High energy density of Sm-doped Na_0.5Bi_0.5TiO₃–Sr_0.7Bi_0.2TiO₃ relaxor ferroelectric ceramics

Zhiqing Li ^a, Bing Xie *^a, Mohsin Ali Marwat ^b, Fei Xue *^c, Zhiyong Liu ^a, Kun Guo ^a, Pu Mao ^a, Huajie Luo *^d and Haibo Zhang ^e
aSchool of Materials Science and Engineering, Nanchang Hangkong University, Nanchang 330063, China. E-mail: xieb@nchu.edu.cn
^bDepartment of Materials Science and Engineering, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi 23640, Khyber Pakhtunkhwa, Pakistan
^cSchool of Information Engineering, Jiangxi University of Technology, Nanchang 330098, China. E-mail: xuefei_work@126.com
^dSchool of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China. E-mail: hjluo@ustb.edu.cn
^eSchool of Materials Science and Engineering, State Key Laboratory of Material Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China

First published on 20th July 2024

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1. Introduction

Dielectric capacitors have great research significance in pulsed power systems, electric vehicles’ electronic devices, and integrated circuits owing to their large power-density and ultrafast charge/discharge speeds.^1–5 However, the relatively low recoverable energy density (W_rec) compared to conventional electrochemical energy storage systems hinders their practical application.^3,6–8 Developing dielectric ceramics that exhibit exceptional energy storage capabilities is imperative. The W_rec of dielectric ceramics is determined by the breakdown strength (E_b) and the strength of polarization using the following equation:^6,9

	(1)

	(2)

	(3)

where W_tot, η, P_r, P_max, and E indicate the total energy density, efficiency, remnant polarization, maximum polarization, and the applied electric field, respectively. High W_rec requires ceramics to have a high E_b and large polarization difference (ΔP = P_max – P_r), and high efficiency requires low P_r and a high degree of relaxor.

In the preceding years, various methods have been developed to improve the energy storage performance of dielectric materials, such as stable antiferroelectric phase,^10,11 domain engineering,^12–14 superparaelectric state regulation,² defect engineering,^15,16 local structure regulation,^6,17,18etc. For instance, by stabilizing the antiferroelectric (AFE) orthorhombic P phase of NaNbO₃ (NN)-based ceramics, enhanced antiferroelectric properties were achieved, resulting in a higher W_rec of 4.4 J cm⁻³.¹⁰ A relatively high W_rec of 3.6 J cm⁻³ was obtained on Na_0.5Bi_0.5TiO₃ (NBT)-based ceramics by constructing ion pairs to induce the formation of polar nanoregions (PNRs).¹² In NBT-based ceramics, high W_rec can also be achieved through defect engineering designs, such as (Bi_0.47Sm_0.03Na_0.42)_0.94Ba_0.06TiO₃ and NBT–(Bi_0.2Sr_0.7)TiO₃–0.07BaTiO₃ ceramics. Nevertheless, their W_rec values were still relatively low (below 5 J cm⁻³).^15,16 Therefore, it is still necessary to improve the W_rec of dielectric ceramics.

NBT-based ceramics offer significant advantages in the realm of energy storage ceramics due to their high polarization. However, the high P_r of NBT-based ceramics results in substantial energy loss. Therefore, it is often necessary to disrupt the long-range ferroelectric order of NBT-based ceramics through chemical doping. For instance, introducing Sr_0.7Bi_0.2TiO₃ (SBT) into NBT effectively disrupts the long-range ferroelectric order and induces PNRs. This incorporation also enhances the relaxor characteristics of the material, resulting in NBT–SBT ceramics exhibiting high energy storage performance.¹³ It should be noted that SBT also inevitably creates vacancies, so the E_b is not high enough (Fig. 1). Reducing vacancies has thus become crucial for enhancing the E_b and energy density, making the doping of simple oxides a sensible choice. Here we choose Sm₂O₃ mainly to consider the following points: (I) the introduction of Sm₂O₃ decreases vacancy and reduces the grain size, resulting in an increase in E_b; (II) the entry of Sm³⁺ into the perovskite lattice leads to a further increase in the disorder of the A-site,^2,19 which is conducive to the improvement of relaxor characteristics and thus energy storage efficiency.

