Impact of Phase Structure on Piezoelectric Properties of Textured Lead-Free Ceramics

: The impact of phase structure on piezoelectric performances of < 001 > textured Na 0.5 Bi 0.5 3 (NBT) based lead-free ceramics was studied, including 3 (88NBT) with morphotropic phase boundary (MPB) composition and 0.90NBT-0.07K 0.5 Bi 0.5 TiO 3 -0.03BaTiO 3 (90NBT) with rhombohedral phase. Both textured ceramics exhibit a high Lotgering factor, being on the order of f~96%. The piezoelectric coe ﬃ cients of the textured 88NBT and 90NBT ceramics are increased by 20% and 60%, respectively, comparing to their randomly oriented ceramics. The piezoelectric enhancement of 90NBT textured ceramic is three times higher than 88NBT, revealing the phase structure plays a signiﬁcant role in enhancing the piezoelectric performances of textured ceramics. Of particular signiﬁcance is that the 90NBT textured ceramic exhibits almost hysteresis-free strain behavior. The enhanced piezoelectric property with minimal strain hysteresis is attributed to the < 001 > poled rhombohedral engineered domain conﬁguration.


Introduction
In recent years, lead-free piezoelectric materials based on Na 0.5 Bi 0.5 TiO 3 (NBT) have attracted extensive attention, which is considered to be a potential candidate due to their good ferroelectric and piezoelectric properties, with high Curie temperature T C of 320 • C and large remnant polarization P r value of 38 µC/cm 2 [1]. However, there is still a need to enhance the properties of NBT-based ceramics before they can replace lead-based materials. Improvements in piezoelectric properties have been studied in NBT-based solid solutions with morphotropic phase boundary (MPB) [2][3][4][5][6][7][8] such as Na 0.5 Bi 0.5 TiO 3 -SrTiO 3 (NBT-ST), Na 0.5 Bi 0.5 TiO 3 -BaTiO 3 (NBT-BT), Na 0.5 Bi 0.5 TiO 3 -K 0.5 Bi 0.5 TiO 3 -BaTiO 3 (NBT-KBT-BT), and Na 0.5 Bi 0.5 TiO 3 -K 0.5 Bi 0.5 TiO 3 -SrTiO 3 (NBT-KBT-ST), but with limited success. It is difficult to increase the piezoelectric performances of NBT-based binary and ternary polycrystalline ceramics further by only composition tuning.
Texturing is a promising approach to enhance the piezoelectric performances of ferroelectric ceramics via controlling the microstructure without drastically changing the
The phase structure and the Lotgering factor were determined by X-ray diffraction (XRD) (PANalytical X´Pert PRO, Holland, Netherlands). The Lotgering factor of <001> textured ceramics was calculated with 2θ over a range of 20-60 • C by Lotgering method [27]. The microstructure of samples was examined by a scanning electron microscopy (SEM) (JSM-7001F, JEOL, Tokyo, Japan). The samples were placed in a silicone oil bath and polarized for 15 min at room temperature under a dc electric field of 50 kV/cm, for measuring the dielectric and piezoelectric properties. The direct piezoelectric coefficient (d 33 ) was determined by a d 33 -meter (ZJ-3A, Jiangsu, China) while the effective piezoelectric coefficient (d 33 *) was calculated from the strain-electric field curves. The strain-electric field (S-E) curves were tested at 10 Hz by a TF Analyzer 2000 piezo-measurement system (aixACCT Systems, Aachen, Germany) with a high-voltage power supply (TREK 610E, NY, USA). For Rayleigh analysis, the maximum electric field with 10 Hz frequency was about half of the coercive field (E C ) of NBT-based ceramics, being on the order of 20 kV/cm. The large signal piezoelectric coefficient d 33 * was obtained from the unipolar strain curves measured at 70 kV/cm.

