Broad-high operating temperature range and enhanced energy storage performances in lead-free ferroelectrics

Zhao, Weichen; Xu, Diming; Li, Da; Avdeev, Max; **g, Hongmei; Xu, Mengkang; Guo, Yan; Shi, Dier; Zhou, Tao; Liu, Wenfeng; Wang, Dong; Zhou, Di

doi:10.1038/s41467-023-41494-1

Broad-high operating temperature range and enhanced energy storage performances in lead-free ferroelectrics

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Published: 15 September 2023

Volume 14, article number 5725, (2023)
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Broad-high operating temperature range and enhanced energy storage performances in lead-free ferroelectrics

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Abstract

The immense potential of lead-free dielectric capacitors in advanced electronic components and cutting-edge pulsed power systems has driven enormous investigations and evolutions heretofore. One of the significant challenges in lead-free dielectric ceramics for energy-storage applications is to optimize their comprehensive characteristics synergistically. Herein, guided by phase-field simulations along with rational composition-structure design, we conceive and fabricate lead-free Bi_0.5Na_0.5TiO₃-Bi_0.5K_0.5TiO₃-Sr(Sc_0.5Nb_0.5)O₃ ternary solid-solution ceramics to establish an equitable system considering energy-storage performance, working temperature performance, and structural evolution. A giant W_rec of 9.22 J cm⁻³ and an ultra-high ƞ ~ 96.3% are realized in the BNKT-20SSN ceramic by the adopted repeated rolling processing method. The state-of-the-art temperature (W_rec ≈ 8.46 ± 0.35 J cm⁻³, ƞ ≈ 96.4 ± 1.4%, 25–160 °C) and frequency stability performances at 500 kV cm⁻¹ are simultaneously achieved. This work demonstrates remarkable advances in the overall energy storage performance of lead-free bulk ceramics and inspires further attempts to achieve high-temperature energy storage properties.

Achieving high energy-storage density in K0.5Na0.5NbO3 optimized Bi0.25Na0.25Ba0.15Sr0.35TiO3 relaxor ferroelectric ceramics

Article 23 August 2023

Enhanced energy-storage performance and temperature-stable dielectric properties of (1 − x)(0.94Na0.5Bi0.5TiO3–0.06BaTiO3)–xNa0.73Bi0.09NbO3 ceramics

Article 08 December 2018

Improved energy storage performances in (1−x)Bi0.5Na0.5TiO3–xSr0.7Bi0.2(Zn1/3Nb2/3)O3 relaxor ferroelectrics

Article 02 July 2024

Introduction

With the continuous growth of the world population and the development of the global economy and society, worldwide energy demand keeps increasing at an alarming rate. Due to the desperate issues, it is vital to exploit a variety of clean and sustainable energy sources^1,2,3,4. Compared with various current energy storage and conversion devices (e.g., lithium-ion batteries, supercapacitors, solid oxide fuel cells), electrostatic capacitors made of dielectric materials have attracted ever-increasing attention up till now owing to their benefits in terms of swift charging-discharging rates, ultrahigh power density, excellent thermal stability, and prolonged storage lifespan^5,6,51,52,53 and Supplementary Table 1. This achievement signifies the substantial potential of BNKT-20SSN ceramic (RRP) as a promising candidate for advanced high-temperature energy storage applications.

**Fig. 2: The energy storage performance under various conditions and charge/discharge characteristics of BNKT-20SSN ceramic (RRP).**

Apart from the ultrahigh W_rec and η, another crucial criterion to determine the availability of high-power pulsed electronic components is the charge/discharge performance. The overdamped discharge property for the BNKT-20SSN ceramic (RRP) under various applied electric fields was measured at room temperature using a purpose-constructed resistance–inductance–capacitance (RLC) load circuit, and the regular overdamped oscillation waveforms reflect steady discharge behavior, as illustrated in Supplementary Fig. 6. Meanwhile, it can be observed that the discharge current rapidly approaches its peak (I_max = 8.2 A, at 500 kV cm⁻¹) and then tends to diminish swiftly. Moreover, the high discharge energy density (W_d) ~5.2 J cm⁻³ can be liberated in a short period of time (t_0.9, 90% of W_d is released) ~244 ns at 500 kV cm⁻¹ (Fig. 2c). According to the foregoing data, the BNKT-20SSN ceramic (RRP) exhibits excellent charge/discharge characteristics, making it a promising candidate for pulsed power applications.

