Excellent energy storage performance in Bi_0.5Na_0.5TiO₃ high-entropy relaxor ferroelectrics modified with multiple aliovalent B-site ions

INTRODUCTION

Dielectric capacitors have attracted considerable attention in energy storage applications owing to their ultrahigh power density, rapid charge-discharge capability, and good temperature/frequency stability. Nevertheless, dielectric capacitors exhibit low energy density compared to current energy storage devices such as fuel cells, batteries, and supercapacitors. Consequently, significant efforts have been made to enhance their energy storage density to meet the requirements for device miniaturization and integration^[1-3]. Generally, the energy storage properties of a dielectric material are evaluated by the recoverable energy density (W_rec) and energy storage efficiency (η), both of which can be calculated via the following formulas:^[4]

where W_tol denotes total energy storage density, P_m is maximum polarization, P_r represents remnant polarization, and E is the applied electric field^[4]. Clearly, low P_r, high P_m, and high breakdown strength (E_b) are critical parameters for achieving superior energy storage performance.

Compared with other dielectric categories, relaxor ferroelectrics (RFEs) exhibit superior energy storage potential due to their high P_m, low P_r, and narrow hysteresis^[5]. In recent years, a series of high-performance RFE systems have been developed, such as Bi_0.5Na_0.5TiO₃-based^[6-8] and BaTiO₃-based^[5,9,10] systems. These distinctive properties originate from the presence of polar nanoregions (PNRs)^[11]. The disruption of long-range ferroelectric order via ionic disorder has been established as an effective way to generate PNRs. The high-entropy strategy has been demonstrated to effectively amplify ionic disorder by constructing a single-phase solid solution of multiple elements, thereby enhancing the relaxor feature^[12].

In contrast to the ceramics designed through conventional multi-component approaches, high-entropy ceramics (HECs) have a unique composition and structure^[13,14]. Through the high-entropy effect, HECs extend the solubility limits of constituent elements, establishing a structural foundation for the stable incorporation of multiple elements^[15,16]. The enhanced solubility limits can be explained from a structural perspective. The ordered anion sublattice creates similar surroundings among cation lattice sites, resulting in minimal site disparity and an abundance of quasi-equivalent sites^[17]. These quasi-equivalent sites prevent the aggregation and segregation of elements at the atomic scale^[15], which enhances multi-cation distribution homogeneity and promotes the formation of a single-phase solid solution^[18]. Through high entropy design, the synergistic multi-element interactions optimize electrical properties by enhancing relaxor characteristics and increasing breakdown strength, leading to superior energy storage performance in HECs^[19,20].

Bismuth sodium titanate (Bi_0.5Na_0.5TiO₃, BNT) is recognized as a suitable matrix for HECs owing to its inherent advantages, including ease of synthesis and high polarization^[21]. In our previous work^[22], Zr⁴⁺ ions were introduced into the B-site of the high-entropy matrix (Na_0.2Bi_0.2Ba_0.2Sr_0.2Ca_0.2)TiO₃ (NBBSCT), which significantly enhanced relaxor behavior and achieved a high W_rec of 6.6 J/cm³ with an excellent η of 93% under 550 kV/cm. This demonstrates that enhancing the entropy of NBBSCT through B-site doping effectively optimizes the energy storage performance of the original high entropy structure. To further push the performance boundaries beyond the current limits, a modified high-entropy strategy is required to enhance configurational entropy (ΔS_config), which is defined as follows^[23]:

where R is the gas constant; N, M, and P represent the number of distinct ionic species occupying the A, B, and O sites in the ABO₃ lattice, respectively; and A_i, B_j and O_q denote their molar fractions. The contribution of anions is excluded, with the entropy dominated by cationic disorder. Obviously, the most direct approach to increase ΔS_config is to introduce the diversity of dopant ions. Notably, entropy quantifies the degree of disorder in a thermodynamic system^[17]. The ΔS_config, as a subset of thermodynamic entropy, can be enhanced by increasing ionic disorder, which is achievable not only through ionic diversity but also via ionic mismatch (e.g., radius/valence disparities)^[24]. Consequently, substituting single isovalent ions with multiple aliovalent ions (e.g., Mg²⁺ and Nb⁵⁺) in the NBBSCT matrix can further boost both ΔS_config and ionic disorder, thereby enhancing relaxor characteristics.

