Figure 1(a) shows the relative permittivity (εr) and dielectric loss (tanδ) of 0.67BF–0.33BT as a function of temperature at various frequencies. The composition shows a relaxor-like dielectric anomaly in the temperature range between 650 K and 750 K. Benefitting from high insulation by Mn modification, the dielectric anomaly at 100 Hz could be clearly observed [8]. The relationship between the temperature (Tm) for the maximum value of εr and measuring frequency can be well described by the Vogel-Fulcher law (Fig. 1b) [30], giving a freezing temperature (Tf) of ~ 627 K, ~ 50 K higher than that reported by Zheng et al. [11]. The relationship between the piezoelectric coefficient (d33) and annealing temperature indicates that the depolarization temperature is ~ 650 K, close to Tf (Fig. 1c). Above 800 K, there is a clear increase in the relative permittivity at 100 Hz and 1 kHz. This should be related to the thermally excited charge carriers. In relaxor ferroelectrics, the polar nano regions (PNRs) appear at the Burns temperature (TB) where the relationship between the reciprocal permittivity and temperature departs from the Curie‐Weiss law when cooled [30]. The high temperature data at 100 kHz, which are less effected by conductivity, were used to define the TB value (Fig. 1d). The TB value was found to be ~ 820 K, ~ 95 K higher than Tm (725 K at 100 kHz). The Curie parameters TCW and C are ~ 746 K and ~ 1.22 ⋅ 106 K, respectively.
The polarization and electro-strain responses during heating were studied to better understand the ferroelectric-like state of 0.67BF–0.33BT (Fig. 2a–c). The detailed experimental results are shown in Fig. S1 in the supporting information. The remnant polarization (Pr) increases clearly with the temperature, accompanied by a reduction in the coercive field (Ec). Above 398 K, the conduction contributes much to the polarization response. We obtained the intrinsic ferroelectric hysteresis loop by deducting the conduction effect, assuming that the relation of leakage current density and electric field is linear [31]. The intrinsic Pr value of 0.67BF–0.33BT is ~ 40 µC/cm2 at 453 K, much higher than that of Bi0.5Na0.5TiO3(BNT) [27]. Most importantly, the heating also induces an enhancement of the electrostrain. At 453 K, the maximum value of unipolar strain (Sm) and large-signal piezoelectric coefficient (d33*) are ~ 0.191% and ~ 477 pm/V, respectively. The trends of the polarization and electrostrain for 0.67BF–0.33BT when heated are identical with those reported in 0.7BF–0.3BT [13, 32]. In addition, the magnitude strain at Ec in the bipolar mode (Sneg) increases from 0.07% at 300 K to 0.17% at 453 K. The finding hints that the heating activates more non-180o domains switching [33].
The first-cycle electrostrain loops in BNT-based nonergodic relaxor materials exhibit two distinctive features [33], which hints the electric-filed-induced transition from the relaxor state to the ferroelectric state induced. (1) The strain increases abruptly above a certain threshold electric field. (2) The minimum strain on the negative side of the bipolar strain curve, which could be named as the “irrecoverable” strain (Sirr) [25], is positive. To further understand the initial state, the first-cycle ferroelectric hysteresis loop and electrostrain loop of 0.67BF–0.33BT were measured (Fig. 3). The composition shows a pronounced increase in the polarization and strain above Ec at room temperature (Fig. 3a). A ~ 0.04% remnant strain could be observed when the poling field was removed. Unlike BNT-based nonergodic relaxor ceramics [22, 25, 33, 34], the Sirr value of 0.67BF–0.33BT is negative. The sign of Sirr is unchanged when the measuring temperature is 453 K. The strain increases clearly when the electric field is imposed. The initial curve of strain and electric field was found to obey the following expression
S = aE + bE2,
where S is the strain, E is the electric field, and a (0.0036 ± 0.0001) and b (0.000110 ± 0.000006) are fitting parameters.
The poling effect on the relationship between the dielectric behavior and log frequency is plotted in Fig. 4. The low dielectric loss in a low frequency range suggests that the leakage current is effectively suppressed near the room temperature by Mn-modification. The relative permittivity of the unpoled sample is frequency dependent. In order to estimate the frequency dispersion, the slope of relative permittivity versus log frequency plots was calculated. The slope of the unpoled sample is approximately − 21. After poling, the relative permittivity increases clearly but the frequency dispersion behaviors are nearly unchanged (slope, approximately − 23).
