Nanoscale structural analysis of Bi_0.5Na_0.5TiO₃ in high-temperature phases

Bismuth sodium titanate (Bi_0.5Na_0.5TiO₃, BNT) with chemical fluctuations at the A site, and related solid solutions, have been extensively investigated owing to their relatively high piezoelectric properties. ^1–6) In response to growing awareness of environmental protection, research and development for practical use of high-performance lead-free piezoelectric ceramics are considered to be urgent and indispensable. ^7–12) Among lead-free piezoelectric ceramics, BNT is attracting attention as one of the candidates in the field of actuator system application, but BNT loses piezoelectricity on the low-temperature side of the Curie temperature, T_C. The depolarization phenomena, which undergoes below T_C, is a diffuse phase transition similar to that of a relaxer. ^13–15) However, there are few reports on the depolarization temperature (T_d ), particularly, no structural changes around T_d have been reported. Research on these compounds provides an opportunity to investigate structural effects and consequent properties when the A-site cations are the primary determining factor of the resulting structure. Similar to PbMg_1/3Nb_2/3O₃ (PMN), in which local structural inhomogeneity has been detected. ^16–19) BNT has similar heterogeneity, with a diffuse phase transition from a partially disordered high-temperature phase to a partially ordered low-temperature phase. ^20–22) To elucidate this phase transition mechanism, both chemical heterogeneity and atomic displacement need to be investigated. We have already performed nanoscale structural analysis of BNT at room temperature and found that there are very large fluctuations in the Ti site, and that the disorder from the average structural position of Ti is the origin of the enormous diffuse scattering. Compared with the highly fluctuating titanium site, the A site occupies almost the average structural position even though Bi and Na are mixed. ²³⁾ Nanoscale structural analysis in the high-temperature phases is necessary to understand the microscopic mechanism of depolarization phenomena. ²⁴⁾ Here, we report the local structural analysis of BNT in the high-temperature phases. BNT comprises Bi and Na with high vapor pressures. Additionally, the loss of these elements during heat treatment has a significant effect on local structure. ^25–29) In recent years, the application of BNT has expanded to photocatalysts and fuel cell electrodes, and the method of synthesizing BNT has greatly evolved. ³⁰⁾ The effect of non-stoichiometry of BNT on the crystal structure caused by Bi and Na defects has not been studied in detail due to the difficulty of synthesizing high-quality BNT. For BNT, where, heterocations occupy the same crystal site, accurate structural analysis can be performed with samples of precisely controlled composition. The results of many local structural analyzes of BNT produced by conventional synthetic methods have been reported. ^23,31) We reexamined the nano-scale order structure of BNT with high-quality samples. The nanoscale-order structural analysis in high-temperature phases was performed by using a pair distribution function (PDF) ^32,33) obtained from the total scattering. In the present work, we reexamined the local structure analysis of high-quality BNT in high-temperature phases. Similar to relaxer ferroelectrics, the diffuse phase transition occurs at T_d due to the locally ordered nanoscale structure. The phase-transition phenomenon of ferroelectrics is generally discussed in terms of macroscale structural changes. Using only Bragg reflection in a disordered system that deviates from the average structure such as BNT, a lot of structural information is missing. By performing PDF analysis obtained from a high-quality BNT sample and synchrotron radiation high-energy X-ray total scattering, local structural analysis without assuming periodicity is performed, and microstructural changes in depolarization phenomena are extracted.

BNT ceramics were synthesized using standard solid-state reaction method with slight modifications introduced by Noguchi et al. ²³⁾ The feed composition was precisely controlled and high-quality ceramics with high sintering density were obtained. Homogeneity and chemical impurities in the synthesized ceramics were examined and no trace elements were found.

The synchrotron X-ray diffraction experiments were carried out at beamlines BL22XU and BL04B2 ³⁴⁾ of SPring-8. The measurements were done on transmission geometry using high-energy X-rays of ∼60 keV. Samples were sealed in cylindrical quartz tubes. The temperature was increased to 600 °C using an electric furnace. The local structure analysis was performed using the PDF technique of the pdffit program ^35,36) and the average structure analysis was performed using the Rietveld refinement of the rietan-fp program. ³⁷⁾ The local structure obtained by PDF analysis was drawn by the vesta program. ³⁸⁾