In this work, Sm₂O₃ is incorporated into the classical NBT–SBT relaxor ferroelectric ceramics (RFCs) for chemical modification. The experimental findings demonstrate that Sm³⁺ is integrated into the perovskite lattice, further enhancing the relaxor behavior. This modification results in improved energy storage performance, leading to the achievement of a high W_rec of 6.1 J cm⁻³ with a η of 78.1% at x = 0.055. The decrease in grain size and vacancies contributes significantly to the increase in breakdown strength, a key factor in achieving high energy density. Additionally, a novel method has been introduced to assess the relaxor properties of RFCs through quantifying the linear fitting of P–E loops. This study introduces an effective approach to develop high-energy-density dielectric ceramics and presents an innovative technique for analyzing the relaxor properties of RFCs.

2. Experimental process

(1 − x)(0.6Na_0.5Bi_0.5TiO₃–0.4Sr_0.7Bi_0.2TiO₃)–xSm₂O₃ [(1 − x)(NBT–SBT)–xSm] (x = 0.025, 0.04, 0.055, 0.07) ceramics were prepared by a solid phase method. Raw materials of Na₂CO₃ (≥99.8%), Bi₂O₃ (≥99%), SrCO₃ (≥99%), TiO₂ (≥98%), and Sm₂O₃ (≥99.9%) (all from Sinopharm Chemical Reagent Co., Ltd, China) were weighed according to the stoichiometric ratio. The powder mixture underwent two rounds of ball milling at 300 rpm for 24 h, with calcination at 850 °C for 6 h in between. The power slush was dried and granulated with 3 wt% polyvinyl alcohol (PVA) as a binder. These powders were pressed into pellets under a pressure of 200 MPa, followed by sintering at 1170–1350 °C for 2 h.

To ascertain the phase composition, XRD (D8 ADVANCE-A25, Bruker, Germany) was used at room temperature. To study the microstructure and element distribution of the ceramics, FE-SEM (Germany's Zeiss Gemini SEM 300) and EDS (Oxford Instruments X-MaxN SN 78861) were used, respectively. Before the test, ceramics were polished and thermally corroded for 0.5 h at 1070–1250 °C. The grain sizes of the ceramics were measured using ImageJ software. The dielectric constant and loss of the samples were determined using dielectric testing equipment (DPTS-AT-600, China) from 25 to 400 °C and 1 to 500 kHz. The breakdown strength of the ceramics was tested using a dielectric breakdown test system (PolyK Technologies, USA) increasing the voltage by 500 V per second. The ceramic lamellas, which were 60–80 μm thick, had P–E loops recorded on them utilizing a device called a ferroelectric test unit (PolyK Technologies, USA). Finally, the behavior of charge and discharge was evaluated with the use of charge and discharge equipment (PolyK Technologies, USA).

3. Results and discussion

The room temperature XRD patterns of the (1 − x)(NBT–SBT)–xSm bulk ceramics are shown in Fig. 2(a). All of these samples exhibit a pure perovskite structure, consistent with the patterns found in ref. 13. Elemental mapping images show that all the elements have a homogeneous distribution over the ceramic, which indicates that Sm₂O₃ diffuses successfully into the NBT–SBT matrix.

Fig. 3(a)–(d) show the SEM micrographs of the as-sintered (1 − x)(NBT–SBT)–xSm (x = 0.025, x = 0.040, x = 0.055 and x = 0.070) ceramics, presenting a relatively compact microstructure with obvious grain boundaries in between the grains. The average grain sizes (G_aver) of these ceramics were determined over 150 to 260 grains using a linear intercept method and showed values of 1.90 μm, 1.50 μm, 1.11 μm, and 2.04 μm, respectively. It is worth noting that the addition of Sm₂O₃ results in a further reduction in grain size. When the Sm₂O₃ is excessive, the grain grows abnormally. According to the equation: (where G is the average grain size),^10,20 a small grain size is favored for increasing E_b as the increased grain boundaries can prevent charge carriers from passing through.²¹ This has been proven to be one of the methods of improving energy storage performance.

