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High energy storage properties of (Nb $_{0.5}$ La $_{0.5}$ ) $^{4 +}$ complex-ion modified (Ba $_{0.85}$ Ca $_{0.15}$ )(Zr $_{0.10}$ Ti $_{0.90}$ )O₃ ceramics

Key Laboratory for Macromolecular Science of Shaanxi Province, Shaanxi Key Laboratory for Advanced Energy Devices, Shaanxi Engineering Laboratory for Advanced Energy Technology, School of Materials Science and Engineering, Shaanxi Normal University, Xi’an 710062, Shaanxi, P. R. China

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Santan Dang

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Zhanhui Peng

https://orcid.org/0000-0003-1000-258X

E-mail Address: pzh@snnu.edu.cn

Corresponding author.

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Bi Chen

School of Chemistry and Chemical Engineering, Yulin University, Yulin 719000, Shaanxi, P. R. China

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Yibing Zhang

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Di Wu

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Pengfei Liang

School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, Shaanxi, P. R. China

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Lingling Wei

School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi’an 710062, Shaanxi, P. R. China

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Xiaolian Chao

https://orcid.org/0000-0003-2957-1192

E-mail Address: chaoxl@snnu.edu.cn

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, and

Zupei Yang

https://orcid.org/0000-0001-5096-2134

E-mail Address: yangzp@snnu.edu.cn

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https://doi.org/10.1142/S2010135X24400101Cited by:4 (Source: Crossref)

This article is part of the issue:

Special Issue on Applications of Ferroelectric Materials in Environment and Energy Fields
Guest Editors: Yanmin Jia (Shaanxi Normal University), Hong Liu (Sichuan University, China) and Yu Chen (Chengdu University, China)

Abstract

In this work, a traditional solid-state method was adopted to prepare dense Ba $_{0.85}$ Ca $_{0.15}$ [(Zr $_{0.1}$ Ti $_{0.9}$ ) $_{1 - x}$ –(Nb $_{0.5}$ La $_{0.5}$ )_x]O₃(BCZT–xNL) lead-free relaxation ferroelectrics with excellent energy storage performance (ESP). Remarkably, a large breakdown field strength of BDS ( $\sim 410$ kV/cm) resulting from decreased grain size by double ions doping at the B-site was achieved in BCZT–xNL ceramics. Especially, the BCZT–0.12NL ceramic displays a good recoverable energy density ( $W_{rec}$ ) of 3.1J/cm³, a high efficiency of 86.7% ( $η$ ) and a superior fatigue resistance, as well as a superior charge–discharge performance ( $C_{D} \sim 1623.14$ A/cm², $P_{D} \sim 162.31$ MW/cm³, $W_{D} \sim 1.30$ J/cm³, $t_{0.9} \sim 49.6$ ns) and good thermal stability. Besides, upon NL doping, the FE to RFE phase transition results in a dielectric behavior traversing the relaxation phase ( $γ \sim 1.84$ ) accompanied by frequency dispersion, which is beneficial to improve ESP. The superior ESP in this work indicates that BCZT–0.12NL ceramics are a promising candidate used in energy storage capacitors.

Keywords:

1. Introduction

The electronics industry and new-generation information industry technologies such as artificial intelligence, the Internet of Things, and 5G are rapidly developing and spreading. The modernization of information science is driving the rapid development of energy storage materials such as batteries and dielectric capacitors toward higher power density and larger energy storage density.^1,2 Due to its advantages of high energy storage density, large power density, extremely fast energy storage speed and miniaturization, environmental protection dielectric ceramic capacitors have attracted extensive attention in pulse power weapons, wind variable propeller system, spacecraft and other high power pulse power systems.^3,4,5 Therefore, the development of dielectric ceramic capacitors with excellent energy storage density and efficiency is imminent. It is widely recognized that the evaluation of energy storage performance (ESP) can be achieved by measuring the hysteresis loops of polarization–electric field (P–E), which can be calculated as follows^6,7:

W tot = \int P m P r E d P, <math display="block" altimg="eq-00030.gif"><msub><mrow><mi>W</mi></mrow><mrow><mstyle><mtext mathvariant="normal">tot</mtext></mstyle></mrow></msub><mo>=</mo><msubsup><mrow><mo>\int</mo></mrow><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>r</mi></mrow></msub></mrow><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>m</mi></mrow></msub></mrow></msubsup><mi>E</mi><mi>d</mi><mi>P</mi><mo>,</mo></math> (1)