Figure 1 represents the temperature dependence of X-ray diffraction profiles with the selected range of 8.3 ≤ 2θ ≤ 8.55°. BNT shows a rhombohedral $R3c$ structure at room temperature, as we have already reported with the same BNT crystal. ²³⁾ The structure changed to tetragonal at 200 °C, and then to cubic at 400 °C, which are generally consistent with the temperature dependence of the Bragg reflection, as shown in Fig. 1. The Bragg reflection shifts to the low angle side due to the elongation of the lattice, but the cubic structure is maintained even at 600 °C. Because the average structure is useful for the initial structure of the local structure analysis, we performed a Rietveld analysis with the X-ray diffraction profiles observed at 200 °C and 600 °C. Figures 2(a) and 2(b) show X-ray diffraction patterns observed at 200 °C and 600 °C along with the corresponding Rietveld refinements assuming tetragonal and cubic structures with the space groups of $P4{bm}$ and ${Pm}\overline{3}m$, respectively. The refined lattice parameters and atomic coordinates were essentially the same as those previously reported by Jones et al. ⁵⁾ The obtained values of the lattice parameters and the atomic coordinates observed at 200 °C and 600 °C are shown in Tables I and II, respectively. In the Rietveld analysis, only the Bragg reflection extracts the periodic structure, despite a large amount of diffuse scattering observed, as shown in Fig. 2(c), which suggests the existence of local structures that deviate from the average structure. The intensity of the diffuse scattering increased with temperature increased. Furthermore, the diffuse scattering intensity is further increased in the high-temperature phases, and structural analysis is required to clarify the disordered structure. We attempted to clarify the deviation from the periodic structure by performing PDF analysis and Rietveld analysis from the same data set.

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Table I. Rietveld refined parameters of Bi_0.5Na_0.5TiO₃ observed at 200 °C. Data were collected at a wavelength of λ = 0.201 693 Å. The refinement was done assuming the space group $P4{bm}$. The parameters obtained are a = 5.4859(6)Å, c = 3.8755(6)Å, R_wp  = 8.293%, R_p  = 6.238%, and goodness of fit (S) = 1.4421.

Atom	x	y	z	UISO (Å2)
Bi/Na	0(−)	0(−)	0.543(2)	0.060(1)
Ti	0(−)	0(−)	0(−)	0.009(1)
O1	0(−)	0(−)	0.535(18)	0.121(7)
O2	0.257(9)	0.231(5)	−0.020(2)	=${U}_{{\rm{O}}1}$

First, the deviation from the average structure is visualized by the PDF obtained using only the diffuse scattering. The Rietveld analysis is performed using the X-ray diffraction pattern with the background subtracted, and components other than Bragg reflection, that is, diffuse scattering can be extracted in the process of the Rietveld analysis, as shown in Fig. 3(a). Figure 3(b) shows a partial PDF extracted from the diffuse scattering of BNT observed at 200 °C. The PDF of the total scattering is also plotted in Fig. 3(b). The PDF obtained from the diffuse scattering also contains data in the high Q region, so it shows sharp PDF peaks that mean sufficient real-space resolution. In the rhombohedral phase at room temperature, the Ti sites fluctuate significantly, indicating that the deviation between average and local structures comes from the misalignment of the TiO₆ octahedral unit brought by the chemical inhomogeneity of Bi/Na. ²³⁾ At 200 °C, the PDF derived from the diffuse component also contains bismuth information because most of the experimental PDF obtained from the total scattering coincides with that obtained from the diffuse component. Beyond 6 Å, the peak positions of the PDFs are different between the diffuse component and the total scattering, indicating that the local structure consists of the network structure with a correlation length of 10 Å and lattice framework. The fluctuations observed during depolarization are caused by the competition between these two types of structures. The short-range order structures are averaged with distance r, so the structure changes with distance. The PDF extracted from diffuse scattering decays and disappeared at approximately 10 Å. Beyond 10 Å, the short-range order structure is negligible for the average structure. A nonperiodic glass-like network structure derived from diffuse scattering modulates the ferroelectric domain, facilitating structural averaging. A local-structure analysis using diffuse scattering for the cubic phase observed at 600 °C was also performed in the same manner. The results are shown in Figs. 4(a) and 4(b). The PDF composed of diffuse scattering observed at 600 °C has even shorter correlation lengths than that observed at 200 °C, terminating at 6 Å. At room temperature, diffuse scattering was mainly caused by the disorder of titanium. ²³⁾ At 200 °C and 600 °C, the short-range order structure within the unit-cell size (r ≤ 4 Å) almost coincides with the PDFs of the diffuse component and the total scattering. Bismuth is also considered to be disordered from the average structural position.

