Quenching‐circumvented ergodicity in relaxor Na
 1/2
 Bi
 1/2
 TiO
 3
 ‐BaTiO
 3
 ‐K
 0.5
 Na
 0.5
 NbO
 3

The regulation on Restriction of Hazardous substances limits the use of Pb2+ in many applications.1,2 In response, several material alternatives, namely (Na1/2Bi1/2TiO3 (NBT)based, K0.5Na0.5NbO3 (KNN)based, BaTiO3based, and BiFeO3based) were identified for specific applications.3,4 NBTbased materials are versatile and have been explored for application in solid state ionics,5 ultrasonic cleaning,6 mechanical energy harvesting,7 ultrahigh temperature multilayer Received: 24 September 2020 | Accepted: 17 January 2021 DOI: 10.1111/jace.17708


| 3317
WEI Et al. capacitors 8 and high strain actuation. [9][10][11] Relaxors, such as (1x)Na 1/2 Bi 1/2 TiO 3 -xBaTiO 3 (NBT-xBT), constitute of polar entities (polar nanoregions, PNRs) below the Burns temperature (T B ) that are dynamic and uncorrelated. Upon cooling, at a critical temperature known as the freezing temperature, T f <<T B , the correlation between the PNRs strengthen (remains the same) leading to non-ergodic (ergodic) character, respectively. 12 Ergodicity (non-ergodicity) is defined as the reversible (irreversible) nature of the relaxor to ferroelectric transformation upon application of external stimuli. Relaxor features in NBT-based materials can be modified by chemical substitution or fabricating a multicomponent solid solution [13][14][15] and in extreme case, can be transformed to a ferroelectric spontaneously. [16][17][18] Recently, quenching has been proposed to promote ferroelectric order in NBT-based materials 19,20 resulting in an enhanced ferroelectric-relaxor transformation temperature (T F-R ). Apart from establishing the practical relevance of the quenching strategy, 21 leveraging an appropriate starting composition (suitably doped, e.g., one with high a mechanical quality factor, Q) could result in further increase in T F-R , beyond that established by the doping limits, with minimal change in the electromechanical response. 16 The stabilized ferroelectric order in quenched NBT necessarily implies changes in the dynamic nature and correlation length of PNRs. However, such a correlation is incomprehensible from investigating non-ergodic relaxors due to the inherent quasi-static nature of PNRs and their increased correlation length.
The Morphotropic Phase Boundary (MPB) of NBT-xBT spans a wide range of compositions 22,23 ; although the core-MPB compositions (6-7 mole% BT) exhibit an average cubic structure, 24 with increasing BT content, tetragonal distortions develop in the MPB compositions albeit retaining relaxor features. 16,17 Assuming a simple composite description of polar (non-cubic) inclusions in a non-polar matrix (cubic), the cubic content decreases with increasing BT content. 16,25 The average structure is then an additional determining factor in stabilizing a relaxor state. Therefore, two different NBT-xBT variants-one with high content of cubic phase at the center of the MPB and another at the edge of the MPB with lower cubic phase content, 16,25 were chosen for the investigation. NBT-xBT-yKNN is reportedly known for its giant strain due to the composition-induced cross over from non-ergodic to ergodic relaxor (>2 mole% KNN), characterized by sproutshaped bipolar strain-field loops in the ergodic state. 9 The giant strain results due to the presence of a non-polar phase destabilizing the induced ferroelectric order 26 and random fields promoting the relaxation of induced ferroelectric order upon application of electric field. 27 The aim of this study is to investigate the effect of quenching on both ergodic and nonergodic NBT-xBT-yKNN and to establish the influence on the dielectric and piezoelectric properties. Further, the results are rationalized based on the random fields due to the A-and B-site disorder of NBT-xBT-yKNN and the increased Bi-O bond length in quenched materials.

