Ceramics with the nominal composition of (1-x)(Bi_0.5Na_0.5)_0.7(Ba_0.3Sr_0.7)_0.3TiO₃-xLa(Mg_2/3Nb_1/3)O₃, hereafter referred to as BNBST-xLMN, were prepared using a conventional solid-state route. The modifier content x was varied from 0 to 0.10 in increments of 0.02. The starting oxides and carbonates, including Nb₂O₅ (99.9%), MgO (99.9%), La₂O₃ (99.9%), BaCO₃ (99.9%), SrCO₃ (99.9%), TiO₂ (98.0%), Na₂CO₃ (99.9%) and Bi₂O₃ (99.9%), were all obtained from a commercial supplier (Sinopharm Chemical Reagent Co. Ltd., Shanghai, China). Each reagent was used in the amount required by the nominal stoichiometry using the purities to correct the batch weights, and the batch was then ball-milled for 24 h in a planetary mill. After drying, the mixtures were calcined at 850 °C for 3 h, milled a second time for 24 h, and granulated with a 5 wt% polyvinyl alcohol solution. The granulated powder was pressed into green disks that were 13 mm in diameter and approximately 1 mm thick under a uniaxial pressure of 120 ± 10 MPa. Binder burnout was performed at 650 °C for 3 h, after which the disks were sintered in air at 1,220-1,240 °C for 2 h.

Phase identification was conducted via X-ray diffraction (XRD; SMARTLAB, Japan) using Cu Kα radiation, and local vibrational features were probed using a Raman spectrometer (in Via, Renishaw, UK). The surface morphologies were examined using scanning electron microscopy (SEM; JSM-6700F, JEOL, Japan). Specimens for transmission electron microscopy (TEM) were cut using a dual-beam focused ion beam workstation (Helios 5 UC, ThermoFisher Scientific, USA). Microstructure and selected-area electron diffraction (SAED) data were recorded using a field-emission TEM (Talos F200X, ThermoFisher Scientific, USA) operated at 200 kV, and the elemental distributions were mapped using the energy-dispersive X-ray spectroscopy detector of the Cs-corrected microscope (Super-X, ThermoFisher Scientific, USA). Atomic-resolution imaging and compositional analysis were performed using double spherical-aberration-corrected scanning TEM (STEM; Spectra 300, ThermoFisher Scientific, USA) with probe- and image-side correctors at 300 kV. Cation positions in the STEM images were refined by two-dimensional Gaussian fitting, and the polarization vectors, magnitudes, and angles were extracted using custom MATLAB routines. Polarization magnitudes above 50 pm were automatically discarded, and all angles were normalized into the 0°-360° range. Ultraviolet-visible (UV-Vis) absorbance spectra were recorded on a UV3600 Plus spectrophotometer (Shimadzu, Japan) using specimens polished to 0.20 mm thickness over a transmission window of 300-700 nm.

The dielectric spectra as a function of temperature were acquired using a precision impedance analyzer (HP4294A, Agilent, USA) between -90 and 400 °C. Complex impedance tests were conducted at 560, 580, 600, 620, and 640 °C using a precision impedance analyzer (HP4294A, Agilent, USA). For ferroelectric testing, the thickness of the specimens was polished to ~100 ± 5 μm and coated with Au to form electrodes with an area of 0.00785 cm². Charge-discharge samples were thinned to the same thickness of ~100 ± 5 μm and printed using a central circular Ag electrode (2 mm in diameter), which was fired at 650 °C for 40 min. The dynamic polarization response was probed by piezoresponse force microscopy (PFM; Jupiter XR, Oxford Instruments, USA) at various fields and relaxation periods. Polarization-electric field (P-E) loops were recorded at 10 Hz on a ferroelectric analyzer (Trek model 609B) wired in the standard Sawyer-Tower configuration, and the frequency-, temperature-, and cycle-dependent loops were collected on a ferroelectric workstation. The temperature-dependent charge-discharge behavior was evaluated using a custom resistor-inductor-capacitor circuit (CFD-003, Tongguo Technology, China) placed inside a temperature-controlled chamber.