W rec = \int P m P r E d P, <math display="block" altimg="eq-00031.gif"><msub><mrow><mi>W</mi></mrow><mrow><mstyle><mtext mathvariant="normal">rec</mtext></mstyle></mrow></msub><mo>=</mo><msubsup><mrow><mo>\int</mo></mrow><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>r</mi></mrow></msub></mrow><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>m</mi></mrow></msub></mrow></msubsup><mi>E</mi><mi>d</mi><mi>P</mi><mo>,</mo></math> (2)

η=WrecWtot×100%,<math display="block" altimg="eq-00032.gif"><mi>η</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>W</mi></mrow><mrow><mstyle><mtext mathvariant="normal">rec</mtext></mstyle></mrow></msub></mrow><mrow><msub><mrow><mi>W</mi></mrow><mrow><mstyle><mtext mathvariant="normal">tot</mtext></mstyle></mrow></msub></mrow></mfrac><mo>×</mo><mn>1</mn><mn>0</mn><mn>0</mn><mi>%</mi><mo>,</mo></math>(3)

where the maximum polarization intensity (

$P_{m}$ ), remnant polarization (

$P_{r}$ ) and electric field intensity (E) directly determine the value of

$W_{rec}$ . However, there is a contradiction between achieving large

$Δ P$ (

$P_{m} - P_{r}$ ) and large breakdown field strength (BDS).^8,9,10 Therefore, it’s necessary to get a balance between

$Δ P$ and BDS to optimize the ESP of dielectric ceramics.¹¹ Relaxor ferroelectrics (RFEs) own large

$P_{m}$ and small

$P_{r}$ accompanied with moderate BDS. It has been shown that the BDS of RFEs can be effectively increased by optimizing the doping strategy of the component design.^12,13,14 Recently, researches of the ESP of BCZT-based ceramics have been widely concerned.^10,15,16,17 Zhao et al. successfully constructed a “relaxation ferroelectric” by introducing (Al

$_{0.5}$ Nb

$_{0.5}$ )

$^{4 +}$ at the B site of calcite structure, realizing improved

$W_{rec}$ of 0.70

J/cm³ in BNBT–xAN ceramics and 1.41

J/cm³ in BNKT–xAN ceramics.^18,19 Zhou et al. introduced the (Ni

$_{1 ∕ 3}$ Nb

$_{2 ∕ 3}$ )

$^{4 +}$ with large ionic radius into BCZT and controlled the grain size to submicron scale to increase BDS.²⁰ Chu et al. reported that Nb₂O₅ as a good firing aid can promote domain wall movement, reduce porosity and increase ceramic densities.²¹ Kumar et al. investigated Nb₂O₅-doped Bi

$_{0.5}$ (Na

$_{0.5}$ K

$_{0.5}$ )

$_{0.5}$ TiO₃ ceramics and reported that the ceramic with 0.4%Nb exhibits relaxation behavior with respect to the degree of diffusivity of the phase transition.²² Similarly, the strong relaxation behavior was observed in the Ba

$_{0.90}$ Ca

$_{0.10}$ Zr

$_{0.10}$ Ti

$_{0.90}$ O₃ system (

$γ \sim 1.85$ ).²³ Further, compared to single-ion doping, double-ion substitution is more likely to achieve high

$W_{rec}$ and

$η$ at low to medium field strengths. The local random field induced by charge and ion radius imbalance breaks the remotely ordered ferroelectric state to produce PNRs, which makes it easier to construct relaxing ferroelectrics. Under the action of electric field, nanodomains are more likely to invert than micro-domains, which leads to a decrease in

$P_{r}$ and an increase in

$η$ . Therefore, the construction of RFEs by B-site double ion substitution is a feasible and effective strategy to improve the ESP of BCZT-based ceramic.

In this work, a new RFE Ba $_{0.85}$ Ca $_{0.15}$ [(Zr $_{0.1}$ Ti $_{0.9}$ ) $_{(1 - x)}$ –(Nb $_{0.5}$ La $_{0.5}$ )_x]O₃(BCZT-xNL) was successfully prepared by the traditional solid-state preparation method. The double ion (Nb $_{0.5}$ La $_{0.5}$ ) $^{4 +}$ replaces the (Zr $_{0.10}$ Ti $_{0.90}$ ) $^{4 +}$ ion with oxygen and cation vacancies to compensate for the charge balance. Charge compensation makes BCZT ceramics able to withstand larger external electric fields without being broken down.^19,24 As shown in Fig. 1, the introduction of large radius ions inhibits the growth of grains, decreases the size of grains and increases the number of grain boundaries, which helps to improve the BDS of BCZT and thus improve the electrostatic properties of ceramics. The experimental results show that BCZT–0.12NL ceramics have large breakdown field strength ( $\sim 410$ kV/cm), good energy storage density ( $\sim 3.1$ J/cm³) and efficiency ( $\sim 86.7$ %). Consequently, NL doping is a new strategy to improve the ESP of BCZT ceramics.

