Correlation between depolarization temperature and lattice distortion in quenched (Bi_1/2Na_1/2)TiO₃-based ceramics

Currently, PbTiO₃-PbZrO₃ (PZT)-based ceramics are widely used for most piezoelectric applications, and PZT contains a large amount of lead oxide (PbO). Research and development of on lead-free piezoelectric materials is considered necessary from the viewpoint of environmental protection, and various lead-free piezoelectric ceramics have been developed so far. (Bi_0.5Na_0.5)TiO₃ (BNT) is an A-site complex perovskite structure ferroelectric with rhombohedral symmetry at room temperature, RT.^1,2) BNT-based solid solution ceramics modified with BaTiO₃ (BT)³⁾ and (Bi_1/2K_1/2)TiO₃ (BKT)^4,5) are reported to have relatively large piezoelectricity near the morphotropic phase boundary. Furthermore, because the mechanical quality factor Q_m of BNT-based ceramics is stable during large-amplitude piezoelectric driving, these ceramics are expected to be one of the superior candidates for lead-free piezoelectric materials for high-power piezoelectric applications such as ultrasonic devices.⁶⁾ However, the temperature at which the piezoelectricity disappears (the depolarization temperature T_d) is approximately 100 °C–200 °C, which is lower than that of PZT-based materials.^7,8) This is a serious disadvantage and hinders the practical applications of this system. Although various studies have so far been conducted to increase the T_d of BNT-based ceramics, piezoelectricity and T_d have a trade-off relationship.⁹⁾

Recently, some researchers have reported that a quenching procedure performed after the sintering process was an effective way of increasing the T_d of pure BNT¹⁰⁾ and BNT-based solid solution ceramics^11,12) without degrading their ferroelectric and piezoelectric properties. For example, the T_d of pure BNT was approximately 180 °C, and that of the BNT sample quenched from 1100 °C was 223 °C, which was almost 40 °C higher than the sample prepared using the ordinary cooling process.¹⁰⁾ In addition, they clarified that the quenching procedure helped increase the rhombohedral distortion (90° − α) and also increased the T_d of the BNT ceramic.^10–12) A similar type of rhombohedral distortion increase was reported by Yoneda et al. in Li-substituted BNT (BNLT) ceramics.¹³⁾ In addition, the BNLT ceramics showed a relatively higher T_d after Li substitution than the pure BNT ceramics.¹⁴⁾ Therefore, it is expected that both Li substitution and the quenching treatment could increase both T_d and the rhombohedral distortion. In fact, 0.92BNT-0.08(Bi_0.5Li_0.5)TiO₃ (BNLT8) showed a high T_d at 237 °C after the quenching treatment from 1100 °C.¹¹⁾

These results are very useful from the standpoint of practical applications of BNT-based ceramics moreover, the phenomena are very interesting from the academic point of view, and raise the question of why the quenching process increases the T_d of BNT-based ceramics. However, currently, not enough is known about the mechanism, and the reason for the T_d increase has not been clearly explained. From the viewpoint of crystal structure, T_d is thought to be the structural phase transition from the rhombohedral (R3c symmetry) to the tetragonal (P4bm symmetry).¹⁵⁾ Previous studies also suggest that the quenching procedure helped increase the rhombohedral distortion (90° − α) and also increased the T_d of the BNT-based ceramic.^10–12) On the other hand, this type of crystal structure analysis was only conducted with laboratory X-ray diffraction (XRD) measurement. Therefore, in this study, high-energy synchrotron X-ray powder diffraction data on quenched and non-quenched BNLT were collected in SPring-8 to analyze their crystal structures in detail, to find a clue for elucidating the mechanism of the T_d increase due to the quenching treatment. In addition, the local atomic structures of these ceramics were also examined with atomic pair distribution function (PDF) analysis¹⁶⁾ by using synchrotron high-energy XRD data.