To ensure steady functioning in complex settings, ideal frequency reliability, and temperature stability must be guaranteed. The frequency-dependent energy storage property of BNKT-20SSN ceramic (RRP) was investigated at 500 kV cm⁻¹, as shown in Fig. 2d, all P–E hysteresis loops are slender with practically unchanged P_max values at various frequencies. The corresponding results are recorded in Supplementary Fig. 7, it can be seen that the BNKT-20SSN ceramic (RRP) exhibits excellent frequency reliability (W_rec ≈ 8.63 ± 0.18 J cm⁻³, ƞ ≈ 94.5% ± 2.4%) across the entire frequency range (1–100 Hz). Likewise, Fig. 2e gives the temperature stability of BNKT-20SSN ceramic (RRP) at 500 kV cm⁻¹, with the attainable P_max value marginally decreasing as the enhancement of the random electric field raises the reaction rate of the PNRs during heating. As expected, this result fits well with the P–E curves derived from phase-field simulations, as presented in Fig. 2f. Simultaneously, the corresponding microstructural evolution in the existence of the external electric field at various temperatures demonstrates that the domain size and polarization strength decrease as temperature increases (Fig. 2f and Supplementary Fig. 8). Of particular significance is that the BNKT-20SSN ceramic (RRP) features not only a wide operating temperature range (25–160 °C) but also an unprecedently high W_rec (≈ 8.46 ± 0.35 J cm⁻³) and ƞ (≈96.4 ± 1.4%) in contrast to certain other cutting-edge lead-free ceramics with excellent temperature stability (Fig. 2g, h)^{6,8,9,18,34,40,46,Full size image}

Atomic-resolution spherical aberration transmission electron microscopy was used in the scanning transmission electron microscopy (STEM) mode along with a high-angle annular dark-field (HAADF) detector in order to analyze the local structure of multiphase-nanoregion coexistence. Precise atom arrangement of the 100/010 plane was captured and fitted by the 2D Gaussian function, see Fig. 3b. The arrangement presents a direct process of the formation of polarization, the coexistence of multiphase PNRs, and nanoregion distribution. The 110-plane atom arrangement could hardly distinguish the R and T phases; the 111-plane atom arrangement shows only the overlap of A and B sites; the higher Miller indices planes projection images present insufficient resolution hindered by the Moiré fringe formation. With the processing by the 2D Gaussian function, the polarization vector could be straightforwardly described by a vector from the B-site cations center to the A-site cations corner, represented by the yellow arrows in Fig. 3b. The R and T phases could be directly identified by the long magnitude arrows, whereas the C phase shows near-zero polarization. The bond lengths calculated from the B-site cations and the A-site cations along vertical and horizontal directions are noted as c and a, and the c/a ratio was then used to distinguish the R phase and the T phase, see Supplementary Fig. 10. Apparently, the captured image presents multiphase PNRs with R and T phases coexisting in the C matrix. The size of the same polarization direction and magnitude PNRs is ~2 nm. The coexistent multiphase-nanoregion destroys the long-range ferroelectric order and produces abundant small-size PNRs, consistent with those predicted by the phase-field calculation. Moreover, the randomly distributed nanoregions of different polarization directions and magnitudes could reduce polarization anisotropy. The enhanced polarization magnitude implies that the internal field is strong. The facts stated above could all lead to a more accessible and quicker polarization response to the external electric field, higher energy efficiency, and better energy storage performance. To better understand the polarizations in the sample, color-filled 2D patterns of summarized polarization directions and magnitudes are plotted in Fig. 3f, g. The patterns are highly corresponding to the phase-field calculation, signifying the reliability and the practical value of the phase-field prediction to design the dielectric materials for energy storage.