Domain evolution in the BNBST-xLMN ceramics was modeled with a phase-field approach in which the local polarization vector P = (P₁, P₂, P₃) describes the domain pattern. The temporal development of P was obtained by solving the time-dependent Ginzburg-Landau equation together with the mechanical and electrical equilibrium conditions for the displacement and electric displacement fields^[49]:

(5) $$ \begin{equation} \begin{aligned} \frac{\partial P_{\mathrm{i}}}{\partial t}=-L \frac{\delta F}{\delta P_{\mathrm{i}}}+E_{\mathrm{i}}^{\text {thermal }} \end{aligned} \end{equation} $$

(6) $$ \begin{equation} \begin{aligned} \frac{\partial}{\partial x_{\mathrm{j}}}\left(\sigma_{\mathrm{ij}}(r, t)\right)=0 \end{aligned} \end{equation} $$

(7) $$ \begin{equation} \begin{aligned} \nabla \cdot \mathrm{D}=\rho_{\mathrm{f}} \end{aligned} \end{equation} $$

In Eq. (5), L is a kinetic coefficient associated with domain-wall mobility and F is the total free energy; σ_ij, ρ_f, r, and t denote the stress tensor, free-charge density, spatial coordinate, and time, respectively. For a bulk system, the total free energy can be calculated using

(8) $$ \begin{equation} \begin{aligned} \begin{array}{l} F&=F_{\text {bulk }}(\boldsymbol{P})+F_{\text {grad }}(\boldsymbol{P})+F_{\text {elastic }}(\boldsymbol{P})+F_{\text {elec }}(\boldsymbol{P}, \boldsymbol{E}) \\ &=\int_{V}\left(f_{\text {bulk }}+f_{\text {grad }}+f_{\text {elastic }}+f_{\text {elec }}\right) d V \end{array} \end{aligned} \end{equation} $$

where the four contributions F_bulk(P), F_grad(P), F_elastic(P) and F_elec(P,E) are the bulk, domain-wall (gradient), elastic, and electrostatic energies, respectively; f_bulk, f_grad, f_elastic, and f_elec are the corresponding densities; and E is the applied static field. The bulk term may be expanded to the sixth order in the polarization:

(9) $$ \begin{equation} \begin{aligned} \begin{array}{l} f_{\text {bulk }}=\alpha_{1}\left(P_{1}^{2}+P_{2}^{2}+P_{3}^{2}\right)+\alpha_{11}\left(P_{1}^{4}+P_{2}^{4}+P_{3}^{4}\right) \\ +\alpha_{12}\left(P_{1}^{2} P_{2}^{2}+P_{1}^{2} P_{3}^{2}+P_{2}^{2} P_{3}^{2}\right)+\alpha_{111}\left(P_{1}^{6}+P_{2}^{6}+P_{3}^{6}\right) \\ +\alpha_{112}\left[P_{1}^{4}\left(P_{2}^{2}+P_{3}^{2}\right)+P_{3}^{4}\left(P_{2}^{2}+P_{1}^{2}\right)+P_{2}^{4}\left(P_{3}^{2}+P_{1}^{2}\right)\right]+\alpha_{123} P_{1}^{2} P_{2}^{2} P_{3}^{2} \end{array} \end{aligned} \end{equation} $$

where α_i, α_ij, and α_ijk are the Landau coefficients. The elastic energy density is f_elastic = 1/2c_ijkl(ε_ij - ε_ij⁰)(ε_kl -ε_kl⁰), where c_ijkl, ε_ij, and ε_ij⁰ are the elastic stiffness, total strain, and eigenstrain, respectively; the eigenstrain is related to the polarization through ε_ij⁰ = Q_ijklP_kP_l where Q_ijkl represents the electrostrictive coefficients. The gradient term f_grad = 1/2G_ijklP_i,jP_k,l involves the gradient coefficients G_ijkl, and the electrostatic contribution is f_elec = -P_i(r)(E_i(r) - 1/2P_i(r)E_iⁱⁿ(r)), where E_i(r) is the applied field and E_iⁱⁿ(r) is the field generated by the dipoles themselves.

The simulations were performed on a 64 × 64 × 64 grid with 1 nm spacing in each direction. The Landau parameters of the (Bi_0.5Na_0.5)_0.7(Ba_0.3Sr_0.7)_0.3TiO₃ host were α₁ = -1.725770 × 10⁸ m²·N/C², α₁₁ = -9.200542 × 10⁷ m⁶·N/C⁴, α₁₂ = 3.213195 × 10⁸ m⁶·N/C⁴, α₁₁₁ = 1.947874 × 10⁸ m¹⁰·N/C⁶, α₁₁₂ = 1.015568 × 10⁹ m¹⁰·N/C⁶, α₁₂₃ = -6.963512 × 10⁹ m¹⁰·N/C⁶, Q₁₁ = 0.070 m⁴/C², Q₁₂ = -0.020 m⁴/C², Q₄₄ = 0.0775 m⁴/C², c₁₁ = 1.746 × 10¹¹ N/m², c₁₂ = 7.937 × 10¹⁰ N/m², and c₄₄ = 1.11 × 10¹¹ N/m². To mimic the experimental conditions, a Gaussian-distributed electric field was superimposed, whose width scales with the entropy-dependent diffusion-doping level. The field has a zero mean and a standard deviation of x MV/cm, where x follows the configurational entropy.

