**Abstract: **Sr_{0.7}Bi_{0.2}TiO_{3} (SBT) by increasing the proportion and size of polar nano-region. Meanwhile, the BDS remains a high level with x ≤ 0.38 attributed to the addition of KBT with a large band gap. As a result, the 0.62SBT-0.38KBT exhibits a high energy storage density of 2.21 J/cm³ with high h of 91.4% at 220 kV/cm and superior temperature stability (-55 ~ 150 °C), frequency stability (10 ~ 500 Hz) and fatigue resistance (10^{5} cycles). Moreover, high pulsed discharge energy density (1.81 J/cm³), high power density (49.5 MW/cm³) and great thermal stability (20 ~ 160 °C) are achieved in 0.62SBT-0.38KBT. Based on these excellent properties, the 0.62SBT-0.38KBT are suitable for pulsed power systems. This work provides a novel strategy and systematic study for improving energy storage properties of SBT.

**Keywords:** Energy storage; (Sr_{0.7}Bi_{0.2})TiO_{3}; K_{0.5}Bi_{0.5}TiO_{3}; Lead-free; Relaxor ferroelectrics; Maximum polarization

**1. Introduction**

The electronics industry is developing rapidly, and electric energy storage elements are crucial for electrical power systems^{ [1]}. Nowadays, dielectric capacitor, electrochemical capacitor and battery are three major electric energy storage devices. Among these energy storage devices, dielectric capacitor is suitable for pulse power system due to high power density, fast charge-discharge rate and long lifetime^{ [2]}. However, the energy storage density of dielectric capacitors is lower than that of electrochemical capacitors and batteries, which prevents its further development^{[3]}. Therefore, it is necessary to research and develop advanced dielectric capacitors with high energy storage density.

Dielectric materials are the key to determine the energy storage properties of pulse energy storage dielectric capacitors. Bulk ceramics in various dielectric energy storage materials have attracted wide attentions and been deeply researched because they can store more absolute energy than thin films^{ [4]}. Meanwhile, bulk ceramics possess good thermal stability and mechanical strength as compared to polymer^{ [5,6]}. However, polymer exhibits better mechanical flexibility and toughness than bulk ceramics^{ [6]}. Therefore, bulk ceramics- and polymer-based dielectric capacitors have different application fields. Bulk dielectric ceramics used for pulse energy storage can be divided into four categories: linear dielectric, ferroelectric, relaxor ferroelectric and anti-ferroelectric. Among them, the relaxor ferroelectric is considered as a kind of ideal materials for the fabrication of pulse dielectric capacitor due to moderate maximum polarization (P_{max}), low remnant polarization (P_{r}), high dielectric breakdown strength (BDS), excellent fatigue property and high energy storage efficiency (η) ^{[7]}.

Sr_{0.7}Bi_{0.2}TiO_{3} (SBT) which adopts perovskite structure is a kind of typical relaxor ferroelectrics. The relaxor behavior comes from Sr site vacancy and Bi^{3+} ion off-centering ^{[1,8]}. The Sr site vacancies result in the distortion of oxygen octahedron, which gives rise to the relaxant movement of Ti^{4+ [9]}. Meanwhile, Bi^{3+} ion with lone pair possesses high stereochemical activity which drives the displacement at the off-centered A-site^{ [10]}. Based on these, SBT shows the relaxor behavior. These relaxation characteristics endow SBT with low P_{r} and coercive field, which contributes to a high h in energy storage application. However, the low Pmax of SBT limits the improvement of energy storage density. Further increasing the BDS is an effective strategy to improve the energy storage properties of SBT. Kong et al. ^{[11]} significantly increased the BDS of SBT to 460 kV/cm by doping with Bi(Mg_{0.5}Hf_{0.5})O_{3} and obtained a high recoverable energy density (W_{rec}) of 3.1 J/cm³ with high h of 93% at 360 kV/cm. Zhao et al. ^{[12]} doped Ca in SBT and increased the BDS to 480.2 kV/cm, and it can enhance the W_{rec} to 2.1 J/cm³ with high η of 97.6% at 290 kV/cm. However, most application areas of dielectric energy storage capacitors are in a relatively low voltage environment. Therefore, it is very important to obtain excellent energy storage properties at moderate electric field, and the enhancement of Pmax for SBT is necessary. The introduction of ferroelectrics with high polarization is expected to improve the P_{max} of SBT by increasing the degree of lattice distortion and changing the structure (such as amount, size and polarity) of nanodomains. Chao et al.^{[13]} obtained high Pmax of 10.1 mC/cm² at 50 kV/cm in (Sr,Pb,Bi)TiO_{3}, but lead is harmful to the environment and human health, which is a disadvantage to the commercial applications. Li et al. ^{[14] }designed 0.6(Sr_{0.7}Bi_{0.2})TiO_{3}-0.4(Bi_{0.5}Na_{0.5})TiO_{3} to obtain high polarizations (~18.45 mC/cm² at 120 kV/cm), but the BDS was deteriorated (only 120 kV/cm in alternating-current (AC) field), which is detrimental to high energy storage density. Therefore, it is necessary to find a better strategy to enhance the P_{max} of SBT and improve the energy storage properties.

K_{0.5}Bi_{0.5}TiO_{3} (KBT) is a kind of lead-free bismuth-based ferroelectric ceramics with large polarization. As reported, the band gap E_{g} of pure KBT is ~3.31 eV, which is higher than other bismuth-based ferroelectric, such as Na_{0.5}Bi_{0.5}TiO_{3} (NBT, ~3.23 eV) and BiFeO_{3} (BF, ~2.67 eV)^{ [15-17]}. It is well known that E_{g} is closely related to the electronic conductivity and intrinsic breakdown^{ [18]}. The higher E_{g} means that electrons are more difficult to jump from valence band into conduction band, which contributes to large BDS. Therefore, a large Pmax with high BDS is expected in SBT-KBT ceramics. In addition, the studies on SBT-KBT ceramics are few, and the effect of KBT addition in SBT matrix is still ambiguous.