Composition-driven and temperature-driven features

Pure BNT and (1-x)BNKT-xSSN ceramics were prepared to understand composition-driven and temperature-driven energy storage properties further. The powder X-ray diffraction (PXRD) patterns at room temperature (Supplementary Fig. 11a) show that all samples exhibit a typical BNT-based perovskite structure without impurities. The Rietveld refinement over PXRD patterns of each component was then processed by GSAS II software to determine the phases, and the results are displayed in Fig. 4a–c and Supplementary Fig. 12⁵⁵. It is widely accepted that the BNT solid solution displays a rhombohedral (R3c) symmetry at room temperature³¹, consistent with the refinement result. The ratio of the R phase and the T phase gradually decreases with the increase of x, and the pure T phase was determined in the 0.82BNT-0.18BKT at 25SSN ceramic, identical to those from previous studies^56,57,58. Temperature-dependent PXRD patterns of the BNKT-20SSN in the temperature range of 25–200 °C (Supplementary Fig. 13) indicate no peak splitting or phase change occurs, suggesting good temperature stability. Furthermore, all elements exhibit homogeneous distribution characteristics with no segregation in BNKT-20SSN ceramic, see Supplementary Fig. 14.

**Fig. 4: Phase analysis, relaxation behavior, dielectric and ferroelectric properties of BNT and (1-x)BNKT-xSSN ceramics, along with their breakdown analysis.**

The genesis of optimum energy storage properties is intimately connected to the dynamic reaction of domain structures to external electric fields^18,28. Here, the dynamic domain response to an applied voltage and the relaxation behaviors of the BNT, BNKT, and BNKT-20SSN ceramics were characterized by employing piezo-response force microscopy (PFM), as displayed in Fig. 4d–i, the schematics of the applied voltage and region are similar to our previous work (Supplementary Fig. 15, 16)⁴⁰. For the BNT ceramics (Fig. 4d, g), significant phase deviations and amplitude signals were observed even at a lower external voltage (10 V), and the overwhelming majority of domains did not flip after a 20 min relaxation time, demonstrating a robust FE characteristic with substantial P_max and P_r. A similar occurrence was also seen in the BNKT ceramic (Fig. 4e, h), albeit the feedback signal (after 20 min) of the BNKT ceramic is slightly weaker than that of the BNT at an applied voltage of 10 V. On the contrary, the phase difference and amplitude signals of the BNKT-20SSN ceramic (Fig. 4f, i) are weak in the entire electrical scan zone and become more potent at higher external voltages. After a 20-min relaxation duration, the signals have significantly decreased. The facts mentioned above could all lead to a negligible P_r and hysteresis loss in the BNKT-20SSN ceramic, thus increasing the energy storage efficiency.

In order to further investigate the mechanism of relaxation polarization behavior over a wide range of temperatures, the temperature (from room temperature to 400 °C) and frequency (from 1 kHz to 1 MHz) dependent dielectric permittivity of pure BNT and (1-x)BNKT-xSSN ceramics were performed and depicted in Fig. 4j and Supplementary Fig. 17. The pure BNT ceramic possesses two typical temperature-dependent dielectric anomalous peaks, labeled as “T_s” (depolarization temperature shoulder) and “T_m” (temperature of the maximum dielectric constant) at low and high temperatures, respectively^59,60,61,62. At the ambient temperature (T_amb), as displayed in Supplementary Fig. 17a, the pure BNT ceramic exhibits a non-ergodic relaxor state and behaves as a normal ferroelectric with a R3c symmetry space group^31,35,63. Afterward, with the addition of BKT (Supplementary Fig. 17b), the BNKT ceramic with R and T phase coexistence at MPB displays a much higher maximum permittivity value (~ 4600 at 1 MHz) than that of the pure BNT ceramic (~2500 at 1 MHz). The T_m of the BNKT ceramic shifts to a lower temperature, and a relatively broad permittivity peak can be detected in the MPB composition⁶⁴. Subsequently, with increasing the content of SSN, the maximum value of the dielectric permittivity decreases step by step, see Fig. 4j. The two dielectric anomaly humps squint towards lower temperatures, and a gradually broaden temperature plateau of the dielectric constant can be observed. The analysis results of ln(1/ε´−1/ε_m´) versus ln(T – T_m) for BNT and (1-x)BNKT-xSSN ceramics are presented in Supplementary Fig. 18. It is observed that the calculated values of γ for (1-x)BNKT-xSSN ceramics lie within the range of 1.86−1.99, indicating the pronounced relaxor behavior. Noteworthy, the dielectric relaxor or frequency dispersion behavior of the BNKT-20SSN ceramic could be noticed around T_amb, which allows for the formation of relaxor ferroelectric (a significant polar order–disorder arrangement) at room temperature and is beneficial to upgrading the energy storage performances³².