Finite-element modeling (COMSOL) was used to map the spatial distributions of the electric potential and local field and thereby assess the field homogeneity in the ceramics. A rectangular two-dimensional geometry of 12.00 µm × 4.63 µm was built, and the grain-boundary thickness was kept identical in all models so that the effect of grain size could be directly compared. The grain/grain-boundary networks were constructed from the SEM images of the x = 0 and 0.08 samples. Dielectric constants assigned to the grains and boundaries were derived from the average grain size together with the overall permittivity measured at 1 kHz, while the breakdown parameters were taken from the impedance results. An external voltage was applied by fixing the electric potential at the upper edge of the model and grounding the lower edge, with periodic boundary conditions on the lateral sides. The electrostatic equations were then solved to obtain the equilibrium potential and field distributions.

Figure 2A shows the XRD patterns of all samples, collected between 2θ = 20° and 80°. The pure BNBST ceramic shows the (001) and (100) diffraction peaks from 22° to 23° [Figure 2A1]. This indicates that the pure BNBST ceramic is mainly composed of the tetragonal (P4bm) phase. As x increases, the (001) and (100) diffraction peaks merge into a single (100) peak, indicating that BNBST-xLMN ceramics gradually transition to a pseudo-cubic (PC)-phase. Additionally, the (200) diffraction peak simultaneously migrates to smaller angles [Figure 2A2], which is consistent with lattice expansion as the La³⁺ radius (1.36 Å, CN = 12) is close to that of the A-site Bi³⁺ (1.38 Å, CN = 12), whereas the average (Mg_2/3Nb_1/3)³⁺ radius (0.69 Å, CN = 6) exceeds that of the B-site Ti⁴⁺ (0.61 Å, CN = 6)^[50]. Additionally, with increasing x value to 0.10, the tolerance factor (t) exhibits a progressive reduction from 0.9731 to 0.9584, while the configuration entropy (S_config) increases from 1.27 to 1.86 R [Supplementary Figure 1]. In perovskites, the oxygen octahedral tilting is governed by t, which is known to construct polar phases such as the rhombohedral R3c and tetragonal P4bm^[30]. As established in the literature, oxygen octahedra maintain a regular undistorted geometry when t > 0.9850, while tilting occurs as t decreases below this critical value^[51]. To quantitatively analyze the phase fractions and competition behavior induced by LMN modification, XRD Rietveld refinements were carried out on all BNBST-xLMN ceramics. A three-phase model incorporating cubic Pm$$\overline{1}$$m, tetragonal P4bm, and rhombohedral R3c phases was employed for the Rietveld refinement process^[52]. The goodness-of-fit indicators, including the chi-square distribution (Chi²) and R-weighted pattern (R_wp), for the optimal BNBST-0.08LMN ceramic are presented in Figure 2B. All refinement results are statistically valid, as the R_wp values for all samples are consistently below the 10% threshold [Supplementary Figure 2]. The evolution of phase fractions with increasing x value is plotted in Figure 2C, providing clear evidence of complex phase competition in the BNBST-xLMN ceramics. When x = 0.04, the ceramic transforms from medium-entropy to high-entropy, which exhibits the highest Pm$$\overline{3}$$m fraction. When x > 0.04, the Pm$$\overline{1}$$m fraction decreases, and the x = 0.08 ceramic exhibits a relatively higher P4bm fraction with similar Pm$$\overline{1}$$m and R3c fractions.

