Figure 1 presents the SEM photographs of the surface morphology of the ceramic samples. All BNT-A and BNT-AN samples show a single phase of rod-like grains. As shown in Fig. 1(a)-(c), BNT-A ceramics with different z values could be well-sintered at 1400 ℃, indicating that the sintering temperature of the BNT-A ceramics is stable at around 1400 ℃, and basically does not change with the doping amount. In comparison, BNT-AN ceramics with z = 2 are well-sintered at 1550 ℃ as shown in Fig. 1(f), illustrating that the sintering temperature of the BNT-AN ceramics increases with increasing doping amounts. Figure 1(d)(e) show that the grain size of the ceramics with the same composition becomes larger as the sintering temperature gets higher.
The XRD patterns of the ceramic samples are shown in Fig. 2. All samples can be confirmed as a single phase with a tungsten-bronze structure (Ba3.99Sm9.34Ti18O54, PDF#89-4356). The detailed XRD data with a 2θ range of 31°~35° are presented in Fig. 2(b), which shows that the peaks shift towards higher degrees as z value increases, indicating that the cell volume decreases. This demonstrates that Al3+ with a smaller ionic radius (0.54 Å, CN = 6) successfully enters into the lattice and substitutes for Ti4+ with a larger ionic radius (0.61 Å, CN = 6). Rietveld refinement was performed to further explore the changes of phase composition and lattice parameters with doping amount. Figure 3(a)-(c) shows the refined results of the BNT, BNT-A (z = 1.25) and BNT-AN (z = 1.25) ceramics as examples, respectively. The fitting results are in good agreement with experimental XRD patterns. Figure 3(d) shows that there are a few peaks that cannot be fitted in the experimental data of the BNT-A ceramics, together with χ2 rises as z value increases, indicating that a small amount of unknown secondary phase appears. In contrast, Fig. 3(e) shows that there is no secondary phase peak in the experimental data of the BNT-AN ceramics. The above-mentioned unknown secondary phase may have an impact on the microwave dielectric properties of the BNT-A ceramics.
The lattice parameters and cell volumes calculated by Rietveld refinement are shown in Fig. 4. The lattice parameters and cell volumes of the BNT-A and BNT-AN ceramics both decrease with the increase in z value, and basically shows the same linear decrease trend as z ≤ 1.25. This indicates that the type of trivalent cations (Al3+ or Nd3+) filling the vacancies at the A1 sites may have less influence on the lattice parameters in the doping process of the BNT ceramics. When z ≥ 1.25, the lattice parameters and cell volumes of the BNT-AN ceramics continuously show a linear decreasing trend, while the decreasing trend of those of the BNT-A ceramics deviates from linearity. Combining with Fig. 3(d)(e), it can be demonstrated that such a deviation is caused by the secondary phase in the BNT-A ceramics. Therefore, the BNT-A ceramics cannot form a complete solid solution phase when more Al3+ ions are added, while the BNT-AN ceramics can form a continuous solid solution in the range of 0 ≤ z ≤ 2. The detailed results of the structural parameters and reliability factors obtained by Rietveld refinement are shown in Table S1 and Table S2.
Figure 5 presents the relative densities and microwave dielectric properties of the BNT-A and BNT-AN ceramics. According to Fig. 5(a), the relative densities of almost all ceramic samples have reached higher than 97%, indicating the ceramics are all well densified. When z ≥ 1, the relative densities of the BNT-AN ceramics is lower than those of BNT-A ceramics with the same doping amount. In addition, the sintering temperature of the BNT-AN ceramics is higher with large z values as illustrated in SEM results. Therefore, the BNT-AN ceramics are more difficult to be well-sintered than the BNT-A ceramics. Figure 5(b)(d) show that the εr and τf values of the ceramics decrease in a similar trend with the increase in z value, which is consistent with the reports of low-valence cations doping at the B sites in BLT system [28–36]. According to Shannon’s rule [41], εr is related to the ionic polarizability (αD) and the molecular volume (Vm):
\(\begin{array}{c}{\alpha }_{\text{D}}=\frac{{V}_{\text{m}}\left({\epsilon }_{\text{r}\text{c}}-1\right)}{\text{b}\left({\epsilon }_{\text{r}\text{c}}+2\right)}\#\left(1\right)\end{array}\)
where εrc is the corrected dielectric constant and b is a constant equal to 4π/3. According to Eq. (1), εrc increases when αD increases or Vm decreases. Although the cell volume of the ceramics decreases slightly when z value increases as shown in Fig. 4, the decrease in αD [α(Al3+)<α(Ti4+)] may mainly dominate the decrease in εr. Reaney et al. [6] reported that τf is usually determined by εr, and the change trends of εr and τf are often similar in the same ceramic system. When z ≥ 1.25, the decrease in εr of the BNT-A ceramics slows down, and may be related to the small amount of secondary phase, consistent with the previous results of Al-doping in BLT system [35]. Figure 5(c) shows that when z ≤ 1.5, the Q×f values of the ceramics significantly increase as z value increases, which may be related to the decline in the activity of \({V}_{\text{O}}^{\bullet \bullet }\) illustrated by TSDC technique in our past research [35]. As z ≥ 1.5, the continuous doping makes the Q×f values of the ceramics decrease slightly. The decrease in the Q×f values of the BNT-A ceramics may be affected by the secondary phase, and that of BNT-AN ceramics may be related to the decline of densification. BNT-AN ceramics with z = 1.25 have reached excellent microwave dielectric properties: εr = 72.2, Q×f = 16480 GHz, and τf = + 14.3 ppm/℃.
