Optimized Breakdown Strength and Crystal Structure for Boosting the Energy Storage Performance of Niobate-Based Glass Ceramics via a B-Site Substitution Strategy

Abstract

Based on the B-site modification strategy, excellent energy storage properties were achieved in this work by substituting Nb with Ta of the same valence in niobate-based glass ceramics. Ta substitution was found to lead to the transformation of crystal structures, and the space point group evolved from the non-centrosymmetric P4bm to the centrosymmetric P4/mbm, resulting in a transition from relaxor ferroelectric to paraelectric glass ceramics. Furthermore, the addition of Ta led to a significant decrease in grain size and interfacial activation energy, as well as an increase in the optical band gap, resulting in a dramatic increase in BDS from 800 kV/cm to 1300 kV/cm. The KBSN-4.0mol%Ta₂O₅ glass ceramic exhibited optimal energy storage properties, including a discharge energy density of ~5.62 J/cm³ and a superfast discharge rate of ~9.7 ns, resulting in an ultrahigh discharge power density of about ~1296.9 MW/cm³ at 1300 kV/cm. Furthermore, this KBSN-Ta glass ceramic also displayed good thermal stability over a temperature range of 20–120 °C, with the W_d decreasing by 9.0% at 600 kV/cm. B-site modification engineering in glass ceramics has proved to be an important way to effectively optimize energy storage performance.

1. Introduction

Inorganic dielectric capacitors are widely used in high-voltage pulse power supply systems due to their high power density, rapid charge and discharge, low cost, and excellent thermal stability [1,2,3]. As one of the main inorganic dielectric capacitors, glass ceramic consists of a nanoscale ceramic phase and an amorphous glass phase, which feature good bulk density, a reasonable dielectric constant, and high electric breakdown strength (BDS) [4,5]. Therefore, glass ceramic dielectric capacitors are a promising candidate in high-voltage, high-power density pulsed devices and have attracted much attention in recent years [6].

Tungsten bronze oxides are the largest class of ferroelectrics with excellent optical and electrical properties; as such, they are the focus of research in the field of ceramic and glass ceramic dielectric energy storage materials. In general, the formula of tungsten bronze oxides can be expressed as ((A1)₂(A2)₄C₄)((B1)₂(B2)₈)O₃₀ [7,8,9,10]. Within this formula, the A1 and A2 sites are usually occupied by cations with large radii, including K⁺, Na⁺, Ba²⁺, Sr²⁺, etc., whereas the B1 and B2 sites are generally occupied by excess metals with smaller ionic radii, such as Nb⁵⁺, Ta⁵⁺, and W⁶⁺, and the C site is usually empty [11]. In general, the impact of the ferroelectric behavior of tungsten bronze structures originates from structural distortions due to A-site cation occupancy; moreover, B-site substitution can directly change the displacement of polar cations, leading to crystal transitions and resulting in transitions in ferroelectric behavior, including the transition from normal ferroelectricity to relaxed ferroelectricity and para-electrics [12,13]. Therefore, special crystal structure transitions can be modulated by the A- or B-site substitution strategy in tungsten bronze structures to optimize the ferroelectric behavior and thus improve the energy storage performance, as has been demonstrated in many recent ceramics with tungsten bronze structures. For instance, by introducing Ag⁺, Ca²⁺, and Gd³⁺ ions into the A-site of SrNaNb₅O₁₅ ceramics, the recoverable energy density can reach 2.37–3.23 J/cm³ at 290–320 kV/cm [14,15,16]. Furthermore, it was found that substituting Nb for Ta in the B-site could optimize the BDS and relaxor nature in Sr₂KNb₅O₁₅ ceramics, thus obtaining a recoverable energy density and efficiency of about 3.84 J/cm³ and 93.2% at 410 kV/cm, respectively [17]. Furthermore, B-site Ta⁵⁺ substitution in Sr₂NaNb₅O₁₅ and Sr_0.25Ba_0.75Nb₂O₆ ceramics can lead to the transformation of the crystal structure and space point group transitions from P4bm and Im2a to P4/mbm, causing the transition from normal ferroelectricity to relaxed ferroelectricity and then to paraelectricity, resulting in a substantial reduction in Pr and providing an important direction for improving energy storage efficiency [7,12]. Although the A/B-site substitution strategy plays an important role in optimizing the ferroelectric behavior and energy storage performance of tungsten bronze ceramics, the BDS of ceramics is generally below 400 kV/cm, which greatly limits the increases in energy storage density and power density compared to those of some high-performance ceramics [18,19,20,21].