To gain deeper insight into the local structural changes induced by LMN modification, Raman spectroscopy measurements were performed on all BNBST-xLMN ceramics, and the resulting spectra are presented in Figure 2D. Each Raman spectrum was deconvoluted into eight distinct peaks using Peakfit software, which can be grouped into four characteristic regions based on their corresponding vibrational modes^[53]: (1) the low-frequency region (< 200 cm^-1) containing v1 and v2 modes, which are characteristic of A-site ion translational vibrations; (2) the mid-low frequency region (200-400 cm^-1) comprising v3 and v4 modes, associated with B-O bond stretching vibrations; (3) the mid-high frequency region (400-700 cm^-1) with v5 and v6 modes, corresponding to oxygen octahedral tilting and bending motions; and (4) the high-frequency region (> 700 cm^-1) featuring v7 and v8 modes, arising from the superposition of A1 LO and E LO modes. A gradual red shift of the v3 and v4 modes to lower wavenumbers is observed with increasing x values, providing direct spectroscopic evidence for weakened B-O bond strength and elongated B-O interatomic distances [Figure 2D1]. Additionally, the progressive increase in peak separation between v3 and v4 results in a significantly broadened and flattened spectral profile. This same evolution behavior is observed for the v5 and v6 modes in the mid-high frequency range [Figure 2D2]. The observed spectral broadening and flattening directly result from the elevated S_config in the HE system, which introduces substantial lattice disordering and creates spatially varying local electric fields, thereby destabilizing long-range ferroelectric domains and favoring the formation of polar nanoregions (PNRs).

To clarify the microstructure at the nanoscale, high-resolution TEM (HR-TEM) imaging was performed on the x = 0.08 ceramic along the [111]_c and [110]_c zone axes [Figure 2E and F], and the corresponding SAED patterns are shown in Figure 2G and H, respectively. The [110]_c pattern contains clear 1/2(ooo) superlattice spots that arise from antiphase a^-a^-a^- tilting of the oxygen octahedra (i.e., the R3c phase^[25]), while the 1/2(ooe) superlattice spots from in-phase a⁰a⁰c⁺ tilting (a P4bm signature) appear in Supplementary Figure 3^[54]. The simultaneous observation of both superlattice spots confirms that antiphase and in-phase octahedral tilts coexist, indicating multiphase coexistence. Moreover, geometric phase analysis (GPA) conducted along the [110]_c zone axis [Figure 2I and J] reveals disordered lattice spacing and localized strain, as evidenced by the alternating red and blue color mapping. Therefore, the introduction of LMN increases S_config, enhances lattice distortion, and eliminates the long-range ferroelectric order.

The atomic-scale structure of the x = 0.08 ceramic was examined by aberration-corrected STEM along the [110]_c zone axis, and the high-angle annular dark-field (HAADF) image is shown in Figure 3A. Moreover, the polarization vectors (yellow arrows) were derived from the displacement of B-site cations relative to the surrounding A-site cations. Based on 2D Gaussian peak fitting, displacement vectors pointing along [001]_c were related to the tetragonal phase (T-phase, blue area), those along [111]_c to the rhombohedral phase (R-phase, pink area), and displacements below 4 pm to the PC-phase, yellow area, corresponding to weak polar or nonpolar regions. The spatial angle and displacement magnitude distributions are presented in Figure 3B and C, respectively. The local structure of the x = 0.08 ceramic exhibits the coexistence of R-T-PC tri-phases, wherein the short-range T- and R-phases are randomly dispersed within the long-range PC-phase. This indicates that short-range polar and long-range nonpolar regions coexist, thereby reducing hysteresis losses while maintaining strong local dipole correlations. Notably, diffuse transition regions (purple area) between different phase domains [Figure 3A], which act as low-energy pathways for polarization rotation and significantly reduce polarization anisotropy. Quantitative analysis of the B-site ion displacements [Figure 3D] shows a slight preferential orientation toward the T-phase direction, which correlates well with the phase fraction results obtained from the Rietveld refinement. The average displacement of B-site ions was measured to be 4.69 pm [Figure 3E], which is smaller than that in typical ferroelectric materials, further confirming the weakened long-range polar component. To directly visualize oxygen octahedral tilting, STEM-annular bright-field (ABF) imaging was performed along the [110]_c zone axis [Figure 3F], enabling clear visualization of oxygen atoms and illustrating the octahedral tilt of ABO₃ perovskite. A magnified view of the red-framed area in Figure 3F (shown in the yellow frame) further elucidates this octahedral tilting, with B-site cations located near the oxygen atoms within the yellow-shaded region. These observations, combined with the statistical oxygen octahedral tilt angle analysis in Supplementary Figure 4, demonstrate that the HE strategy induces random oxygen octahedral tilting. This tilting generates local random elastic and electric fields, which effectively pin domain walls and moderate the polarization reorientation dynamics of this system.