Based on the above considerations, aliovalent combination ions (Mg_1/3Nb_2/3)⁴⁺ (MN) were selected to substitute the B site of the high-entropy matrix NBBSCT in this work. The newly designed HECs, (Na_0.2Bi_0.2Ba_0.2Sr_0.2Ca_0.2)[Ti_1-x%(Mg_1/3Nb_2/3)_x%]O₃ with 3 mol% MN, exhibited enhanced relaxor feature with a high W_rec of 7.1 J/cm³ and ultrahigh η of 93% under an electric field of 610 kV/cm. This demonstrates that the high-entropy strategy combined with aliovalent B-site ions regulation is an effective approach to achieving superior energy storage properties in RFEs.

MATERIALS AND METHODS

(Na_0.2Bi_0.2Ba_0.2Sr_0.2Ca_0.2)[Ti_1-x%(Mg_1/3Nb_2/3)_x%]O₃ (x is 0, 1, 2, 3 and 4, abbreviated as NBBSCT-xMN) ceramics were fabricated via conventional solid-state synthesis. The raw materials Na₂CO₃ (99.8%), Bi₂O₃ (99%), BaCO₃ (99%), SrCO₃ (99%), CaCO₃ (99%), TiO₂ (98%), MgO (99.9%), and Nb₂O₅ (99.9%) were precisely weighed according to stoichiometric calculations. The mixed powders were ball milled at 200 rpm for 12 h in anhydrous ethanol using zirconia balls as milling media. After drying, the precursor mixtures were calcined at 950-1,000 °C for 4 h. The calcined powders were ball milled with consistent parameters and subsequently dried. The milled powders were pressed into disks with 7 mm in diameter and 1 mm in thickness, followed by cold isostatic pressing at 300 MPa for 10 min. Finally, the green pellets were heated to 1,200-1,250 °C for 4 h in air.

Phase structure characterization was conducted via X-ray diffraction (XRD, SmartLab-3 kW, Rigaku Ltd., Japan) employing Cu Kα radiation with a scanning range of 10-120° at 0.01° step size. Phase composition and structural parameters were resolved via Rietveld refinement using GSAS software. To further characterize the crystal structure, Raman spectroscopy was conducted using a laser confocal Raman micro spectroscope (LabRAM HR800, Horiba JobinYvo) with 532 nm excitation. The temperature-dependent dielectric properties were measured by a precision impedance analyzer (E4990A, Keysight, Bayan, America) with temperatures ranging from -100 to 400°C at various frequencies. The microstructure of the as-sintered samples was observed via a scanning electron microscope (SEM, Gemini Sigma 300, ZEISS, Germany) operated at 5 kV, with elemental distribution concurrently analyzed by Energy Dispersive Spectroscopy (EDS). Quantitative grain size distribution was statistically analyzed using Nano Measurer software through the intercept method. The breakdown electric field was measured using a voltage breakdown tester (RK2671AM, Meiruike Electronic Technology Co. Ltd, Shenzhen, China) with electric field ramping rates maintained within 100-300 V/s. The impedance spectra were measured by an electrochemical impedance spectrometer (1260AC and 1287AC, UK) in the temperature range of 625-725°C at 0.1 Hz-1 MHz. The P-E loops were characterized using a ferroelectric tester (TF Analyzer 3000, aixACCT, Germany) at 10 Hz. The discharge energy density and speed were evaluated using a capacitor charge-discharge test system (PK-CPR1801-10015, Polyk Technology, USA), employing a load resistance of 10,260 Ω. For dielectric property characterization, the as-sintered pellets were polished down to a thickness of 0.6 mm and uniformly coated with Ag electrodes on both surfaces. In the case of breakdown strength, P-E, and charge-discharge measurements, the samples were polished down to 0.1 mm in thickness and coated with an Ag electrode of 2 mm in diameter. All samples equipped with Ag electrodes were heat-treated at 600 °C for 30 min.

RESULTS AND DISCUSSION

Normally, a material is classified as high entropy material when ΔS_config exceeds 1.5R^[23]. Figure 1A illustrates the evolution of ΔS_config, calculated using Equation (4). The addition of MN dopants increases ΔS_config progressively from 1.61 to 1.80R, confirming all compositions as HECs. The XRD patterns of NBBSCT-xMN ceramics are shown in Figure 1B. All compositions exhibit single-phase perovskite structures without secondary phases, indicating MN is well dissolved within the high-entropy matrix. From the enlarged view of the diffraction peaks, the peak position gradually shifts to lower angles with the increase of MN content, attributed to the substitution of smaller Ti⁴⁺ (0.605 Å, CN = 6) by larger Mg²⁺ (0.72 Å, CN = 6) and Nb⁵⁺ (0.64 Å, CN = 6). Notably, the single-peak profiles of the (200) reflections indicate that the pseudo-cubic phase is the main phase across all compositions^[25]. To further determine the phase structure, Rietveld refinement was performed; the fitting parameters for NBBSCT-xMN ceramics are presented in Figure 1C and Table 1. The refinement parameters for all compositions (R_wp < 7.5%, χ² < 1.3) confirm the fitting reliability. The NBBSCT-xMN ceramics conform to a pure tetragonal phase with the P4bm space group, indicating structural stability upon MN doping. This stabilization may arise from the entropy-driven reduction of Gibbs free energy^[13,15]. The lattice parameters a, b, c, and unit cell volume (V) increase with MN content, attributed to larger ionic radii of Mg²⁺ and Nb⁵⁺ compared to Ti⁴⁺.