In this work, the structure, dielectric and relaxor properties of (1-x)SBT-xKBT (x = 0 ~ 0.58) system were systematically investigated. The introduction of KBT significantly enhances the dielectric constant and the relaxor behavior of SBT. In particular, the P_{max} of SBT obviously enhances with the increasing KBT content because the proportion and size of PNRs increase. Meanwhile, the BDS maintains high values when 0 ≤ x ≤ 0.38 due to the additive of KBT with large E_{g}. The enhancement of P_{max} with the high BDS effectively improves the energy storage density of SBT. Therefore, a high energy storage density of 2.21 J/cm³ with high h of 91.4% was achieved at 220 kV/cm in 0.62SBT-0.38KBT, and the 0.62SBT-0.38KBT shows superior and stable energy storage properties under various temperatures (-55 ~ 150 °C), frequencies (10 ~ 500 Hz) and cycle numbers (1 ~ 10^{5}). Moreover, the 0.62SBT-0.38KBT exhibits excellent pulsed charging-discharging performance with high W_{d} of 1.81 J/cm³ and P_{D} of 49.5 MW/cm³, and both W_{d} and P_{D} show excellent thermal stability in the range of 20 ~ 160 °C at 100 kV/cm. The above results signify the great promise of 0.62SBT-0.38KBT for energy storage applications.

**2. Experimental**

**2.1. Fabrication of SBT-KBT ceramics**

(1-x)SBT-xKBT (x = 0, 0.09, 0.19, 0.28, 0.38, 0.48, 0.58) was fabricated using SrCO_{3}, Bi_{2}O_{3}, TiO_{2} and K_{2}CO_{3} powders as raw materials (purity ≥ 99%). The SrCO_{3}, Bi_{2}O_{3} and TiO_{2} were weighted based on stoichiometric ratios (Sr excess 3% to obtain pure SBT) and ball milled 8 h with ethyl alcohol and zirconia balls. The slurries were dried and calcined at 950 °C for 3 h to form SBT powder. The Bi_{2}O_{3}, K_{2}CO_{3} and TiO_{2} were mixed to form KBT powder in a similar way and the slurry is calcined at 800 °C for 4 h. After that, the powders consisting of SBT and KBT were weighted and ball milled for 6 h in ethyl alcohol. After drying, the powder were mixed with 10 wt.% solution of polyvinyl alcohol (PVA) and pressed into disks with 9 MPa (~12 mm of diameter and ~1 mm of thickness). Finally, the disks were buried in stabilized ZrO_{2} powder and sintered in the alumina crucible at 1185 °C ~ 1275 °C for 3 h after burning out the PVA at 600 °C.

**2.2. Characterization**

The crystalline structure of SBT-KBT was determined by X-ray diffraction (XRD) with Cu Kα radiation (PANalytical, Netherlands) and Raman spectroscopy (RENISHAW, In Via reflex) using 514.5 nm laser excitation. The micro-morphology was observed by fieldemission scanning electron microscopy (FESEM, FEI Inspect F50). The crystal structure and domain structure were investigated by transmission electron microscopy (TEM, FEI Tecnai G2 F30 S-TWIN,USA). The temperature and frequency dependence of dielectric properties were tested by LCR meter (Agilent 4284A, U.S.A.) over a temperature range of -55 ~ 200 °C and a frequency range of 100 ~100 kHz. Dielectric breakdown strength (BDS) was tested by a voltage withstand test instrument (RK2671AM, China) at room temperature. The diffuse reflectance and transmittance spectra of samples were obtained by using a UV-VIS-NIR spectrophotometer (MAPADA, UV 6100) over the wavelength of 300 ~ 800 nm. Polarization-electric field (P-E) hysteresis loops, current density vs. electric field (J-E) loops and leakage current densities of samples were tested by a ferroelectric test system (Radiant Precision, U.S.A.). Charge-discharge properties were obtained using a commercial charge-discharge platform (Tongguo (TG) technology, Pulsed Charge-discharge System, CFD-003). The samples used in the ferroelectric test system, charge-discharge platform and voltage withstand test instrument were polished to ~0.12 mm in thickness and the Ag electrode is ~0.2 cm² in area.

Energy density and energy efficiency are evaluated using following equations:

where W is the energy storage density, E is the external electric field.

**3. Results and discussion**

**3.1. Crystal structure and micro-morphology analyses of SBT-KBT**

The XRD patterns of (1-x)SBT-xKBT (x = 0 ~ 0.58) are shown in Fig. 1a. All samples exhibit main perovskite phase (SrTiO_{3}, PDF#35e0734). The second phase K_{4}Ti_{3}O_{8} can be detected for x ≥ 0.09 because of the volatilization of the bismuth element in the sintering process^{ [19,20]}, and it is common to observe the K_{4}Ti_{3}O_{8 }phase in KBT-based materials. The magnified profile for (111) and (200) diffraction peaks is shown in Fig. 1b, and no splitting of (111) and (200) is observed, indicating that the pseudo-cubic phase is formed in all samples. Meanwhile, the diffraction peaks (111) and (200) shift towards lower degree as x increases, indicating that the lattice parameters of samples gradually increase. The high-resolution transmission electron microscopy (HR-TEM) and selected area electron diffraction (SAED) patterns along several zone axis for SBT and 0.62SBT-0.38KBT are shown in Fig. 1(c ~ f), which can visually reflect the changes in the crystal structure with KBT content increasing. It can be seen that both the SBT and the