To further elucidate the correlation between the dynamic polarization response and local structural features under an applied electric field, PFM testing was conducted on the x = 0 and 0.08 ceramics. The PFM measurement protocol involved applying a negative DC voltage to a 5 µm × 5 µm area using a conductive tip, followed by a positive DC voltage of equal magnitude to the central 2 µm × 2 µm region. Phase images of pure BNBST captured in the out-of-plane mode at various relaxation times are shown in Figure 3G1-G3. When subjected to 30 V, the BNBST ceramic exhibits a nearly 180° polarization reversal; however, a significant fraction of the switched domains remains in their reversed states even after 10 min of relaxation. This demonstrates that the polarization switching is slow and largely irreversible, which relates to the strong hysteresis losses. By contrast, the BNBST-0.08LMN ceramic demonstrates a highly dispersed, punctate polarization switching pattern at 30 V, where most domains swiftly recover their original orientations within 10 min of voltage removal [Figure 3H1-H3]. This fast, reversible switching stems from highly dynamic PNRs with minimized polarization anisotropy, which is consistent with the previous phase-field results and local structural analysis.

The temperature dependence of the dielectric properties was measured at different frequencies for all samples [Figure 4A-F], and the 1 kHz curves are overlaid in Figure 4G for direct comparison. A clear frequency dispersion is observed with increasing x value, accompanied by a downward shift of the temperature of the permittivity maximum (T_m). In particular, a thermal evolution peak (T_s) appears at low temperatures when x ≥ 0.04 and is attributed to the temperature-driven phase transition. This observation demonstrates that the competing phases not only transform due to the introduction of LMN, but also interconvert as the temperature increases. This dynamic phase competition effectively broadens and flattens the dielectric constant peak.

The temperature stability for capacitor applications was evaluated through the TCC, calculated by^[55]

(10) $$ \begin{equation} \begin{aligned} \text { TCC }=\frac{\varepsilon-\varepsilon_{\mathrm{R}}}{\varepsilon_{\mathrm{R}}} \times 100 \% \end{aligned} \end{equation} $$

where ε is the permittivity at the measurement temperature, and ε_R is the permittivity at the reference temperature of 150 °C, which corresponds to the operation temperature for automotive engine-compartment electronics and industrial switching power supplies. All samples satisfy the Electronic Industries Alliance requirement of TCC within ±15% over a certain temperature window [Figure 4H]. The BNBST-0.08LMN ceramic keeps TCC within ±15% from -30.5 to 252.6 °C [Figure 4I], a markedly broader range than that of pure BNBST.

The ferroelectric and energy-storage behavior was characterized through bipolar P-E hysteresis loops [Figure 5A] and the corresponding current-electric field (I-E) curves [Figure 5B]. The pure BNBST ceramic shows a high P_max and a large P_r value because its polarization switching is irreversible, and the associated sluggish response generates pronounced current peaks in the I-E curves. As x increases, the loops become progressively slimmer, P_r markedly decreases, and the current peaks flatten, indicating that the high S_config and dynamic PNRs delay polarization saturation and suppress hysteresis loss. Figure 5C presents the unipolar loops of the BNBST-0.08LMN ceramic under different electric fields. At 450 kV/cm, this ceramic combines a low P_r of 3.20 μC/cm² with a high P_max of 40.43 μC/cm² and strongly reduced hysteresis compared with pure BNBST, owing to the HE strategy and the simultaneous presence of short-range polar and long-range nonpolar regions. Furthermore, E_b values were repeatedly measured, and the measurement reliability was assessed via the Weibull statistical analysis using^[56]:

(11) $$ \begin{equation} \begin{aligned} X_{\mathrm{i}}=\ln \left(E_{\mathrm{i}}\right) \end{aligned} \end{equation} $$

(12) $$ \begin{equation} \begin{aligned} Y_{\mathrm{i}}=\ln (\ln (1 /(1-\mathrm{i} /(\mathrm{n}+1)))) \end{aligned} \end{equation} $$