In our previous work, we added Ag₂O to the composition of K₂O-BaO-SrO-Nb₂O₅-B₂O₃ glass to provide Ag⁺ for A-site substitution during precipitation [22]. It was found that Ag⁺ substitution in the A-site could exacerbate the structural distortion of the NbO₆ octahedra, resulting in optimized dielectric, ferroelectric, and energy storage properties. For example, when the doping of Ag⁺ was 1.0 mol%, the glass ceramic increased the Pmax while maintaining a smaller residual polarization (P_r), resulting in an increase in W_rec from 4.7 J/cm³ to 5.8 J/cm³ under 800 kV/cm while maintaining efficiency above 90%. In addition, the actual charge–discharge performance was also significantly improved, i.e., discharge energy density (W_d) increased from 2.82 J/cm³ to 3.62 J/cm³ while also exhibiting an ultrahigh power density (P_d) of 1054.8 MW/cm³ under 800 kV/cm.

Based on our previous work, different contents of Ta₂O₅ were introduced into the composition of K₂O-BaO-SrO-Nb₂O₅-B₂O₃ glass with the aim of providing Ta⁵⁺ for B-site substitution during crystallization. Subsequently, the effects of B-site substitution on the phase structure, microstructure, and dielectric, ferroelectric, and energy storage properties of the glass ceramics combined with impedance analysis were studied systematically.

2. Materials and Methods

2.1. Fabrication of Glass Ceramics

Glass with a composition of 10K₂O-7BaO-16SrO-34Nb₂O₅-33B₂O₃-xTa₂O₅ (simplified as KBSN-xTa₂O₅, x = 0.0, 1.0, 2.0, 4.0, and 8.0 mol%) was prepared by the method of melt quenching. Raw materials, i.e., K₂CO₃ (≥99%), BaCO₃ (≥99%), SrCO₃ (≥99%), Nb₂O₅ (≥99.9%), H₃BO₃ (≥99.5%), and Ta₂O₅ (≥99.5%), were used for the glass preparation. All of the raw materials were weighed proportionally, mixed with anhydrous ethanol as a dispersant in a ball mill for 12 h, and then dried at 100 °C for 3 h. The dried mixtures were placed in a corundum crucible (≥99.7%) and melted at 1450 °C for 2 h. The melt was poured into a preheated copper plate to press into shape and then annealed at 550 °C for 6 h to obtain the mother glass. The mother glass was cut into pieces of 1 × 1 × 0.2 cm and crystallized at 740 °C for 2 h to obtain glass ceramics, which was then thinned and polished to about 0.07 mm. Finally, a silver electrode of about 2 mm diameter was coated on both sides of the glass ceramics and then sintered at 550 °C for 40 min to obtain the glass ceramic capacitors for dielectric, ferroelectric, and charge-discharge performance tests.

2.2. Characterization

The phase structures were determined via X-ray diffraction (XRD, Bruker D8 Advance, Karlsruhe, Germany) at room temperature with Cu-Ka radiation. The local structure was studied using a LabRAM HR Evolution Raman spectrometer (HORIBA, Palaiseau, France, 532 nm excitation) at room temperature. The microstructures were obtained using a scanning electron microscope (FE-SEM, Quanta 450 FEG, FEI, Miamisburg, OH, USA), and the samples were treated with 20% HF about 60 s before testing. High-angle annular dark field (HAADF) images and elemental distribution spectra were acquired using a field-emission transmission electron microscope (TEM, Talos F200X, FEI, Pasadena, CA, USA) at 200 kV. The UV-vis absorption spectra were tested with a UV-visible spectrophotometer (Jingdao UV-200, Ōsaka shi, Japan). The impedance spectra were measured via LCR meter (2838A, Tonghui, Changzhou, China) at temperatures from 460 °C to 540 °C and a frequency test range from 0.5 kHz to 1000 kHz. The dielectric temperature spectra were obtained at 0.5, 1.0, 10, 100, and 1000 kHz using an LCR tester (Th 2832, Tonghui, Changzhou, China) with a measurement temperature range of −150 °C to 200 °C. The P-I-E loops were measured using a ferroelectric tester (TF ANALYZER 2000, aixACCT, Aachen, Germany). The charge–discharge properties were studied using an RLC testing circuit (Gogo Instruments, CFD-003, Shanghai, China) with a load resistance of approximately 200 Ω.