0.62SBT-0.38KBT exhibit cubic phase. Moreover, the spacing between (100) planes (d_{100}) of 0.62SBT-0.38KBT is 0.399 nm, which is larger than that of SBT (d_{100} = 0.391 nm). This finding is due to the larger average ionic radius of (Bi_{0.5}K_{0.5}) ^{2+} (1.51 Å, 12 coordination number (C.N.)) than that of (Sr_{0.7}Bi_{0.2}) ^{2+} (1.284 Å, 12 C.N.) ^{[21]}. Therefore, these TEM results are consistent with the XRD analysis.

Fig. 1. (a) XRD patterns of (1-x)SBT-xKBT (x ¼ 0 ~ 0.58) ceramics and (b) the magnified (111) and (200) diffraction peaks. (c ~ d) The HR-TEM images and SAED patterns of lattice fringes along [1-10]_{C} (c) and [001]C (d) for the SBT ceramics. (e ~ f) The HR-TEM images and SAED patterns of lattice fringes along [1-10]_{C} (e) and [111]_{C} (f) for the 0.62SBT-0.38KBT ceramics.

To further investigate the micro-structural evolution of (1-x) SBT-xKBT ceramics with increasing doping content, the Raman spectroscopy is depicted and shown in Fig. 2a and b. The Raman spectroscopy can be divided into three parts: (1) modes below 200 cm^{-1} are related to vibrations of perovskite A sites; (2) 200 ~ 400 cm^{-1} Raman shifts are associated with the vibration of BeO bond; (3) modes in the range of 400 ~ 700 cm1 are classified as the vibrations of BO_{6}-octahedra [20]. The Raman peaks are deconvoluted (Lorentzian Area type) by PeakFit software to better distinguish the Raman vibration modes. After the appropriate deconvolution, there are seven peaks detected in the Raman spectra, and five main active modes are consistent with related reports^{ [20,22-24]}. With KBT addition, the peak at 151 cm^{-1} is obviously broadened, indicating the enhanced cation disorder in the A sites due to the introduction of Bi^{3+} and K^{+ [25]}. The mode at 236 cm^{-1} becomes flatter, whereas the mode at 287 cm^{-1} that regarded as the ferroelectric characteristic peak becomes sharper, indicating the enhanced ferroelectricity with increasing KBT content ^{[24]}. With the increase of x, the mode at 515 cm^{-1} becomes flat and the mode at 569 cm^{-1} becomes visible, implying an increase in polar nano-region (PNR) size^{ [22]}. Meanwhile, this change also indicates the change of polar state due to the electric dipole moment, local polarization and BO_{6}-octahedra distortion produced by the introduction of (Bi_{0.5}K_{0.5})^{2+}, which is related to the enhancement of ferroelectricity. The blue shift of the modes at 287 cm^{-1} and 569 cm^{-1} and the red shift of the mode at 515 cm^{-1 }are evidence of the distortion of BO_{6}-octahedra vibration^{[20,22,26]}, which may be affected by the enhancement of the disorder in A sites. In addition, when x = 0.58, the E1(TO) mode, A1 mode and the mode at 280 cm^{-1} become apparent, which are assigned to the vibration of BieO bond, KeO bond and TieO bond. The appearance of these three modes which are usually detected in KBT-based ceramics is attributed to a high doping content of KBT, further suggesting an increased PNR size and enhanced ferroelectricity with the increasing x.

Fig. 2. Raman spectra of (1-x)SBT-xKBT (x= 0 ~ 0.58) ceramics at room temperature.

Fig. A1(a ~ g) show the micrographs of the cross-section of (1-x) SBT-xKBT, and all samples exhibit dense microstructure. The gran size slightly decreases with the increasing x because of the gradual decrease of sintering temperature. Fig. A2 shows the EDS mapping of 0.62SBT-0.38KBT ceramics, and the even distribution of Ti, O, Sr, Bi and K elements is believed to contribute to high BDS. In addition, the rod-like second phase can be only observed in the sample with x = 0.58 (Fig. A1g) due to the high relative amount in this composition. The EDS mapping indicates that this second phase observed in Fig. A1g is rich in K, Ti and O element (Fig. A3), which is consistent with the result of XRD.

**3.2. Dielectric properties and relaxor behavior analyses of SBT-KBT**

Fig. A4 shows the dielectric properties of (1-x)SBT-xKBT (x = 0 ~0.58) ceramics as a function of temperature under different frequencies. All samples exhibit the broad peaks of dielectric constant and dielectric loss around Tm (the temperature of maximum dielectric constant ε_{m}) with the phenomenon of frequency dispersion and diffuse phase transition, which is regarded as the typical characteristic of relaxor ferroelectrics ^{[27]}. Fig. 3a and b show the temperature dependence of dielectric constant and the change of T_{m} and ε_{m} of (1-x)SBT-xKBT ceramics with an increasing x at 100 kHz. It can be observed that the Tm shifts toward higher temperatures and the εm increases with the increasing addition of KBT, which is attributed to the high Tm and large ε_{m} of KBT ceramics. The increase of T_{m} and εm indicates the existence of polar nanoregions (PNRs) and a relaxation of PNRs ^{[28]}. Furthermore, the factors, such as the enhanced polarization of electron displacement, space charges, domain wall vibrations and dipolar defects after the introduction of KBT, can all contribute to the increase of ε_{m} ^{[29]}. The introduction of KBT decreases the A-site structural vacancy and enhances the coupling effect of [TiO_{6}] octahedron, which increases the structural stability of the materials and thus leads to a higher T_{m}^{[30]}.

