Mechanism of enhanced energy storage density in AgNbO 3 -based lead-free antiferroelectrics

The mechanisms underpinning high energy storage density in lead-free (AFE) ceramics have been investigated. Rietveld reinements of in-situ synchrotron X-ray data reveal that the structure remains quadrupled and orthorhombic under electric ield ( E ) but adopts a non-centrosymmetric space group, Pmc2 1 , in which the cations exhibit a ferrielectric coniguration. Nd and Ta doping both stabilize the AFE structure, thereby increasing the AFE-ferrielectric switching ield from 150 to 350 kV cm − 1 . Domain size and correlation length of AFE/ferrielectric coupling reduce with Nd doping, leading to slimmer hysteresis loops. The maximum polarization (P max ) is optimized through A-site aliovalent doping which also decreases electrical conductivity, permitting the application of a larger E . These effects combine to enhance energy storage density to give W rec = 6.5 J cm − 3 for Ag 0.97 Nd 0.01 Ta 0.20 Nb 0.80 O 3 .


Introduction
Dielectric capacitors have attracted interest for pulsed power applications due to their high power densities and fast charge-discharge rates [1,2] but their low energy storage densities have restricted their use [3]. For a dielectric capacitor, the total energy density (W), recoverable energy density (W rec ), energy storage eficiency (η) and the energy loss (W loss ) are: Antiferroelectric (AFE) ceramics are promising candidates for high energy density due to their large P max and small remanent polarization (P r ) [4]. Extensive research has been carried out on lead-based AFEs over the last decade [5,6] (e.g. lead lanthanum zirconium titanate), due to their high W rec ~6.4 J cm −3 [7] but their toxicity drives an environmental and commercial need for lead-free equivalents [8]. Recently, many studies have focused on lead-free relaxor-type ceramic dielectrics based on, e.g. Na 0.5 Bi 0.5 TiO 3 , BaTiO 3 and BiFeO 3 [9][10][11][12][13]. Generally, these materials offer promising properties at E > 500 kV cm −1 in multilayer ceramic capacitors (MLCCs) with dielectric layer thickness < 10 µm. Lead free AFE ceramics, such as AgNbO 3 , also offer the potential of high energy density due to the delayed onset of an AFE-ferroelectric transition but optimum properties are typically achieved at lower E than relaxors (<500 kV cm −1 ) [14]. AgNbO 3 has the prototype perovskite structure but exhibits a complex sequence of phase transitions on cooling, Table S1 [15,16]. In 2016, Zhao et al. [17] demonstrated that MnO 2 increased W rec , which the authors ascribed to enhanced AFE stability, prompting several further studies [18][19][20][21][22]. W rec of 2.6 J cm −3 was obtained for Bi-doped AgNbO 3 and Ca-doped AgNbO 3 achieved W rec = 3.55 J cm −3 , which was attributed to enhanced breakdown strength (BDS), smaller grain size, Ag vacancies and a reduced tolerance factor (t) [18,21]. W rec of 4.4 J cm −3 and 4.5 J cm −3 were attained for La and Gd doped AgNbO 3 ceramics, respectively [19,22], with the authors quoting similar reasons to those in references [17,20]. The assertion that decreasing t increases AFE stability has been stated by several other researchers [23,24], but W and Ta doping, which lower B-site polarizability but not t, also enhance AFE stability, giving W rec of 3.3 J cm −3 and 4.2 J cm −3 , respectively [25][26][27].
X-ray diffraction (XRD) on ceramic samples was performed using a Bruker D2 phaser benchtop system. The surface morphology of thermally etched polished samples was examined using a FEI Inspect F50 scanning electron microscope (SEM) with a backscattered electron (BSE) detector. Thermal etching of polished samples was conducted at 90% of the sintering temperature for 20 min. Samples for transmission electron microscopy (TEM) were ground manually to a thickness of ~50 µm using a SiC slurry. Ion thinning was conducted at 0.5-3 kV using an Ar ion mill set at an incidence angle of 6 • (PIPS II 695, Gatan, USA). TEM images and electron diffraction patterns were acquired using a JEOL JEM 2100F (Tokyo, Japan) operated at 200 kV.