Results and Discussion
XRD patterns of 88NBT and 90NBT ceramics are shown in Figure 1A. All samples present the perovskite structure with no secondary impurity phase. The (003)/(021) and (002)/(200) peaks appear at 2θ of 40 • and 46.5 • in randomly oriented 88NBT ceramic, respectively, demonstrating an MPB region Crystals 2020, 10, 367 3 of 10 with the coexistence of rhombohedral-tetragonal phases, which is in good agreement with the results reported earlier [28]. For the randomly oriented 90NBT ceramic, on the contrary, the (003)/(021) and single peak of (200) can be observed at around 40 • and 46.5 • , respectively, confirming the presence of rhombohedral phases. In all textured ceramics, the intensities of the (200) peaks are higher than other diffraction peaks, demonstrating a strongly preferred grain orientation in the 88NBT and 90NBT textured ceramics along <00l> direction. Based on the XRD results, the Lotgering factor (f) of the textured ceramics can be estimated by Lotgering equations [27]. The f values of the 88NBT and 90NBT textured ceramics are on the order of 96%. This result indicates that the textured 88NBT and 90NBT ceramics possess the same high Lotgering factor. Crystals 2020, 10, 367 3 of 10 higher than other diffraction peaks, demonstrating a strongly preferred grain orientation in the 88NBT and 90NBT textured ceramics along <00l> direction. Based on the XRD results, the Lotgering factor (f) of the textured ceramics can be estimated by Lotgering equations [27]. The f values of the 88NBT and 90NBT textured ceramics are on the order of 96%. This result indicates that the textured 88NBT and 90NBT ceramics possess the same high Lotgering factor. Figures 1B-E show the cross-section SEM micrographs of the 88NBT and 90NBT ceramics. As shown in Figures 1B and D, the average grain sizes of the randomly oriented 88NBT and 90NBT ceramics are observed to possess similar values, being on the order of ~1 μm, suggesting the composition/phase has minimal impact on the grain size of the randomly oriented ceramics. Meanwhile, the 88NBT and 90NBT textured ceramics are observed to possess the brick-like shaped grains, which is in good agreement with the crystallographic orientation, as demonstrated by XRD patterns shown in Figure 1A, further clarify the strong grain orientation. It is obvious that the textured ceramics have much larger grain size in contrast to the randomly oriented ceramics, being on the order of ~10 um.  Figure 2 shows the temperature-dependent of dielectric constant and dielectric loss of poled 88 and 90 NBT ceramics. The maximum temperature (Tm) at which the dielectric constant reached a maximum value is assigned to the Curie temperature. The broad peaks at Tm are observed, either on randomly oriented or textured ceramics. Notably, the peaks at Tm of textured ceramics are flattened, comparing to the randomly oriented ceramics because of the stress induced by the embedded templates. The depolarization temperature (Td) for textured and randomly oriented ceramics are confirmed by the first inflection point of dielectric loss curves. For 88 NBT ceramics, the Td are about 80 °C, which are below the Td of 90 NBT ceramics. The Td of textured and randomly oriented ceramics are about 100 and 120 °C, respectively.
To further explore the relationship between phase and piezoelectric response, Rayleigh analysis of NBT-based ceramics was carried out. Under the low electric field, the Rayleigh law can be expressed by the following formulas [29]: where E0 denotes the level of electric-field, S(E) denotes the ac electric-field-induced strain. In the piezoelectric response, the reversible piezoelectric response, resulting from the intrinsic (lattice) and reversible motion of internal interfaces, is described by coefficient dinit. The contribution of the latter is relatively small in the ferroelectric materials [29,30]. Therefore, in the study, the coefficient dinit is considered to be caused by the intrinsic contribution. The extrinsic contribution to the total piezoelectric response αE0 is arising from the irreversible domain walls motion, where the measured   Figure 1B,D, the average grain sizes of the randomly oriented 88NBT and 90NBT ceramics are observed to possess similar values, being on the order of~1 µm, suggesting the composition/phase has minimal impact on the grain size of the randomly oriented ceramics. Meanwhile, the 88NBT and 90NBT textured ceramics are observed to possess the brick-like shaped grains, which is in good agreement with the crystallographic orientation, as demonstrated by XRD patterns shown in Figure 1A, further clarify the strong grain orientation. It is obvious that the textured ceramics have much larger grain size in contrast to the randomly oriented ceramics, being on the order of~10 um. Figure 2 shows the temperature-dependent of dielectric constant and dielectric loss of poled 88 and 90 NBT ceramics. The maximum temperature (T m ) at which the dielectric constant reached a maximum value is assigned to the Curie temperature. The broad peaks at T m are observed, either on randomly oriented or textured ceramics. Notably, the peaks at T m of textured ceramics are flattened, comparing to the randomly oriented ceramics because of the stress induced by the embedded templates. The depolarization temperature (T d ) for textured and randomly oriented ceramics are confirmed by the first inflection point of dielectric loss curves. For 88 NBT ceramics, the T d are about 80 • C, which are below the T d of 90 NBT ceramics. The T d of textured and randomly oriented ceramics are about 100 and 120 • C, respectively.
