Nature of polar state in 0.67BiFeO3–0.33BaTiO3

This study was conducted to understand the nature of the polar state in the morphotropic phase boundary composition 0.67BiFeO3–0.33BaTiO3 (0.67BF–0.33BT). Both the unpoled and poled specimens exhibit an average cubic structure. The poling induces a 0.14% increase in the lattice parameter. Macrodomains are absent both in the initial and polar state of 0.67BF–0.33BT. A typical relaxor-type dielectric anomaly was observed (Tf = ~ 627 K, TB = ~ 820 K). The remnant polarization (Pr), maximum value of electrostrain (Sm), and magnitude strain at Ec in the bipolar mode (Sneg) increase clearly during heating (Pr, ~ 40 µC/cm2; Sm, 0.191% under 40 kV/cm at 453 K). Unlike Bi0.5Na0.5TiO3-based nonergodic relaxors, the first-cycle bipolar electrostrain loops indicate that the minimum strain on the negative side of the bipolar strain curves is negative. Furthermore, the slopes of the relative permittivity versus log frequency plots in unpoled (− 21) and poled (− 23) specimens are similar. The transition between the relaxor state and ferroelectric-like state does not involve a clear dielectric anomaly even in the poled specimen.

Despite the intensive studies, the controversy on the origin of MPB has continued. The early research suggested that a cubic phase appeared when the BaTiO 3 content reached 33 mol% [1,2]. Leontsev et al. held that the BaTiO 3 -rich phase should be pseudocubic, considering the presence of the ferroelectric and piezoelectric properties [5]. The study by Lee et al. highlighted the similarity in MPB between BF-BT and Pb(Zr,Ti)O 3 [9]. In 2017, Wang et al. found that the electrostrain of 0.7BF-0.3BT increases clearly when heated [13]. A field-induced relaxor-ferroelectric transition was presumed to interpret this enhancement. However, the in situ synchrotron X-ray diffraction (XRD) in combination with Rietveld refinement of pseudocubic BF-BT suggested that there was no apparent peak splitting when the poling field was imposed [31,32]. The recent study suggested that the enhancement in electrostrain should be related to the nanodomains and thermal depolarization [33].
To understand the origin of MPB, the nature of the initial state in the MPB compositions of BF-BT should be verified. There are three models to interpret their initial state (Fig. 1). (a) It is a nonergodic relaxor state, which is related to the frozen polar nanoregions (PNRs) and develops into a long-range ferroelectric state under the poling field. (b) It is a long-ranged ferroelectric state with small tetragonal distortion. (c) It is a ferroelectric state with nanodomains that adopts pseudocubic symmetry on the global length scale. Due to their ferroelectric and piezoelectric properties, we could refer to the initial state of MPB compositions as the ferroelectric-like state. The structure changes based on the above three models are too similar to be resolved by X-ray diffractions.
The analyses of the first-cycle electrostrain loop and structure-property relationship of the poled sample are essential. If the transition from the nonergodic relaxor state to the ferroelectric state occurs, we could observe its effect on the first-cycle electrostrain loop, domain structure, and dielectric properties like Bi 0.5-Na 0.5 TiO 3 -based ceramics [34][35][36][37]. Based on the above thought, the initial state of 0.67BF-0.33BT was studied. We found a significant difference in the structural and electrical characteristics among 0.67BF-0.33BT, typical nonergodic relaxors, and ferroelectrics with macrodomains.

Experimental
Solid solution ceramics 0.67BF-0. 33BT [38]. The starting reagents were carefully weighed in stoichiometric ratios and wet mixed thoroughly by ball-milling for 10 h. The mixture was then dried and calcined at 1073 K for 2 h in a covered corundum crucible. The calcined powder was ball-milled and dried. Pellets with a diameter and thickness of 12 and 1-2 mm, respectively, were pressed using a 10% polyvinyl alcohol binder. The pellets were sintered in a covered corundum crucible at 1273 K for 3 h. For the electrical measurements, the silver paste was coated and fired at 823 K for 10 min. For the property characterization of the polar state, the specimens were poled in the silicone oil for 10 min under a dc field of 40 kV/cm at 298 K.
The crystal structures were detected using an X-ray diffractometer (XRD, D2 PHASER, Bruker AXS, Karlsruhe, Germany). The Rietveld refinement analysis (using the FullProf software) was performed to study the poling effect on the structure. The brightfield images and selected area electron diffraction SAED patterns were obtained by the transmission electron microscopy (TEM, JEM-2100Plus; JEOL, Tokyo Metropolis, Japan). Before TEM observation, the unpoled and poled specimens were prepared by polishing, dimpling, and ion milling. The dielectric data were measured using an LCR meter (4294 A, Agilent, Santa Clara, America) with a temperaturecontrolled cell. The piezoelectric coefficients (d 33 ) were measured using a piezo-d 33 meter (ZJ-3AN; Institute of Acoustics, Beijing, China). The poled specimen was annealed at selected temperatures below 760 K for 10 min to obtain the relationship between d 33 and the annealing temperature. The ferroelectric properties and electrostrain responses at 1 Hz were measured using a ferroelectric test system (TF Analyzer 2000E, aixACCT, Aachen, Germany).