Fig. 1. Strategy of BCZT to obtain high ESP.

2. Experimental Procedures

Ba $_{0.85}$ Ca $_{0.15}$ [(Zr $_{0.1}$ Ti $_{0.9}$ ) $_{1 - x}$ –(Nb $_{0.5}$ La $_{0.5}$ )_x]O₃ ( $x = 0.0$ , 0.025, 0.06, 0.09, 0.12, 0.15) ceramics were prepared using the traditional solid-state method. Reagent grade raw materials of BaCO₃ (99%), CaCO₃ (99.99%), ZrO₂ (99.99%), TiO₂ (99.99%), Nb₂O₅ (99.99%) and La₂O₃ (99.5%) with an accurate stoichiometric ratio were mixed by ball milling for 24h in anhydrous ethanol. After drying, the mixtures were pre-sintered for 2h at $120 0^{\circ}$ C. Next, the powder added with PVA was ground for 2h and pressed into a 10mm disks at 6MPa, then the cold isostatic pressing technology was used to hold the pressure at 220MPa for 5min. Finally, the disks were sintered at 1400– $145 0^{\circ}$ C for 4h in air to obtain BCZT–xNL ceramics. The manufactured round flake ceramic samples were ground, polished, and tested after being electrodeposited. The specification of the samples for dielectric test is 8mm in diameter, 0.6mm in thickness, and the upper and lower surfaces are coated with electrodes; the specification of the samples for ferroelectric test is 8mm in diameter, 0.15mm in thickness, and the electrode area is 0.0314cm².

The crystal structure of ceramic samples was characterized by X-ray diffractometer (MiniFlex 600, Rigaku, Japan) with Cu $K_{α 1}$ radiation ( $λ = 1.540562$ Å) in a $2 θ$ range of 20– $8 0^{\circ}$ . The surface micromorphology of ceramics was observed by cold field emission scanning electron microscope (SU-8020). The dielectric properties’ temperature dependence was tested by Dielectric/Impedance spectrometer (TH2827A, Tonghui, TZDM-200-300) in the frequency range from 1kHz to 200kHz. Impedance spectra were obtained by high temperature dielectric impedance measurements (DMS-2000, BALAB). The P–E loops were measured via a ferroelectric analyzer (Model11610E, Radiant, America). The charge–discharge performances of BCZT–xNL ceramics were characterized via a pulse charge–discharge instrument (CFD-001, Shanghai Tongguo Intelligent Technology Co. Ltd., China).

3. Results and Analyses

Figure 2 illustrates the XRD patterns of BCZT–xNL ( $x = 0.0$ , 0.025, 0.06, 0.09, 0.12, 0.15) ceramics in a $2 θ$ range of 20– $8 0^{\circ}$ . The XRD patterns exhibit a single perovskite phase without secondary phase formation, indicating that (Nb $_{0.5}$ La $_{0.5}$ ) $^{4 +}$ entirely diffuses into BCZT lattice and forms a stable solid solution.²⁵ With the increase of (Nb $_{0.5}$ La $_{0.5}$ ) $^{4 +}$ content, the positions of (200) peaks shift slightly toward lower angles. This indicates a distortion of the lattice, which may be attributed to the larger ionic radius of (Nb $_{0.5}$ La $_{0.5}$ ) $^{4 +}$ with 6-coordination (0.835Å), compared to (Zr $_{0.10}$ Ti $_{0.90}$ ) $^{4 +}$ (0.692Å).²⁶ To further investigate the crystal structure of ceramics, XRD data of BCZT–xNL ( $x = 0$ , 0.12) ceramics were refined by GSAS (General Structure Analysis System) software, and the data are presented in Table 1. Pure BCZT ceramic has the coexistence of rhombohedral (R) and tetragonal phases (T) for MPB composition near room temperature.²⁷ As shown in Fig. 2(c), pure BCZT ceramics show the structure of Rhombohedral ( $R 3 m$ ) and Tetragonal ( $P 4$ mm), with the weighing fraction accounting for 69.50% and 30.50%. With the introduction of (Nb $_{0.5}$ La $_{0.5}$ ) $^{4 +}$ , when $x = 0.12$ , the phase structure of the ceramic sample becomes a pseudo-cubic phase, as shown in Fig. 2(d). Finally, according to the finishing results, the relative densities of components $x = 0$ and 0.12 are calculated, and the calculation results are shown in Table 1. The calculation formula is as follows :