3. Results and Discussion

Figure 1a displays the room temperature X-ray diffraction patterns of the KBSN-xTa₂O₅ (x = 0.0, 1.0, 2.0, 4.0 and 8.0 mol%) glass ceramics. It can be seen that a pure KBaSrNb₅O₁₅ phase with a tungsten bronze structure precipitated in all samples, and no second phase was observed. The inset of Figure 1a depicts an enlarged diffraction peak around 46°. Notably, the diffraction peak began to split when the Ta content increased to 4.0 and 8.0 mol%. Considering the changes in polarization behavior of KBSN-xTa₂O₅ glass ceramics which are discussed in the following sections, the non-centrosymmetric point group of P4bm was used for the x = 0.0, 1.0, and 2.0 components, and the centrosymmetric point group of P4/mbm was used for the x = 4.0 and 8.0 components in the structure refinement program. The structure refinement results are shown in Figure S1, and the lattice parameters of all samples are displayed in

Table 1. The Rietveld refinement results for XRD of KBSN-xTa₂O₅ glass ceramics.

Ta Content	x = 0.0	x = 1.0	x = 2.0	x = 4.0	x = 8.0
Space group	P4bm	P4bm	P4bm	P4/mbm	P4/mbm
a (Å)	12.52019	12.520752	12.517999	12.509094	12.50440
b (Å)	12.52019	12.520752	12.517999	12.509294	12.50440
c (Å)	3.95194	3.949690	3.950870	3.947899	3.946172
c/a	0.315645	0.315451	0.315615	0.315597	0.315583
Rp (%)	3.45	3.39	3.52	4.13	4.06
Rwp (%)	4.32	4.32	4.42	5.25	5.14

(R_p is the residual variance factor of the graph and R_wp is the weighted residual variance factor of the graph). As the content of Ta increased, lattice parameter a increased and c decreased, leading to a reduced value of tetragonality c/a [12]. In particular, the trend of the a value for the x = 2.0 component was opposite to that of x = 1.0, with a decreasing and c increasing, but the value of c/a was still lower than the x = 0.0 component. This anomaly may have been caused by the coexistence of the two structures at the beginning of the phase transition, which led the peaks around 46° to shift to a lower angle. As shown in Table 1, when x ≥ 4.0 mol%, both the lattice parameter a and c decreased, although the radii of Nb⁵⁺ (0.64 Å, coordination number (CN) = 6) and Ta⁵⁺ (0.64 Å, CN = 6) were the same [7]. This lattice contraction may be attributed to the higher electronegativity of Ta and the stronger covalent Ta-O bond (shorten bonding length) due to the enhancement of hybridization between oxygen 2p orbitals and Ta d orbitals; that is, the shortened Ta-O bonds may have enhanced the degree of electronic localization and reduced the driving force of polarity distortion, leading to the lattice contraction. Combined with the clear splitting of the diffraction peak that appeared at x ≥ 4.0, it is reasonable to speculate the symmetry deviation arose from the crystal structure changing from a non-centrosymmetric P4bm to a centrosymmetric P4/mbm space group [16].