The modified Curie-Weiss law was used to evaluate the dielectric dispersio:

where γ is the indicator of the relaxor degree and C is the Curie-Weiss constant. γ = 1 represents the ideal ferroelectric while γ = 2 reflects the excellent relaxor characteristic. The values of γ fitted by Equation (4) for (1-x)SBT-xKBT ceramics at 100 kHz are shown in Fig. 3c. The γ increases from 1.50 to 1.84 with the gradual increase of x, indicating the enhanced degree of relaxor after doping with KBT. Although SBT possesses certain relaxation characteristics, the degree of long-range paraelectric order is still relatively high. After the introduction of KBT, the submission of Bi^{3+}, K^{+} and Sr^{2+} at A-site destroys the long-range dipolar interaction and forms a local distortion of the polar region (PNRs) due to their different valence and ionic radii ^{[31]}. This enhances compositional fluctuation and structural disorder in the arrangement of cations, leading to an increase in the degree of relaxor ^{[32]}. The strong relaxor characteristic for ceramics contributes to obtain the slim P-E loop which benefits the energy storage.

Fig. 3. (a) Temperature dependence of (1-x)SBT-xKBT (x ¼ 0 ~ 0.58) ceramics with increasing of the value x under -55 °C ~ 200 °C at 100 kHz. (b) The change of T_{m} and ε_{m} (100 kHz) with increasing of the value x. (c) The diffuseness parameter γ which reveals the degree of relaxor for (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics by fitting with the modified Curie-Weiss law (Equation (4)) recorded at 100 kHz. (d) The frequency dependence of the dielectric constant and loss for (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics from 100 Hz to 100 kHz at room temperature.

The frequency dependence of dielectric properties for (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics in the frequency range of 100 ~100 kHz under room temperature is shown in Fig. 3d. For x ≤ 0.28, the ε shows excellent stability within the measured frequencies. But for x ≥ 0.38, the ε gradually decreases with increasing frequency due to the frequency dispersion caused by relaxor behavior. The increased variation of ε depending on frequency with the increasing x is because the T_{m} shifts toward higher temperatures with the increasing KBT addition. Based on this phenomenon, at 100 Hz, the ε of (1-x)SBT-xKBT increases with increasing x and reaches a maximum value of ~2783 with x = 0.58, which is 2.2 times higher than that of SBT (~1267). The tanδ of the samples gradually rises as the frequency increases, and this trend becomes obvious with the KBT content increasing, indicating the relaxor behavior in (1-x)SBT-xKBT ceramics ^{[33]}. Meanwhile, all the samples exhibit low dielectric loss (tanδ < 0.15) in 100 ~ 100 kHz, which contributes to low energy loss^{ [34]}.

**3.3. BDS and conduction mechanism analyses of SBT-KBT**

BDS is a vital parameter to evaluate the energy storage properties, which directly affects the energy storage density of ceramics. The BDS can be analyzed by Weibull distribution by Equations (5) and (6):

where E_{i} is the breakdown voltage of each sample, i is the serial number of sample and n is the total amount of samples. All date points of the samples fit well with the Weibull distribution (Fig. 4a). The shape parameters β are more than 9 for all samples, indicating the reasonable fitting results. With the increase of KBT, the average BDS decreases from 360.6 kV/cm for x = 0 to 274.8 kV/cm for x = 0.58, which can be attributed to the gradually increased ε of (1-x)SBT-xKBT. This is the experimental relationship between BDS and ε according to the model developed by McPherson (the BDS should show an approximate (ε)^{-1/2} dependence over a wide range for high dielectric constant materials) ^{[35]}. In addition, the decreased BDS and conduction mechanism can also be analyzed by the leakage current density of (1-x)SBT-xKBT ceramics, as shown in Fig. 4b. With increasing the applied electric field, the leakage current density of all samples increases because the number and kinetic energy of charged carriers (such as free electrons and oxygen vacancies) increase. This means that the charged carriers contribute to electric conduction based on Ohmic conduction mechanism after getting enough energy as the electric field increases ^{[36,37]}. For all compositions, the leakage current density shows the increasing trend with the increase of x. This can be attributed to two aspects: on the one hand, the increased amount of A-site elements (B_{i} and K) with low melting points promotes the volatilization during sintering, which increases the concentration of oxygen vacancies to maintain the valence balance^{ [38]}; on the other hand, the increased lattice parameter causes the loose lattice after doping KBT, leading to an easy diffusion of charge carriers^{ [39]}. These reduce the resistance and increase the leakage current density, leading to the deterioration of BDS.

Fig. 4. (a) The Weibull distribution of BDS for (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics, the inset shows the change of the average BDS values with different x. (b) Leakage current density of (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics as a function of electric field with different x. (c) The variation of the bandgap E_{g} of (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics with different x.