BNLT8 ceramics have been fabricated by using a conventional solid-state-reaction method (ordinary fired: OF). The sintering conditions are 1140 °C for 2 h. The details are described elsewhere.¹¹⁾ On the other hand, in the rapid cooling process, a sample is removed from the furnace when the temperature of the furnace reaches 1100 °C during the main firing, and rapidly cooled by blowing with a fan. The temperature at which the sample is removed from the furnace for quenching is called "quench temperature." And the quench temperature at 1100 °C was optimized and determined in a previous work.¹¹⁾ The physical and electrical properties of the produced ceramics were measured by conventional methods.^13–15) A synchrotron XRD experiment was conducted at SPring-8 (BL14B1). After grinding the samples, the powders were encapsulated in a Kapton capillary. High-energy synchrotron X-ray powder diffraction data were collected with 60 keV X-rays at 300 K. Long-range structural parameters were subjected to Rietveld refinement with the RIETAN-FP program.¹⁷⁾ The pseudo-Voigt peak shape function was chosen. In addition, the local structure was refined with the PDFFIT program using the atomic PDF technique.¹⁶⁾

The physical and electrical properties of OF and quenched BNLT8 ceramics are summarized in Table I. The relative density ratios of both ceramics are the same: 98.7%. Further, the electromechanical coupling factors k₃₃ of OF and quenched BNLT8 ceramics are almost the same: 0.48 and 0.49, respectively. The free permittivity ε₃₃^T/ε₀ and piezoelectric constant d₃₃ decreased slightly after the quenching treatment. On the other hand, T_d was elevated greatly from 152 °C to 237 °C by the quenching treatment, determined from measurement of the temperature dependence of k₃₃. The detailed properties have been reported in our previous paper.¹¹⁾

The observed and calculated diffraction profiles and difference plots for the OF and quenched BNLT at RT are shown in Figs. 1(a) and 1(b), respectively. The short vertical markers represent the calculated peak positions. The XRD profiles of both OF and quenched BNLT8 exhibit rhombohedral symmetry with the space group R3c, which is similar to the previous reports.¹⁵⁾ Sometimes, pure BNT can be fitted easily with the space group Cc rather than R3c.¹⁸⁾ On the contrary, one of the advantages of using Li-substituted BNT in this study is that R3c is preferable for fitting the observed profiles. The R_wp and R_F values represent the misfit between the calculated and observed XRD profiles and is used to evaluate the reliability of the model. R_wp values of both OF and quenched BNLT indicate an order of 5%. The refined structure parameters are summarized in Table II. The lattice constant is almost the same. On the other hand, it was found that the rhombohedral distortion (90° − α) was significantly increased by the quenching treatment. Figure 1(c) is an enlarged view of OF and quenched BNLT8 at approximately 5.2°–5.4°, indicating a clear splitting of 111-related reflections in the quenched BNLT8. This type of difference was also observed in the previous report,^10–12) in which measurements were taken from laboratory-level X-ray equipment. In addition, when the quench temperature was changed from 800 °C to 1100 °C, T_d and (90° − α) tended to increase simultaneously.¹⁰⁾ In other words, T_d tended to increase proportionally as (90° − α) increased. Considering these results together with the (90° − α) values from high-energy synchrotron XRD in this work, we could confirm that there is a strong correlation between T_d and (90° − α). We can then conclude that an increase in the rhombohedral distortion by the quenching treatment can promote the T_d elevation of BNT. Dorcets et al. conducted an in situ transmission electron microscopy (TEM) study on BNT that focused on the rhombohedral phase and T_d.¹⁹⁾ The ferroelectric domains of R3c at approximately RT are disappeared with temperature rise, and Pnma orthorhombic sheets appeared within the R3c matrix at around 200 °C. They stated that the increase in the density of the Pnma sheets led to a reorientation of the polar vector within the R3c, that is, "depolarization." Their conclusion was that "destabilization of R3c phase" corresponds to "depolarization." Similar studies have also been conducted by X. Tan's group.²⁰⁾ They also carried out an in situ TEM study on the phase transitions in BNT-BaTiO₃ ceramics. Their study also showed that the BNT-side compositions have R3c rhombohedral ferroelectric domains at RT, and modulated P4bm tetragonal nanodomains developed within the R3c phase at approximately T_d. From these TEM studies, because the rhombohedral phase instability corresponds to T_d, we can reasonably conclude that an increase in the rhombohedral distortion (i.e. stabilization of the rhombohedral phase) affects the T_d increase.