To further explore the relationship between phase and piezoelectric response, Rayleigh analysis of NBT-based ceramics was carried out. Under the low electric field, the Rayleigh law can be expressed by the following formulas [29]: where E 0 denotes the level of electric-field, S(E) denotes the ac electric-field-induced strain. In the piezoelectric response, the reversible piezoelectric response, resulting from the intrinsic (lattice) and Crystals 2020, 10, 367 4 of 10 reversible motion of internal interfaces, is described by coefficient d init . The contribution of the latter is relatively small in the ferroelectric materials [29,30]. Therefore, in the study, the coefficient d init is considered to be caused by the intrinsic contribution. The extrinsic contribution to the total piezoelectric response αE 0 is arising from the irreversible domain walls motion, where the measured coefficient α represents the Rayleigh parameter. From Rayleigh analysis, the electric field dependent d 33 is calculated by d 33 = S p-p /2E 0 , where the S p-p is peak-to-peak strain. The d 33 of the randomly oriented and textured ceramics were plotted as a function of ac electric field E 0 and given in Figure 3. The d 33 had a good linear correlation with E 0 , indicating the piezoelectric response follows the Rayleigh law. According to Equation (1) d33 is calculated by d33 = Sp-p/2E0, where the Sp-p is peak-to-peak strain. The d33 of the randomly oriented and textured ceramics were plotted as a function of ac electric field E0 and given in Figure 3. The d33 had a good linear correlation with E0, indicating the piezoelectric response follows the Rayleigh law. According to Equation (1), dinit values are on the order of 67, 124, 72, 141 pm/V for randomly oriented and textured 88NBT and 90NBT ceramics, respectively. α are found to be 2.61 cm/kV, 2.36 cm/kV, 2.06 cm/kV, 1.52 cm/kV, respectively.  Based on the Rayleigh analysis, αE 0 /(αE 0 + d init ), the ratios of extrinsic contribution were calculated and given in Figure 4. The ratios of extrinsic contributions for randomly oriented and textured 88NBT and 90NBT ceramics are found to be on the order of~43%, 27%, 37%, and~18% at an electric field of 20 kV/cm, respectively. The results indicate that textured 88NBT ceramic possesses a lower extrinsic contribution of 27% comparing to the randomly oriented 88NBT ceramic. In ferroelectric materials, it is known that ferroelastic domain-wall motion, is the main factor for extrinsic contribution [31,32]. Thus, in contrast to the randomly oriented ceramics, textured 88NBT ceramic possesses lower ferroelastic domain-wall motion. It can be noted that the extrinsic contribution of ceramics is usually accompanied by strong nonlinearity and large strain hysteresis, according to the results of Rayleigh analysis. Similarly, when the extrinsic contribution is reduced, the corresponding strain hysteresis is expected to reduce.   Based on the Rayleigh analysis, αE0/(αE0 + dinit), the ratios of extrinsic contribution were calculated and given in Figure 4. The ratios of extrinsic contributions for randomly oriented and textured 88NBT and 90NBT ceramics are found to be on the order of ~43%, 27%, 37%, and ~18% at an electric field of 20 kV/cm, respectively. The results indicate that textured 88NBT ceramic possesses a lower extrinsic contribution of 27% comparing to the randomly oriented 88NBT ceramic. In ferroelectric materials, it is known that ferroelastic domain-wall motion, is the main factor for extrinsic contribution [31,32]. Thus, in contrast to the randomly oriented ceramics, textured 88NBT ceramic possesses lower ferroelastic domain-wall motion. It can be noted that the extrinsic contribution of ceramics is usually accompanied by strong nonlinearity and large strain hysteresis, according to the results of Rayleigh analysis. Similarly, when the extrinsic contribution is reduced, the corresponding strain hysteresis is expected to reduce. The principle piezoelectric