In-situ high-energy synchrotron XRD experiments were performed at the I15 Diamond light source with a photon energy of 72 keV (λ=0.1722 Å). Ceramic samples were cut into rectangular bars (L5.0 × W1.0 × T0.2 mm), annealed 2 h at 800 • C to eliminate residual stresses and sputter coated with Au to form electrode (area of L4.0 × W0.8 mm) on top and bottom surface. The bar-shaped samples were placed in silicone oil in a custom-designed polyimide holder. During in-situ experiments, the sample holder was electrically connected to a high voltage ampliier (Matsusada EC-10). The X-ray beam was focused and collimated to 70 µm diameter. Transmission and 2-D diffraction patterns were collected using Pilatus 2M detector located ~1 m downstream of the sample prior, during and after application of external E. Collected XRD patterns were calibrated, integrated to eliminate the texture effect and converted into conventional onedimensional XRD patterns using Dawn software. Full-pattern Rietveld reinements were conducted using Topas 6 software to obtain Impedance spectroscopy (IS) data were collected using an Agilent E4980A (Agilent Technologies Inc., Palo-Alto, CA) from 20 Hz to 2 MHz and from 400 to 600 • C at 100 mV. Resistivity was obtained by itting the experimental data using ZView software (Scribner Associates, Inc., Southern Pines, NC). Temperature dependence of dielectric properties was measured using an Agilent 4184A precision LCR meter from room temperature (RT) to 600 • C at 1, 10, 100, 250 kHz and 1 MHz. IS and LCR data were corrected by a geometric factor (thickness/surface area). To obtain polarization-ield (P-E) loops, ceramic samples were ground to ~0.15 mm and gold sputtered to give a circular electrode with an area of 7 mm 2 . Bipolar P-E loops were obtained using an aixACCT TF 2000E ferroelectric tester at 1 Hz.

Results and discussions
All peaks in XRD patterns (Fig. S1) were indexed according to a single orthorhombic perovskite structure with Pbcm symmetry. An enlarged view of the {200} c peak (Fig. S1a) illustrates that splitting decreases with increasing Nd concentration. As Ta concentration increases however, a reduction in splitting is also accompanied by peaks shifting to higher 2θ values (Fig. S1b), suggesting smaller d-spacings. Ta 5+ and Nb 5+ have the same effective ionic radius (0.64 Å, CN = 6) [28] and it is most likely the decrease in ionic polarizability from Nb to Ta which reduces the average off-centering of the B-site ion in the octahedra and modiies the cell parameters [23].
SEM images of thermally-etched polished ceramic samples are shown in Fig. S2, which reveal equiaxed grains with minimal porosity, consistent with a relative density ~95%. The average grain size of all studied samples was < 5 µm, with the smallest (~2 µm) in x = 0.02. Nd doping with x = 0.01 and 0.02 inhibits grain growth but for x ≥ 0.03, the grain size increases, and secondary phases emerge. The grain size increases from ~2.5 µm in Nd 0.01 to ~5 µm in Nd 0.01 Ta 0.10 as a result of the higher sintering temperature employed for the latter. The average grain size decreases slightly with further increasing Ta concentration ( Fig. S2e-h), which may be associated with the more refractory nature of Ta 2 O 5 in comparison with Nb 2 O 5 [29].
Fig. 1a-d shows [210] c (c = cubic) zone axis electron diffraction patterns and the corresponding dark ield images obtained using fundamental (001) c perovskite relections for Ag 1-3x Nd x NbO 3 compositions. As Nd concentration increases to 0.03, the domain width decreases from ~1 µm (Fig. 1b) to < 0.3 µm (Fig. 1d) which is attributed to disruption of the antipolar order due to the presence of Nd •• Ag and V ′ Ag . The disruption in antipolar order is also manifest in electron diffraction patterns as elongation and streaking of the ± ¼{00l} c relections in the [001] c direction as x increases from 0 ( Fig. 1a) to 0.03 (Fig. 1c). The streaking (highlighted by circles in Fig. 1a and c) and decrease in domain width (highlighted by dashed lines in Fig. 1b and d) are Typical Z* plots, combined Z" and M" spectroscopic plots, and Arrhenius plots of Ag 1-3x Nd x NbO 3 and Ag 0.97 Nd 0.01 Ta y Nb 1-y O 3 ceramics are given in Fig. S3. Only one semicircle was observed in the Z* plot for all compositions, as shown in Fig. S3a and b, and one Debye peak in both Z" and M" spectroscopic plots locates at the same frequency ( Fig. S3c and  d), indicating that all samples are electrically homogeneous [30]. The total resistivity of the ceramics (obtained from low frequency intercepts in Z* plots) increases with increasing Nd and/or Ta concentration, together with an increase in activation energy ( Fig. S3e and f), suggesting potential enhancement of BDS [31].