An important factor in attaining high W_rec is the maximum electric field that a dielectric material can withstand. By using the following equations, one may determine the breakdown strength (E_b) of the (1 − x)(NBT–SBT)–xSm bulk ceramics by a Weibull distribution analysis:²

Xi = ln(Ei)	(4)

Yi = ln(ln(1/(1 − i/(n + 1))))	(5)

In the above equations, E_i represents the breakdown strength of the corresponding specimen, and i and n are, respectively, the sequence number and total number of specimens. Fig. 4(a) shows that the Weibull modulus β values (an index of the dispersion of data distribution) of the (1 − x)(NBT–SBT)–xSm ceramics are >6, underscoring the reliability of the Weibull distribution. Based on Fig. 4(b), the ceramic with x = 0.055 achieves a maximum E_b of 470 kV cm⁻¹. The β value for this sample reaches 13.29, indicating the ceramic possesses a relatively dense microstructure with few defects and the potential to withstand high voltage. Investigation into the breakdown mechanism of (1 − x)(NBT–SBT)–xSm bulk ceramics and the relationship between grain size and electric field distribution was systematically conducted. The G_aver decreases first and then increases with increasing x (Fig. 4(c)). Meanwhile, doping with Sm₂O₃ effectively impedes charge emission, reducing leakage current, which promotes the improvement of E_b.² The introduction of Sm₂O₃ into the NBT–SBT matrix results in the substitution of some A-site ions and a reduction in oxygen vacancies,² for example:

	(6)

	(7)

The reduction of oxygen vacancies effectively decreases the defect content and enhances the improvement of the E_b. The x = 0.055 ceramic reaches the highest E_b in comparison with the other compositions. With the further increase of Sm₂O₃ (x > 0.055), the E_b decreases gradually.

To further confirm the effect of grain size on the E_b of the ceramic, the finite element method was used to simulate the local electric field and leakage current. This simulation focuses on the effect of microstructure on electric field distribution, and the microstructural models required for simulation were obtained from SEM maps (Fig. 5(a)–(c)). An external electric field of 100 kV cm⁻¹ was applied along the direction indicated by the arrow as shown in Fig. 5(a). Fig. 5(d)–(f) show a simulation of the dielectric constant, where the blue curves indicate the grain boundaries, and the grains in red, cyan, and yellow represent the dielectric constants for x = 0.025, 0.055, and 0.070, respectively. It can be observed that the dielectric constant of the material decreases significantly with the increase of Sm₂O₃, which provides the basis for high electric field. The grain dielectric constant in polycrystalline ceramics is 10 times higher than the dielectric constant of the grain boundary, resulting in higher external electric fields at the grain boundaries.²² As can be seen from Fig. 5(g)–(i), with the increase in the number of grain boundaries, the local electric field is more evenly distributed among the ceramics, which effectively improves the electrical breakdown performance of the ceramics. Fig. 5(j)–(l) show the simulation results of local leakage current, and the decreased grain size makes the current density distribution more uniform and less likely to go through the early breakdown caused by the high current density.^23,24 The simulation results of the local electric field and the leakage current are consistent with the conclusions drawn from the Weibull distribution, thus confirming the reliability of the experimental results.

The temperature-dependent constant (ε_r) and loss tangent (tanδ) of the (1 − x)(NBT–SBT)–xSm bulk ceramics are shown in Fig. 6(a)–(d). T_s and T_m anomaly peaks, respectively, appear in lower and higher temperature ranges, and the former shows an obvious frequency dispersion which is characteristic of relaxor ferroelectrics.¹³ A combination of rhombohedral (R3c) and tetragonal (P4bm) PNRs undergoes relaxor thermal development, giving rise to T_s. The structural transition of the PNRs from R3c to P4bm and the thermal development of the P4bm phase PNRs are the sources of the other dielectric anomaly peak, T_m,^14,15 which is a typical process of the dielectric response of NBT-based RFCs.¹³ As shown in Fig. 6(e), with increasing Sm₂O₃ content, the two dielectric peaks move towards room temperature (RT). Meanwhile, the ε_r decreases throughout the entire temperature range with this compositional change. The widened temperature range of the ergodic phase is generally believed to be the reason for the lowering of ε_r produced by the doping concentration.¹⁵ The reason both ε_r and tanδ decrease as the frequency increases is that the space charge at the grain boundary contact is inefficient.

