Designing lead-free antiferroelectrics for energy storage

Abstract

Dielectric capacitors, although presenting faster charging/discharging rates and better stability compared with supercapacitors or batteries, are limited in applications due to their low energy density. Antiferroelectric (AFE) compounds, however, show great promise due to their atypical polarization-versus-electric field curves. Here we report our first-principles-based theoretical predictions that Bi_1-xR_xFeO₃ systems (R being a lanthanide, Nd in this work) can potentially allow high energy densities (100-150 J cm^-3) and efficiencies (80-88%) for electric fields that may be within the range of feasibility upon experimental advances (2-3 MV cm^-1). In addition, a simple model is derived to describe the energy density and efficiency of a general AFE material, providing a framework to assess the effect on the storage properties of variations in doping, electric field magnitude and direction, epitaxial strain, temperature and so on, which can facilitate future search of AFE materials for energy storage.

Figure 1. Schematic illustrations.

(a) The definition of stored energy density and energy loss from the typical polarization-versus-electric field double hysteresis loop of antiferroelectrics. The arrows indicate the charging and discharging processes. E_up and E_down denote the critical field at the AFE–FE and FE–AFE transitions, respectively. E_C is the electric field at which the FE and AFE phases have precisely the same energy. (b) The energetic paths and barriers connecting the AFE and FE phases with increasing E-field.

Figure 2. Relevant structures of Bi_1−xNd_xFeO₃.

(a) The antiferroelectric orthorhombic Pnma phase (AFE phase), characterized by the anti-polar distortions along the pseudo-cubic [110] direction, and oxygen octahedral tiltings (a⁻a⁻c⁺ in Glazer notations14). (b) The ferroelectric R3c phase (R phase), characterized by polar distortions and anti-phase tiltings about the [111] direction (a⁻a⁻a⁻). (c) The ferroelectric tetragonal P4mm phase (T phase), characterized by polar distortions along the [001] direction and no tiltings (a⁰a⁰c⁰). (d) The ferroelectric Amm2 orthorhombic phase (O phase), characterized by polar distortions along the [110] direction and no tiltings (a⁰a⁰c⁰). The VESTA code is used for the visualization. Arrows represent local electric dipoles.

Figure 3. Calculated P–E hysteresis curves of Bi_1−xNd_xFeO₃ solid solutions.

Nd composition ranges between 0.4 and 1.0, and four different electric field orientations are considered. (a) [001]. (b) [100]. (c) [110]. (d) [111]. The displayed polarization is the projected component of the total polarization along the direction of the applied E-field. The arrows inside the boxes (on the sides of each panel) schematize the direction of the long-range-ordered electric dipoles in the initial and final states. The different colours used for the solid lines denote compositions ranging from x=0.4 to 1.0, as shown by the legend on the right.

Figure 4. Energy-storage performance and model parameters.

(a,b) The calculated energy density and efficiency of Bi_1−xNd_xFeO₃ solid solutions at various compositions (x=0.4–1.0) and under various electric field orientations, with the maximum applied E-field (E_max) being 2.6 MV cm⁻¹ (larger than the AFE–FE transition field for all cases). The discrete data are calculated from the effective Hamiltonian simulations based on the predicted P–E curves. The solid lines come from a least square fit of W and η to the simple model mentioned in the text (equations (6) and (7)) and Supplementary Note 6, with being the variable for each E orientation with linear dependence on the composition. (c–e) Model parameters at various compositions and E-field orientations. (c) The zero-field energy difference between the AFE and FE phases. (d) The FE-to-AFE barrier at E=0 (δ⁰, dashed lines), E_down (, dotted lines) and E_C (, solid lines). (e) The dielectric susceptibility.

Figure 5. The computed energy storage performance of selected Bi_1−xNd_xFeO₃ solid solutions.

(a) The P–E hysteresis curves. (b) The energy density as a function of the magnitude of the maximum applied electric field, with the discrete symbols representing the best available experimental data from different types of materials, that is, lead-based (PbZrO₃ (PZO), PLZT, (Pb,La)(Zr,Sn,Ti)O₃ (PLZST) and Pb(Zn_1/3Nb_2/3)O₃-Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (PZN-PMN-PT)33), and lead-free (BNLBTZ and HZO11) systems. (c) The efficiency as a function of the magnitude of the maximum applied electric field. The dotted vertical line denotes the estimated intrinsic breakdown field for BFO.