ρb=m1m1−m2(ρ0−ρl)+ρl,<math display="block" altimg="eq-00138.gif"><msub><mrow><mi>ρ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo stretchy="false">(</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>l</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>,</mo></math>(4)

where

$ρ_{l}$ is the density of air (0.0012

g/cm³),

$m_{1}$ is the mass of the sample in air,

$m_{2}$ is the wet weight of the sample in distilled water, the

$ρ_{0}$ is the density of distilled water at the test temperature. The theoretical density (

$ρ_{th}$ ) of ceramic samples is calculated as follows :

ρth=Z⋅MV⋅NA,<math display="block" altimg="eq-00145.gif"><msub><mrow><mi>ρ</mi></mrow><mrow><mstyle><mtext mathvariant="normal">th</mtext></mstyle></mrow></msub><mo>=</mo><mfrac><mrow><mi>Z</mi><mo>⋅</mo><mi>M</mi></mrow><mrow><mi>V</mi><mo>⋅</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>A</mi></mrow></msub></mrow></mfrac><mo>,</mo></math>(5)

where M is the molar mass of the compound; V is the cell volume of the compound; Z is the number of molecules in the unit cell;

$N_{A}$ is Avogadro’s constant. According to the bulk density (

$ρ_{b})$ and theoretical density (

$ρ_{th}$ ) of the ceramic sample, its relative density (

$ρ_{r})$ can be calculated :

ρr=ρbρth×100%.<math display="block" altimg="eq-00150.gif"><msub><mrow><mi>ρ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mstyle><mtext mathvariant="normal">th</mtext></mstyle></mrow></msub></mrow></mfrac><mo>×</mo><mn>1</mn><mn>0</mn><mn>0</mn><mi>%</mi><mo>.</mo></math>(6)

Figure 3 displays the SEM micrographs of NL co-doped BCZT ceramic samples after thermal corrosion recorded. The grain of all ceramic samples was dense and homogeneous micromorphology. Large densities are a key factor in obtaining high breakdown field strengths in ceramics, and large pores and many cracks lead to large leakage currents and thus low breakdown field strengths. Cold isostatic pressure technology can make ceramic samples in all directions by 220

Mpa uniform pressure. The sintering, before the use of physical pressure to tighten the ceramic powder particles, can effectively reduce the sintering of large pores that cannot be a discharged phenomenon, thus greatly reducing the pores and cracks. Relative density can reflect the porosity and compactness inside the ceramic. The closer the relative density is to 1, the lower the porosity and the better the compactness. According to Table 1, BCZT–0.12NL has the best densification. Besides, the grain size distribution is recorded by Nano Measurer software, as shown in Figs. 3(a)–3(f). Compared with pure BCZT (

$\sim 22.95 μ$ m), the grain size of doped ceramic sample is significantly reduced, which is caused by the large ionic radius of the (Nb

$_{0.5}$ La

$_{0.5}$ )

$^{4 +}$ B-site complex-ion.^15,16,28 The low diffusivity of La

$^{3 +}$ as a rare earth ion retards the mass transfer of particles during ceramic sintering.^29,30 The reduced grain size and high density would contribute to the enhanced dielectric breakdown field strength, which is a key factor benefiting the high ESP. The results of the Weibull distribution show the change tendency of BDS, as Fig. 3(g). Weibull plots, which need eight sets of sample breakdown data are used to interpret BDS data.^31,32 the average value of BDS can be expressed by the following formula^19,33:

X i = ln (E i), <math display="block" altimg="eq-00157.gif"><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mo>ln</mo><mo stretchy="false">(</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>,</mo></math> (7)

Yi=ln(−ln(1−i1+n)).<math display="block" altimg="eq-00158.gif"><msub><mrow><mi>Y</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mo>ln</mo><mfenced separators="" open="(" close=")"><mrow><mo>−</mo><mo>ln</mo><mfenced separators="" open="(" close=")"><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><mi>i</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>n</mi></mrow></mfrac></mrow></mfenced></mrow></mfenced><mo>.</mo></math>(8)

where

$X_{i}$ and

$Y_{i}$ correspond to the x- and y-axes of the Weibull distribution,

$E_{i}$ is BDS of each specific at the ith time, i is the rank of specimens, and n is the sum of specimens. The average BDS determined by the fitting lines increases with the (Nb

