Pyrochlore-based high-entropy ceramics for capacitive energy storage

High-performance dielectrics are widely used in high-power systems, electric vehicles, and aerospace, as key materials for capacitor devices. Such application scenarios under these extreme conditions require ultra-high stability and reliability of the dielectrics. Herein, a novel pyrochlore component with high-entropy design of Bi1.5Zn0.75Mg0.25Nb0.75Ta0.75O7 (BZMNT) bulk endows an excellent energy storage performance of Wrec ≈ 2.72 J/cm3 together with an ultra-high energy efficiency of 91% at a significant enhanced electric field Eb of 650 kV/cm. Meanwhile, the temperature coefficient (TCC) of BZMNT (∼ −220 ppm/°C) is also found to be greatly improved compared with that of the pure Bi1.5ZnNb1.5O7 (BZN) (∼ −300 ppm/°C), demonstrating its potential application in temperature-reliable conditions. The high-entropy design results in lattice distortion that contributes to the polarization, while the retardation effect results in a reduction of grain size to submicron scale which enhances the Eb. The high-entropy design provides a new strategy for improving the high energy storage performance of ceramic materials.


Introduction 
The rapid development in electronic and electrical power systems has put forward more demands on electrostatic capacitors including ultrafast charging/discharging speed and long cycling life [1][2][3][4]. Although some progress has been made, further improvements in energy density are still required to achieve the miniaturization of capacitors. [5][6][7]. Recently, the strategy utilizing configurational entropy to modulate material with tailormade properties with wide application has received much attention [8][9][10]. The high-entropy oxide (HEO) follows [21]: (1) stabilization of the solid-solution formation through promoting dissolution limit among various elements; (2) retardation of the grain growth and reduced grain size; (3) strengthened and hardened structure which contributes to the lattice distortion brought by the mismatch of ionic radii; and (4) unpredictable properties brought by mixing various component elements which is called cocktail effect.
Pyrochlore structure with A 2 B 2 O 7 (A 2 B 2 O 6 O') formula contains a larger-sized cation A which usually has a preferred site coordination number of 8, and a smaller cation B with coordination number of 6 which locates in its octahedral site point [22]. Owing to the compositional and structural flexibility, homovalent or heterovalent ions of different sizes can be doped into the structure. Bismuth-based pyrochlore, typically Bi 1.5 ZnNb 1.5 O 7 (also can be written as (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 in the form of A 2 B 2 O 7 ) with moderate dielectric constants (ε r ≈ 180), low dielectric loss (~10 −4 ), and low temperature coefficient of resonance frequency (τ f ), has been comprehensively studied in the field of high-frequency and microwave dielectrics [23]. Moreover, the relative low sintering temperature makes it more compatible with Ag electrodes when taking its application in multilayer ceramic capcitors (MLCC) into account [24]. Over the past few decades, investigations related to BZN concentrated on their fabrication methods, phase structure, tenability, and dielectric properties; however, few efforts were made in exploring their energy storage performance [25][26][27][28].
Herein, by utilizing high-entropy concept, we have successfully synthesized the high-entropy pyrochlorebased bulk ceramics. It was the first time to study their performance in the capacitive energy storage field systematically. The effects of configurational entropy design on structure, microstructure, dielectric properties, and ferroelectric energy storage performance were studied.

Experimental
The Bi 1 5 were used as raw reactants with proper mass ratio. After the ball-milling process, the samples were dried and calcined at 800-850 ℃ for 3 h. Then, the calcined powders were ball milled again and pressed into disks with PVA binder (φ = 12 mm). Finally, the pellets were sintered at temperature range of 1000-1150 ℃.
The crystal structure and lattice parameters of the four samples were characterized by an X-ray diffractometer (XRD, PANalytical). The microstructure images were obtained by scanning electron microscopy (SEM, Zeiss Gemini). Before the SEM observation, the samples were thermally etched at 50 ℃ lower than each sintering temperature for 20 min. For the dielectric measurements, the polished pellets were pasted with high-temperature silver (φ = 4 mm) on both sides, and tested by a temperature chamber and LCR meter system (Novocontrol, Concept 80). The electrical characterization (P-E loop and breakdown strength) was measured by a ferroelectric tester (PK-CPE1701PolyK Tech), the disk samples were polished down to a thickness range of 80-100 μm, and the sputtered Au electrodes were used as electrodes.