Interestingly, the BDS values change slowly and remain at high level (above 300 kV/cm) with x ≤ 0.38. Meanwhile, the leakage current density of the samples with x ≤ 0.38 is low and similar, and then increases rapidly when x ≥ 0.48. These can be analyzed from the aspect of bandgap (E_{g}). The E_{g} is considered as the underlying intrinsic factors affecting the BDS at the electron level^{ [11]}, and a large E_{g} usually results in a high BDS for energy storage ceramics. The E_{g} of (1-x)SBT-xKBT ceramics was calculated from the UVevis absorption spectrum, as shown in Fig. A5 and Fig. 4c. The E_{g} value decreases from 3.13 eV for x = 0 to 2.96 eV for x = 0.58, which is consistent with the variation tendency of BDS. However, the E_{g} of samples with x ≤ 0.38 exhibits large values (above 3.03 eV) and relatively gentle variation owing to the larger E_{g} of additive KBT

(~3.31 eV) than that of SBT (~3.13 eV). The large E_{g} means that it is difficult for electrons to jump from the valence band to the conduction band, leading to the high resistance, high leakage current and low possibility of breakdown^{ [40]}. Therefore, the introduction of a moderate amount (x ≤ 0.38) KBT with large E_{g} compensates the deterioration of BDS in (1-x)SBT-xKBT ceramics.The high BDS contributes to achieve the high energy storage density. However, when x ≥ 0.48, this compensation effect disappears, and the BDS seriously deteriorates, which may be related to the increasing amount of secondary phase, excess number and kinetic energy of charged carriers and large tan d. The tan d of the samples is lower than 0.01 with x ≤ 0.38 at 100 Hz (Fig. 3d). It is beneficial for the ceramics with low tan d to generate low heat during the charge-discharge process, resulting in a low probability of thermal breakdown and high BDS ^{[11]}. When x ≥ 0.48, the rapid increase in tan d (tanδ = 0.04 for x = 0.48, tanδ = 0.09 for x = 0.58) causes the sharp decline of BDS.

**3.4. Energy storage properties of SBT-KBT**

The unipolar P-E loops, P_{max} and P_{r} of (1-x)SBT-xKBT (x = 0 ~0.58) at 170 kV/cm and 10 Hz are shown in Fig. 5a and b. All samples exhibit relaxor ferroelectric behavior with slim P-E loops and low P_{r}. This owes to the existence of PNRs, which contains many nanodomains with fast response of aligning and back-switching under external electric fields^{ [41]}. With the increase in x, the Pmax and P_{r }gradually increase from 14.92 mC/cm² to 30.48 mC/cm² for P_{max} and from 0.14 mC/cm² to 2.2 mC/cm² for Pr, indicating the enhanced ferroelectric properties, which can be attributed to two factors^{[10,42]}: (1) When the Sr site is occupied by K^{+} and Bi^{3+}, the K^{+} site and Bi^{3+} site can be regarded as the center of negative charge and positive charge, respectively. This produces the electric dipole moment with the local electrical field between K^{+ }site and Bi^{3+} site, leading to the large lattice distortion and local broken-symmetry. The production of Bi^{3+}-K^{+} ionic pair induces the local polarization, and more Bi^{3+} doping can drive more displacements at the offcentered A-site. These factors contribute to the increase in the proportion of the PNRs, leading to the increased P_{max} and P_{r} (Fig. 5c and d). Meanwhile, the decreased ramp rate of the normalized P_{max }indicates the aggravating polarization saturation (Fig. A6a). This also demonstrates the increase in the dynamic PNRs and the enhancement of ferroelectricity ^{[43]}. (2) Based on the discussion of (1), the electric dipole with the same orientation increases, resulting in an increase in the size of PNRs (Fig. 5c and d), which is also reflected in Raman spectra (Fig. 2). Furthermore, the change of the size of PNRs can be observed in TEM, as shown in Fig. 5e and f.

The nanodomains can be obviously observed in the TEM of the sample with x = 0.38 but are difficult to be found in the TEM of SBT at the same scale, suggesting that the PNRs with a larger size exist in 0.62SBT-0.38KBT. Herein, the increase in the size of PNRs contributes to the enhanced P_{max} and P_{r}.

Fig. 5. (a) The unipolar P-E loops of (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics at 170 kV/cm and 10 Hz. (b) P_{max }and P_{r} of (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics at 170 kV/cm and 10 Hz.The schematic diagram of the amount and size of PNRs for SBT (c) and 0.62SBT-0.38KBT (d). The TEM images of SBT (e) and 0.62SBT-0.38KBT (f).

The J-E loops of (1-x)SBT-xKBT (x ¼ 0 ~ 0.58) at 160 kV/cm and 10 Hz are shown in Fig. 6a. All J-E loops show the gentle slope with the bulge shape, which is regarded as a typical characteristic of relaxor ferroelectric [44]. The two broad current peaks that near zero electric field are linked to PNRs switching: the random PNRs can be oriented along the direction of the external electric field and lose the orientation when removing the electric field^{ [45]}. With the increase of KBT doping content, the electric current peak enhances gradually, demonstrating that the higher proportion and larger size of PNRs switching happens and the ferroelectricity is enhanced ^{[46]}. These are consistent with the analysis results of P-E loops, and the enhanced ferroelectricity for SBT is beneficial to improve the energy storage properties. However, the increase of current peak discloses the enhanced dynamics of PNRs, resulting in the large strain and heat dissipation, which deteriorates the BDS and η ^{[20,47]}. Furthermore, the energy loss caused by electric conductivity (σ) can be reflected by the difference value between the charge current density (J_{charge}) and the discharge current density (J_{discharge}) at the maximum electric field [44]. The values of (J_{charge} - J_{discharge}) for (1-x) SBT-xKBT (x = 0 ~ 0.58) ceramics are shown in Fig. A6b. With the increase of x, the increasing tendency of (J_{charge} - J_{discharge}) means the increasing energy loss caused by σ, which is attributed to the increased s originated from the enhanced concentration and kinetic energy of oxygen vacancies, leading to the decrease of η and the deterioration of BDS. Meanwhile, the values of (J_{charge} - J_{discharge}) change slowly for the samples with 0 ≤ x ≤ 0.38, and then significantly increase for the samples with x > 0.38. This is related to the obviously decreased E_{g} and increased leakage current density when x > 0.38. The energy storage properties of (1-x)SBT-xKBT (x = 0 ~0.58) at 170 kV/cm and 10 Hz are shown in Fig. A6c. With the increase in x, the η gradually decreases from 96.6% to 83.1% because of the increasing Pr. The Wrec gradually increases from 1.1 J/cm³ to 1.76 J/cm³ for the samples with 0 ≤ x ≤ 0.48 due to the increased (P_{max} - P_{r}), and then decreases for x ¼ 0.58 (1.68 J/cm³) due to the large Pr and low η. Therefore, high Pmax with low hysteresis characteristics (large (P_{max} - P_{r})) is conducive to the improvement of energy storage properties.