In order to investigate the change in the local structure of the glass ceramics with the addition of Ta₂O₅, the Raman spectrum was tested, as shown in Figure 1b. Similar to other ceramics with tungsten bronze structures reported in the literature, KBSN-xTa₂O₅ (x = 0.0, 1.0, 2.0, 4.0 and 8.0 mol%) glass ceramics exhibited the same vibration modes [23]. The Raman peaks in the region below 200 cm⁻¹ (the two deconvoluted peaks marked by dark yellow and green in Figure 1b) were closely related to the vibrations of A-site cations, including K⁺, Ba²⁺, and Sr²⁺ [23]. The Raman peaks in the wavenumber range of 200–1000 cm⁻¹ could be attributed to the internal mode of the BO₆ octahedron, including Nb⁵⁺ and Ta⁵⁺. The peaks around 250 cm⁻¹ (the deconvoluted peak marked in blue in Figure 1b) were attributed to the bending vibration of O-B-O bonds, while the peaks around 630 cm⁻¹ (the two deconvoluted peaks marked in cyan and magenta in Figure 1b) and 840 cm⁻¹ (the deconvoluted peak marked by yellow in Figure 1b) were associated with the stretching vibrations of B-O bonds [14,22,24]. As shown in Figure 1b, the Raman peaks of B-bonds became weaker in intensity and wider in shape with increasing Ta₂O₅ content, which indicated the weakening of Nb-O and O-Nb-O bonds; additionally, the disorder of B-site increased and the polarity of units decreased, leading to a decrease in the dielectric constant [25,26]. Furthermore, as shown to Figure 1c, the peaks around 200 cm⁻¹ shifted to lower wavenumber values, associated with the displacement of B-site cations, due to the higher atomic mass of Ta compared to Nb [20]. Figure 1d shows the absolute value (ΔFWHM) of the FWHM difference between the two subpeaks in the 600 cm⁻¹ band; it can be clearly observed that the ΔFWHM increased sharply when x ≥ 4.0, which could be attributed to the weakening of one of the peaks and the enhancement of the other. Furthermore, two peaks gradually merged into one peak, indicating a changing structural symmetry. This change may have been related to the change of the space point group from the non-centrosymmetric of P4bm to the centrosymmetric of P4/mbm owing to the transformation of the crystal structure due to Ta substitution.

An element distribution diagram of the KBSN-4.0mol%Ta₂O₅ sample is displayed in Figure 1e. The results show that all the elements were uniformly distributed in the nanograins, indicating that the precipitated crystals were pure KBaSrNb₅O₁₅ ceramic phase with uniform composition, and that Ta⁵⁺ had entered the lattice, replacing Nb⁵⁺ at the B-site. In addition, the grains were not purely tetragonal, showing that the substitution of Ta led to a crystallographic transformation, consistent with previous XRD analysis.

Scanning electron microscope (SEM) images of the KBSN-xTa₂O₅ (x = 0.0, 1.0, 2.0, 4.0 and 8.0 mol%) glass ceramics are displayed in Figure 2a–e. Obviously, for all samples, the crystal grains were uniformly embedded in the glass matrix, forming a dense microstructure without obvious pores and crystal grain aggregation. The inset of Figure 2a–e shows the grain size distribution; it is clear that the crystal particles were at the nanoscale in all samples. Furthermore, the grain size became more uniform and smaller after the addition of Ta₂O₅. Notably, when the Ta₂O₅ addition was 4.0 mol%, the average grain size was significantly reduced to 90 nm, i.e., nearly 60% less than that of the sample without the addition of Ta₂O₅. A dense internal structure and small grain size are conducive to a high electric breakdown strength (BDS) [22,27,28,29]; thus, the KBSN-4.0mol%Ta₂O₅ glass ceramics may have had the highest BDS among all samples. The UV-vis absorption spectra of KBSN-xTa₂O₅ glass ceramics and corresponding optical band gaps (E_g) are shown in Figure 2f. Obviously, with an increase of Ta₂O₅ content, the trend of E_g increased first and then decreased; this is the same trend as the average grain size variation observed by SEM. When the addition amount of Ta₂O₅ was 4 mol%, the maximum value of E_g reached 3.205 eV. A wider band gap makes it more difficult for electrons in the valence band to jump into the conduction band, which served to improve the BDS [30].

As we all know, glass ceramics are composed of a glass phase and a ceramic phase. When an electric field is applied, the huge relative permittivity gap between the glass and ceramic phases induces an inhomogeneous distribution of the electric field, resulting in charge aggregation, thus triggering dielectric breakdown, which is the interfacial polarization phenomenon of glass ceramics [31,32]. The activation energy (E_a) calculated from the complex impedance spectrum can be used to analyze the charge migration, illustrating the intrinsic relationship between interfacial polarization and BDS [33,34]. E_a can be obtained from the Arrhenius formula:

$$ln\tau ={\displaystyle \frac{E_a}{k_{B}T}}+ln{\tau }_0$$

(1)

where T, k_B, τ, and τ₀ represent absolute temperature, the Boltzmann constant, the relaxation time, and the pre-exponential factor, respectively [35,36,37], and τ is related to the frequency of the impedance and can be calculated using the following equation:

$$\tau ={\displaystyle \frac{1}{2\pi f_{max}}}$$

(2)

where f_max represents the frequency of the crest value of the imaginary part of impedance (−Z″) [38]. Figure 3a–e shows −Z″ as a function of frequency at various test temperatures for KBSN-x Ta₂O₅ (x = 0.0, 1.0, 2.0, 4.0 and 8.0 mol%) glass ceramics. For all samples, only one peak could be observed for each test temperature, and the crest value decreased with the increase of the test temperature, indicating a rise in conductivity [24]. In addition, it should be noted that the peak shifted to a high frequency with the increase of the test temperature, resulting in changes in the value of τ. According to Formula (1), the E_a of the relaxation process can be calculated by a linear function of lnτ with 1/T, as displayed in Figure 3f. Commonly, E_a reflects the space charge mobility at the interface [39]; a smaller E_a indicates higher space charge mobility and less likelihood of local agglomeration, which leads to a higher BDS [31,34]. As the Ta₂O₅ content increases, E_a first decreased and then increased. In particular, E_a reached a minimum value of 1.47 eV when the Ta₂O₅ content was 4.0 mol%; this was related to the small grain size observed via SEM. Owing to the fact that a smaller grain size leads to a smaller relative permittivity, the difference in relative permittivity between the glass and ceramic phases was smaller, resulting in higher charge mobility, less susceptibility to local agglomeration, more uniform electric field distribution, and less susceptibility to dielectric breakdown. Therefore, it can be considered that the KBSN-4.0mol%Ta₂O₅ glass ceramics exhibited the highest BDS, which is consistent with the former analysis, as shown in Figure 4a.

Figure 5a–e shows the temperature dependent spectrum of the dielectric constant and loss for the KBSN-xTa₂O₅ (x = 0.0, 1.0, 2.0, 4.0 and 8.0 mol%) glass ceramic at various frequencies. For all samples, a unique dielectric peak could be observed with varying degrees of frequency dispersion. ΔT_m (the difference of T_m between 1 MHz and 100 Hz) was then introduced to characterize the degree of frequency dispersion; the variations of ΔT_m with x are shown in Figure 5f. As shown in Figure 5f, a large ΔT_m of KBSN-xTa₂O₅ (x = 0.0, 1.0 and 2.0 mol%) indicated strong frequency dispersion over a wide temperature range, revealing the typical relaxor ferroelectric features of these samples [40,41]. Interestingly, when the addition of Ta₂O₅ was greater than 2.0 mol%, ΔT_m decreased sharply, indicating that the dielectric frequency dispersion had been substantially weakened, as shown in Figure 5d,e. This allowed us to predict the phase transition from relaxor ferroelectric to paraelectric; a similar phenomenon appeared in the Sr₂Na(Nb_1−xTa_x)₅O₁₅ ceramics [7]. The above results indicate that the introduction of a certain amount of Ta₂O₅ induced a transition from relaxor ferroelectric to paraelectric in KBSN glass ceramics, which may be beneficial for the energy storage performance. Notably, the dielectric constants of glass ceramics without the addition of other dopants were inconsistent when comparing our previously reported work and this paper, although their ratios, as well as the preparation methods, were the same. We give an explanation for this discrepancy in the Supporting Information.

The unipolar P-E loops of KBSN-xTa₂O₅ (x = 0.0, 1.0, 2.0, 4.0 and 8.0 mol%) glass ceramics at a critical electric field and the corresponding variation of recoverable energy density (W_rec) and efficiency (η) are displayed in Figure 4a and Figure 4b, respectively. Eb improved from 800 kV/cm to 1300 kV/cm as the Ta₂O₅ increased from 0.0 to 4.0 mol%, which greatly contributed to obtaining high energy storage density, as illustrated in the equation of $W_{rec}={\int }_{P_r}^{P_m}EdP$, where P_r is the residual polarization and P_m is the maximal polarization [3]. The significant increase in E_b could be attributed to the decrease of the interfacial activation energy (E_a) and the increase of the bandgap width (seen Figure 2f and Figure 3f). For the x = 4.0 component sample, the maximum value of W_rec reached about 6.20 J/cm³, i.e., about 1.68 times higher than that of the x = 0.0 component sample (3.69 J/cm³), and also kept a high η of about 82%. The room temperature I-E loops of KBSN-xTa₂O₅ (x = 0.0, 1.0, 2.0, 4.0 and 8.0 mol%) glass ceramics under 400 kV/cm are presented in Figure 4c. For the I-E loops, there was only one broader current peak near 0 kV/cm for components with x = 0.0, 1.0, and 2.0; this was related to the relaxation ferroelectric characteristics of the glass ceramics [42]. With an increase in the Ta₂O₅ content, this current peak disappeared and the shape of the I-E loop approximated a rectangle without spontaneous polarization, indicating a transition from a relaxation ferroelectric to a paraelectric phase, corresponding to an anomalous weakening of the frequency dispersion in the dielectric temperature spectrum.