| EXPERIMENT
Na 1/2 Bi 1/2 TiO 3 -xBaTiO 3 -yK 0.5 Na 0.5 NbO 3 (NBT-xBT-yKNN), where x and y denote mole% was prepared using the solid state route. Stoichiometric amounts of Na 2 CO 3 (99.5%), K 2 CO 3 (99%), Bi 2 O 3 (99.975%), TiO 2 (99.6%), and Nb 2 O 5 (99.9%) (all Alfa Aesar) were milled in ethanol for 12 h using zirconia balls in a planetary ball mill. The dried powders were then calcined at 900°C for 3 h and remilled in ethanol for 6 h. The samples were sintered at 1180°C for 2 h, denoted as FC (short for furnace cooled). Samples were quenched by removing them from the furnace after the sintering dwell time of 2 h and were rapidly cooled in ambient air (denoted as Q, short for quenched). This procedure was determined to decrease the surface temperature to less than 300°C in ~300 s as verified from experiment and simulation. 21 Two different NBT-xBT variants-NBT-6BT and NBT-9BT were chosen. Since the development of ergodicity is dependent on the KNN content, y was selected as 3 mole%, since NBT-6BT was demonstrated to exhibit ergodic features beyond 3 mole% KNN. 9 High resolution diffraction data was acquired from powders (obtained by crushing a pellet and annealing) in transmission geometry using a Stadi P (Stoe & Cie. GmbH) diffractometer equipped with MYTHEN1K (Dectris Ltd.) detector and monochromatized Cu-Kα 1 radiation (λ = 1.540598 Å, Ge[111]-monochromator). The microstructure was characterized by scanning electron microscopy (Philips XL30 FEG). The sintered samples were ground and electroded with silver. Prior to all measurements, samples were annealed at 400°C for 30 min to relieve grinding induced mechanical stresses. Poling was done at 6 kV/mm for 20 min. Temperature-and frequency-dependent permittivity measurements were performed using an impedance analyzer (4192A LF; Hewlett-Packard). T F-R was determined from the first anomaly in the temperature-dependent permittivity plots of poled samples. Polarization and strain hysteresis were quantified with a triangular field up to 6 kV/mm at 1 Hz using a Sawyer-Tower circuit equipped with an optical sensor and a temperature stage. The thermally stimulated depolarization current (TSDC) was measured in a short circuit mode, utilizing a constant heating rate of 3 K/min, while the discharge currents were monitored by an electrometer (Model 617; Keithley).

| RESULTS AND DISCUSSION
The phase pure perovskite structure of the synthesized materials can be confirmed from Figure 1. Quenching does not alter the microstructure and the average grain size is 1.2-1.7 μm for both the FC and Q samples ( Figure 2).
The ergodicity in NBT-xBT-3KNN is exemplified in the temperature-and frequency-dependent dielectric spectra (Figure 3), wherein a strong frequency dispersion is observed for all the samples in the unpoled state at low temperatures. 28,29 The reversible/irreversible nature of the field-induced (poled) relaxor-ferroelectric transformation is established from the permittivity response of poled samples. For FC-NBT-6BT-3KNN, the frequency dispersion is present in both the poled and unpoled state ( Figure 3A), indicating ergodic relaxor features. In contrast, FC-NBT-9BT-3KNN exhibits a recognizably weakened frequency dispersion upon poling ( Figure 3B). Upon quenching, a stark contrast is observed in the dielectric spectra for both Q-NBT-6BT-3KNN and Q-NBT-9BT-3KNN in the poled state, wherein the frequency dispersion is obviously suppressed at low temperatures, indicative of non-ergodic relaxor character. 20,30 The first anomaly in the dielectric spectra, characteristic of the ferroelectric-relaxor transformation temperature (T F-R ) is 80°C and 136°C for Q-NBT-6BT-3KNN and Q-NBT-9BT-3KNN, respectively ( Figure 3C,D). Dielectric loss (tan δ) in the quenched samples are comparable to FC samples, similar to the observations made previously. 20 Note that the maximum in temperature-dependent permittivity, T m remains majorly unaltered upon quenching and mimics the trend of FC-counterparts (Table 1; Figure 3).