The unipolar P-E loops, Pmax and Pr of (1-x)SBT-xKBT (x = 0 ~0.58) with critical electric fields under 10 Hz are shown in Fig. 6b and Fig. A6d. All samples display slim P-E loops, indicating excellent relaxor behavior. With the increasing x, the P_{max} and P_{r} gradually increase due to the enhanced ferroelectricity. The critical electric fields are similar and high for the samples with 0 ≤ x ≤ 0.38 (220 ~ 230 kV/cm), and then decrease to 170 kV/cm for the samples with x ≥ 0.48, which is consistent with the change of BDS. In particular, the samples with x ≥ 0.48 exhibit relatively higher Pmax than other samples, which may originate from the larger space-charge polarization due to the lower E_{g}, higher second phase content and more charge carriers (ion vacancies). Meanwhile, the larger space-charge polarization in the samples with x ≥ 0.48 may enhance the local electric field at the interface, leading to the relatively lower critical electric fields. The energy storage properties of (1-x)SBT-xKBT (x = 0 ~ 0.58) with critical electric fields under 10 Hz are shown in Fig. 6c. The W_{rec} increases first due to the increased (P_{max} - P_{r}) and then decreases due to the high P_{r} and low BDS with increasing x. The Wrec reaches the maximum value with x = 0.38 due to simultaneously obtained large Pmax (26.01 mC/cm²), low P_{r} (0.77 mC/cm²) and high BDS (220 kV/cm). The h gradually decreases with the increase in x due to the increased P_{r}, but the values of η are still higher than 90% for (1-x)SBT-xKBT (x ≤ 0.48), which contributes to energy storage. The P-E loops, P_{max}, P_{r} and energy storage properties of 0.62SBT-0.38KBT under 50 ~ 220 kV/cm at 10 Hz are shown in Fig. 6d, Fig. A6e and Fig. 6e, respectively. The slim P-E loops and the gentle J-E loops with bulge shape (Fig. A6f) under different electric fields suggest the excellent relaxor behavior of 0.62SBT-0.38KBT. The P_{max} gradually increases with low P_{r} due to the enhanced interaction of PNRs with electric field enhancing ^{[48]}, leading to the increase in Wand Wrec. The h slightly decreases due to the increased energy loss with the increasing electric field, but it still maintains a high value of 91.4% at 220 kV/cm. Meanwhile, similar charge and discharge current density of symmetrical J-E loops implies the low thermal loss and high h ^{[44]}. The high h means that less energy is wasted to heat from the stored energy, which contributes to the excellent reliability of dielectric energy storage capacitors. The high W (2.21 J/cm³) and W_{rec} (2.02 J/cm³) with high η of 91.4% were achieved in 0.62SBT-0.38KBT at 220 kV/cm. Fig. 6f shows the comparison of energy storage properties between 0.62SBT-0.38KBT ceramics with other SrTiO_{3} (ST)- and SBT-based ceramics in recent years. The specific dates and related references are shown in Table A1. The 0.62SBT-0.38KBT possesses high W_{rec}, η and BDS simultaneously, which is superior to many ST- and SBT-based energy storage ceramics. Therefore, a much higher energy storage density can be obtained by increasing P_{max} while maintaining low P_{r} and high BDS in (1-x)SBT-xKBT ceramics.

Fig. 6. (a) The J-E loops of (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics at 160 kV/cm and 10 Hz. (b) The unipolar P-E loops of (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics with critical electric fields under 10 Hz. (c) The energy storage properties of (1-x)SBT-xKBT (x = 0 ~ 0.58) ceramics with critical electric fields under 10 Hz. (d) The P-E loops of 0.62SBT-0.38KBT at 50 ~220 kV/cm and 10 Hz. (e) The energy storage properties of 0.62SBT-0.38KBT at 50 ~ 220 kV/cm and 10 Hz. (f) Comparisons of the energy storage properties of 0.62SBT-0.38KBT and other ST- and SBT-based energy storage ceramics.