A more thorough comprehension of the dielectric characteristics was achieved by using the revised Curie–Weiss law. For this purpose, dielectric spectra of (1 − x)(NBT–SBT)–xSm ceramics were recorded at 1 kHz and used to calculate the dispersion coefficient (γ): , where ε_r, ε_m, T_m, and C represent the dielectric constant, maximum dielectric constant, corresponding temperature of ε_m, and Curie constant, respectively. The γ values of the x = 0.025, 0.040, and 0.055 ceramics are, respectively, 1.73, 1.80, and 1.94, which are in the range of 1 (normal ferroelectrics) to 2 (ideal relaxor).^{7,12,14,21,25} Together with the broadened dielectric peaks, this signifies that relaxor behavior was improved in these ceramics by Sm₂O₃.

To study the influence of Sm₂O₃ content on the ferroelectric properties of (1 − x)(NBT–SBT)–xSm ceramics, as shown in Fig. 7(a)–(d), unipolar P–E loops were recorded from 100 kV cm⁻¹ to E_b. The results indicate that increasing the Sm₂O₃ content helps to greatly enhance the relaxor properties and delay the polarization saturation. When x > 0.025, the relaxor properties were further improved, resulting in slim P–E loops and enhanced E_b, implying that the energy storage performance of ceramics is enhanced with the increase of x. The optimal polarization saturation delay was observed at x = 0.055. When combined with the dielectric temperature spectra, it is evident that the T_m peak sharply transitions to lower temperature as x increases from 0.025 to 0.07, gradually decreasing to below room temperature, as depicted in Fig. 6(e). The phenomenon is analogous to what happens in superparaelectric systems.² Moreover, the straightness of all P–E loops was confirmed by the functional curvature, enabling an analysis of how the curve changes with increasing Sm₂O₃ content. As shown in Fig. 8(a), nonlinear fitting was performed on the discharging paths of the P–E loops. The curvature of the fitted data is calculated using the formula:

	(8)

where K represents the curvature of the fitted curve at each point, the obtained data points were carefully selected, and the maximum values for each component are compared in Fig. 8(b). The curvature exhibits a significant decrease with x increasing from 0.025 to 0.07. At this point, the corresponding P–E loop exhibits a similar superparaelectric phase character, which contributes to the delay in polarization saturation and the increase in E_b.² As the Sm₂O₃ content increases further, the curves become more and more straight, indicating the quasi-linear characteristics.

The introduction of Sm³⁺ with a smaller ionic radius into the NBT–SBT matrix promotes the development of local chemical, structural, and electrical heterogeneity. This process leads to the disruption of long-range ferroelectric order and the formation of PNRs.^2,14 With increasing Sm₂O₃ concentration, the P–E loops become narrower, and P_max and P_r gradually decrease (as shown in Fig. 7(f)). These phenomena are attributed to the improvement of the relaxor behavior, which is a result of the continuous refinement of the domains.²⁶ The increase in the applied electric field results in a further enhancement of P_max, attributed to the induction of long-range ferroelectric orders by the electric field. During the unloading of the electric field, the long-range ferroelectric orders break down rapidly into PNRs. This reversible process leads to a slow increase in P_r and consequently an increase in ΔP. Moreover, Fig. 9(a) displays a comparison of W_rec under different electric fields for the (1 − x)(NBT–SBT)–xSm ceramics. The x = 0.055 ceramic reaches its optimal breakdown strength at 470 kV cm⁻¹, along with a high ΔP, resulting in W_rec reaching a maximum value of 6.1 J cm⁻³. The 0.945(NBT–SBT)–0.055Sm lead-free ceramics for energy storage outperform other materials based on NBT in terms of breakdown strength and polarization.^{13–15,27–29} The advantage of adding the Sm₂O₃ dopant is that it results in strong local chemical, structural, and electrical inhomogeneities,² disrupting the stable ferroelectric ordering and decreasing the P_r. The addition of Sm ions also improves the relaxor properties of the ceramics, delaying the polarization saturation of the ceramic, causing the η to steadily rise from 68.4% at x = 0.025 to 78.1% at x = 0.055. The improvement of η effectively reduces energy loss and facilitates energy recovery. Fig. 9(c) contrasts W_rec and E_b for various lead-free ceramics.^{10–12,14,15,21,22,25–34} When compared to other lead-free energy storage ceramics, the 0.945(NBT–SBT)–0.055Sm RFE ceramic exhibits certain advantages in energy density (>5 J cm⁻³) and breakdown strength (>450 kV cm⁻¹).