The bipolar P–E hysteresis loops of all components mentioned above were performed under 100 kV cm⁻¹ at room temperature, and the results are shown in Fig. 4k. The pure BNT ceramic exhibits a canonical FE behavior with large P_max, P_r, considerable hysteresis, and a fully saturated P–E loop. A lower coercive electric field (E_c) and a slightly improved P_max were obtained in the BNKT (MPB) ceramic, indicating a softened FE activity. The hysteresis losses decrease dramatically, accompanied by slimmer P–E loops seen in the SSN-introduced compositions, and are consistent with those calculated from the phase-field simulation method (Fig. 4l). To better understand composition-driven breakdown strength, the values of theoretical E_b of all ceramic samples were evaluated by the Weibull distribution experiments, see Fig. 4m. With increasing the SSN concentration, the theoretical E_b values first increased and then decreased, reaching a maximum at the BNKT-20SSN ceramics. To investigate the energy storage performance of the ceramics, the P–E hysteresis loops were performed on a ferroelectric analyzer. As depicted in Supplementary Fig. 19, the room-temperature P–E loops of the BNKT-20SSN ceramic were measured from 100 kV cm⁻¹ to the critical electric field (385 kV cm⁻¹) at 10 Hz. As a consequence, a great W_rec of 5.23 J cm⁻³ along with a high energy efficiency of 90.2% are simultaneously achieved in the BNKT-20SSN ceramic, demonstrating a substantial promotional impact of combinatorial-optimization strategy guided by phase-field simulations on energy storage performance.

Discussion

The selection of promising dielectric materials to combine is a foundational but inevitable procedure in material science. The presented phase-field method assistant strategy could be used to investigate dielectric material with high energy storage performance upon a wide working temperature range^5,40. By learning the structural evolution, polarization distribution, and characteristics of PNRs in combinations of BNT-BKT-SSN at morphotropic phase boundary that affords possibly engineerable ceramic materials from the phase-field calculation simulation strategy, we could initiatively decide and select the optimal composition for further study to achieve the remarkable performances.