where E_i is the breakdown strength of the i-th measurement and n is the total number of tests. Additionally, X_i and Y_i denote the transformed horizontal and vertical coordinates of the Weibull plot, respectively. The Weibull shape parameter β, which indicates the dispersion of the breakdown strength data, is greater than 10 for all samples [Figure 5D], indicating good measurement reliability and uniform sample quality. Notably, Eb progressively increases with increasing x and reaches a maximum at x = 0.08; the underlying mechanisms for this enhancement will be discussed later. Figure 5E depicts the electric field dependence evolution of W_rec and η of the BNBST-xLMN ceramics, and Figure 5F compares the W_rec and η values at their respective E_b values. Under these conditions, pure BNBST exhibits W_rec = 0.83 J/cm³ with η = 44.45% at 100 kV/cm, whereas BNBST-0.08LMN achieves W_rec = 6.50 J/cm³ with η = 86.42% at 450 kV/cm. These values correspond to relative increases of approximately 683.1% in W_rec and 94.4% in η [Figure 5G]. A comprehensive comparison with recent studies of lead-free energy storage ceramics demonstrates that the BNBST-0.08LMN ceramic achieves excellent ESP under moderate electric fields [Supplementary Table 1, Figure 5H], making it highly attractive for next-generation compact and integrated power electronic systems.

SEM analysis was performed on all samples to elucidate the mechanism of the improved E_b in the BNBST-xLMN ceramics. The surface morphologies of the BNBST-xLMN ceramics without any additional processing are shown in Figure 6A-F. The pure BNBST ceramic has an average grain size of 1.36 μm, and a small number of pores are visible in the cross-sectional micrograph [Supplementary Figure 5A]. The average grain size of BNBST-0.02LMN ceramic is smaller than that of pure BNBST, which is due to the increased S_config value. However, for 0.06 ≥ x ≥ 0.04, the average grain size increases. This seems contradictory to the grain refinement commonly observed in the HE strategy. In addition, the average grain size decreases when x ≥ 0.08, and the BNBST-0.08LMN ceramic shows a smaller average grain size (≈ 1.23 μm) than the pure BNBST ceramic, with reduced pore structures in the cross-section [Supplementary Figure 5B]. Moreover, Mg oxide compounds (such as MgO and MgTiO₃) are observed at the grain boundaries [Figure 6G-K]. At moderate x values (such as 0.04 and 0.06), Mg²⁺ ions enter the lattice, lowering the strain energy barrier.

$$ \begin{equation} \begin{aligned} \Delta G_{\text {strain }}=4 \pi \mathrm{MN}_{\mathrm{A}}\left[\frac{r_{0}}{2\left(r_{\mathrm{d}}-r_{0}\right)^{2}}+\frac{1}{3\left(r_{\mathrm{d}}-r_{0}\right)^{3}}\right], \end{aligned} \end{equation} $$

where M is Young’s modulus, N_A is the Avogadro constant, r₀ is the ionic radius of the host lattice site, and r_d is the ionic radius of the dopant. This occurs because the radius (r_d) of the dopant ions is larger than that (r₀) of the substituted ions^[57]. This lower energy barrier enhances the mass transport kinetics across grain boundaries during sintering, leading to more pronounced grain growth, which also conceals the effect of the HE strategy on grain refinement. When x ≥ 0.08, some Mg²⁺ ions start to segregate and form Mg oxide compounds at the grain boundaries. These compounds act as pinning centers, hindering grain boundary motion and inhibiting further grain growth. Therefore, the average grain size is related not only to the HE strategy, but also to the existence of the Mg oxide compounds at the grain boundaries.

In addition to the grain size, the impedance characteristics and electrical homogeneity between grains and grain boundaries also affect E_b. To clarify these factors, complex impedance spectroscopy measurements were conducted on the BNBST-xLMN ceramics [Figure 7A and B, Supplementary Figure 6]. All Nyquist plots exhibit depressed semicircular arcs rather than perfect semicircles, which is a typical signature of non-Debye relaxation behavior. Notably, the radius of the impedance semicircular arc monotonically increases with x up to x = 0.08, indicating a progressive enhancement in the insulating resistance of the ceramics. The BNBST-0.08LMN ceramic demonstrates the best insulation performance, with the largest semicircular arc radius. However, the insulation performance slightly decreases at x = 0.10. This means that an excess of Mg oxide compounds at the grain boundaries can lead to deterioration. To further analyze the electrical homogeneity, the frequency positions of the imaginary impedance (Z″) and imaginary modulus (M″) peaks were compared. For pure BNBST, these peaks are separated by 112 Hz [Figure 7C], signaling strong electrical heterogeneity. By contrast, the BNBST-0.08LMN ceramic shows nearly overlapping Z″ and M″ peaks with a frequency difference of only 17 Hz [Figure 7D], indicating improved electrical homogeneity^[58,59].