and dielectric properties are listed in Table 1. As shown in Table 1, d33 are 150 and 110 pC/N for the 88NBT and 90NBT randomly oriented ceramics, respectively, increasing to the value of ~185 pC/N and ~175 pC/N for the textured ceramics, respectively, demonstrating 20% and 60% enhancements, respectively. This result shows that the piezoelectric properties of 90NBT textured ceramic have been significantly improved, compared to the 88NBT textured ceramic with MPB composition. The enhanced piezoelectric performance in textured 90NBT ceramic is closely associated with the domain configurations and crystallographic structure. Analogous to <001> oriented single crystals, as shown in Figure 4B, specific domain configuration "4R" (where 4 means the number of degenerated polarization directions while R represents rhombohedral phase) can also be expected to form in <001> textured 90NBT, accounting for the enhanced piezoelectric properties and reduced dielectric loss as compared to its randomly oriented ceramics. The principle piezoelectric and dielectric properties are listed in Table 1. As shown in Table 1, d 33 are 150 and 110 pC/N for the 88NBT and 90NBT randomly oriented ceramics, respectively, increasing to the value of~185 pC/N and~175 pC/N for the textured ceramics, respectively, demonstrating 20% and 60% enhancements, respectively. This result shows that the piezoelectric properties of 90NBT textured ceramic have been significantly improved, compared to the 88NBT textured ceramic with MPB composition. The enhanced piezoelectric performance in textured 90NBT ceramic is closely associated with the domain configurations and crystallographic structure. Analogous to <001> oriented single crystals, as shown in Figure 4B, specific domain configuration "4R" (where 4 means the number of Crystals 2020, 10, 367 6 of 10 degenerated polarization directions while R represents rhombohedral phase) can also be expected to form in <001> textured 90NBT, accounting for the enhanced piezoelectric properties and reduced dielectric loss as compared to its randomly oriented ceramics. In order to explore the impact of phase structure on strain behavior at large electric field, the unipolar strain curves were measured as a function of electric fields up to 70 kV/cm at 1 Hz, as shown in Figure 5. At 70 kV/cm, the strain of randomly oriented 88NBT ceramic, textured 88NBT ceramic, randomly oriented 90NBT ceramic, and textured 90NBT ceramic can reach 0.18%, 0.18%, 0.13% and 0.14% respectively. The d 33 * are calculated to be 205 pm/V for the textured 90NBT ceramic at 70 kV/cm as compared with that of 180 pm/V for the randomly oriented 90NBT ceramic, i.e., the textured ceramics show an improvement about 13% in d 33 *. Compared to the 88NBT composition, the d 33 * of 90NBT composition with rhombohedral phase has been clearly improved, while the strain level and d 33 * of 88NBT with MPB composition are comparable in randomly oriented and textured samples, due to the extrinsic contribution, i.e., the domain wall motion, in 88NBT with coexisted rhombohedral and tetragonal phases dominates the large field piezoelectric. These results can also be confirmed by the strain hysteresis H, where the value for rhombohedral randomly oriented 90NBT ceramic is about 26% at large field of 70 kV/cm, lower than the MPB 88NBT ceramics, owing to the facilitated domain wall motion in tetragonal phase, thus higher extrinsic contribution and higher strain hysteresis. Of particular significance is that the 90NBT textured ceramic exhibits almost linear behavior even at a high electric field of 70 kV/cm, with strain hysteresis being on the order of 12%. In contrast to randomly oriented ceramics, the textured ceramics possess less than half of the strain hysteresis, which can be explained by the <001> texturing characteristics, leading to engineered domain configuration "4R" after polarizing along <001> direction, accounts for the greatly reduced strain hysteresis [9,12,20].