Figure 1. (A) Composition-dependent ΔS_config for NBBSCT-xMN ceramics. (B) XRD patterns of NBBSCT-xMN ceramics with an enlarged view of the (200) diffraction peaks. (C) Rietveld refinement results for NBBSCT-3MN ceramics. (D) Raman spectra and fitting results for NBBSCT-xMN ceramics.

To illustrate the local ionic configuration changes, Raman spectra of NBBSCT-xMN ceramics were measured and deconvolved into eight Gaussian-Lorentzian peaks, as shown in Figure 1D. Based on vibrational mode assignments, the spectra are divided into four regions: < 200, 200-400, 400-650, and 650-950 cm^-1, corresponding to A-site cation vibrations, B-site cation vibrations, BO₆ octahedra distortions, and oxygen displacements in BO₆ octahedra, respectively^[20,26,27]. All compositions exhibit broad Raman peaks, reflecting high local structural disorder induced by multi-cation occupation at A and B sites^[28]. Furthermore, the consistent peak positions and line shapes across the NBBSCT-xMN ceramics indicate no significant structural variations, in agreement with the XRD refinement results.

Figure 2A-E displays the microstructure morphology and grain size distributions of all ceramic samples. All NBBSCT-xMN ceramics exhibit dense microstructures with grain sizes ranging from 1.0-2.0 μm. Figure 2F quantifies the average grain size across all compositions. The average grain size decreases progressively from 1.33 μm for NBBSCT-0MN ceramic to 1.00 μm for NBBSCT-2MN ceramic. This grain refinement originates from retarded atomic diffusion during sintering, caused by the increase of ΔS_config^[28]. Notably, NBBSCT-4MN ceramics exhibit abnormal grain growth, resulting from the elevated sintering temperature due to the high melting point of MN. This thermal condition accelerates atomic diffusion, thereby promoting abnormal grain growth^[29]. To evaluate the elemental homogeneity, EDS mapping was performed on the NBBSCT-3MN ceramic, as shown in Figure 3. The constituent elements exhibit a uniform distribution without any detectable segregation. This directly confirms the homogeneous incorporation of dopant ions into the ceramic matrix. Such chemical homogeneity conforms to the characteristics of HECs. The combined effects of refined grain structure and homogeneous element distribution enhance breakdown strength, which lays the foundation for superior energy storage performance^[30].

Figure 2. SEM images of (A) NBBSCT-0MN, (B) NBBSCT-1MN, (C) NBBSCT-2MN, (D) NBBSCT-3MN, and (E) NBBSCT-4MN ceramics. Insets present the corresponding grain size distributions. (F) Average grain size of all compositions.

Figure 3. The EDS elemental mapping of NBBSCT-3MN ceramic.

The temperature-dependent dielectric permittivity (ε_r) and loss (tanδ) of NBBSCT-xMN ceramics are presented in Figure 4A-E. A distinct dielectric peak (labeled T_m) is observed for all compositions, indicating a phase transition from the FE to the paraelectric (PE) phase. Notably, the T_m peak exhibits pronounced frequency dispersion, shifting to higher temperatures with increasing frequency. This behavior is a defining characteristic of the RFEs. Furthermore, as the MN content increases, the T_m peak progressively broadens and shifts toward room temperature, accompanied by a reduction in dielectric maximum (ε_m), as summarized in Figure 4F. This collective evolution of T_m characteristics directly demonstrates diffuse phase transition behavior.

Figure 4. Temperature-dependent ε_r and tanδ for (A) NBBSCT-0MN, (B) NBBSCT-1MN, (C) NBBSCT-2MN, (D) NBBSCT-3MN, and (E) NBBSCT-4MN ceramics. (F) Composition dependence of ε_r at 500 Hz.