The performance of the optimized combination of the KBSN-4.0mol%Ta₂O₅ glass ceramics exhibited great superiority in terms of energy storage. Hence, KBSN-4.0mol%Ta₂O₅ glass ceramics were chosen for further investigation. Variations in the I-E and P-E loops as the electric field increased are displayed in Figure 4d,e, and the energy storage density combined with the energy storage efficiency calculated from P-E loops under different electric field strengths are exhibited in Figure 4f. As shown in the Figure 4d, with an increase in the electric field, the current increased but the shape of the I-E loops remained rectangular, without any spontaneous polarization behavior, indicating that the sample remained in a paraelectric state, without phase transition. Furthermore, all P-E loops yielded slim features with large P_m and small P_r, as well as excellent resistance to electric fields, as shown in Figure 4e, all of which are advantageous for achieving high energy storage performance. As expected, W_rec improved considerably from 0.0426 to 6.20 J/cm³, and the efficiency remained high, i.e., >80%. When the electric field reached 1300 kV/cm, excellent energy storage performance was achieved with KBSN-4.0 mol%Ta₂O₅, including a W_rec value of 6.20 J/cm³, as well as efficiency of about 82%.

Generally, a P-E circuit is measured in a quasi-static electric field, so it is impossible to calculate the actual discharge rate and discharge power density of the capacitor [19]. In contrast, the pulse charge–discharge test takes place in an RLC oscillation circuit, applying an electric field to charge the capacitor, and discharging it via a load resistor for a short time after removing the electric field. The pulse charge–discharge performance of the capacitor can be obtained by collecting the current change in this process. Therefore, it is necessary to carry out pulse charge–discharge tests on glass ceramics dielectric capacitors to simulate the operating conditions in practical applications. The discharge energy density (W_d) can be calculated by:

$$W_d=R\int i^2\left(t\right)dt/V$$

(3)

where R is the load resistance (200 Ω), V is the volume of glass ceramic dielectric capacitor, and i(t) is the current in the circuit [43,44]. Figure 6a,b comprises the room temperature overdamped discharge current and energy density (W_d) over time curves for the KBSN-4.0mol%Ta₂O₅ glass ceramic under different electric fields. In particular, a sharp current peak emerged, as shown in Figure 6a, indicating the unique pulsed charge–discharge characteristics of the glass ceramic. With an increase in the electric field, the value of the maximum current and W_d increased sharply, and a value of W_d of about 5.62 J/cm³ was reached at 1300 kV/cm. Typically, t_0.9 is defined as the time required for the release of 90% of the stored energy [45]. It can be seen that a t_0.9 of about 9.7 ns was maintained when the electric field increased to 1300 kV/cm, revealing a superfast discharge rate of the capacitor. The W_d values of other KBSN-xTa₂O₅ glass ceramics with x = 0.0, 1.0, 2.0, and 8.0 mol% can be found in Figure S2 in the Supporting Information for reference. The discharge power density is particularly important in pulsed power supplies. The overdamped instantaneous discharge power density (P_d) is obtained using the following equation:

$$P_d=i^2\left(t\right)R/V$$

(4)

where the meanings of V, R, and i(t) are all described in Equation (3) [46]. The instantaneous discharge power densities over time of the KBSN-4.0mol%Ta₂O₅ glass ceramic are shown in Figure 6c. As expected, P_d was positively correlated with the electric field. The highest P_d was 1296.9 MW/cm³ under a 1300 kV/cm electric field. Commonly, the underdamped discharge behavior is used to determine whether the discharge behavior of the capacitor is linear or not [47]. The underdamped discharge period (T) can be expressed as:

$$T\approx 2\pi \sqrt{LC}$$

(5)

where L is the inductance and C is the capacitance of the sample. In the RLC oscillation circuit, L can be considered as a constant [48]. Therefore, the discharge period (T) is proportional to the root of the square of C. Figure 6d displays the underdamped discharge current curves over time for the KBSN-4.0mol%Ta₂O₅ glass ceramic. Significantly, the discharge period (T) remained constant with an increasing electric field, indicating that the capacitance of the glass ceramics also remained constant, according to Formula (5). Thus, it can be concluded that the KBSN-4.0mol%Ta₂O₅ glass ceramic was linear dielectric.

Furthermore, it was necessary to explore the thermal stability of the charge–discharge performance for dielectric capacitors. Figure 7a–c shows the overdamped discharge current, energy density, and instantaneous power density curves versus time at different measured temperatures of KBSN-4.0mol%Ta₂O₅ glass ceramics under 600 kV/cm. Obviously, all curves show a minor variation with increasing temperature from 20 °C to 120 °C. Figure 7d reveals the maximum values of the discharge current (I_max), energy density (W_d), and power density (P_d) as a function of the measured temperature. As the measured temperature increased from 20 °C to 120 °C, I_max, W_d, and P_d decreased from 18.3 A, 1.385 J/cm³, 322.4 MW/cm³ to 18 A, 1.302 J/cm³, and 293.7 MW/cm³, respectively, representing decreases of about 2%, 9%, and 6%, indicating that the KBSN-4.0mol%Ta₂O₅ glass ceramics possessed favorable thermal stability.

A comparison of the W_d, P_d, and BDS values observed in this work and those from other recently reported research for glass ceramic dielectrics is displayed in Figure 8 [23,31,32,36,46,47,49,50,51,52,53,54]. Significantly, most of the glass ceramic dielectrics had a BDS below 600 kV/cm, resulting in their W_d and P_d being generally lower than 2.0 J/cm³ and 500 MW/cm³. In contrast, the KBSN-Ta glass ceramic in this work simultaneously achieved a W_d of 5.62 J/cm³ and a P_d of 1296.9 MW/cm³ by virtue of its ultra-high BDS of 1300 kV/cm, which is superior to those reported in previous works, revealing it to be a promising candidate glass ceramic dielectric material for high-voltage and high-power capacitors. A comparison of the W_rec in this work and those in ceramic and polymer based dielectrics reported elsewhere is shown in Figure S3 [55,56,57,58,59,60,61,62,63,64,65,66,67,68,69], illustrating that the glass ceramic fabricated by B-site modification engineering is a promising candidate for dielectric energy storage applications.

4. Conclusions

In this work, KBSN-xTa₂O₅ lead-free glass ceramics were designed and fabricated based on B-site engineering to optimize the energy storage properties. The results show that the KBSN-samples simultaneously achieved record-high W_d (5.62 J/cm³) and P_d (1296.9 MW/cm³) at 1300 kV/cm, as well as a super-fast discharge time, i.e., about 9.7 ns. The XRD, element distribution, and Raman analyses revealed that Ta entered the KBaSrNb₅O₁₅ crystal lattice and replaced Nb in B-sites, leading to a change in the cell constant, a decrease in tetragonality, an increase in cation displacement in the BO₆ octahedra, and a distortion of structural symmetry, resulting in a dramatic change in ferroelectricity. The P-E loops shows that the addition of Ta₂O₅ improved the BDS from 800 kV/cm to 1300 kV/cm, and the KBSN-4.0mol%Ta₂O₅ sample exhibited an excellent W_rec of about 6.20 J/cm³ and a favorable energy storage efficiency of about 82%. The SEM, UV-Vis absorbance spectrum, and impedance analyses revealed that the excellent BDS of the KBSN-4.0mol%Ta₂O₅ sample was a result of the reduced grain size, modified band gap, and the decreased interfacial activation energy (E_a). Moreover, the KBSN-4.0mol%Ta₂O₅ sample also presented superior thermal stability in the temperature range of 20 °C to 120 °C. The above results indicate that the KBSN-4.0mol%Ta₂O₅ glass ceramics showed superior, comprehensive performance and have promise for application in high voltage pulse power systems.