Temperature stability is the crucial factor to evaluate the application prospect in harsh temperature conditions. The temperature dependence of unipolar P-E loops, P_{max}, P_{r} and energy storage properties of 0.62SBT-0.38KBT under the temperature ranging from -50 ~ 150 °C at 100 kV/cm and 10 Hz are shown in Fig. 7a, b and c. All slim P-E loops exhibit the temperature-stable relaxor behavior. With the increasing temperature, the size of PNRs becomes small and the dynamics of PNRs increases, which leads to the slightly decrease of P_{max} and P_{r} ^{[49]}. Moreover, this phenomenon may also be attributed to the decrease of the ε at 10 Hz and the enhanced thermal fluctuation. The decreasing P_{max} and P_{r} cause the trend of a slight decrease of W_{rec} and a slight increase of η. As a result, the stable W_{rec} of 0.66 ~ 0.74 J/cm³ (~5.7% variation) with stable and high h of 92.3% ~ 95.3% (~1.6% variation) is achieved in 0.62SBT-0.38KBT. The small variation for W_{rec} and h indicates that the 0.62SBT-0.38KBT exhibits excellent temperature stability in the measured temperatures, which is due to the broad diffusive phase transition. Frequency stability is another vital evaluation of energy storage properties. The frequency dependence of unipolar P-E loops, P_{max}, P_{r} and energy storage properties of 0.62SBT-0.38KBT in the frequency ranging from 10 ~ 500 Hz at 100 kV/cm and room temperature are shown in Fig. 7d, e and f. The 0.62SBT-0.38KBT exhibits slim P-E loops in the measured frequencies. The P_{max} is almost constant and the P_{r} slightly increases with the increasing frequency, resulting in the almost no changed W_{rec} (~0.73 J/cm³) and slightly decreasing η from 95.6% to 92.8%. The slight increase of P_{r} is resulted from the lag of domain wall motions and domain switching behind the increased frequencies^{[14]}, thus leading to a slight decreasing η. However, the variation of η is only ~1.5%, so the 0.62SBT-0.38KBT exhibits excellent frequency stability due to the fast response of PNRs. In addition, excellent fatigue resistance is necessary for ceramics capacitors applied in long term repeated cycles. The fatigue test of the 0.62SBT-0.38KBT was performed up to 10^{5} cycles at 100 kV/cm and 10 Hz. The fatigue cycle number dependence of unipolar P-E loops, Pmax, P_{r} and energy storage properties of 0.62SBT-0.38KBT are shown in Fig. 7g, h and i. The P-E loops do not change significantly and maintain slim shape after 10^{5} cycles. The P_{max} and P_{r} show the trend of slight increase with the increasing fatigue cycles. The Wrec is around 0.73 J/cm³ (with variation below 1%) with a high h of ~94.3% (with variation of~1%). Therefore, the 0.62SBT-0.38KBT shows the outstanding cycling endurance, which may be related to the highly dynamic nano-scale domain structure, the dense microstructure and the less oxygen vacancies ^{[50]}. Based on these, the excellent stability of temperature, frequency and cycling demonstrate that the 0.62SBT-0.38KBT is potential for energy storage application in harsh environments.

Fig. 7. (a ~ c) The temperature dependence of unipolar P-E loops, Pmax, Pr and energy storage properties of 0.62SBT-0.38KBT in the temperature ranging from -50 ~ 150 C at 100 kV/cm and 10 Hz. (d ~ f) The frequency dependence of unipolar P-E loops, P_{max}, P_{r} and energy storage properties of 0.62SBT-0.38KBT in the frequency ranging from 10 ~ 500 Hz at 100 kV/cm and room temperature. (g ~ i) The fatigue cycle number dependence of unipolar P-E loops, P_{max}, P_{r} and energy storage properties of 0.62SBT-0.38KBT performed up to 10^{5 }cycles at 100 kV/cm and 10 Hz under room temperature.

**3.5. Pulsed charging-discharging performance of SBT-KBT**

High power density and energy storage density and fast charge-discharge rate are required for high power applications. Therefore, the pulse charge-discharge measurements are conducted by the overdamped and underdamped resistance-capacitance circuit (RC circuit). The overdamped current-time curves of the 0.62SBT-0.38KBT under various electric fields (20 ~ 220 kV/cm) are shown in Fig. 8a. With the electric field increases, the similar discharge behaviors are achieved, and the current peak (I_{max}) increases from 1.6 A at 20 kV/cm to 16.67 A at 220 kV/cm (inset). The linearly increasing peak current suggests an excellent relaxor behavior of the 0.62SBT-0.38KBT. The discharge energy density (W_{d}) can be evaluated by the following formula:

where R is the load resistance (102 Ω) and V is the sample volume. Fig. 8b shows the time dependence of W_{d} with different electric fields. The t0.9 is defined as the time when 90% stored energy (W_{d}) has been released, and it is used to evaluate the discharge rate. The electric field dependence W_{d} and t0.9 are shown in Fig. A7a, where the W_{d} increases while t0.9 shows the opposite manner. The 0.62SBT-0.38KBT exhibits the high W_{d} of 1.81 J/cm³ with the t_{0.9} of 0.36 ms at 220 kV/cm. It is noted that the W_{d} is slightly lower than the W_{rec} calculated by P-E loops, which originates from their different mechanisms. There is the loss of discharged energy in the equivalent series resistor, and the enhancement of viscous force clamps the domain walls ^{[20,51]}. In addition, the energy storage density obtained by P-E loops is idealized because the load resistance will inevitably lose energy in practice. Therefore, the W_{d} obtained by pulse charge-discharge measurements is more practical^{ [52,53]}. The underdamped pulsed discharge current waveforms of the 0.62SBT-0.38KBT under various electric fields (20 ~220 kV/cm) are shown in Fig. 8c. The 0.62SBT-0.38KBT exhibits similar discharge behaviors, and the stored energy releases rapidly with a short time about 0.6 ms under different electric fields. Meanwhile, the period time of T is nearly unchanged (Fig. A7b). T can be expressed as follows based on the circuit theory:

where ω is the radian frequency, R and L are the resistance and inductance, which are constant in the same circuit. C is the capacitance and affects T. The electric field-stable T of the 0.62SBT-0.38KBT demonstrates the weak dielectric nonlinearity for various electric fields, indicating a very low energy loss in the charge-discharge process^{ [54,55]}. The corresponding maximum current (I_{max}), current density (C_{D}) and power density (P_{D}) are shown in Fig. 8d. The C_{D} and P_{D} are calculated by equations (9) and (10), respectively:

where S is the area of electrode, E is the electric field strength. The I_{max}, C_{D} and P_{D} increase with the increasing electric field, and reach their maximum of 90 A, 450 A/cm² and 49.5 MW/cm³ at 220 kV/cm, respectively. Fig. 8e shows the contrast of charge-discharge performance of various lead-free energy storage ceramics in recent years. The specific dates and related references are shown in Table A2. The 0.62SBT-0.38KBT possesses high W_{d}, P_{D} and BDS simultaneously in the pulse charge-discharge measurements, which is superior to many lead-free energy storage ceramics.