It is noticed from Fig. 5(b)(c) that when z ≤ 1.5, the εr and Q×f values of the BNT-AN ceramics are both higher than those of the BNT-A ceramics with the same doping amount, indicating that Al/Nd co-doping may be a superior strategy for substitution in the BNT ceramics. The comparison of the εr and Q×f values of these ceramics is visually presented in Fig. 6. This important difference in microwave dielectric properties may be related to factors such as the composition, structure and defects of the ceramics. The trivalent cations filling the vacancies at the A1 sites have different polarizabilities [α(Al3+) < α(Nd3+)], which results in higher εr values of BNT-AN ceramics according to Shannon’s rule [41]. As for the Q×f values, the determinants may become more complicated: in addition to the secondary phase and porosity that have been discussed, the defects and stability of crystal lattice may also play an important role [6, 42]. Bond length, bond valence and bond energy are important factors that reflect the stability of crystal lattice, and have been used to explore the relationship between the structure and properties of microwave dielectric properties [43–45]. However, according to the results of Rietveld refinement, the variation of the average bond length of the ceramics related to z value is less than 0.01 Å, which is roughly equivalent to the uncertainty of Rietveld refinement method (~ 0.006 Å). The average bond length of A1-O is shown in Fig. S1 as an example. These data could hardly be used for further analysis. Therefore, Raman spectroscopy and TSDC technique are performed to further explore the relationship among the crystal structure, defects and Q×f values of the ceramics.
Raman spectroscopy can reflect the lattice vibration information of materials. The polarization mechanism of dielectrics in the microwave frequency band is mainly ion displacement polarization [46], which is closely related to the vibration of ions in the crystal lattice. Therefore, Raman spectroscopy is a powerful tool for studying the relationship between the structure and properties of microwave dielectric ceramics [20, 32, 47–53]. The space group of the BLT superlattice with tungsten-bronze structure is Pbnm (No. 62), and there are 24 Raman active vibration modes: 7Ag + 7Bg + 5B2g + 5B3g [54]. The Raman spectra results of the BNT-A and BNT-AN ceramics are presented in Fig. 7. A total of 17 Raman vibration modes were observed in the experimental data. As the Raman spectra of the BLT system are excessively complex, previous studies had different opinions on the identification of Raman modes. Nevertheless, most studies considered that the Raman vibration modes in the region of 100 ~ 200 cm− 1 correspond to A-site cations translation. The vibration modes in the regions of 200 ~ 400 cm− 1 and 400 ~ 600 cm− 1 were attributed to the rotation and the internal vibration of the TiO6 octahedra, respectively. The mode at 757 cm− 1 might correspond to the second order scatter [20, 32, 51–53]. Limited by the test conditions, vibration modes between 50 cm− 1 and 100 cm− 1 in BLT system have not been reported yet. Previous studies on perovskite systems such as SmAlO3, NdNiO3, LaGaO3 and BaCeO3, which also have the space group symmetry Pbnm, reported Raman modes in the region of 50 ~ 100 cm− 1 and identified all those modes as A-site cations translation [54–59]. Therefore, in the BNT-A and BNT-AN systems, the vibration modes between 50 cm− 1 and 100 cm− 1 are identified as A-site cations translation as well as the vibration modes between 100 cm− 1 and 200 cm− 1. It is reported that the mode at 234 cm− 1 was considered as the tilting vibration of the TiO6 octahedra when the A sites are occupied by Ba2+ [48, 54]. The doping methods in the present work have not made any changes to the Ba2+ cations occupying the A2 sites, so it can be considered that this mode does not change significantly. In order to compare the intensities of the Raman modes, the relative intensities of the Raman spectra in Fig. 7 were obtained by normalizing the experimental intensities based on the peak values of the Raman mode at 234 cm− 1.