The temperature dependence of permittivity (ε r vs T) and loss (tanδ vs T) at 100 kHz of Ag 1-3x Nd x NbO 3 and Ag 0.97 Nd 0.01 Ta y Nb 1-y O 3 ceramics are shown in Fig. 2. A sequence of dielectric anomalies is  observed, consistent with the phase transitions reported for undoped AgNbO 3 (Table S1) [16].  Fig. S4, suggesting that the M 2 -M 3 phase transition is frequency independent. P-E and current-electric ield (I-E) loops as a function of composition under maximum applied ield (E max ) for Ag 1-3x Nd x NbO 3 and Ag 0.97 Nd 0.01 Ta y Nb 1-y O 3 ceramics are shown in Fig. 3a-d. All compositions exhibit double hysteresis loops, typical AFE behavior. For Nd doped samples (Fig. 3a), E max increases with Nd concentration to 300 kV cm −1 for Nd 0.02 and then decreases to 240 kV cm −1 for Nd 0.03 possibly due to the presence of secondary phases, Fig. S2i. The variation of E max as a function of Nd concentration is consistent with IS data and SEM images and contiguous with a reduced grain size and increased resistivity each of which has been reported to enhance dielectric BDS [33,34].
As Nd concentration increases, P max and P r irst increase (Nd 0.01 ) but then decrease for x > 0.01, as shown in Fig. 3e. The antipolar to polar switching ield may be used to estimate the AFE phase stability. The dependence of the forward switching ield (E F ), the backward switching ield (E A ) and its difference (E F -E A ) are shown as a function of Nd concentration in Fig. 3g. E F increases from 147 kV cm −1 for AgNbO 3 to 241 kV cm −1 for Nd 0.02 but decreases for Nd 0.03 , presumably due to the presence of secondary phases, Fig. S2i. E A increases from 47 to 136 kV cm −1 for AgNbO 3 and Nd 0.03 , respectively. The increase in E F and E A suggests that Nd stabilizes the antipolar with respect to polar phase.
For Ta doped samples, P max and P r decrease since the polarizability of Ta is lower than Nb [25], but the increase in P max for x = 0.01 in the Ag 1-3x Nd x NbO 3 solid solution series suggests that it is already optimized, as shown in Fig. 3f. E F and E A increase with Ta concentration establishing that the antipolar is stabilized with respect to the polar phase at zero ield, Fig. 3h. Fig. 4a-c show representative energy storage properties of Ag 1-3x Nd x NbO 3 and Ag 0.97 Nd 0.01 Ta y Nb 1-y O 3 ceramics at different E with data from further compositions shown in Fig. S5. The corresponding P-E loops are presented in Fig. S6. Generally, η decreases and W rec increases with the increasing E. W rec however, reaches a maximum of 6.5 J cm −3 at 370 kV cm −1 with η of 71% for Ag 0.97 Nd 0.01 Ta 0.20 Nb 0.80 O 3 , decreasing slightly at higher Ta concentrations. These values are superior or equivalent to current lead-free AFE ceramics, Fig. 4f and the reported values of the commercial lead-based incumbents [7,10,17-19, 21,22,25-27,31,33-64].
In-situ synchrotron XRD was employed to study the crystal structure of Ag 0.97 Nd 0.01 Ta 0.25 Nb 0.75 O 3 ceramics prior, during and after application of E. This composition has the highest BDS from Fig. 3b and was thus least likely to breakdown during in-situ poling experiment. Fig. 5a shows the effect of E on a) two XRD representative peaks (indexed using cubic prototype cell); b) illustrates the full-pattern reinements of the zero-ield and ield-induced phases and c) reveals the schematic structures at zero ield and 380 kV cm −1 in which the relative ion displacements are represented as arrows. The best reinement of AFE phase at zero ield was obtained using orthorhombic Pbcm symmetry with Goodness of Fit (GoF) = 1.07, however, small changes in the intensity of the peaks were observed (Fig. 5a) at 380 kV cm −1 (above E F ). Several symmetries were used to try and reine XRD patterns under ield, including Pbcm (orthorhombic, space group 57, GoF = 1.10) but Pmc2 1 (orthorhombic, space group 26, GoF = 1.02) provided a marginally better description of the symmetry compared with the others, as shown in Fig. 5b. We note however, in Pbcm, the long axis is c (≈4a c , where a c is cubic perovskite cell parameter) but in Pmc2 1 , a has the largest lattice parameter. The reinement parameters are listed in Table S2. Given the marginally better GOF and that P-E loops open and exhibit hysteresis above a threshold value, E F , we conclude that the noncentrosymmetric, Pmc2 1 space group best describes the symmetry of Ag 0.97 Nd 0.01-Ta 0.25 Nb 0.75 O 3 at 380 kV cm −1 . Fig. 5c shows schematics of the zero ield and ield induced structures with b Pbcm //c Pmc21 , emphasizing the relative cation displacements (arrows) and how they differ in the centro-(Pbcm) and noncentrosymmetric (Pmc2 1 ) space groups, In the centrosymmetric Pbcm cell, Ag and Nb atoms averagely displace ± 0.019 and . The Ag sub-lattice therefore, exhibits a net polarization along the c axis (equivalent to the b axis in the Pbcm setting). The four pairs of Nb 5+/ Ta 5+ ions exhibit unequal antiparallel displacements along [001]/[001] to give a further net contribution to polarization along the c axis. The ield-induced transition may therefore, be considered to occur between a quadrupled, orthorhombic AFE to a ferrielectric phase whose average structure does not involve a change in crystal class or in the number of perovskite formula units per unit cell. In contrast, in Pb(Zr,Ti)O 3 (PZT)-based AFE materials, a rhombohedral polar structure is stabilized at high ield which involves a change in crystal class and a large strain (0.45% at 60 kV cm −1 ) [65]. The total strain for Ag 0.97 Nd 0.1 Ta 0.25 Nb 0.75 O 3 was calculated as 0.06% at 380 kV cm −1 from representative relections in in-situ XRD data using the Daymond method [12].