Results and discussion
The XRD patterns of unpoled and poled powdered specimens for 0.67BF-0.33BT are shown in Fig. 2a, b. An average cubic perovskite phase was found both in the unpoled and poled specimens, consistent with the in situ synchrotron radiation XRD analyses [31,32]. 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 lattice parameter (a, Table 1) for the poled specimen (* 3.9970 Å ) is larger than that for the unpoled specimen (* 3.9916 Å ). The expansion of the unit cell might be related to the intrinsic displacements of the ferroelectrically active Bi 3? and Ti 4? cations [32]. The bright-field TEM images of many grains were examined to understand the micropolar order. No viable ferroelectric domains were detected both in the unpoled (Fig. 2c) and poled state (Fig. 2d). The finding reveals that macrodomains are absent in the initial state of 0.67BF-0.33BT, and the poling field hardly induces the formation of macrodomains, which could also be supported by the average cubic phase in the poling state. Nanodomain structures rather than macrodomains have been also observed in the similar BF-BT compositions, such as 0.64Bi 1.05 Fe 0.99 Sc 0.01 O 3 -0.35BaTiO 3 -0.01Bi 1.05 (Zn 0.5-Hf 0.5 )O 3 [33] and 0.63BiFeO 3 -0.32BaTiO 3 -0.05Bi(Mg 2/3 Nb 1/3 )O 3 [39].
To further understand the poling effect on the structure, the SAED patterns with [110] zone axis were obtained (Fig. 2e, f). The absence of the superlattice reflection spots 1/2(111) c suggests that there is no ordered octahedral tilting both in the initial and poled state of 0.67BF-0.33BT [35]. In the case of typical nonergodic relaxor ceramics (Pb,La)(Zr,Ti)O 3 8/65/35 (PLZT) [40], the appearance of (311) and (331) superlattice reflections after poling have been demonstrated, which results from an electric fieldinduce irreversible change from the R3m structure to the R3c structure. Despite the average cubic structure, the unpoled 0.94Bi 1/2 Na 1/2 TiO 3 -0.06BaTiO 3 (0.94BNT-0.04BT) ceramic exhibits the presence of the 1/2{ooo} and 1/2{ooe} superlattice reflections in the SAED patterns, hinting that the R3c and P4bm structures coexist on the local scale [35]. Differently, the R3c structure should be eliminated if the rhombohedral distortions are present on the local scale in 0.67BF-0.33BT. The increase in the tolerance factor (t = 0.968 for 0.75BF-0.25BT, t = 0.970 for Bi 1/2 Na 1/ 2 TiO 3 and t = 0.978 for 0.67BF-0.33BT) [41,42] and the degree of disorder with increasing BaTiO 3 content leads to the disappearance of the ordered octahedral tilting. Figure 3a shows the relative permittivity (e r ) of 0.67BF-0.33BT as a function of temperature at various frequencies. The composition shows a relaxor-like dielectric anomaly between 650 and 750 K. Benefitting from high insulation by Mn modification, the dielectric anomaly at 100 Hz could be observed [8].
The temperature (T m ) for the maximum value of relative permittivity (e m ) is dependent on the frequency and shifts from 700 K (100 Hz) to 725 K (100 kHz). The temperature dependence of dielectric loss is shown in the inset of Fig. 3a. The dielectric loss anomaly could also be observed, and the loss anomaly temperature is lower than T m .
The relationship between T m and the measuring frequency can be well described by the Vogel-Fulcher law (Fig. 3b) [43], giving a freezing temperature (T f ) of * 627 K, * 50 K higher than that reported by Zheng et al. [11]. The relationship between the piezoelectric coefficient (d 33 ) and annealing temperature indicates that the depolarization temperature is * 650 K, close to T f (Fig. 3c). Above 800 K, there is an abrupt increase in the relative permittivity at 100 Hz and 1 kHz. The finding should be related to the space charge effect. In relaxor ferroelectrics, the polar nanoregions (PNRs) appear at the Burns temperature (T B ) on cooling. Above T B , the relationship between the reciprocal permittivity and temperature obeys Curie-Weiss law [43], where T CW and C are Curie contents. The high-temperature data at 100 kHz, which are less affected by conductivity, were used to define the T B value (Fig. 3d). The T B value was found to be * 820 K, * 95 K higher than T m (725 K at 100 kHz). The Curie  contents T CW and C are * 746 K and * 1.22 Á 10 6 K, respectively. The polarization and electrostrain responses during heating were studied to understand the ferroelectric-like state of 0.67BF-0.33BT (Fig. 4a-c). The remnant polarization (P r ) increases clearly with the temperature, accompanied by a reduction in the coercive field (E c ). 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 relationship between the leakage current density and electric field is linear [44], where r is electronic conductivity. The value of r was found to be 8.0 9 10 -7 S/m at 453 K, and the intrinsic P r value of was * 40 lC/cm 2 , much higher than that of Bi 0.5 Na 0.5 TiO 3 (BNT) [36]. Analogous to 0.7BF-0.3BT [13,45], the heating also induces an enhancement of the electrostrain. At 453 K, the maximum value of unipolar strain (S m ) and largesignal piezoelectric coefficient (d 33 * ) are * 0.191% and * 477 pm/V, respectively. Besides, the magnitude strain at E c in the bipolar mode (S neg ) increases from 0.07% at 300 K to 0.17% at 453 K. It is generally known that the magnitude of S neg is dependent on the competition between 180°and non-180°domain switching processes [46]. The increase in S neg hints