As shown in Fig. 7, with the increase in z value, most of the Raman modes present a blue-shift, which indicates that the cell volume decreases [20, 32, 46, 49, 52, 53, 60], consistent with the XRD results. The relative intensities of the vibration modes in the region of 300 ~ 400 cm− 1 increase slightly as z value increases, implying that the tilting vibration of the TiO6 octahedra becomes stronger, and the decline of τf is related to this phenomenon [48, 51, 53]. The more obvious changes appear in the vibration modes between 50 cm− 1 and 200 cm− 1, which are identified as A-site cations translation. As z value increases, the relative intensities of these Raman modes are significantly reduced, where the variation of relative intensities of the Raman modes at 80 cm− 1 and 94 cm− 1 is shown in Fig. 8 as an example. It represents that the A-site cations translation is weakened, indicating that the binding force towards the A-site cations is strengthened, and accordingly the contribution to the microwave dielectric loss is reduced and the Q×f values increase. Comparing the Raman spectra of BNT-A and BNT-AN ceramics with the same z value, it is found that the relative intensities of the Raman modes at 80 cm− 1 and 94 cm− 1 of the BNT-AN ceramics are lower than those of the BNT-A ceramics, as shown in Fig. 8. It is implied that the strength of the A-site cation vibration in the BNT-AN ceramics is weaker, so the contribution to the microwave dielectric loss is lower and the Q×f values is higher. Briefly, the relationship between the Q×f values and the strength of the A-site cation vibration in the BNT-A and BNT-AN systems has been established through Raman spectroscopy.
TSDC technique can provide valuable information on the types and concentrations of defects in dielectrics, and has been widely used to explore the dielectric response mechanism of ceramics [35, 61–68]. Liu et al. [61] firstly reported the method for determining the types of defects in inorganic dielectrics through the changes in peak position (Tm, the temperature at which the absolute value of current density is maximized) and peak intensity (Jm, the maximum of the absolute value of current density) of the TSDC curves with various polarization conditions (Tp and Ep), and Zhang et al. [66] applied this method to microwave dielectric ceramics for the first time. Figure 9 shows the TSDC curves of the BNT, BNT-A (z = 1.25) and BNT-AN (z = 1.25) ceramics. The curves of all samples show three or four TSDC peaks, indicating that there are at least three or four defect relaxation mechanisms, respectively. In the range of 50 ℃ < Tm < 150 ℃, there is a weak peak (referred to as peaks A1, A2 and A3) in each figure. And peaks similar to each other (referred to as peaks B1, B2 and B3) are displayed in the range of 160 ℃ < Tm < 200 ℃. The TSDC curves of different samples are quite different in the high temperature section above 200 ℃. The curves of undoped sample exhibit a very strong peak (referred to as peak D1), and its Tm values have exceeded the test range. The curves of two doped samples both show peaks with similar changes (referred to as peaks C2 and C3) at around 240 ℃. The TSDC curves of the BNT-A (z = 1.25) ceramics also show a weak peak (referred to as peak D2) with Tm > 280 ℃.