To explore further the microscopic origin of energy storage properties in Nd/Ta co-doped AgNbO 3 lead-free AFE ceramics, irst-principles density functional theory (DFT) calculations and Landau--Ginzburg-Devonshire (LGD) phenomenological theory were carried out. The detailed information can be obtained in Fig. S7 (supplementary information) but in summary, preliminary DFT calculations and LGD phenomenological theory both concur that Nd/Ta co-doping stablizes the AFE structure, thereby increasing the ield required for the onset of the AFE-ferrielectric induced phase transition. Ag decreases long-range coupling of antipolar and thereby induced ferrielectric order. This effect is manifested in a reduction of splitting in {200} c peaks in XRD patterns, smaller AFE domains and streaking of ± ¼{00l} c relections in electron diffraction patterns, respectively, as Nd concentration increases. The induced ferrielectric portion of the P-E loop becomes slimmer and the area to its left increases. iv) Nd and Ta increase the stability of the AFE phase. Enhanced AFE stability increases E F and improves W rec by increasing the area to the left of the P-E loop.
Nd/Ta co-doping in AgNbO 3 thus create a set of crystallo-chemical criteria which in combination optimize W rec . Importantly, the AFE to ferrielectric transition does not involve a change in crystal class so potentially offers minimum strain (0.06% at 380 kV cm −1 ) in comparison with lead-based analogs such La doped PZT (0.71% at 300 kV cm −1 ) [66]. We note that enhancement of W rec for lead-free relaxors has been reported for ilms and multilayers with respect to ceramics due to the larger BDS [9,67]. It remains to be elucidated whether multilayers of Nd/Ta co-doped AgNbO 3 achieve a similar enhancement with respect to bulk ceramic properties. A schematic illustrating how these principles combine to optimize W rec is shown in Fig. 6.

Conclusions
In summary, W rec of 6.5 J cm −3 , equivalent to lead-based ceramics, was achieved in Ag 0.97 Nd 0.01 Ta 0.20 Nb 0.80 O 3 , at an applied E of 370 kV cm −1 . The factors which result in such a large W rec in Nd/Ta codoped AgNbO 3 are complex but are ascribed to four key points: (i) an increase in resistivity which increases BDS and permits the application of larger E, (ii) optimization of P max through A-site aliovalent doping, (iii) slimmer portion of the P-E loop in the induced ferrielectric region due to the presence of Nd •• Ag and V ′ Ag defects, and iv) stabilization of the AFE phase, giving higher E F . Fig. 6. Schematic diagram illustrating how W rec is optimized through doping in AgNbO 3 . Gray, yellow, green, dark green and red spheres represent Ag, Nd, Nb, Ta and O atoms, respectively. Gray squares represent silver vacancies. (For interpretation of the references to color in this igure legend, the reader is referred to the web version of this article.) CRediT authorship contribution statement D.W., S.L., and I.M.R. supervised the research. Z.L. wrote the article and carried out the electrical and energy storage property. Z.L., G.W., L. L., D.W. and A.K.K. contributed to the in-situ synchrotron X-ray experiment. S.S. conducted the SEM characterizations. W.B. and F.X. conducted the TEM characterizations. J.L., H.Y., H.J. and A.F. contributed to data discussion and to write the article. D.L. and S.L. developed the theory and performed the computations. All the authors discussed the results and commented on the manuscript.

Declaration of Competing Interest
The authors declare that they have no known competing inancial interests or personal relationships that could have appeared to inluence the work reported in this paper.