The ergodic nature of FC-NBT-6BT-3KNN is unambiguously established from the pinched and slim polarization-field (P-E) response and sprout-shaped strain-field (S-E) response, with a lower remanent polarization (P r ) and remanent strain (S r ) ( Figure 4A,C). 31 In contrast, Q-NBT-6BT-3KNN is characterized by a 60% increase in P r and approximately a threefold increase in S r . In addition, the square-shaped P-E and butterfly shaped S-E response confirm the non-ergodic character of Q-NBT-6BT-3KNN. The increase in P r signifies increased ferroelectric order for Q-NBT6BT-3KNN. The total strain is not significantly altered, but note that there is a distinctive poling field reflected in the inflection point in the S-E response at 2 kV/mm ( Figure 4C). The lower transformation field and sharp inflection for the relaxor→ferroelectric transformation imply the ease of developing long-ranged ferroelectric order upon quenching. FC-NBT9BT-3KNN and Q-NBT9BT-3KNN are non-ergodic relaxors demonstrating similar S-E and P-E response, with comparable P r and S r at 30 μC/cm 2 and 0.3%, respectively ( Figure 4B,D), in accordance with prior reports. 20 Albeit the weak frequency dispersion in the permittivity response of poled FC-NBT-9BT-3KNN ( Figure 4B), the hysteresis response reveals a strong non-ergodic character.
Since quenching the ergodic compositions has been demonstrated to induce non-ergodic features, it becomes imperative to track the thermal depolarization behavior ascertained by the depolarization current and hysteresis response. To this end, TSDC spectra were measured for the samples. FC-NBT-6BT-3KNN exhibits a broad peak in the current density, resulting from the culmination of depolarization of uncorrelated PNRs in the ergodic relaxor ( Figure 5A). The resulting polarization obtained from TSDC measurements by integration of depolarization current density over time ( Figure  5B) is also weak, in correspondence to the lower P r as noted previously. In contrast, all the other samples exhibit a single sharp peak in the depolarization current density, corresponding to the depolarization temperature (T d ). T d of Q-NBT-6BT-3KNN is 85°C and comparable to T F-R (80°C) established from temperature-and frequency-dependent permittivity response; this is tantamount to the T d of furnace-cooled nonergodic NBT-6BT. 20 The polarization of NBT-6BT-3KNN exhibits a fourfold increase upon quenching similar to the trend in P r . Note that, the non-ergodic nature of FC-NBT-9BT-3KNN is evident from the clear depolarization peak at 62°C ( Figure 5A). T d exhibits approximately a twofold increase to 133°C upon quenching NBT-9BT-3KNN. The increase in polarization remains marginal and is in accordance with previous reports on quenching non-ergodic relaxors. 20 Figure 6 depicts the high resolution diffraction data obtained from unpoled powders and highlights select diffraction profiles. A singlet in the diffraction profile is expected for cubic symmetry. All the samples indicate non-cubic symmetry reflected in the additional peaks or tails in the diffraction profile (marked by arrows in the figure). However, a notable feature is the development of tetragonal distortions as highlighted in 200 pc for Q-NBT-6BT-KNN ( Figure 6B).
