nincreasing temperature.”\nReviewer #3 (Remarks to the Author):\nThis communication reports a technique to utilize the anisotropy of precipitation-\nhardened LNN piezoceramics via precipitate alignment, which was realized by\napplying a uniaxial stress during the aging process. The precipitate alignment was\npredicted by a mechanical simulation and verified by a TEM study. The precipitate-\nrelated electrical anisotropy was determined by both small- and large-signal electrical\nmeasurements. This technique is of great novelty and well matches the scope of Nature\nCommunications. The manuscript is well organized with theoretical simulation, solid\nexperimental results and in-depth discussions. I suggest to accept the manuscript to be\npublished on Nature Communications after addressing the following comments.\n1. In Figs, lc and Id, the authors sorted the order of the possibilities of precipitate\nvariants Pl to P6 in <110> -oriented and <100> -oriented cells. How was the\nPC PC\npossibility order derived?\nResponse: It is a rough estimation based on misfit strain change under a compressive\nstress. The LNN ceramics contain precipitates with a plate-like shape, where the largest\nface of the plate is a coherent interface (Figure R6). The reason is that the misfit strain\nof the coherent interface is the smallest (~0.84%). When applying a uniaxial stress, the\nmisfit strain will change. Since the lattice of the precipitate is smaller and softer than\nthat of the matrix, the misfit strain would increase in the stress axis. Then, the precipitate\nvariant with its coherent interface parallel to the stress axis should have higher elastic\nenergy since the misfit strain of its largest interface increases (Figure R7). This leads to\na smaller energy preference of such variant. On the other hand, the elastic energy\nincrease of the precipitate variant with its coherent interface perpendicular to the stress\naxis should be least influenced by the stress, thus this variant is most energetically\nfavored. A rough assumption is made that the elastic energy of the coherent interface\ndecreases with the angle between the precipitate´s long axis and the stress axis (largest\nfor 0° and smallest for 90°). Based on this assumption, the possibility of different\nprecipitate variants can be sorted as shown in Figures 1c and 1d.\nFigure R6. Definition of interface coherency between precipitate and matrix.\nFigure R7. Schematic of misfit strain change under uniaxial stress.\n2. The authors stated that the nucleation energy barriers of precipitates can be\ndecreased by applying stress in the introduction section, which should result in an\nincreased precipitate number density. In Figs. 3a and 3b, the number density of\nprecipitates in the samples aged with and without stress look similar. Please explain\npossible reasons.\nResponse: Two possible reasons could contribute to this: a) the samples in Figs. 3a and\n3b were aged with different temperature profiles in different furnaces. Fig. 3a were\nreprinted from our previous work and the sample was aged with 500 °C-24 h + 600 C-\n6 h, while the sample in Fig. 3b was aged with 550 °C-24 h + 650 C-8 h; b) the aging\nin both samples almost reached equilibrium, thus the difference between the two cases\nis subtle. The main purpose of Figs. 3a and 3b is to demonstrate how stress affects the\norientation of precipitates, thus the effect of stress on the number density of precipitates\nis out of the scope of this work and may need further studies.\n3. In Figs. 5c-5d, the polarization loops exhibit an enhanced polarization with\nincreasing temperature, while in many papers it was reported that the piezoceramics\nexhibited opposite trend (KNN-based: 10.1039/C9DT02042J, 10.1007/sl0854-019-\n01654-w; PT-based: 10.1080/21870764.2020.1824317;). Please explain the\ndifference.\nResponse: Please refer to the response to the Comment 4 from the Reviewer #2.\n4. The significance of this work can be highlighted by introducing potential\napplications based on the piezoceramics. However, related theoretical research\nendeavors have also been undertaken in other materials systems, as exemplified in\nreference (Science, 373 (6561), 1353-1358 (2021); Nature Communications 4, 2224\n(2023); Advanced Materials 34, 2203283, (2022)). These endeavors significantly\ncontribute to enhancing the theoretical depth and rigor of this paper.\nResponse: Thanks for the suggestion. Some of the abovementioned references were\ncited in proper positions.\nPage 2, line 14: “Recently, investigations of cutting-edge two-dimensional infrared imaging\nequipment have been made by Hu et al.4, where the pressing challenge of piezoelectric hardening\nin such necessitates prompt attention and resolution.”\nPage 3, line 14: “Milestone advancements have been achieved by Wang et al. in delving into the\nelectrical characteristics5.”\nReferences\n1. Ardell, A. J. Precipitation hardening. Metall. Trans. A. 16, 2131-2165 (1985).\n2. Zhao, C. et al. Coherent Precipitates with Strong Domain Wall Pinning in Alkaline Niobate\nFerroelectrics. Adv. Mater. 34, 2202379 (2022).\n3. Zhao, C. et al. Precipitation Hardening in Ferroelectric Ceramics. Adv. Mater. 33, 2102421 (2021).\n4. Wang, F., Zhang, T., Xie, R., Wang, Z. & Hu, W. How to characterize figures of merit of two-\ndimensional photodetectors. Nat. Commun. 14, 2224 (2023).\n5. Wang, F. et al. Fully Depleted Self‐Aligned Heterosandwiched Van Der Waals Photodetectors. Adv.\nMater. 34, (2022)."}, {"round": 2, "reviewer_comments": {"reviewer_2": "The authors have fully addressed my questions/comments and added adequate information in the revised manuscript to elvate the importance and completeness of this work. Therefore, I recommend its publication in Nature Communications.", "reviewer_3": "The authors properly addressed my concerns in the last round. There may be still several concerns remained for the manuscript. I would suggest to accept the manuscript for publication on Nature Communications after a minor revision. My comments are listed as follows:\n1. The abbreviation \"EELS\" is not specified when it appears in the text for the first time.