The degree of diffuse phase transition is quantified through normalized dielectric permittivity analysis [Figure 5A]. Two characteristic parameters, T_R-L and T_R-H (R = 1/2, 2/3), are defined to quantify the temperature intervals between T_m and T_R (R = ε_r/ε_m) in the low- and high-temperature range^[31,32]. Figure 5B reveals the progressive broadening of both T_R-L and T_R-H, indicating slow phase transition and enhanced phase transition diffuseness. This variation can be attributed to the random occupation of equivalent crystallographic sites by multiple cations, induced by the high-entropy effect^[33,34]. To quantitatively evaluate the relaxor characteristics, the diffuseness parameter (γ) was determined using the modified Curie-Weiss law^[35],

where T_c denotes the Curie-Weiss temperature. The value of γ typically ranges from 1 to 2, where a larger γ indicates enhanced relaxor behavior. Figure 5C presents the fitting lines based on Equation (5), in which high fitting factors are observed. It is interesting that high γ is observed in all ceramics, which increases from 1.73 for NBBSCT-0MN to 1.90 for NBBSCT-4MN ceramics with the increase in MN content, demonstrating a progressive enhancement of relaxor behavior. This conclusion is corroborated by the frequency dispersion (ΔT = T_m (1 MHz)-T_m (1 kHz))^[31], which increases constantly from 39 to 48°C [Figure 5D]. These trends demonstrate that the high-entropy strategy effectively enhances the relaxor feature. The increased ΔS_config via MN doping promotes structural disorder, thereby enhancing relaxor characteristics^[12].

Figure 5. (A) ε_r/ε_m vs. T-T_m for all compositions. (B) Composition dependence of T_R-L and T_R-H (R = 1/2, 2/3). (C) ln(1/ε_r-1/ε_m) vs. ln(T-T_m) at 10 kHz. (D) Composition-dependent γ and ΔT.

The E_b of NBBSCT-xMN ceramics was evaluated using Weibull distribution following the formulations:^[36]

where n represents the total number of tested samples, and E_i denotes the E_b value of the i-th samples sorted in descending order^[36]. Figure 6A displays strong linear correlation between ln(ln(1/(1-(i/(n+1))))) and ln(E_i), confirming the high reliability of the linear fitting. Figure 6B presents the Weibull-fitted E_b, which first increases and then decreases with MN doping. The optimal E_b reaches 610 kV/cm for NBBSCT-3MN ceramics. To elucidate the enhanced E_b, impedance spectra were presented in Figure 6C. The semicircular arcs exhibit a trend of initial expansion followed by contraction, with NBBSCT-3MN ceramic showing the largest arc radius, corresponding to its highest resistivity. According to the Arrhenius law^[26], the relationship between lnf_max and 1,000/T was fitted [Figure 6D], revealing a strong linear correlation. The activation energy (E_a) increases from 1.89 eV for NBBSCT-0MN ceramic to 1.97 eV for NBBSCT-3MN ceramic [Figure 6E]. The increased E_a may originate from suppressed oxygen vacancy mobility^[36]. B-site substitution by larger-radius cations (e.g., Mg²⁺/Nb⁵⁺), together with lattice distortion arising from the high-entropy strategy, collectively increases the energy barrier for oxygen vacancy migration^[37]. However, a high MN content (> 3%) lowers E_a, possibly because Bi and Na volatilize at the elevated sintering temperatures required due to the high melting points of MN. This volatilization increases the concentration of oxygen vacancies, which in turn enhances ionic conductivity but degrades the insulation performance^[26]. Furthermore, NBBSCT-3MN ceramics exhibit the lowest leakage current density among all compositions [Figure 6F], directly corroborating its superior insulation performance. This reduction in leakage current likely originates from the enhanced electrical homogeneity enabled by the high entropy design^[13,16,20]. The synergy between its refined grain structure (1.06 μm) and optimized electrical properties leads to the highest breakdown strength in NBBSCT-3MN ceramics, thereby enhancing energy storage performance.

Figure 6. Electrical properties of NBBSCT-xMN ceramics. (A) Weibull distribution of E_b. (B) Composition dependence of E_b. (C) Complex impedance spectra at 625 °C. (D) Arrhenius lines of lnf_max vs. 1,000/T. (E) Composition dependence of E_a. (F) Leakage current density.