It is concluded that different phase structures have a significant impact on the performances of textured ceramics. Based on the concept of domain engineering, significantly enhanced piezoelectric response and reduced strain hysteresis could be expected in highly <001> textured ceramics with rhombohedral phase, as a result of promoted polarization rotation owing to the formation of "4R" domain configuration [12,33,34], this also is confirmed by the above Rayleigh analysis. The textured 90NBT ceramic has a lower extrinsic contribution of 18% as well as lower H comparing to the textured 88NBT ceramics and the randomly oriented 90NBT ceramic. The greatly decreased extrinsic contribution and reduced strain hysteresis observed in textured 90NBT are inherently associated with the engineered domain configuration, domain wall density and the number of possible directions of spontaneous polarizations. Both textured ceramics were found to possess one order larger grain size when comparing to their random ceramic counterparts, as shown in Figure 1, revealing the domain size in textured ceramics is greater than that in random ceramics due to the fact that domain size is proportional to the square root of grain size [35,36], leading to lower domain wall density, accounting for the smaller extrinsic contribution and strain hysteresis in the textured ceramics comparing to their randomly oriented counterparts. On the other hand, the textured 88NBT and 90NBT ceramics possess similar grain size and the same Lotgering factor, suggesting the grain size and Lotgering factor are not the dominant factors responsible for the lower extrinsic contribution of the textured 90NBT ceramic comparing to textured 88NBT. In the <001> textured 90NBT ceramic with the rhombohedral phase, all the grains are aligned along crystallographic <001> direction. Analogous to <001> oriented rhombohedral single crystals, the <001> textured 90NBT ceramic with rhombohedral phase will form the engineered-domain configuration after poled along <001> direction (even the textured ceramic is transversely isotropic material which possesses a plane of isotropy vertical to <001> direction, being different from single crystal), where the coexistence of the four degenerated domain states can stabilize the domain wall, thus less domain wall motion. The smaller extrinsic piezoelectric response and minimal strain hysteresis at a high electric field of the textured 90NBT ceramic are associated with the "4R" domain engineered configuration [37].
0.14% respectively. The d33* are calculated to be 205 pm/V for the textured 90NBT ceramic at 70 kV/cm as compared with that of 180 pm/V for the randomly oriented 90NBT ceramic, i.e., the textured ceramics show an improvement about 13% in d33*. Compared to the 88NBT composition, the d33* of 90NBT composition with rhombohedral phase has been clearly improved, while the strain level and d33* of 88NBT with MPB composition are comparable in randomly oriented and textured samples, due to the extrinsic contribution, i.e., the domain wall motion, in 88NBT with coexisted rhombohedral and tetragonal phases dominates the large field piezoelectric. These results can also be confirmed by the strain hysteresis H, where the value for rhombohedral randomly oriented 90NBT ceramic is about 26% at large field of 70 kV/cm, lower than the MPB 88NBT ceramics, owing to the facilitated domain wall motion in tetragonal phase, thus higher extrinsic contribution and higher strain hysteresis. Of particular significance is that the 90NBT textured ceramic exhibits almost linear behavior even at a high electric field of 70 kV/cm, with strain hysteresis being on the order of 12%. In contrast to randomly oriented ceramics, the textured ceramics possess less than half of the strain hysteresis, which can be explained by the <001> texturing characteristics, leading to engineered domain configuration "4R" after polarizing along <001> direction, accounts for the greatly reduced strain hysteresis [9,12,20].   