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Figure 2 shows schematic illustrations of the average structure position estimation of each element in OF and quenched BNLT-8 ceramics, using the program VESTA.²¹⁾ Changes in the average structure position of Bi ions were observed in OF and quenched samples, and Bi ion were displaced along the 〈111〉 direction away from Na ion by the quenching treatment. Table II shows an atomic distance between Bi and Na along 〈111〉 direction, which indicates a Bi–Na distance determined from the average structure position of each element. This value in the quenched sample was longer than that in OF sample. Therefore, from the Rietveld refinement, Na ions occupy the center position of the A-site of perovskite structure, which means the displacement of Bi ions on the off-center position along the 〈111〉 direction after the quenching treatment. Some previous papers have also reported that the Bi ion introduces significant structural distortion into the crystal of BNT.^22–24) Furthermore, Kitamura et al. also described the atomic configuration and local structure of BNT,²⁵⁾ suggesting that Na behaves as a pillar of the A-site in the perovskite structure and Bi is located on the off-center positions of the A-site. These results also support our speculation about Bi-ion off-centering around the A-site. We assume that this displacement of the Bi ion in the 〈111〉 direction increases both rhombohedral distortion and the stability of R3c phase, due to the quenching treatment. These behaviors then lead to the elevation of T_d. Further, Moriyoshi et al. reported the off-centering of Bi ion even in the cubic phase at 1000 K on BNT.²⁶⁾ They indicated that the off-center displacement of Bi-ion at this temperature was approximately 0.39 Å. This value is larger than that of our displacement result (∼0.14 Å) however, it is on the same order of magnitude. This correspondence is quite important as a clue regarding the mechanism of the quenching behavior in BNT. This is because, even in the high-temperature state, Bi ions were already displaced on the off-center position of the A-site before the quenching treatment, after which the temperature suddenly cooled down to the ground state at RT with maintenance of the off-center position of the Bi ions. This is equivalent to a "freezing" of Bi-ion off-centering by the quenching treatment.

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One of the additional interesting features in Table II is the atomic displacement parameter of Bi ions in OF and quenched BNLT8. Although the diffraction data of BNLT8 can be indexed unambiguously, the displacement parameter of A(Bi)-site atoms was relatively large (>1.4 Ų) as compared with the parameters of other B-site and oxygen atoms (<1.0 Ų). This tendency is also reported in a previous paper,¹³⁾ which reported similar values to those reported by this study. The displacement parameter tends to couple with static local atomic displacements. Therefore, the large displacement parameters indicate that Bi ions are disordered from the average lattice point. The displacement parameter of the quenched sample was smaller and almost half that in the OF sample. This means that the OF sample has a disordered structure around the A-site of the perovskite structure, and the quenched sample has a more ordered structure. Again, the average displacement parameter from XRD is strongly related to the static local atomic displacement. Thus, further local structure analysis was conducted by using the PDF method to confirm the disordered or ordered structures in OF and quenched BNLT8. Figure 3 shows the observed PDFs in the range 1.0 ≤ r ≤ 10 Å for OF and quenched BNLT8 at 15 K. The G(r) in PDF analysis indicates the probability of finding an atom at a distance r from another atom. It can be seen from the figure that the PDF peaks at approximately 3.9 and 3.2 Å correspond to the unit cell size in the perovskite structure and (Bi/Na)-Ti bonds, respectively. In the case of unit cell length of 3.9 Å of the perovskite structure, the effect of the quenching treatment was hardly observed, and the PDF amplitudes of these peaks are almost the same. This is because the Na ions behave as a pillar of the A-site positions in the perovskite unit cell as discussed in the previous paragraph, and Na ions are not affected by the quenching treatment. On the other hand, the PDF amplitude of OF-BNLT8 at approximately 3.2 Å from the (Bi/Na)-Ti bonds is smaller and wider than that of the quenched sample. The higher PDF amplitude indicates a more ordered structure with better crystallinity and/or larger grain size. The grain sizes are almost the same in both OF and quenched samples. Therefore, local structure analysis also suggests that the quenched sample has a more ordered structure. In particular, the peak position at approximately 3.2 Å corresponds to the (Bi/Na)-Ti bonds in the 〈111〉 direction, suggesting enhanced ordering behavior of Bi ions. This result also explains the smaller displacement parameter of Bi ions in the average structure after the quenching treatment as shown in Table II. Therefore, it is confirmed from the local structure analysis that the OF sample has a disordered structure around the Bi ion along 〈111〉 in the perovskite structure, and the quenched sample has a more ordered structure. In summary, in the quenched sample, it can be imagined that Bi ions are more ordered at off-center positions displaced in the 〈111〉 direction.