The irreversible strain (S irr ) in the electrostrain loops is an important parameter which could identify the electric field-induced phase transition. To further understand the initial state, the first-cycle ferroelectric hysteresis loop and electrostrain loop of 0.67BF-0.33BT were measured (Fig. 5). The composition shows a pronounced increase in the polarization and strain above E c at room temperature (Fig. 5a). A * 0.04% remnant strain could be observed when the poling field was removed. The S irr value of 0.67BF-0.33BT is negative. The sign of S irr is unchanged when the measuring temperature is 453 K. The strain increases clearly when the electric field is imposed. The finding should be related to the promotion of the domain wall movements induced by heating. The initial curve of the strain versus the electric field obeys the following expression.
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 positive S irr values have been found in Bi 1/2 Na 1/ 2 TiO 3 -BaTiO 3 [34] [48] (ferroelectrics, d 33 [ 300 pC/N). The electric field-induced phase transition of the above compositions has also been evidenced by the XRD measurement. On the other hand, the negative S irr values are usually observed in normal ferroelectrics (e.g., pure BaTiO 3 [46], soft Pb(Zr,Ti)O 3 [34]). In particular, relaxor PLZT, as a typical nonergodic relaxor, shows a negative S irr value. The further study indicates that both the unpoled (R3m) and poled (R3c) phases are rhombohedral [40]. In the case of 0.67BF-0.33BT, there are no differences in the XRD patterns between the unpoled and poled specimens, and the superlattice reflections are absent in the poled state. So we can safely conclude that the negative S irr may hint that there is no fieldinduced change in the crystallographic system. For normal ferroelectrics, the relative permittivity is usually frequency-independent in the frequency range between 100 and 1 MHz. However, when the long-range ferroelectric state is disrupted, the relative permittivity is profoundly affected by the frequency [43]. If the poling could alter the polar state, a significant difference might be observed in the frequency dependence of the relative permittivity. The poling effect on the relationship between the dielectric behavior and log frequency is plotted in Fig. 6. 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. The slope of relative permittivity versus log frequency plots was calculated to estimate the frequency dispersion. The slope of the unpoled specimen is approximately -21. After poling, the relative permittivity increases clearly, but the frequency dispersion behaviors are nearly unchanged (slope, approximately -23). Unlike typical nonergodic relaxors [35], the poling field may not change the polar state of 0.67BF-0.33BT.
The temperature dependence of relative permittivity suggests that the T m value shifts to the hightemperature side after poling (Fig. 7a). At 100 kHz, the poling induces a 4 K increase in T m . The increase in T m by poling was also observed in PbMg 1/3 Nb 2/ 3 O-PbTiO 3 [49]. Most importantly, there is no apparent dielectric anomaly related to the transition point between ferroelectric-like state and relaxor state in the poled specimen [50,51]. It may be because that the temperature-induced change in the polar states does not involve any phase transitions on the global length scale. The poling effect on the relationship between dielectric loss and temperature is shown in Fig. 7b. The dielectric loss anomaly temperature also increases after poling. Besides, 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 resonance effect due to poling.
(1) Both the structures of the unpoled and poled states could be well understood as the pseudocubic symmetry [31,32].  (6) The heating leads to an increase in P r , S m , and S neg , even the maximum measuring temperature is * 200 K lower than T d . (7) The frequency dependence of T m is apparent and well fitted by the V-F functions. (8) The difference between T m and T B is about * 95 K, higher than that in 0.64PMN-0.36PT but lower than that in 0.94BNT-0.06BT.
Our studies reveal that the initial state of 0.67BF-0.33BT is not a long-range ferroelectric state with macrodomains. There are also apparent differences between 0.67BF-0.33BT and typical nonergodic relaxors in the poling effects on the structure and dielectric behaviors. We tend to believe that the nanodomains (possibly induced by the increased local heterogeneity) are present in 0.67BF-0.33BT and play a leading role in the structure-property relationship.

Conclusions
The poling does not change the average structure of 0.67BF-0.33BT but leads to a definite increase in the lattice parameter. We did not observe the presence of the macrodomains both in the initial and polar state. The temperature dependence of dielectric properties of 0.67BF-0.33BT shows typical relaxor features, with T f and T B of * 627 K and * 820 K. P r , S m , and S neg increase with temperature. The intrinsic P r reaches * 40 lC/cm 2 at 453 K. The S irr values in the initial strain loops at 300 K and 453 K are both negative, suggesting the absence of electric field-induce change in the crystallographic system. The frequency dispersion behavior remains unchanged after poling.
Our studies indicate that there are distinct differences in the polar states among 0.67BF-0.33BT, normal ferroelectrics, and typical nonergodic relaxors.