The P-E loops of all samples measured at 400 kV/cm are shown in Figure 7A. As the MN content increases, the delayed polarization saturation becomes progressively pronounced. Meanwhile, P_m decreases slightly from 36.7 to 33.8 μC/cm², while P_r shows a marked reduction from 2.7 to 1.6 μC/cm², favoring W_rec under electric fields. Furthermore, the NBBSCT-xMN ceramics exhibit slim P-E loops with low hysteresis loss, which is characteristic of RFEs. Combined with these characteristics, NBBSCT-3MN ceramics achieve the optimal energy storage performance with W_rec of 7.1 J/cm³ and η of 93% at the highest E_b of 610 kV/cm, as shown in Figure 7B and C. Figure 7D presents the P-E loops of NBBSCT-3MN ceramics under varying electric fields, with the corresponding energy storage parameters quantified in Figure 7E. Obviously, η exhibits electric field insensitivity, maintaining an ultrahigh level (> 90%) across all tested electric fields. Concurrently, the continuous substantial growth in P_m drives a nearly linear enhancement of W_rec with increasing electric field. Figure 7F compares the W_rec and η of NBBSCT-3MN ceramic with other lead-free bulk dielectrics, including BNT^[8,26,38-41], NaNbO₃ (NN)^[36,42-47], AgNbO₃ (AN)^[29,48-54], and BaTiO₃ (BT)^[55-60] -based ceramics. Among these, NBBSCT-3MN ceramic demonstrates superior energy storage performance.

Figure 7. (A) P-E loops of all NBBSCT-xMN compositions under 400 kV/cm. (B) P-E loops measured at respective breakdown electric fields for each composition. (C) Composition-dependent energy storage properties. (D) Electric field dependence of P-E loops and (E) calculated W_rec and η for NBBSCT-3MN ceramics. (F) Comparison of W_rec and η between NBBSCT-3MN ceramic and reported lead-free perovskite bulk ceramics^{[8,26,36,38-47]}.

To evaluate the stability of NBBSCT-3MN ceramics in various operational conditions, the frequency- and temperature-dependent P-E loops were measured under 400 kV/cm. The P-E loops retain slim shapes across 1-200 Hz, with negligible variations in both P_m and P_r, as shown in Figure 8A. Therefore, W_rec exhibits excellent frequency stability, ranging from 4.2 to 4.4 J/cm³ with merely 3% fluctuation, as shown in Figure 8B. The η also maintains a high level remaining above 85%. Similarly, the P-E loops show minor variations but a gradual increase in hysteresis loss from room temperature to 120 °C [Figure 8C]. As a result, the W_rec and η exhibit temperature-induced variations below 10% and 20%, respectively, which confirms good thermal stability [Figure 8D].

Figure 8. Operational stability of NBBSCT-3MN ceramics. (A) Frequency dependence of P-E loops and (B) the corresponding W_rec and η. (C) Temperature dependence of P-E loops and (D) the corresponding W_rec and η.

The charge-discharge performance serves as a critical metric for evaluating dielectric capacitors in practical applications. Figure 9A and B presents the discharge energy density (W_dis) and the discharge time (t_0.9, defined as the time to release 90% of stored energy). W_dis increases rapidly and saturates within t_0.9 less than 11 μs. Specifically, W_dis increases linearly from 1.0 to 6.9 J/cm³ with varying electric fields, showing excellent consistency with the calculated W_rec derived from the P-E measurement. Figure 9C and D shows the temperature-dependent charge-discharge performance from room temperature to 120 °C. W_dis reaches a plateau with a short t_0.9 in less than 10 μs across the entire temperature range. The temperature-induced variation in W_dis remains below 10%, demonstrating exceptional thermal stability. These combined merits establish NBBSCT-3MN ceramic as a promising candidate for energy storage applications.

Figure 9. Charge-discharge performance of NBBSCT-3MN ceramics. (A) Time dependence of W_dis under varying electric fields, and (B) field-dependent W_dis and t_0.9. (C) Time dependence of W_dis at various temperatures, and (D) temperature-dependent W_dis and t_0.9.

CONCLUSIONS

Herein, by introducing aliovalent ions (Mg_1/3Nb_2/3)⁴⁺ into NBBSCT, a series of new high-entropy relaxor ferroelectric ceramics with compositions of (Na_0.2Bi_0.2Ba_0.2Sr_0.2Ca_0.2)[Ti_1-x%(Mg_1/3Nb_2/3)_x%]O₃ were successfully prepared. The phase structure maintained stability as the MN content increased, where ΔS_config increased from 1.61 to 1.80R, resulting in enhanced frequency dispersion and diffuse phase transition. The NBBSCT-3MN ceramics exhibited a high W_rec of 7.1 J/cm³ and superior η of 93% at 610 kV/cm. Additionally, they exhibited excellent frequency stability in W_rec, showing less than 3% variation from 1 Hz to 200 Hz, while maintaining temperature stability with less than 10% variation from room temperature to 120 °C. Meanwhile, the ceramics delivered a rapid t_0.9 of 11 μs and a high W_dis reaching 6.9 J/cm³. The excellent energy storage properties demonstrate that NBBSCT-3MN high entropy ceramics have great potential for energy storage capacitor applications.