$_{0.5}$ La

$_{0.5}$ )

$^{4 +}$ addition. This may be due to the complex-ion substitution in B-site, which leads to charge imbalance, and oxygen vacancy compensation charge balance, which leads to greater breakdown field strength.^19,20,24 In addition, according to the work of Tunkasiri, the effect of grain size on BDS can be expressed by

$E \propto G^{- α}$ , where E is the field strength, G is the grain size, and

$α$ is a constant.³⁴ As a result, the large compactness, small grains and charge compensation enable the doped BCZT ceramics to obtain a higher breakdown electric field. The results show that BCZT–0.12

NL ceramics have the best density

$ρ_{b}$ up to 5.72

g/cm³, BDS up to 400

kV/cm, and an average grain size of 0.7

$μ$ m.

Fig. 2. (a) XRD patterns of BCZT-xNL ceramics, (b) XRD curves near 38– $4 6^{\circ}$ , (c)–(d) BCZT-xNL ( $x = 0$ , 0.12) refinement results.

Fig. 3. (a)–(f) Scanning electron micrographs of BCZT-xNL ceramics after thermal corrosion, (g) Weibull distribution of BDS of BCZT-xNL ceramics, and (f) bulk density, average grain size and BDS of BCZT-xNL ceramics.

**Table 1. Refinement results of BCZT-xNL ( $x = 0$ , 0.12) ceramic XRD data.**
Sample		$x = 0$			$x = 0.12$
Crystal system	Atoms	Rhombohedral	Tetragonal	Atoms	Cubic
Space group		$R 3 m$	$P 4 m m$		$P m 3 m$
Cell parameters	$a = b$	4.627Å	4.024Å	$a = b = c$	4.0193Å
	c	4.003Å	3.997Å
	$c ∕ a$	0.866	0.993	$c ∕ a$	1
		$α = β = 9 0^{\circ}$ , $γ = 12 0^{\circ}$	$α = β = γ = 9 0^{\circ}$		$α = β = γ = 9 0^{\circ}$
Weigh fraction		69.50%	30.50%		100%
R-factors	$R_{p}$	7.27%		$R_{p}$	6.04%
	$R_{w p}$	9.72%		$R_{w p}$	8.84%
	$χ^{2}$	1.32		$χ^{2}$	1.07
Relative density	93.18%			95.52%

As illustrated in Figs. 4(a)–4(f), the changes of dielectric constant and dielectric loss of BCZT-xNL ceramics with temperature were measured at different frequencies (1, 10, 50, 100 and 200kHz). Pure BCZT ceramics show two obvious phase transition peaks at $3 2^{\circ}$ C and $82 . 5^{\circ}$ C, namely the phase transition from rhombic to tetragonal ( $T_{R - T}$ ) and from tetragonal to cubic ( $T_{C}$ ), as shown in Fig. 4(a).^27,35 The ceramic phase structure is altered by the transformation of two-phase transition peaks into one peak after doping with (Nb $_{0.5}$ La $_{0.5}$ ) $^{4 +}$ . At room temperature, when $x = 0.12$ , the paraelectric structure of the pseudo-cubic phase is observed, which is consistent with the refinement results. With the increase of doping amount, dielectric relaxation behavior with frequency dispersion effect becomes more obvious, which is due to the doping of double ions disrupting the long-range ordered structure inside the BCZT ceramics and forming short-range ordered structure polar nanoregion (PNR).^36,37,38,39 In Fig. 4(a), the dielectric properties of BCZT–xNL ( $x = 0.0$ , 0.025, 0.06, 0.09, 0.12, 0.15) ceramic at 1kHz and −160– $20 0^{\circ}$ C were compared. With the increase of x value, the maximum permittivity dropped sharply, and the dielectric peak widened, $T_{C}$ moved to the low temperature region. Numerous studies have shown that dielectric with medium dielectric constant is beneficial to high energy density.^40,41,42,43 In addition, dielectric loss also decreases with the decrease of doping and is stable over a wider temperature range, which facilitates the reduction of thermal losses and the possibility of thermal breakdowns.^44,45 Diffusion factor $γ$ is an important parameter describing the degree of relaxation of ferroelectric ceramics, which is generally calculated by modified Curie–Weiss law^46,47 :