To state, various combinations in perovskite structure have been considered to acquire substantial polar nanoregions in the structure to enhance energy storage performances. The initial BNT ceramic shows a considerable ferroelectric performance, but the P_r is too large for energy storage applications^31,32,37; following the BNKT binary system at the morphotropic phase boundary is an ideal fundament for massive afterward studies^56,61. We intentionally choose ionic radius and valence distinguishable cation pairs as guests for targeting a solid solution and thus enable the discovery of diverse ferroelectric/energy storage performances. The phase-field method supports an efficient strategy of rational design of a targeted material with relaxor behavior by implying reduced PNRs, thermal stability, reversible response to the external electric field, high P_max, and low P_r, all of which could effectively optimize the ferroelectric/energy storage performances. The designed BNKT-20SSN ceramic (RRP) shows extraordinary performances of giant W_rec and ultrahigh η, unprecedented temperature, and frequency stabilities. Multi-methods analysis describes the occurrence of the performances. The small, uniform, dense grain structures by the RRP process method guarantee the breakdown strength and subsequent applications. The coexisting R/T/C multiphase nanoregions confirmed by atomic-scale TEM provide small-scaled PNRs with different polarization distributions in both magnitude and orientation, suggesting a relaxor-behavior FE with large P_max of energy storage density and small P_r of energy loss and allowing the polarization of nanoregions flip** along the same directions with lower energy and higher dynamics. The PNRs of the BNKT ceramic were confirmed with a size of ~200 nm, and the guest-invited BNKT-20SSN reduced the size to ~2 nm⁶⁵. Notably, typical relaxor REs present only minor differences in polarization magnitude but only in orientation, which differs from what we reported here^1,66. This phenomenon may be because of the considerable amount of SSN concentration, x = 0.20, and the fact that the A site is composed of 0.42Bi-0.34Na–0.08K–0.16 Sr, introducing considerably strong local heterogeneity and destabilizing the polarization ordering. The system retains the original PNRs of BNKT, but the PNRs are reduced and dissociated, forming a local order–disorder coexistence system. The metastable order–disorder system in BNKT-20SSN presents a lower P_max than BNKT, but the abundant PNRs promote the performance of energy storage. Moreover, BNKT-20SSN ceramic (RRP) exhibits unprecedented temperature and frequency stabilities where the W_rec and η typically decrease when temperature increases, indicated by the decrease of P_max and the occurrence of the non-negligible P_r. This case may come from a series of benefits. First, the average structure is stable upon temperature change to 200 °C. Second, the heterogeneity in the metastable order–disorder system may act as a pinning effect and hinder further atom thermal vibration-induced local structure change^67,68. Finally, the randomly distributed PNRs also show some order–disorder, inviting a suitable local energy barrier to the external electric field and frequencies, indicated by the flat temperature-dependent dielectric response.

In summary, a rational phase-field calculation guided dielectric material designing method is presented to achieve small-scale and stable PNRs with overall well-behaved energy storage performance theoretically and experimentally. The so-calcined BNKT-20SSN guided by calculations with improved RRP techniques shows a W_rec of 9.22 J cm⁻³ and an ultrahigh ƞ of ~96.3% at large external electric field 535 kV cm⁻¹, accompanied with excellent temperature-insensitive (W_rec ≈ 8.46 ± 0.35 J cm⁻³, ƞ ≈ 96.4 ± 1.4%, 25–160 °C) and frequency stability (W_rec ≈ 8.63 ± 0.18 J cm⁻³, ƞ ≈ 94.5% ± 2.4%, 1–100 Hz) at 500 kV cm⁻¹. This research provides a paradigm for the synergistic development of lead-free dielectric materials with enhanced comprehensive energy storage capacity over a broad operating temperature range to fulfill the pressing demands of modern energy storage components.

Methods

Ceramics preparation

The lead-free ceramics with the composition of (1-x)Bi_0.5(Na_0.82K_0.18)_0.5TiO₃-xSr(Sc_0.5Nb_0.5)O₃ (abbreviated as BNKT-xSSN, where x = 0, 0.05, 0.10, 0.15, 0.20, and 0.25) were fabricated via a conventional solid-state reaction method. The pre-dried oxides and carbonate powders of Bi₂O₃ (≥99.9%), Na₂CO₃ (≥99.8%), K₂CO₃ (≥99.5%), TiO₂ (≥99.9%), SrCO₃ (≥99.5%), Sc₂O₃ (≥99.9%) and Nb₂O₅ (≥99.99%) (Aladdin Chemical Reagent Co., Ltd., CN) were used as the starting materials. The raw powders were weighed according to the stoichiometric ratio, and 2 wt.% excess of Bi₂O₃, Na₂CO₃, and K₂CO₃ were added to compensate for the weight loss at high temperatures. The mixtures were planetarily ball-milled for 24 h at 300 rpm with ethanol in nylon jars using Y-stabilized zirconia balls as milling media. After drying, the mixtures were calcined at 800–850 °C for 4 h in an alumina crucible and ball-milled again similarly. After drying and sieving, the powders were uniaxially pressed into pellets at 10 MPa in a 12 mm diameter stainless steel cylindrical die. Then, the preformed green ceramic sheets were pressed at 300 MPa for 3 min through cold isostatic pressing. Finally, the samples were sintered at 1140–1200 °C for 4 h with a heating rate of 4 °C min⁻¹ in closed alumina crucibles. To minimize the evaporation of the volatile elements Bi, Na, and K, the samples were embedded in powders of the same composition. For the electrical measurements, the silver paste was coated on both surfaces of the sintered samples and fired at 650 °C for 20 min to form electrodes.