The temperature dependence of relative permittivity suggests that the Tm value shifts to the high-temperature side after poling (Fig. 5a). At 100 kHz, the poling leads to an increase of Tm from 725 K to 729 K. The increase in Tm by poling was also observed in PbMg1/3Nb2/3O–PbTiO3 [35]. Most importantly, there is no clear dielectric anomaly related to the transition point between ferroelectric-like state and relaxor state in the poled specimen. The poling effect on the relationship between dielectric loss and temperature is shown in Fig. 5(b). The dielectric loss anomaly temperature also increases after poling. In addition, there is another loss anomaly at 500 kHz around 650 K. The anomaly point is corresponding to the depolarization temperature. This loss anomaly is only observed in the measuring frequency that is close to the resonant frequency. Therefore, it could be understood as the resonant effect due to poling.
The XRD patterns of unpoled and poled powdered specimens for 0.67BF–0.33BT are shown in Fig. 6(a) and (b). A cubic-like perovskite phase was found both in unpoled and poled specimens, consistent with the in-situ synchrotron radiation XRD analyses [20, 21]. The reflection peak shifts to the low-angle side after poling. Rietveld refine analysis suggests that the structures could be well described by the cubic symmetry with the space group of Pm_3m. The poling leads to a 0.14% increase in the lattice parameter (a). The increase in the lattice parameter by dc electric field poling is much larger than the observed remnant strain (~ 0.04%) (Fig. 3a).
The bright-field TEM images of many grains were examined to understand the micro polar order. No viable ferroelectric domains were detected both in the unpoled (Fig. 6c) and poled state (Fig. 6d). It reveals the difficulty in the formation of long-range ferroelectric domains under the poling field.
To further understand the poling effect on the structure, the SAED patterns with [110] zone axis were obtained (Fig. 6e and f). The absence of the super-lattice reflection spots 1/2(111)c suggests that there is no ordered rotation of the octahedral both in the initial and poled state of 0.67BF–0.33BT [36]. That is, the R3c structure should be eliminated if the rombohedral distortions are present on the local scale. The increase in the tolerance factor (t = 0.968 for 0.75BF–0.25BT, t = 0.970 for Bi1/2Na1/2TiO3 and t = 0.978 for 0.67BF–0.33BT) and the degree of disorder with increasing BaTiO3 content leads to the difficulty in the ordered rotation of the octahedral.
We compared 0.67BF–0.33BT with 0.64PbMg1/3Nb2/3O3–0.36PbTiO3 (0.64PMN–0.36PT) [37] and 0.94Bi1/2Na1/2TiO3–0.06PbTiO3 (0.94BNT–0.06BT) [22, 23, 38–40] near MPB (Table 1) to better understand its structural and electrical characteristics. The eight main differences in 0.67BF–0.33BT are summarized as below.
(1) Both the structures of the unpoled and poled states could be well understood as the pseudocubic symmetry [20, 21].
(2) No visible ferroelectric domains could be detected in the unpoled state. The poling field hardly triggers the formation of the long-range ferroelectric domains.
(3) The frequency dispersion behavior is obvious in the unpoled specimen. Poling does not induce distinct change in the frequency dispersion behavior.
(4) The frequency dependence of Tm is obvious and well fitted by the V-F functions.
(5) The difference of Tm and TB is about ~ 95 K, higher than that in 0.64PMN–0.36PT but lower than that in 0.94BNT–0.06BT.
(6) The relationship between the relative permittivity and temperature in the poled sample lacks the clear anomaly related to the transition from the relaxor state to the ferroelectric-like state.
(7) Different from typical nonergodic ralaxors, the initial electrostrain loops show a negative Sirr.
(8) The heating leads to an increase in Pr, Sm and Sneg, even the maximum measuring temperature is ~ 200 K lower than Td.
Our studies reveal the complexity of 0.67BF–0.33BT. This is possibly caused by the mixtures of the ferroelectrically active and non-ferroelectrically active cations both on the A site and B site. We hope our study could promote the understanding in the polar state of 0.67BF–0.33BT.