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Figure 5(a) shows the observed PDF for BNT observed at 200 °C in the range of 1 ≤ r ≤ 200 Å. First, in order to extract the deviation from the average structure, PDF fitting was performed using the tetragonal structure model obtained by Rietveld analysis. To characterize the length scale dependence of the crystal structure in BNT, a sequential PDF refinement of increasing r-ranges (box-car method) was performed. ³⁹⁾ Figures 5(b) and 5(c) are an enlarged view of Fig. 5(a) in the range of 1.5 ≤ r ≤ 20 Å, and 1.5 ≤ r ≤ 8 Å, respectively. The structure model for the PDF fit was a tetragonal structure, which was refined using the Rietveld refinement. The observed PDF is mostly reproduced by the average structural model. in the range of r ≥ 10 Å, as shown in Fig. 5(b). In the region of r ≥ 10 Å, the average structure and the local structure are almost the same. In the region of r ≤ 10 Å, there is a large discrepancy between the experimental and the calculated PDFs, the cause of the discrepancy in this r-range was the characteristic diffuse component. In the X-ray diffraction pattern, total scattering consists of Bragg reflection and diffuse scattering. Therefore, in the real space, the PDF composed of total scattering is the sum of the partial PDF reflecting the periodic structure composed of Bragg reflection and that reflecting the local structure composed of diffuse scattering. That is, the residuals of the calculated PDF obtained using the average structure model from the total PDF should match the partial PDF composed of the diffuse scattering. As shown in Fig. 5(c), the residuals between the calculated PDF using the tetragonal model and the experimental PDF are coincide with the PDF obtained from the diffuse scattering. Similar local-structural analysis was performed in the cubic phase at 600 °C, as shown in Figs. 6(a)–6(c). In the cubic phase, the deviation between the calculated PDF obtained by the average structure model and the experimental PDF is very large, especially in the range of 1.5 ≤ r ≤ 6 Å. The difference PDF is exactly the same as the PDF obtained from diffuse scattering, as shown in Fig. 6(c). Even though there is three orders intensity difference between Bragg reflection and diffuse scattering, the agreement of the difference PDF and the partial PDF of the diffuse scattering shows the high reliability of our experimental data.

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Because we have confirmed the high reliability of our data, we need a local-structure model that reproduces the experimental PDF. We modified the initial structure model based on the rhombohedral structure, which is the average structure of BNT at room temperature. ²³⁾ The bond length of Ti–O is clearly split into two and the peak splitting is also retained in the high-temperature tetragonal and cubic phases, as shown in Fig. 7(a). The doublet peak of the Ti–O bond length is characteristic of the rhombohedral structure. Thus, the atomic coordinates of the TiO₆ octahedral unit were refined in the rhombohedral symmetry. The atomic positions of Bi atoms were modified by changing the bond distribution between Bi and O. The decrease in the peak amplitude at approximately at 4 Å corresponding to the primitive unit cell, which is a feature of the phase transition triggered by the displacement of the A-site atom. ²⁴⁾ The model structure around Bi atoms breaks the rhombohedral symmetry. The result of PDF refinement for BNT observed at 200 °C is shown in Fig. 7(b). The PDF peak near 2 Å related to Ti and O is reproduced by the model structure based on the rhombohedral structure. The observed PDF peaks above 3 Å are reproduced quite well. At 200 °C, a slight Bi site disorder occurs while maintaining the rhombohedral structure. The tetragonal structure of the average structure is a disordered structure caused by the misalignment of the rhombohedral unit and the slight displacement of the Bi site from the rhombohedral position. We also attempted to reproduce the experimental PDF observed at 600° in the same manner. Reasonable results were obtained, as shown in Fig. 7(c). As a result of fitting at 600 °C, a large shift from the rhombohedral positions of the Bi site was found to have deviated from the unit cell, and Bi formed a new correlation around 3.7 Å. This is very similar to the appearance mechanism of the cubic phase in the relaxor. ⁴⁰⁾ A huge diffuse component was observed at 600 °C, which was due to the large displacement of the Bi site in addition to the averaging out of the rhombohedral structure. The characteristic diffuse scattering lying approximately at Q ≈ 8–12 Å⁻¹ in Fig. 2(c) is associated with the displacement of Bi. At room temperature, the atomic coordinates of Bi and Na did not shift but remained in the average structural positions of the rhombohedral (Bi,Na)O₁₂ cage. The position of the Bi atoms shifted with temperature increase, as shown in Fig. 8(a). At room temperature, both the average and the local structures are rhombohedral structures, and the Bi atom is in the position assigned by the average structure. This position was set to zero, and the deviation from the position where the rhombohedral symmetry was maintained was plotted from 200 °C. The displacement of Bi atoms from the rhombohedral lattice framework reduced the PDF peak of 4 Å. This decrease is due to the irregularity of rhombohedral symmetry caused by the shift of Bi atoms, and the loss of atomic correlation of unit cells. In Fig. 7(a), it is considered that the peak at 3.7 Å that appears at 400 °C and 600 °C, which is the cubic phase, deviates from the unit cell and a new Bi–O–Bi correlation is established. To reproduce the experimentally obtained PDF, a rhombohedral structural model was required at all temperatures from room temperature to 600 °C in the region below 5 Å. The schematic diagram of the refined local structure around Bi atoms is shown in Fig. 8(b).