Repeated rolling processing

The green ceramic tapes with BNKT-20SSN composition were prepared by a repeated rolling processing (RRP) method, in which the pre-sintered powders were used as raw materials. After sieving, the calcined powders of BNKT-20SSN were thoroughly mixed with polyvinyl alcohol (PVA). The extrusion force generated by the two tightly contiguous rollers could greatly improve the density of the green ceramic tape and also help to form a dense structure during sintering with minimal porosity, resulting in a significant increase in E_b. And then, the ceramic tapes prepared by RRP were punched into disks with a diameter of 12 mm and then calcined at 650 °C for 2 h to burn out the PVA. Subsequently, the green disks were embedded in the pre-sintered powders of the same composition and sintered at 1070–1140 °C for 2 h using a double crucible method, so that the volatilization of Bi, Na, and K elements during high-temperature sintering could be suppressed.

Structural characterization

The phase purity and crystalline structure were characterized at an X-ray diffractometer (SmartLab-3 kW, Rigaku, Tokyo, Japan) with Cu Kα radiation. Neutron diffraction patterns were collected on the high-resolution powder diffractometer ECHIDNA at ANSTO over the angular range 8 ≤ 2θ/° ≤ 160, using a step size Δ2θ = 0.05° and a wavelength of 1.622 Å at room temperature. The Rietveld refinements on PXRD and NPD were analyzed using the program GSAS II⁵⁵. The microstructure of the ceramics was observed by field-emission scanning electron microscopy (FE-SEM, FEI Quanta 250 FEG, Hillsboro, Oregon, USA). The Nano Measurer software was used to calculate the average grain size of the samples based on the SEM images. The HAADF atomic-scale images were acquired using an atomic-resolution STEM (aberration-corrected Titan Themis G2 microscope) and processed by 2D Gaussian fitting in MATLAB scripts to evaluate the polarization vector, magnitude, and angle maps.

Dielectric measurements

For the dielectric measurements, the silver paste was coated on both surfaces of the sintered samples and fired at 650 °C for 20 min to form electrodes. Temperature and frequency-dependent dielectric permittivity and tanδ were tested by an accurate inductor–capacitance–resistance (LCR) meter (E4980A, Agilent, USA) with a 3 °C min⁻¹ heating rate.

Ferroelectric measurements

The room-temperature P–E loops with a triangle signal of 10 Hz and temperature and frequency-dependent P–E loops were measured on a ferroelectric analyzer (aix ACCT, TF Analyzer 2000, Aachen, Germany). For the P–E loops measurements, the sintered disks were polished to ≈35 μm and then sputtered with gold electrodes on both surfaces.

Pulsed charge–discharge test

The change–discharge properties of ceramics with a thickness of ≈50 μm were investigated via a specially designed resistance, inductance, and capacitance (RLC) load circuit.

Dielectric breakdown test

The breakdown performances were measured via a ferroelectric analyzer (aix ACCT, TF Analyzer 2000, Aachen, Germany). The statistical E_b properties for perovskite structure ceramics are generally estimated by Weibull distribution equations: X_i = ln(E_i), Y_i = ln(ln(1/(1-P_i))), P_i = i/(n + 1), where E_i is the experimental breakdown strength of each sample in ascending order, P_i is the cumulative probability of dielectric breakdown, n represents the total number of samples for ceramics. The Weibull distribution modulus, which can estimate the value of E_b, was represented by the slope of the fitting line.

PFM characterization

The surface morphology, dynamic response, and relaxation behavior of the domains under external voltages were investigated by piezoelectric force microscopy (PFM, MFP-3D, Asylum Research, USA). The surfaces of each ceramic specimen used for PFM measurement were finely polished with polycrystalline diamond polishing paste.