\n2. About the dimension of the precipitates, the authors state that it is of several hundreds nanomaters in length and several tens of nanomater in thickness. In my opinion, 100 nm and 900 nm has a large difference. The precipitates in the TEM images look quite uniform in size. Can the authors minimize the dimension range so readers can have a more straightforward feeling about the precipitate size?\n3. There should be proper citations on the sentence of \"The permittivity close to E=0V/mm is almost solely contributed by the reversible mechanisms and is independent of field amplitude. In comparison, εr-ε0 represents the contributions from the irreversible mechanisms and depends onthe field amplitude\".\n4. Error bars are missing for Figure 5f.\n5. What does the long and short axes in Figures 2a-2c represent? It is not clear which cross-section of precipitates the ellipses represent for. Please specify them.\n6. I suggest to insert more TEM images of stress-aged samples in Figure 3. Only one figure is not convincing enough to support the main demonstration of the manuscript that the long axes of precipitates tend to align perpendicular to the stress axis."}, "author_response": "Response letter\nReviewer #2 (Remarks to the Author):\nThe authors have fully addressed my questions/comments and added adequate information in the\nrevised manuscript to evaluate the importance and completeness of this work. Therefore, I recommend\nits publication in Nature Communications.\nResponse: We thank the reviewer for his careful review and constructive suggestions.\nReviewer #3 (Remarks to the Author):\nThe authors properly addressed my concerns in the last round. There may be still several concerns\nremained for the manuscript. I would suggest to accept the manuscript for publication on Nature\nCommunications after a minor revision. My comments are listed as follows:\n1. The abbreviation \"EELS\" is not specified when it appears in the text for the first time.\nResponse: Thanks for pointing out the mistake. We have corrected it in the revised manuscript.\nPage 8, line 32: “Energy Dispersive Spectroscopy (EDS) analysis reveals…”\nPage 9, line 2: “…is detected by Electron Energy Loss Spectroscopy (EELS)…”\n2. About the dimension of the precipitates, the authors state that it is of several hundreds nanomaters\nin length and several tens of nanomater in thickness. In my opinion, 100 nm and 900 nm has a large\ndifference. The precipitates in the TEM images look quite uniform in size. Can the authors minimize\nthe dimension range so readers can have a more straightforward feeling about the precipitate size?\nResponse: We apologize for the confusion. We have reported a rough range because the TEM images\npresented in this paper (including SI) were taken with different zone axes. The projection of\nprecipitates varies with zone axis, thus the dimension measured from the images change. We have now\nnarrowed down the range according to a set of TEM images.\nPage 8, line 26: “…approximately measuring 200—400 nm in length and 10—30 nm in thickness can\nbe observed…”\n3. There should be proper citations on the sentence of \"The permittivity close to E=0V/mm is almost\nsolely contributed by the reversible mechanisms and is independent of field amplitude. In comparison,\nεr-ε0 represents the contributions from the irreversible mechanisms and depends on the field amplitude\".\nResponse: Citation Ref. [43] (M Morozov, D Damjanovic, N Setter, J. Eur. Ceram. Soc., 25(12): 2483-\n2486, 2005) has been added to this sentence.\nPage 10, line 9: “The permittivity close to E = 0 V/mm (εʹ ) is almost solely contributed by the\n0\nreversible mechanisms and is independent of field amplitude. In comparison, εʹ−εʹ represents the\nr 0\ncontribution from the irreversible mechanisms and depends on the field amplitude43.”\n4. Error bars are missing for Figure 5f.\nResponse: Error bars were added to Figure 5f, as the reviewer suggested.\n5. What does the long and short axes in Figures 2a-2c represent? It is not clear which cross-section of\nprecipitates the ellipses represent for. Please specify them.\nResponse: The shape of precipitates is suggested to be plate-like, a 3-D schematic is depicted in Figure\nR1a. With the coordinate configuration in Figure R1a, the ellipses in Figures 2a-2c correspond to the\nprojection of precipitates on the x-z plane, as depicted in Figure R1b.\nFigure R1. Schematic of the cross-section of precipitates.\nWe have added a description about the ellipses used in the calculation model.\nPage 7, line 2: “The ellipse represents the cross-section of the plate-like precipitate, where the long\naxis corresponds to the length direction and the short axis corresponds to the thickness direction.”\n6. I suggest to insert more TEM images of stress-aged samples in Figure 3. Only one figure is not\nconvincing enough to support the main demonstration of the manuscript that the long axes of\nprecipitates tend to align perpendicular to the stress axis.\nResponse: Thanks for the suggestion. We have also noticed this problem in the last revision round so\nwe inserted additional TEM images to the SI. All the TEM images (Figures 3b, 3c, 3d, S2a and S3a-\nS3d) indicate that the stress axis is perpendicular to the long axis of precipitates. These TEM images\nwere taken at several spots and we think they should be convincing enough to support our conclusion."}, {"round": 3, "reviewer_comments": {"reviewer_3": "The authors have made significant improvements to the paper and recommends its publication in Nature Communications."}, "author_response": "Response: We thank the reviewer for all his constructive suggestions which make our\nmanuscript improve a lot."}]

Decision letter