1ε′−1ε′r=(T−Tm)γC,<math display="block" altimg="eq-00214.gif"><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mi>′</mi></mrow></msup></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>′</mi></mrow></msubsup></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mrow><mo stretchy="false">(</mo><mi>T</mi><mo>−</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mi>γ</mi></mrow></msup></mrow><mrow><mi>C</mi></mrow></mfrac><mo>,</mo></math>(9)

where C represents the modified Curius coefficient,

$γ$ is the diffusion factor, taking a value between 1 and 2, the closer to 2 the stronger the relaxation. Figure 5(b) shows the

$γ$ value obtained from the calculation of the permittivity at 1

kHz. With the addition of the doping, the

$γ$ factor increases and remains above 1.8. It can be seen that the appropriate addition of (Nb

$_{0.5}$ La

$_{0.5}$ )

$^{4 +}$ B-site complex-ion can effectively lead to the generation of PNRs, which can increase the relaxation and ESP.^15,48,49

Fig. 4. (a)–(f) Temperature dependence of the dielectric constant and dielectric loss for BCZT-xNL ceramics with $x = (a)$ 0, (b) 0.025, (c) 0.06, (d) 0.09, (e) 0.12, (f) 0.15.

Fig. 5. (a) Temperature dependence of the dielectric constant and dielectric loss for BCZT-xNL ceramics at 1kHz, (b) $ln (1 ∕ ε_{r} - 1 ∕ ε_{m})$ versus $ln (T - T_{m})$ for BCZT-xNL ( $x = 0$ , 0.025, 0.06, 0.09, 0.12) ceramics.

The microstructure of polycrystalline dielectric ceramics has a significant influence on their electrical properties.^50,51 Complex impedance analysis (CIA) is a major means to study the internal electrical properties of ceramics. Figure 6 shows the Nyquist plots as well as the fitted curves for the BCZT–xNL ceramics. The semicircular arcs of all samples decrease with increasing temperature, which indicates a decrease in resistivity.^9,52 The complex impedance profile of ideal polycrystalline ceramics shows three semicircular arcs⁵³ and only the high-frequency section arcs contributed by the grains and the low-frequency section arcs contributed by the grain boundaries when the frequency range of the test is not sufficiently low, as shown in Figs. 6(a) and 6(b). In order to obtain the values of $R_{g}$ and $R_{gb}$ , two equivalent circuits consisting of a resistor in parallel with a capacitive phase element (CPE) in series are used to fit. Generally speaking, grain boundaries of ceramics have stronger insulation and capacitance than grains, mainly due to the existence of nonstoichiometric distributed oxygen and dangling bonds on the grain boundaries, which act as charge carrier traps and barrier layers.^54,55 When the (Nb $_{0.5}$ La $_{0.5}$ ) $^{4 +}$ is doped, the two arcs gradually merge into one and grain boundary conduction dominates while containing mixed, ionic and electronic conduction.⁵⁶ BCZT–0.15NL ceramics show arcs at low frequencies, which can be caused by ionic spatial polarization and oxygen vacancies being blocked at the electrodes.^57,58 The grain resistance ( $R_{g}$ ) and grain boundary resistance ( $R_{gb}$ ) were obtained by fitting the data for all samples within 440– $50 0^{\circ}$ C using Z-View software. In all cases, the fitted data matched well with the test data. The conductivity of the BCZT–xNL ceramics is in accordance with the Arrhenius equation⁵⁹ :

σ=σ0exp(−EaKT),<math display="block" altimg="eq-00236.gif"><mi>σ</mi><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>exp</mo><mfenced separators="" open="(" close=")"><mrow><mfrac><mrow><mo>−</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>a</mi></mrow></msub></mrow><mrow><mi>K</mi><mi>T</mi></mrow></mfrac></mrow></mfenced><mo>,</mo></math>(10)

where

$σ_{0}$ is a constant,

$σ$ stands for the conductivity value,

$E_{a}$ is the activation energy, K is the Boltzmann’s constant and T is the Kelvin temperature. Figures 7(a) and 7(b) show the variation curves of grain conductivity and grain boundary conductivity with

$1000 ∕ T$ , respectively. It can be seen that

$E_{g}$ (

$\sim 1.99$

eV) and

$E_{gb}$ (

$\sim 2.96$

eV) are maximum when

$x = 0.12$ . Therefore, the doping of ions leads to grain reduction and increase in grain boundaries. Carriers need to penetrate past the grain boundaries for transport within the ceramic, which leads to an increase in activation energy, which helps increase BDS to some extent.