Phase-field simulations

Phase-field simulations have been employed to investigate a single crystal undergoing the Cubic (C) to Tetragonal (T) to Rhombohedral (R) ferroelectric transition. This study encompasses varying defect do** concentrations in the range of x = 0 to 0.30, denoted as BNKT-xSSN. The comprehensive evaluation of the ferroelectric system’s total free energy is expressed as follows:

$$F={\int }_{\!\!V}\left({f}_{{bulk}}+{f}_{{grad}}+{f}_{{couple}}\right){dV}+{\int }_{\!\!V}\left({f}_{{elas}}+{f}_{{elec}}\right){dV}$$

(1)

where f_bulk represents the bulk free energy density,

$${f}_{{bulk}}= {\alpha }_{1}\left({P}_{1}^{2}+{P}_{2}^{2}+{P}_{3}^{2}\right)-{\alpha }_{11}{\left({P}_{1}^{2}+{P}_{2}^{2}+{P}_{3}^{2}\right)}^{2}+{\alpha }_{12}\left({P}_{1}^{2}{P}_{2}^{2}+{P}_{2}^{2}{P}_{3}^{2}+{P}_{1}^{2}{P}_{3}^{2}\right) \\ +{\alpha }_{112}\left({P}_{1}^{4}{P}_{2}^{2}+{P}_{2}^{4}{P}_{3}^{2}+{P}_{1}^{4}{P}_{3}^{2}+{P}_{1}^{2}{P}_{2}^{4}+{P}_{2}^{2}{P}_{3}^{4}+{P}_{1}^{2}{P}_{3}^{4}\right)+{\alpha }_{113}\left({P}_{1}^{2}{P}_{2}^{2}{P}_{3}^{2}\right) \\ +{\alpha }_{111}{({P}_{1}^{2}+{P}_{2}^{2}+{P}_{3}^{2})}^{3}$$

(2)

where α_ij represents the coefficient, the value of which is contingent upon both concentration c and the temperature T.

f_grad represents the gradient energy density.

$${f}_{{gradient}}= \frac{1}{2}{G}_{11}[{\left({P}_{1,1}\right)}^{2}+{\left({P}_{1,2}\right)}^{2}+{\left({P}_{1,3}\right)}^{2}+{\left({P}_{2,1}\right)}^{2}+{\left({P}_{2,2}\right)}^{2}+{\left({P}_{2,3}\right)}^{2}\\ +{({P}_{3,1})}^{2}+{({P}_{3,2})}^{2}+{({P}_{3,3})}^{2}]$$

(3)

where G₁₁ signifies the coefficient for gradient energy, while f_couple pertains to the dipole effect induced by do**.

${f}_{{{{{{\rm{couple}}}}}}}=-\int {d}^{3}x{\sum}_{i={{{{\mathrm{1,2,3}}}}}}{P}_{i}(x)\cdot {\varphi }_{{loc}}(x)$, where ${\varphi }_{{loc}}(x)$ is the dipolar field generated through do**, expected to exhibit a random distribution and remain unchanged during the cooling process. f_elas corresponds to the energy density associated with long-range elastic interactions, and f_elec pertains to the energy density attributed to electrostatic interactions. ${f}_{{elas}}=\frac{1}{2}{c}_{{ijkl}}{e}_{{ij}}{e}_{{kl}}=\frac{1}{2}{c}_{{ijkl}}({\varepsilon }_{{ij}}-{\varepsilon }_{{ij}}^{0})({\varepsilon }_{{kl}}-{\varepsilon }_{{kl}}^{0})$, where c_ijkl denotes the elastic constant tensor, ε_ij signifies the total strain, and ε⁰_kl represents the electrostrictive stress-free strain, i.e., ε⁰_kl = Q_ijklP_kP_l. f_elec = f_dipole + f_depola + f_appl, where f_dipole is the dipole-dipole interactions arising from polarization, f_depola, represents the depolarization energy density, and f_appl, denoting the energy density resulting from an applied electric field. The temporal evolution of the spontaneous polarization field (P) can is determined by solving the time-dependent Ginzburg-Landau (TDGL) equation: $\frac{{{dP}}_{i}(x,{t})}{{dt}}=-\!M\frac{\delta F}{\delta {P}_{i}(X,t)}$, i = 1, 2, 3, where M represents the kinetic coefficient, F signifies the total free energy, and t denotes time^5,69.