Figure 6A-D shows the unipolar strain curves of 88NBT and 90NBT ceramics at 40 kV/cm, with temperatures ranging from room temperature (RT) to 160 • C. The corresponding strain and d 33 * of ceramics are plotted in Figure 6E. As shown in Figure 6A-D, the textured ceramics show relatively linear unipolar strain curves at different temperatures in contrast to the random ceramics of the same composition, which corresponds to smaller strain hysteresis. In contrast to the 88NBT ceramics, the 90NBT ceramics exhibit more linear unipolar strain curves, owing to the domain wall motion in the tetragonal phase. Herein as the temperature increases, the strain and d 33 * (at 40 kV/cm) of all ceramics both increase to maximum values at first and then decrease approaching to depolarization temperature T d . This phenomenon has also been observed in NBT-BT-ST and NBT-KBT-BT ceramics [38,39]. For 88NBT randomly oriented ceramic, the unipolar strain increases gradually as the temperature rises to 100 • C, which is higher than the depolarization temperature T d (~80 • C). The maximum unipolar strain and d 33 * of 88NBT randomly oriented ceramic are 0.26% and 660 pm/V, respectively, which can be achieved at a temperature of 100 • C, being associated with the coexistence of ferroelectric order and ergodic relaxor phase in NBT-based ceramics. Above 100 • C, the strain and d 33 * of 88NBT randomly oriented ceramic decrease. Meanwhile, it is worth noting that the 88NBT randomly oriented ceramic has relatively small strain hysteresis at high temperatures. In contrast, the strain and d 33 * of 88NBT textured ceramic increase gradually from RT to 60 • C, followed by a sharp increase to 0.27% and 675 pm/V at 100 • C, respectively, above which, the strain and d 33 * values of the 88NBT textured ceramic are reduced, showing a phenomenon similar to that of 88NBT randomly oriented ceramic. At RT to 140 • C, the strain and d 33 * of the 90NBT randomly oriented ceramic increase gradually, then sharply increase to 0.27% and 680 pm/V at 160 • C, respectively. For 90NBT textured ceramic, the maximum unipolar strain and d 33 * is 0.32% and 800 pm/V at 140 • C, respectively. In summary, the 90NBT textured ceramics exhibit a linear strain linear behavior with enhanced temperature stability when the temperature below the Td in contrast to the 88 NBT textured ceramics.

Conclusions
Highly <001>-textured 88NBT (MPB) and 90NBT (rhombohedral phase) ceramics with Lotgering factor f~96% were prepared via the TGG method. The piezoelectric coefficients of 88NBT textured and 90NBT textured ceramics are increased by 20% and 60%, respectively, compared to their randomly oriented ones. Additionally, the d33* of 90NBT textured ceramic possess 13% enhancement compared to its randomly oriented counterpart; however, the d33* of textured 88NBT ceramic maintains a similar value. These results demonstrate that the different phase structures have a significant impact on the properties of textured ceramics. Based on the Rayleigh analysis and strain behavior, the enhancement of piezoelectric properties and minimal strain hysteresis of 90NBT textured ceramics can be explained by the increased rhombohedral phase and "4R" domain engineered configuration comparing to 88NBT textured ceramics.

Conflicts of Interest:
The authors declare no conflicts of interest.

Conclusions
Highly <001>-textured 88NBT (MPB) and 90NBT (rhombohedral phase) ceramics with Lotgering factor f~96% were prepared via the TGG method. The piezoelectric coefficients of 88NBT textured and 90NBT textured ceramics are increased by 20% and 60%, respectively, compared to their randomly oriented ones. Additionally, the d 33 * of 90NBT textured ceramic possess 13% enhancement compared to its randomly oriented counterpart; however, the d 33 * of textured 88NBT ceramic maintains a similar value. These results demonstrate that the different phase structures have a significant impact on the properties of textured ceramics. Based on the Rayleigh analysis and strain behavior, the enhancement of piezoelectric properties and minimal strain hysteresis of 90NBT textured ceramics can be explained by the increased rhombohedral phase and "4R" domain engineered configuration comparing to 88NBT textured ceramics.