Fig. 6. BCZT-xNL ceramic Nyquist plot at different temperatures along with the fitting results using (a) $x = 0.00$ , (b) $x = 0.025$ , (c) $x = 0.06$ , (d) $x = 0.09$ , (e) $x = 0.12$ , (f) $x = 0.15$ .

Fig. 7. (a) Grain conductivity and (b) grain boundary conductivity as a function of $1000 ∕ T$ , the variation of the fitted activation energy with x in the inset figure.

Figure 8(a) illustrates the bipolar P–E circuits of BCZT–xNL ceramics at 100Hz, 90kV/cm. It can be seen that, as expected by the design, the P–E curves become elongated with NL doping, and the BCZT–xNL ceramics transform from typical ferroelectrics to relaxation ferroelectrics, which is in agreement with the dielectric results.^10,16 Figure 8(b) shows the unipolar P–E loops of BCZT–xNL ceramic under critical breakdown. It can be preliminarily seen that the P–E loop of BCZT–0.12NL ceramic is thinner and has the largest BDS. The variations of $P_{m}$ , $P_{r}$ and BDS with component of x in BCZT ceramics are shown in Fig. 8(c). As the amount of x increases, the $P_{m}$ and $P_{r}$ continue to decrease, while the BDS continues to increase. The decrease in $P_{r}$ is mainly due to the construction of relaxation ferroelectrics and may also be related to the introduction of NL to produce PNRs. The increase in $P_{r}$ at $x = 0.15$ may be due to the generation of niobium vacancies as a result of over-doping. Niobium vacancies, as negatively charged defects, tend to pair with oxygen vacancies to form defective dipoles, which can be aligned with spontaneous polarization in the presence of an applied electric field.^60,61 The removal of the applied electric field resulted in the formation of high residual polarization in BCZT–0.15NL ceramics. The ESP of ceramics are calculated by Eqs. (2) and (3), and the results are shown in Fig. 8(d). It can be seen that BCZT–0.12NL ceramic has the best ESP, reaching an energy storage density ( $W_{rec}$ ) of $\sim 3.11$ J/cm³, an energy storage efficiency ( $η$ ) of $\sim 86.7 %$ , and a breakdown field strength of $\sim 410$ kV/cm.

Fig. 8. (a) Bipolar P–E loops of BCZT-xNL ceramics at 90kV/cm, (b) unipolar P–E loops of BCZT-xNL ceramics at breakdown field strength, (c) $P_{m}$ , $P_{r}$ , and BDS of BCZT-xNL ceramics, and (d) energy storage density and efficiency computed from the (b) plot.

Considering the practical applications, the frequency stability and anti-fatigue characteristics of ferroelectric properties of BCZT–0.12NL ceramic were investigated at 150kV/cm as shown in Fig. 9. In the range 5–150Hz, the $W_{rec}$ fluctuation is within 11.4%, and the $η$ fluctuation is within 10.8%. Under the $1 0^{5}$ cycles test, the $W_{rec}$ fluctuation is only 3.3%, and the $η$ fluctuation is only 2.7%. Therefore, BCZT–0.12NL ceramics have good frequency stability and excellent anti-fatigue characteristics. It has practical applications value in pulse power systems and high energy storage capacitors.

Fig. 9. (a), (b) Frequency stability of BCZT–0.12NL ceramic ESP, (c), (d) Fatigue stability of BCZT–0.12NL ceramic ESP.

Power density and current density are important evaluation indexes of ceramic capacitors in practical applications. Figure 10 displays the discharge behavior of 100–200kV/cm of BCZT–0.12NL ceramic measured in a DC electric field. The power density ( $C_{D}$ ) and current density ( $P_{D}$ ) of ceramics can be calculated by using the I–t curve under underdamped conditions (load resistance is 0):

CD=ImaxS,<math display="block" altimg="eq-00290.gif"><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mo>max</mo></mrow></msub></mrow><mrow><mi>S</mi></mrow></mfrac><mo>,</mo></math>(11)

PD=EImax2S,<math display="block" altimg="eq-00291.gif"><msub><mrow><mi>P</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>E</mi><msub><mrow><mi>I</mi></mrow><mrow><mo>max</mo></mrow></msub></mrow><mrow><mn>2</mn><mi>S</mi></mrow></mfrac><mo>,</mo></math>(12)

where

$I_{max}$ is the maximum current in the I–t curve, S is the electrode area of the test sample, and E is the field voltage. As illustrated in Fig. 10(a), the current underdamping increases with the electric field increase. Figure 10(b) is calculated from Fig. 10(a). When the external electric field is 200

kV/cm, the

$I_{max}$ (

$\sim 50.97$

A),

$C_{D}$ (

$\sim 1623.14$

A/cm²) and

$P_{D}$ (

$\sim 162.31$

MW/cm³) of BCZT–0.12

NL ceramics reach the maximum value. The high power density indicates that BCZT–0.12

NL ceramics have great application potential in pulsed power systems.