The Tm and Jm of peaks A1 and A3 both increase with an increase in Ep, indicating that these peaks are likely related to the relaxation of \({V}_{\text{O}}^{\bullet \bullet }\). As Ep increases, the Jm of peak A2 increases while the Tm decreases, indicating that peak A2 may be related to the relaxation of trapped charges. Using the initial rise method [66, 69], the activation energies of peaks A1, A2 and A3 are calculated as 0.43 ~ 0.50 eV, 0.14 ~ 0.17 eV and 0.24 ~ 0.36 eV, respectively. Based on previous results [35, 64, 65], the activation energies of peaks A1 and A3 are close to those of the in-grain \({V}_{\text{O}}^{\bullet \bullet }\), and it can be inferred that these peaks are related to the relaxation of the in-grain \({V}_{\text{O}}^{\bullet \bullet }\). The Tm and activation energy of peak A2 are similar to those of peaks A1 and A3, and it is speculated that peak A2 may correspond to trap charges associated with the in-grain \({V}_{\text{O}}^{\bullet \bullet }\). Peaks B1, B2, B3, C2 and C3 have Tm values which basically unchanged with polarization conditions, while their Jm values increase with an increase in Ep, indicating that they may be related to the relaxation of defect dipoles. The calculated activation energies of peaks B1, B2 and B3 are 0.58 ~ 0.80 eV, 0.64 ~ 0.75 eV and 0.59 ~ 0.75 eV, respectively. According to the results from previous studies [35, 63, 70], it can be inferred that peak B is related to the relaxation of the \({\text{T}\text{i}}_{\text{T}\text{i}}^{\text{'}}-{V}_{\text{O}}^{\bullet \bullet }\) defect dipoles. Although the activation energies of peaks C2 and C3 are difficult to calculate by the initial rise method, the type of defects related to peak C could be determined by the defect reactions in the doping process, considering that peak C appears only after doping. During the substitution process of Al3+ for Ti4+ at the B sites, \({\text{A}\text{l}}_{\text{T}\text{i}}^{\text{'}}\) point defects are formed. Meanwhile, excess trivalent cations (Al3+ or Nd3+) were added to fill the vacancies at the A1 sites, forming \({\text{A}\text{l}}_{A1}^{\bullet \bullet \bullet }\) or \({\text{N}\text{d}}_{A1}^{\bullet \bullet \bullet }\) point defects. Thus the condition of charge balance could be ensured, without ion valence changing or \({V}_{\text{O}}^{\bullet \bullet }\) producing. Therefore, peak C2 and C3 are considered as the relaxation peaks of the \({\text{A}\text{l}}_{\text{T}\text{i}}^{\text{'}}-{\text{A}\text{l}}_{A1}^{\bullet \bullet \bullet }\) and \({\text{A}\text{l}}_{\text{T}\text{i}}^{\text{'}}-{\text{N}\text{d}}_{A1}^{\bullet \bullet \bullet }\) defect dipoles, respectively. As for peak D1, the current density rises slower when Ep is higher, indicating that it will reach a peak value at a higher temperature with higher Ep, which signifies that peak D1 may be related to the relaxation of \({V}_{\text{O}}^{\bullet \bullet }\). The calculated activation energy of peak D1 is 0.98 ~ 1.19 eV, similar to that of the across-grain-boundary \({V}_{\text{O}}^{\bullet \bullet }\) (1.1 eV) [35, 62]. It is implied that peak D1 is likely related to the relaxation of the across-grain-boundary \({V}_{\text{O}}^{\bullet \bullet }\). Since the position of peak D2 is similar to peak D1, it is speculated that the relaxation mechanisms of the two are the same, so that it can be considered that peak D2 is also related to the relaxation of the across-grain-boundary \({V}_{\text{O}}^{\bullet \bullet }\).
TSDC peaks with higher Jm imply a higher concentration of the corresponding defects [68, 71]. Comparing the TSDC curves of the three ceramic samples, the BNT ceramics with peak D1 in Fig. 9(a) show an extremely high concentration of the across-grain-boundary \({V}_{\text{O}}^{\bullet \bullet }\), while the BNT-A (z = 1.25) ceramics with peak D2 in Fig. 9(b) show only a small amount of across-grain-boundary \({V}_{\text{O}}^{\bullet \bullet }\), and the BNT-AN (z = 1.25) ceramics show no peaks corresponding to across-grain-boundary \({V}_{\text{O}}^{\bullet \bullet }\) in Fig. 9(c). It is generally believed that oxygen vacancies could cause the extrinsic loss of dielectric ceramics and affect the Q×f values at microwave frequency bands [6]. The TSDC results in the present work are consistent with it. It is noticed that each O2− in the crystal lattice is adjacent to several A-site cations in BLT system. Associating the results of TSDC with the aforementioned Raman spectroscopy of the BNT-A and BNT-AN ceramics, it can be found that with the strengthening of binding force between the A-site cations and O2−, the formation of \({V}_{\text{O}}^{\bullet \bullet }\) becomes difficult, indicating that the results of TSDC and Raman spectroscopy are consistent. It is demonstrated for the first time that in the structural and defect modulation of the BNT ceramics, the formation of \({V}_{\text{O}}^{\bullet \bullet }\) in the crystal lattice is closely related to the strength of the A-site cation vibration, and \({V}_{\text{O}}^{\bullet \bullet }\) affects the lattice vibration then affects the microwave dielectric loss.