Results and discussion
The BZN, BZMN, BZNT, and BZMNT were fabricated via solid-phase method. The configurational entropy can be described as [29]: where R is the gas constant, and the mole fractions of elements present in the cationic and anionic sites can be represented as x i and x j , respectively. The entropy of BZN, BZMN, BZNT, and BZMNT are calculated to be 1.12, 1.30, 1.64, and 1.81, respectively only when considering 25% Mg 2+ ions substituting for Zn 2+ in single A-or B-site. In this case, the firing temperatures of the samples with Mg 2+ and/or Ta 5+ dopants exhibit about 50-100 ℃ higher than bare BZN ceramic. All the samples show relative high density over 98%.
The XRD patterns of bismuth niobium zinc oxide pyrochlore ceramic BZN and its high-entropy derivates are displayed in Fig. 1. Four samples all exhibit pure A 2 B 2 O 7 phase (PDF No. 52-1770, Fd3m) without detectable impurity. The Ta 5+ and Nb 5+ show the same ionic radii of 0.64 Å in the coordination number of 6 in B-site, while the ionic radius of Mg 2+ with 8 coordination (0.89 Å) is smaller than that of the Zn 2+ (0.90 Å), leading to the shrinkage of lattice volume as well as the shift of diffraction peaks to a higher degree. The complete dissolution of both Mg 2+ and Ta 5+ ions and the phase structural stability may be both ascribed to the improved solubility limit introduced by the highentropy design. The single-phase structure is preferred in the formation of a highly disordered and multicomponent material with high-entropy system. Figure 2 displays the SEM images of the four samples. Since the samples all exhibit similar sinterability, it can be clearly observed from the graph that the BZMNT component possesses the most desirable dense microstructure with grains closely adjacent to each other. From the grain size distribution plots inserted into their corresponding graphs, the grain size is reduced from ~3 μm on average to submicron size, which can be illustrated by the retardation effect in grain growth brought by the high-entropy effect. With the increasing designed entropy, the optimum sintering temperature increases for the other three samples, indicating a continuously slowing kinetics in the system [30]. Benefiting from the sluggish diffusion, formation of the crystal structure as well as the crystal fusion, growth, and coarsening are retarded, resulting in a stable structure and reduced grain size of the materials. Figure 3(a) shows the frequency-dependent dielectric properties of the components which were fabricated at their optimized temperatures. For all samples, both the dielectric constants and loss tangent exhibit frequency independent characteristic in a wide measured frequency range from 1 to 10 5 Hz, which can be considered for use in high-frequency application scenarios. Furthermore, all the components show the similar dielectric behavior of ultra-low loss tangent in the order of 10 −4 . Figure  3(b) displays the temperature dependence of dielectric constant and loss tangent of BZMNT ceramic measured ranging from 10 Hz to 1 MHz. The dielectric constant has a minor drop over the experimental temperature range from −100 to 200 ℃. Generally, many factors affect dielectric properties (e.g., the grain size effect [31], sintering conditions [32], dopants [33], etc.). In this case, the higher configurational entropy components show a relative higher dielectric constant, i.e., ε r(BZMN)~ 300 > ε r(BZN)~2 50, and ε r(BZMNT)~2 20 > ε r(BZNT)~1 90, at room temperature and 1 kHz. Considering the difference  in microstructure, the higher dielectric constant may be related to the lattice distortion caused by the introduction of multi-elements. Besides, the dielectric properties of pyrochlore had a strong correlation with their BO 6octahedra structure, where B-site ions played the unneglectable roles (e.g., Ta 5+ ) [34]. Moreover, the dielectric temperature coefficient (τ ε ) of BZMNT ceramic is calculated to be ~ −220 ppm/℃ from −100 to 200 ℃, which is much higher than that of pure BZN ceramic (τ ε = ~ −300 ppm/℃) over this wide temperature range. The highly structural disorder and lattice distortion brought by high-entropy design may affect the permittivity temperature coefficient of BZN materials to a more positive value.
The energy storage properties of the high-entropy components are shown in Fig. 4. It can be seen that all the samples possess slim and linear shape P-E loops measured at 300 kV/cm and 100 Hz ( Fig. 4(a)). Similar ferroelectric behaviors were also proven by other researchers [35,36]. Moreover, the BZMNT ceramic exhibits good frequency stability with negligible polarization and minimal narrowing of the P-E loops under different frequencies, as shown in Fig. 4(b). To further illustrate the energy storage behavior of BZMNT   Fig. 4(c), and the summarized energy storage performance is shown in Fig. 4(d). It can be seen that, the BZMNT is able to undergo a continuously elevated applied field without visible deformation of the P-E curves. The maximum W rec was obtained at 650 kV/cm of 2.72 J/cm 3 with a high efficiency of 91%. Figure 4(e) displays the Weibull distribution of breakdown strength under direct current (i.e., the E b of BZN, BZMN, BZNT, and BZMNT are 460, 530, 590, and 670 kV/cm, respectively). Figure 4(f) shows the negative correlation between the BDS and the statistic average grain size of the four samples. The increase in configurational entropy of the materials leads to a smaller average grain size, which is beneficial to the improvement of the BDS in energy storage field.
To evaluate reliability and stability in harsh conditions, fatigue cycling endurance as well as high-temperature stability study were carried out. Figures 5(a) and 5(b) display stable P-E loops and the corresponding energy storage performance for BZMNT ceramic under a high temperature range from 100 to 200 ℃. BZMNT exhibits a temperature-insensitive behavior that the efficiency can be still maintained at 92%, and the recoverable energy density has a minor loss of 6.7% at 200 ℃.
Likewise, shapes of the P-E hysteresis loop of BZMNT remain the same over the cycling, which can also be perceived from Figs. 5(c) and 5(d). The efficiency maintains 95% without obvious fatigue loss after a cycling number of 10 5 , indicating its superior cycling stability (Fig. 5(c)). Whether the cycling or the temperature stability, the excellent performance of the BZMNT ceramic can be attributed to its intrinsically superior properties inherited from base BZN as well as stable structure introduced by high-entropy design, which is beneficial for its application at high temperature and high reliable scenario.

Conclusions
In this study, bismuth-based pyrochlore ceramic (BZN) and its three derivates with different configurational entropy were synthesized for the first time utilizing the high-entropy concept. The high-entropy component of BZMNT (S = 1.82R) exhibits a moderate dielectric constant (~225) as well as a relatively low loss tangent (~0.0003) at 1 kHz, both of which are beneficial for the enhancement of energy storage properties. The recoverable energy density of 2.72 J/cm 3 and excellent energy efficiency of 91% under an applied electric field of 650 kV/cm are achieved in BZMNT, which is 2 times higher than the origin BZN component. Furthermore, the BZMNT also exhibits superior cycling endurance (no energy density and efficiency loss after 10 5 cycles) as well as temperature-insensitive character (with high energy efficiency of 92% at 200 ℃). All these outcomes demonstrate BZMNT ceramic with high-entropy design a potentially promising dielectric material that can be utilized at high temperatures.