These results establish quenching as a means of tailoring both T d and ergodicity, as an alternative to chemical modification (higher BT content, doping, new solid solution etc.). Quenching-induced enhancement in tetragonal distortion can be rationalized to result from the anomalous increase in Bi-O bond distance as recently noted in quenched Li-modified-NBT. 32 For NBT-6BT-3KNN, temperature-dependent polarization-and strain-hysteresis response is used to further track the ferroelectric-relaxor transformation ( Figure 7). As indicated previously, FC-NBT-6BT-3KNN is in the ergodic state and retains the sprout-shaped S-E loops and slim, pinched P-E loops in the temperature range of investigation ( Figure 7A,C). 33 a change of the shape of the hysteresis response close to T F-R ( Figure 7B,D). The negative strain (S neg ) is close to zero in the ergodic state and is a definite gauge to establish the ferroelectric-relaxor transformation. At room temperature, S neg for FC-NBT-6BT-3KNN is close to zero; however, for Q-NBT-6BT-3KNN, it is roughly three times higher at −0.09% (Figure 8). Further, with increasing temperature, S neg for Q-NBT-6BT-3KNN remains consistently higher than that of FC-NBT-6BT-3KNN and decreases to zero close to T F-R . The temperature at which S neg is zero is marginally higher, since the applied field promotes the ferroelectric order even at T F-R ; however, once the depolarization fields cannot be compensated any longer, the material transforms back to the relaxor state. 34 Canonical relaxors upon cooling may result in two extreme possibilities-at the critical freezing temperature, the PNRs get frozen into the non-ergodic state or percolate the material and integrate into a ferroelectric solid. 28,35 Such transitions into the ferroelectric state has been previously reported for Pb(Sc 1/2 Ta 1/2 )O 3 as a result of cation ordering in the system. 36 The stabilization of a ferroelectric order 20 upon quenching has been reported previously for nonergodic NBT-based relaxors, which enhances the T F-R (and T d ) and reflects as an enhanced lattice distortion. 19,20,32,37,38 Non-ergodic relaxor NBT-9BT-3KNN conforms to this observation, wherein the T d increased from 62°C to 133°C. The mechanism that enables the ferroelectric equilibrium upon quenching has been debated to result from increased oxygen vacancy concentration 20,38 or changes in the local structure 21 resulting in an enhanced Bi-O off-centered displacements. 32 For higher quenching rates, the role of transient thermal stresses has been elucidated based on thermal shock induced microcracking 39,40 These observations indirectly imply a strong correlation between the PNRs that enable the onset of new polar regions or growth of existing PNRs. This work is an experimental evidence for the same, exemplifying the inception of non-ergodic features upon quenching ergodic samples, reflected in the onset of T F-R and S neg . This then entails an increased correlation between the existing PNRs apart from providing means of tailoring ergodicity as an alternative to new solid solutions or chemical doping. A similar increase in the correlation length of PNRs was facilitated in ergodic relaxor (Ba, Ca)(Ti, Zr)O 3 -K 1/2 Bi 1/2 TiO 3 by quenching; although driven by chemical heterogeneity (unlike the present study), the quenched samples exhibited enhanced non-cubic (tetragonal) phase fraction as opposed to the slowcooled specimens. 41 In NBT-6BT, it has been demonstrated that Bi-O and Bi-Ti bond distances feature an abrupt change at T m but not at T F-R , indicating the transformation from rhombohedral to tetragonal phase to occur gradually. However, a recent report indicated that quenching results in enhanced Bi 3+ offcentering as opposed to furnace-cooled specimens, 32 which can alter the local structure. In the present work, it was observed that quenching significantly affects T F-R , but does not alter T m (Figure 3; Table 1) and the quenched compositions exhibit an increased tetragonal distortion. This indirectly implies that quenching promotes a stabilization of tetragonal PNRs and increases the ferroelectric order, thus increasing T F-R .
Total scattering X-ray and neutron investigations on the A-site disordered NBT revealed that both Na + and Bi 3+ shift from their average crystallographic position, 42 with consequently larger Bi-O bond lengths in comparison with Na-O bond distances, 43 that can potentially influence the polarizability of the lattice. Quenching non-ergodic relaxor 0.92NBT-0.08(Bi 0.5 Li 0.5 )TiO 3 results in off-centered displacements of Bi 3+ . 32 This work demonstrates that quenching induced longrange order is a potent means to negate the effect of the increased disorder at the A-and B-site random fields due to the introduction of K + and Nb 5+ in NBT-xBT-3KNN, that usually promotes ergodicity.

| CONCLUSION
Quenching ergodic relaxor NBT-6BT-3KNN is demonstrated to develop non-ergodicity that manifests as onset of T F-R , enhanced negative strain, increased remanent polarization and higher tetragonal distortion. The increase in correlation between the PNRs is rationalized to result from quenching-induced off-centered displacements of Bi 3+ that circumvents the ergodicity promoted by the Asite disorder.