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From room temperature to 600 °C, three phases appear: rhombohedral, tetragonal, and cubic. The PDF amplitude changes with the phase transition. The change in PDF amplitude is the change in atomic correlation. The PDF amplitude shows characteristic changes in each phase. We can obtain PDFs up to 200 Å. The peak amplitude of the observed PDFs increases or decreases as temperature increased. This behavior also depends on the r range. Figure 9(a) shows the observed PDFs up to 200 Å divided into three blocks. Envelopes of the main PDF peak every 10–20 Å were plotted in Fig. 9(b) to capture the relative changes of PDF amplitude in each phase. In the region up to 60 Å, the PDF amplitude obtained at room temperature is the largest and decreases with temperature. In addition, the shape of the PDF also changes with temperature, causing a relatively large change in the local structure, as shown in Fig. 7(a). In the region of 60–100 Å, the PDF amplitude is approximately the same level at all temperatures. Furthermore, in the region after 100 Å shown in Fig. 9(b), the amplitude of the PDF obtained at 30 °C was the smallest, which was the opposite of the tendency in the range of r ≤ 60 Å. At room temperature, there is a ferroelectric domain with the rhombohedral structure, and the local polarizations are aligned within the domain. The PDF amplitude reflects a strong atomic correlation due to the high coherence within the ferroelectric domain. The decrease in the PDF amplitude in the large r-region observed at 30 °C is due to the dielectric domain disrupting the long-range order correlation. Because the Bi atom shifts as the temperature rises, the rhombohedral structure is disordered, and the tetragonal structure appears due to averaging by coupling with static disorder and temperature factors. The appearance of the tetragonal structure increases the PDF amplitude in the range r ≥ 100 Å, indicating that the rhombohedral domain configuration has changed. Long-range correlation is terminated by ferroelectric clusters in the rhombohedral phase. In the tetragonal and cubic phases, the local disorder facilitates structural averaging. As a result, long-range order atomic correlations can be established in the tetragonal and cubic phases, as disordered phases.

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The T_d peculiar to BNT is caused by the various local structures depending on the distance, r. The T_d is lower than the rhombohedral-tetragonal phase transition temperature (200 °C). The T_d is caused by local structural changes before long-range order is established. The T_d of BNT can be increased by quenching, ^13–15) that is, the rhombohedral structure stabilizes due to quenching. Regarding the phase transition from the rhombohedral to the tetragonal phase, we found three structural changes. First is the change in the global average structure, the second is the change in the local structure owing to the shift of the Bi atom, and the third is the increase in PDF amplitude around 170–200 Å due to the change in the domain configuration. Shifts of the Bi atoms are sensitive to local structures, but a large amount of shift is required for changes in local structures to propagate to changes in the domain and average structures. The nanoscale structural change that causes T_d is the replacement of the disordered sites from Ti to Bi. Consequently, the deviation between the average and local structures exists at all temperatures. While the average structure is a change in long-range-order correlation, there is a discrepancy in temperature between the change in the polarization mechanism caused by the disorder of bismuth in short-range order and the change of the global average structure in the long-range order. The transient phenomenon in which the change in the local structure caused by the shift of Bi propagates to the long-range-order structure is considered to be the depolarization phenomenon.

High-quality BNT polycrystalline ceramics were examined by synchrotron total scattering techniques at high-temperature phases. The positions of A-site cations of Bi/Na were shifted from the rhombohedral atomic positions of the (Bi,Na)O₁₂ cage in the high-temperature phases. The high-temperature tetragonal and cubic phases appeared as disordered rhombohedral phases. Subtracting the components of the average structure obtained by Rietveld analysis from the PDF obtained by total scattering, it exactly matched the partial PDF composed only of diffuse scattering. If the structural change remains in the nanoscale order region without forming a long-range order structure, it causes a relaxer-like diffuse phase transition such as depolarization temperature. This study demonstrates that X-ray PDF analysis can be used to investigate the mechanism of anomalous properties that deviate from the average structure found in dielectric and ferroelectric materials.

The author would like to thank Dr. F. Izumi for his insightful discussions. The research used resources of the SPring-8. The synchrotron radiation experiments were performed at BL22XU and BL04B2 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI Proposal Nos. 2019A1217, 2019A3607, 2019B1194, 2021A3701, and 2021A1134). This project was supported by a Grant-in-Aid for Scientific Research (C) (No. 19K04502) from the Ministry of Education, Culture, Sports, Science and Technology.