A major source of electrical inhomogeneity is Maxwell-Wagner interfacial polarization, which is caused by the permittivity and conductivity mismatch between grains and boundaries. The resulting space charge accumulation at the interfaces enhances the local field and lowers E_b. To quantify this, the impedance data were fitted with a dual resistor-constant phase element equivalent circuit that separates the contributions of each component. The degree of electrical heterogeneity can be quantified using the activation energy difference considering the insulation performances of the grains and grain boundaries (ΔΦ = |E_G - E_GB|), which is directly proportional to the strength of Maxwell-Wagner interfacial polarization^[54]. A decrease in ΔΦ suppresses space charge buildup at grain-grain boundary interfaces, thus making a smaller ΔΦ beneficial for enhancing E_b. The activation energies for grains (E_G) and grain boundaries (E_GB) were calculated by fitting the temperature-dependent impedance data to the Arrhenius equation (σ = σ₀exp(-E_a/k_BT), where σ is the measured conductivity, σ₀ is a pre-exponential constant, E_a is the activation energy, k_B is the Boltzmann constant, and T is the absolute temperature). As shown in Figure 7E, pure BNBST demonstrates ΔΦ = 0.3010 eV, reflecting pronounced heterogeneity, while BNBST-0.08LMN shows ΔΦ = 0.0319 eV, which is an order of magnitude smaller and indicates a much more uniform electrical response. These results show that LMN modification simultaneously enhances the insulating properties of both grains and grain boundaries, leading to improved overall insulation and electrical homogeneity. The enhanced grain boundary insulation arises from the formation of a highly resistive Mg oxide compound at the grain boundaries, while the improved grain insulation is associated with the widening of the optical band gap (E_opt). To verify this, the E_opt value was extracted from UV-Vis absorbance data via Tauc plots based on the Kubelka-Munk function [Figure 7F]^[56,60]. The E_opt values increase with increasing x value, and then converge when x ≥ 0.06. Notably, the previous analysis suggests that Mg²⁺ ions enter the lattice when x ≤ 0.06, thus increasing the E_opt value. At high x values, Mg²⁺ ions not only enter the lattice, but also form Mg oxide compounds at the grain boundaries, thereby resulting in a smaller variation in the E_opt value. In addition, the increased E_opt values increase the energy required for electron excitation, reducing the intrinsic carrier concentration and improving the insulating properties of the grains.

Finite-element simulations were conducted using realistic 2D microstructural models derived directly from the experimental SEM images to investigate the microscopic mechanisms governing dielectric breakdown and electric tree propagation. An electric field of 350 kV/cm was applied, and all relevant material parameters, including permittivity and conductivity, were carefully calibrated based on the dielectric and impedance properties. Figure 7G shows the time-resolved electrostatic potential and local electric field distributions obtained during tree initiation and growth in the pure BNBST ceramic. The simulation results clearly demonstrate that the permittivity contrast between high-permittivity grains and low-permittivity grain boundaries leads to a significant electric-field concentration at the grain boundaries. Due to the higher intrinsic breakdown strength of grain boundaries compared to grains, the electric trees initiate near the high-potential area and preferentially propagate through the weaker grain interiors. Notably, the BNBST-0.08LMN ceramic shows a slower electrical tree propagation than that of the pure BNBST ceramic [Figure 7H]. Moreover, the electric tree in the BNBST-0.08LMN ceramic displays a highly branched morphology with multiple bifurcations emerging around the main trunk, in contrast to the relatively simple tree shape observed in the pure BNBST ceramic. This behavior indicates that the retarded electric tree propagation arises not only from the smaller grain size and the larger fraction of grain boundaries, but also from the formation of multiple branching propagation paths that stem from the improved electrical homogeneity. These branched paths dissipate the electric-tree energy and force it to follow a more difficult route, significantly increasing the time to breakdown. Therefore, the superior insulation characteristics, combined with the multiply branched propagation routes, synergistically contribute to the enhanced E_b value of the BNBST-0.08LMN ceramic.