Fig. 10. BCZT–0.12NL ceramic (a) underdamped impulse discharge current profile, (b) corresponding $C_{D}$ and $P_{D}$ .

To better represent the storage capacity of the ceramic, the overdamped (nonzero load) discharge current waveform is shown in Figs. 11(a)–11(c). The discharge energy density ( $W_{D}$ ) of dielectric storage materials is as follows^62,63,64 :

WD=R∫i(t)2dtV,<math display="block" altimg="eq-00308.gif"><msub><mrow><mi>W</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>R</mi><mo>∫</mo><msup><mrow><mi>i</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>t</mi></mrow><mrow><mi>V</mi></mrow></mfrac><mo>,</mo></math>(13)

where R (300

$Ω$ ) is the load resistance, i is the current, t is the discharge time and V is the single volume of the test sample.

$t_{0.9}$ is defined as the time required when

$W_{D}$ reaches 90%, and is generally used to measure the speed of discharge.^65,66,67 Similarly, with the E increases,

$W_{D}$ increases from 0.42

J/cm³ to 1.30

J/cm³, and

$t_{0.9}$ eventually remains at 49.6

ns. Finally, the temperature stability of the overdamped charge–discharge performance of BCZT–0.12NL ceramic (30–

$19 0^{\circ}$ C) was explored, as shown in Figs. 11(d)–11(f). The results show that the

$W_{D}$ and

$t_{0.9}$ of BCZT–0.12NL ceramic overdamping fluctuate moderately in the temperature range of 30–

$19 0^{\circ}$ C with good temperature stability.

Fig. 11. (a)–(c) Overdamped pulse performance for BCZT–0.12NL ceramic, (d)–(f) variable temperature overdamped pulse performance for BCZT–0.12NL ceramic.

4. Conclusions

In this paper, BCZT–xNL ceramics were successfully synthesized by the traditional solid-state method. XRD showed a single pseudo-cubic phase perovskite structure and SEM images showed a compact uniform microstructure. The introduction of the B-site double ion (Nb $_{0.5}$ La $_{0.5}$ ) $^{4 +}$ inhibited the grain growth. The small grain size (0.70 $μ$ m) and more grain boundaries result in a large breakdown field strength ( $BDS \sim 410$ kV/cm). The wide dielectric peak is accompanied by frequency dispersion and strong relaxation behavior ( $γ \sim 1.84$ ). The FE to RFE phase transition leads to low $P_{r}$ , thin hysteresis loop, high energy storage efficiency ( $\sim 86.7 %$ ) and high energy storage density (3.1J/cm³). At the same time, it has good frequency stability and excellent fatigue resistance. In addition, the maximum $C_{D}$ ( $\sim 1623.14$ A/cm²), $P_{D}$ ( $\sim 162.31$ MW/cm³), $W_{D}$ ( $\sim 1.301$ J/cm³) and extremely low discharge speed $t_{0.9}$ ( $\sim 49.6$ ns) are suitable for applications in pulse power capacitors.

Acknowledgment

This work was supported by the National Science Foundation of China (NSFC) (Grant Nos. 52272119 and 52202143). The authors would also like to thank the Natural Science Basic Research Plan in the Shaanxi Province of China (Grant No. 2022JQ338), Young Talent Fund of University Association for Science and Technology in Shaanxi, China (20230415), the Fundamental Research Funds for the Central Universities (Grant No. GK202401009), Key Research and Development Program of Shaanxi Provincial Science and Technology Department (Grant No. 2023-YBGY-162) and the Fundamental Innovation Project in School of Materials Science and Engineering (SNNU).

ORCID

Zhanhui Peng https://orcid.org/0000-0003-1000-258X

Xiaolian Chao https://orcid.org/0000-0003-2957-1192

Zupei Yang https://orcid.org/0000-0001-5096-2134

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Vol. 14, No. 04

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History

Received 18 January 2024

Revised 28 March 2024

Accepted 30 March 2024

Published: 16 May 2024

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This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Abstract

1. Introduction

2. Experimental Procedures

3. Results and Analyses

4. Conclusions

Acknowledgment

ORCID

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