Fig. 8. (a) The overdamped current-time curves of the 0.62SBT-0.38KBT under various electric fields (20 ~ 220 kV/cm), the inset shows the change of the current with different electric fields. (b) The time dependence of W_{d} with different electric fields (20 ~ 220 kV/cm). (c) The underdamped current-time curves of the 0.62SBT-0.38KBT under various electric fields (20 ~ 220 kV/cm). (d) The change of I_{max}, C_{D} and P_{D} as functions of the electric fields (20 ~ 220 kV/cm). (e) Contrast of charge-discharge performance of various lead-free energy storage ceramics

The thermal stability of pulsed charging-discharging performance is important for applying in pulsed power systems. The temperature dependence of overdamped current-time curves of the 0.62SBT-0.38KBT under various temperatures (20 ~ 160 °C) and 100 kV/cm are shown in Fig. 9a. All curves show the similar shape, and the current peak remains stable at ~8.5A (inset) in the measured temperature range. The W_{d} as a function of time under different temperatures at 100 kV/cm is shown in Fig. 9b, which shows a similar time dependence trend and maintains relatively stable. The W_{d} fluctuates within the range of 0.64 ~ 0.72 J/cm³ with the variation of less than 6% as the temperature increases (inset). The t0.9 with small variation gradually decreases (Fig. A7c) due to the enhanced polarization response caused by the decreasing size of PNRs with the increasing temperature^{ [56]}. The temperature dependence of underdamped current-time curves of the 0.62SBT-0.38KBT under various temperatures (20 ~ 160 °C) and 100 kV/cm are shown in Fig. 9c. The amplitude of the first peak current is almost unchanged, but the positions of the rest of peak exhibit a lag due to the dielectric nonlinearity for various temperatures. The T increases firstly and decreases later with the increase in temperature (Fig. A7d), which reflects the same tendency of C. This indicates the nonlinear relationship between ε and temperature, which is consistent with the results of Fig. A4e. As shown in Fig. 9d, the Imax, C_{D} and P_{D} increase firstly and decrease later with the increasing temperature at 100 kV/cm. This is attributed to the decreasing size and increasing dynamics of PNRs with the temperature increasing. After the temperature increases to 140 °C, the enhanced local random field impedes the full PNRs alignments, leading to a low current ^{[48]}. However, both C_{D} (267 ~ 290 A/cm²) and P_{D} (13.5 ~14.5 MW/cm³) show a small variation of ~4%. The above results strongly signify the excellent and stable pulsed chargingdischarging performance of the 0.62SBT-0.38KBT, suggesting the high application potential in pulsed power systems.

Fig. 9. (a) The overdamped current-time curves of the 0.62SBT-0.38KBT under various temperatures (20 ~ 160 °C) at 100 kV/cm, the inset shows the change of the current with different temperatures at 100 kV/cm. (b) The time dependence of Wd with different temperatures (20 ~ 160 °C), the inset shows the change of W_{d} with different temperatures at 100 kV/cm. (c) The underdamped current-time curves of the 0.62SBT-0.38KBT under various temperatures (20 ~ 160°C) at 100 kV/cm. (d) The change of Imax, C_{D }and P_{D} as functions of the temperatures (20 ~ 160 °C) at 100 kV/cm.

**4. Conclusions**

In summary, the novel (1-x)SBT-xKBT (x = 0 ~ 0.58) lead-free relaxor ferroelectric ceramics were synthesized by the solid-state reaction methods. The dielectric constant and relaxor behavior of SBT can be enhanced with the addition of KBT. The incorporation of Bi^{3+} and K^{+} increases the proportion and size of PNRs, resulting in an enhanced Pmax of SBT. Meanwhile, the samples with x ≤ 0.38 remain a relatively large band gap (E_{g} ≥ 3.03 eV) and low leakage current due to the introduction of KBT with a large band gap, leading to the high BDS more than 327.3 kV/cm with x ≤ 0.38. Based on these synergistic effects, the 0.62SBT-0.38KBT exhibits excellent energy storage properties with high energy storage density of 2.21 J/cm³ and high h of 91.4% at 220 kV/cm. Moreover, superior temperature stability (~5.7% variation of Wrec with ~1.6% variation

of h in -50 ~ 150 °C), frequency stability (almost unchanged W_{rec }with ~1.5% variation of h in 10 ~ 500 Hz) and fatigue resistance (almost unchanged Wrec and h within 10^{5} cycles) are obtained at 100 kV/cm for 0.62SBT-0.38KBT. In addition, the 0.62SBT-0.38KBT also exhibits high Wd of 1.81 J/cm³ and PD of 49.5 MW/cm³ at 220 kV/cm, which possesses excellent temperature stability with a variation less than 6% for W_{d} and a small variation of ~4% for PD in 20 ~ 160 C at 100 kV/cm. These advantages indicate that the 0.62SBT-0.38KBT is a promising candidate for advanced pulse energy storage applications.