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In addition, a similar tendency (more ordering behavior by the quenching treatment) was also observed in the temperature dependence of various electrical characteristics. Figure 4 shows the temperature dependences of the dielectric constant ε_s and loss tangent tan δ for OF and quenched BNLT8 after the poling treatment. The peak temperatures in tan δ correspond to T_d.²⁷⁾ We can thus confirm that the quenched sample has a higher T_d as compared with the OF sample. One of the interesting aspects of the temperature dependence of tan δ is the diffuseness around T_d. The tan δ of the OF sample indicates broad behavior, but that of the quenched sample has a sharp peak at around T_d. In other words, the OF sample shows a more diffuse phase transition as compared with the quenched sample. In the case of Pb-based relaxor materials such as Pb(Sc, Ta)O₃ (PST),²⁸⁾ Pb(In, Nb)O₃ (PIN),²⁹⁾ etc., the compositional order-disorder may greatly affect the dielectric and ferroelectric properties. For example, Setter and Cross²⁸⁾ demonstrated that the degree of B-site order in PST can be controlled by heat treatment. A well-ordered single crystal, obtained after long-time annealing at 1000 °C, exhibits a normal first-order ferroelectric phase transition. By contrast, a disordered sample shows a broad peak in ε_s with strong dispersion, which is typical for relaxor ferroelectrics. In the case of BNLT8 in this study, the temperature dependences of dielectric properties in the quenched sample indicate a sharp peak at approximately T_d, which is similar to the first-order phase transition with a more ordered structure. This tendency is diametrically opposite to the behavior in Pb-based relaxors. However, this sharp peak in quenched BNLT8 is an experimental fact. One of the big differences in BNT and Pb-based relaxor materials is the complex site of the material elements, such as the A-site complex in BNT or the B-site complex in Pb-based relaxors. The A-site of BNT consists of Bi and Na. The Na ions make a framework of perovskite unit cells at the center position of the A site,²⁵⁾ and they are not strongly affected by the quenching treatment. On the other hand, Bi ions are displaced on the off-center positions of the A-site with a small displacement fluctuation after the quenching treatment. Therefore, the behavior of Bi ions appears to be one of the key points for understanding the mechanism of this strange behavior in BNT. Kitanaka and Noguchi reported that the stabilization of the R3c phase for BNT stems from the low-lying valence states arising from the Bi-6p and O-2p hybridization.^30,31) Moriyoshi et al. mentioned that the Bi ion tends to go to the off-center site to hybridize with the O ion even in the high-temperature cubic phase,²⁶⁾ and the Bi–O distance in the off-center structure is key to understanding the off-centering behavior of the Bi ion in Bi-based perovskite systems.^30,31)

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From this discussion, we assume that the mechanisms for OF and the quenched process in BNLT ceramic are as follows. In the case of the OF sample, the Bi ions tend to undergo a large displacement fluctuation due to the change in the oxygen vacancy concentration surrounding the A-site during slow cooling. The result is a disordered structure with a large displacement parameter, whereas the average Bi position is near the center of the A-site. On the other hand, in the case of the quenched sample, the Bi ions are frozen at large off-center positions with a more ordered structure. Then, Bi ion off-centering on average leads to an increase in rhombohedral distortion (stabilization of R3c phase), and finally T_d is elevated. It is still necessary to conduct more studies on topics such as the distribution of oxygen vacancies, formation of chemical order regions and domain structures, etc., to support this mechanism. However, if this speculation is true, the quenching treatment should be able to control the material properties of Bi-based A-site complex perovskites in general, without being limited to rhombohedral structures. In fact, even in (Bi_1/2K_1/2)TiO₃ (BKT) and BNT-BKT systems having tetragonal symmetry, it has been confirmed that the phase transition temperature is increased by the quenching treatment.¹²⁾ Therefore, we can state that the "quenching treatment" is a unique method and a powerful tool for controlling the physical and electrical properties of bismuth-based A-site complex perovskite ferroelectrics.