The commercial viability of dielectric materials critically depends on their ability to maintain a consistent performance under the diverse and demanding conditions encountered in real-world applications. To comprehensively evaluate the operational stability and durability of the BNBST-0.08LMN ceramic, its unipolar P-E loops were assessed over a range of frequencies, temperatures, and fatigue cycles. The frequency dependence of the ESP, illustrated in Figures 8A and B, demonstrates good stability. Between 1 and 100 Hz, the P-E loops show negligible change, with η varying by less than 2%. This frequency insensitivity is highly desirable for applications requiring operation over a broad frequency spectrum. The temperature-dependent performance, presented in Figure 8C and D, shows that the BNBST-0.08LMN ceramic maintains a good ESP over a wide temperature range. From 20 to 160 °C, η stays within 7% of its room-temperature (20 °C) value, and W_rec slightly decreases. To investigate the microscopic origin of this slight W_rec reduction at high temperatures, in situ Raman spectroscopy measurements were performed from 20 to 200 °C [Figure 8E]. No new peaks appear as the temperature increases, indicating good structural stability at high temperatures. In addition, a gradual decrease in the peak intensities of the v3, v4, v5, and v6 modes at elevated temperatures is observed [Figure 8E1 and E2], which is due to the weakening of dipole correlations and smaller PNRs and hence slightly reduced P_max and W_rec values. Furthermore, the fatigue resistance of the BNBST-0.08LMN ceramic was evaluated by subjecting it to 10⁵ unipolar polarization switching cycles [Figure 8F and G]. It also exhibits excellent fatigue resistance, with no significant degradation in the P-E loop shape and η varying by less than 3% even after 10⁵ cycles. This good fatigue performance is attributed to the highly dynamic nature of the PNRs, which can easily switch their polarization direction without causing permanent damage to the material. Overall, the BNBST-0.08LMN ceramic combines a high ESP with stable operation over wide frequency, temperature, and cycling ranges, making it an attractive candidate for advanced dielectric energy-storage devices.

The ultimate test of any dielectric energy storage material is its performance under realistic operating conditions. To evaluate the practical charging-discharging properties of the BNBST-0.08LMN ceramic, we performed measurements in both overdamped and underdamped circuit conditions, which represent the two most common operating modes for pulsed power applications. In the overdamped circuit regime, which is typical for applications requiring controlled energy release, the two most important performance metrics are the discharge energy density (W_d) and the discharge rate (t_0.9). W_d was quantitatively determined by integrating the power dissipated across a 100 Ω load resistor using^[61]

(13) $$ \begin{equation} \begin{aligned} W_{d}=\frac{R \int I^{2} \mathrm{~d} t}{V} \end{aligned} \end{equation} $$

where R is the load resistance, V is the effective electrode volume, and I is the discharge current. The peak discharge current increases with the applied electric field and reaches its highest value at 240 kV/cm [Figure 9A], where W_d = 2.79 J/cm³ [Figure 9B]. The deviation of W_d from the theoretical recoverable energy density W_rec results from unavoidable energy losses originating from the external circuit load and the microstructural imperfections within the ceramic. Furthermore, the discharge rate, which is critical for pulsed power applications requiring rapid energy delivery, was characterized using the t_0.9 value, which is defined as the time required to release 90% of the total discharge energy. Notably, an ultrafast discharge rate is observed in the BNBST-0.08LMN ceramic, with t_0.9 remaining at approximately 45 ns over a wide electric field range. Moreover, the overdamped discharge performance stability was also investigated at 200 kV/cm over a wide temperature range [Supplementary Figure 7A and B, Figure 9C]. Within the tested temperature range, W_d shows only slight fluctuations between 2.07 and 2.29 J/cm³, and the discharge time remains below 40.5 ns, demonstrating the good thermal stability of the fast discharge properties.

In the underdamped circuit regime, the current density (J) and power density (P_D) are key performance indicators. These parameters were calculated using^[62]:

(14) $$ \begin{equation} \begin{aligned} J=\frac{I_{\text{max}}}{S} \end{aligned} \end{equation} $$

(15) $$ \begin{equation} \begin{aligned} P_D=\frac{E \times I_{\text{max}}}{2S} \end{aligned} \end{equation} $$

where S and I_max are the electrode area and maximum current, respectively. Figure 9D shows the underdamped discharge curves as a function of the applied electric field. At 240 kV/cm, the BNBST-0.08LMN ceramic obtains J = 789.80 A/cm² and P_D = 94.77 MW/cm³ [Figure 9E]. The temperature-dependent curves measured at 200 kV/cm are shown in Supplementary Figure 7C. With increasing temperature, the discharge current exhibits more pronounced oscillatory behavior. At 100 °C, the J and P_D values reach maxima of 757.96 A/cm² and 75.79 MW/cm³, respectively [Figure 9F]. These results demonstrate an exceptional charge-discharge performance in both circuit modes, positioning BNBST-0.08LMN as a strong candidate for advanced pulsed-power systems.