The energy storage properties discussed above were obtained at room temperature, while in the actual applications, having good frequency and temperature stabilities for W_rec and η is quite important.^35–37 The unipolar P–E loops were recorded at different frequencies and temperatures for the 0.945(NBT–SBT)–0.055Sm ceramic (Fig. 10(a) and (b)). Their W_tot, W_rec, and η results are shown in Fig. 10(c) and (d). Over a broad frequency range of 10–1000 Hz (Fig. 10(c)), the W_rec ∼ 1.6–1.8 J cm⁻³ and η ∼ 81–85% imply excellent frequency stability at 200 kV cm⁻¹ and RT. At high electric field and high measurement frequency, the P_r of the ceramic appears to be slightly enhanced. This enhancement is primarily attributed to the rapid reorientation of domain walls, resulting in increased viscous force and consequently higher energy loss.³⁸ Similarly, within an operating temperature range of 25–180 °C, the ceramic exhibited W_rec ∼ 1.3–1.6 J cm⁻³ and η ∼ 74–81% (Fig. 10(d)), implying good stability of this ceramic. The slight decline of η at high temperatures is likely linked to the thermally stimulated conduction loss.^2,39 The aforementioned investigation demonstrates that the 0.945(NBT–SBT)–0.055Sm ceramic has commendable temperature and frequency stability.

The possible practical applicability of the x = 0.055 ceramic was evaluated using charge–discharge testing. The discharge energy density (W_dis) curves at room temperature for x = 0.055 under different electric fields are shown in Fig. 11(a). The W_dis quickly achieves its maximum value in less than 10 μs and can be determined using the current–time waveforms and the following equation:^20,40

	(9)

where R, t, I, and V are the load resistor, time, current, and sample volume, respectively. When the electric field increases from 50 kV cm⁻¹ to 275 kV cm⁻¹, the W_dis rises from 0.15 J cm⁻³ to 1.95 J cm⁻³. It is worth noting that the W_dis calculated through the charge–discharge method typically appears lower compared to the W_dis derived from the integrated area of P–E loops at an equivalent electric field. This discrepancy arises from the distinct mechanisms of the dynamic discharge current at varying frequencies and the quasi-static nature of P–E loops.^18,38 Furthermore, the parameter t_0.9 represents the discharge time needed to discharge 90% of the stored energy density, as indicated by the red line in Fig. 11(a). The power density (P_D) reaches its maximum value of 224 mW L⁻¹ under 275 kV cm⁻¹, as shown in Fig. 11(b). The high P_D and ultrashort t_0.9 demonstrate the great potential application of the 0.945(NBT–SBT)–0.055Sm bulk ceramic in advanced high power/pulsed systems.

4. Conclusions

In summary, a high W_rec of 6.1 J cm⁻³ and E_b value of 470 kV cm⁻¹ were obtained in 0.945(NBT–SBT)–0.055Sm RFCs. The experimental results demonstrate that the introduction of Sm₂O₃ is beneficial to reduce the grain size and vacancies of ceramics, thereby increasing the E_b. Furthermore, the incorporation of Sm³⁺ into the perovskite lattice induces disorder at the A-site, thereby enhancing the relaxor properties of the ceramic and reducing the value of P_r. The substantial improvement in W_rec is attributed to the significantly increased E_b and the large ΔP. Moreover, the ceramics exhibit excellent frequency/temperature stability. Moreover, a novel method has been proposed to evaluate the relaxor properties of relaxor ferroelectric ceramics (RFCs) by quantifying the linear fitting of P–E loops. In this work, an effective strategy for designing high-energy-density dielectric ceramics is proposed and an innovative method for analyzing the relaxor properties of ceramics is presented.

Data availability

The data are available from the corresponding author on reasonable request.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52162018 and 52162017), the Science Fund for Distinguished Young Scholars of Jiangxi Province (Grant No. 20224ACB214007), the Aeronautical Science Foundation of China (Grant No. 2020Z056056001) and the Key-Area Research and Development Program of Guangdong Province (Grant No. 2023B0101200001).

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