Data availability

All data supporting this study and its findings are available within the article and its Supplementary Information. The data that support the findings of this study are available on request from the corresponding authors.

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Acknowledgements

This work was supported by the National Key R&D Program of China (2021YFB3800602), the International Cooperation Project of Shaanxi Province (2021KWZ-10), the Fundamental Research Funds for the Central University, the 111 Project of China (B14040), Zhejiang Provincial Science and Technology Program under Grant LGG20F010007. The SEM work was done at the International Center for Dielectric Research (ICDR), **’an Jiaotong University, **’an, China. The authors thank Dr. Yan-Zhu Dai for her help with SEM.

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Electronic Materials Research Laboratory & Multifunctional Materials and Structures, Key Laboratory of the Ministry of Education & International Center for Dielectric Research, School of Electronic Science and Engineering, **’an Jiaotong University, 710049, **’an, Shaanxi, China
Weichen Zhao, Diming Xu, Da Li, Yan Guo & Di Zhou
Australian Nuclear Science and Technology Organization, Lucas Heights, 2234, NSW, Australia
Max Avdeev
School of Physics and Information Technology, Shaanxi Normal University, 710062, **’an, Shaanxi, China
Hongmei **g
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, **’an Jiaotong University, 710049, **’an, Shaanxi, China
Mengkang Xu
Department of Chemistry, Zhejiang University, 310027, Hangzhou, Zhejiang, China
Dier Shi
School of Electronic and Information Engineering, Hangzhou Dianzi University, 310018, Hangzhou, Zhejiang, China
Tao Zhou
State Key Laboratory of Electrical Insulation and Power Equipment, **’an Jiaotong University, 710049, **’an, Shaanxi, China
Wenfeng Liu
Frontier Institute of Science and Technology and State Key Laboratory for Mechanical Behavior of Materials, **’an Jiaotong University, 710049, **’an, Shaanxi, China
Dong Wang

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Weichen Zhao
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Da Li
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Yan Guo
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Dier Shi
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Tao Zhou
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Wenfeng Liu
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The work was conceived and designed by W.C.Z., D.Z., and W.C.Z. fabricated the samples, tested the energy storage, dielectric, structure, stability, and other properties, and processed related data, assisted by D.Z., D.X., and D.L. The SEM images were filmed and processed by G.Y. and T. Z. The HAADF-STEM images were filmed and processed by H.M.J. and D.X. The PFM images were filmed and processed by M.K.X. and W.F.L. The neutron diffraction data were processed and analyzed by D.X. and M.A. Temperature-dependent XRD data were processed and analyzed by D.E.S. The manuscript was drafted by W.C.Z. and revised by D.Z. and D.X. The phase-field simulations were performed by D.W. and discussed with D.Z. and W.C.Z. All authors participated in the data analysis and discussions.

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Correspondence to Diming Xu, Dong Wang or Di Zhou.

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Zhao, W., Xu, D., Li, D. et al. Broad-high operating temperature range and enhanced energy storage performances in lead-free ferroelectrics. Nat Commun 14, 5725 (2023). https://doi.org/10.1038/s41467-023-41494-1

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Received: 15 March 2023
Accepted: 06 September 2023
Published: 15 September 2023
DOI: https://doi.org/10.1038/s41467-023-41494-1
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Broad-high operating temperature range and enhanced energy storage performances in lead-free ferroelectrics

Abstract

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Introduction

Composition-driven and temperature-driven features

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Methods

Ceramics preparation

Repeated rolling processing

Structural characterization

Dielectric measurements

Ferroelectric measurements

Pulsed charge–discharge test

Dielectric breakdown test

PFM characterization

Phase-field simulations

Data availability

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