Critical ionic transport across an oxygen-vacancy ordering transition

Abstract

Phase transition points can be used to critically reduce the ionic migration activation energy, which is important for realizing high-performance electrolytes at low temperatures. Here, we demonstrate a route toward low-temperature thermionic conduction in solids, by exploiting the critically lowered activation energy associated with oxygen transport in Ca-substituted bismuth ferrite (Bi_1-xCa_xFeO_3-δ) films. Our demonstration relies on the finding that a compositional phase transition occurs by varying Ca doping ratio across x_Ca ≃ 0.45 between two structural phases with oxygen-vacancy channel ordering along <100> or <110> crystal axis, respectively. Regardless of the atomic-scale irregularity in defect distribution at the doping ratio, the activation energy is largely suppressed to 0.43 eV, compared with ~0.9 eV measured in otherwise rigid phases. From first-principles calculations, we propose that the effective short-range attraction between two positively charged oxygen vacancies sharing lattice deformation not only forms the defect orders but also suppresses the activation energy through concerted hopping.

Fig. 1. Real-time observation of V_O migration in BCFO films.

a Schematic of a BCFO channel protected by a LaAlO₃ capping layer with a pair of 400-μm gapped coplanar electrodes. Optical microscopic video and real-time current were simultaneously monitored while a constant voltage was applied. V_Os migrated toward the ground electrode, thereby extending a conducting dark-colored formed phase. b Time evolution of the optical contrast along the centerline of the channel during the electroforming process at x_Ca= 0.45. The orange dashed line represents the boundary between the intermediate dark-yellow phase and the completely-formed dark-colored phase. c Trajectories of the boundary position as a function of elapsed time at selected Ts. Horizontal and vertical error bars represent the full-width-at-half-maximum (FWHM) of differential color change Gaussian profiles along the position and time coordinates. The green fitting curves indicate that the simplified model (described in the main text) matches the experimental data well. d The fitting variables of ionic mobility and time offset were evaluated from the fitting in c. e Arrhenius plots of V_O diffusivity in BCFO films of different x_Cas (0.1 ~ 0.6). Solid lines indicate the linear relationship between logarithmic diffusivities and inverse Ts. f Arrhenius plots of ionic conductivity times T. Filled dots were obtained using the optical visualization. Empty dots were obtained using AC impedance spectroscopy of N₂ gas annealed BCFO films. g The E_A of V_O diffusivity with respect to x_Ca. Both filled dots (from the optical visualization) and empty dots (from the AC impedance spectroscopy) are well matched on the red guide line. h Prefactor of diffusivity (D₀) as a function of x_Ca. i Correlation between logarithmic D₀ and linear E_A. Error bars in d–i represent the standard errors of fittings or the values calculated from them based on error propagation for the derived parameters.

Fig. 2. Observation of V_O channels and the compositional phase transition point in BCFO films.

a Schematics of three types of oxygen ion migration in 2D potentials. Oxygen ions avoid residing on the 1D atomic-scale channels because the potential therein is not relatively deep. Ionized V_Os are mainly present in the channel regions, which offer more positive potential in a self-consistent way. Free energy landscapes over the ionic configuration indicate competition between two types of channels along [100] or [110]. Configuration fluctuations can be significantly large at the phase transition point, leading to enhancement of generalized susceptibilities such as elastic compliance and ionic conductivity. b, c Representative ABF-STEM images along [010] ([$\overline{1}$10]) in the V_O layers present in BCFO (x_Ca = 0.3, 0.45 and 0.6), and corresponding intensity line profiles. The intensity line profiles averaged over 15 pixels were extracted from the ABF-STEM images along the [100] ([110]) direction, i.e., across the Fe/O–O atomic columns. The black arrows in b indicate that the intensity of the oxygen atomic columns is not uniform, instead V_O ordering is observed. The black arrows in c show that the Fe–Fe distances are not uniform; instead two clearly different Fe–Fe distances alternate along the [110] direction. The Fe–Fe distances are 0.24 ± 0.02 and 0.33 ± 0.02 nm for the x_Ca = 0.6 phase, and 0.27 ± 0.01 and 0.30 ± 0.01 nm for the x_Ca = 0.3 and 0.45 phases. d Schematics of the atomic configuration of the BCFO films with V_O channels.

Fig. 3. DFT calculation results for collective ion diffusion.

a Schematic diagram of individual or collective diffusions of vibrating oxygen ions in the [110] channel of the phase I (as-grown BCFO with 3V_O) and phase II (intermediate phase with 2V_O). b Electronic structures of four possible phases, phase 0 with 4V_O, as-grown phase I with 3V_O, phase II with 2V_O, and phase III without V_O, in a representative BCFO (x_Ca = 0.25) with fixing n_period = 6. Red and blue lines are spin-up and spin-down bands, respectively. Here, the reciprocal positions of the supercell are denoted by A = (0.5, 0.5, 0.5), Γ = (0.0, 0.0, 0.0), M = (0.5, 0.5, 0.0), and X = (0.5, 0.0, 0.0). c E_A of V_O migration for phases I and II. Both comparative calculations use periodic boundary conditions to mimic a sufficiently long coherence length of ions positional fluctuations (longer than the relaxation length). Only the phase II shows a significant reduction in E_A, indicating the high defect density in the intermediate phase, which appears in the nonequilibrium situation after electroforming, is a necessary condition for the correlative migration.

Fig. 4. Structural softness in the compositional phase transition point in BCFO films.

a Force versus distance curve of BCFO at x_Ca = 0.45, obtained by characterizing the elastic property using an AFM technique. (Inset) The measured force (F) was evaluated by cantilever bending against surface depth deformation (δ_d). Zero cantilever deflection, i.e., F = 0, corresponds to the situation where the attractive adhesive force (F_adh ≤ 0) between the sample and tip is fully compensated by the tip pressing force. So, the real tip-driven force on the sample surface is F−F_adh. Magenta and cyan indicate approach and retreat modes. b Tip-driven force (F−F_adh) versus δ_d curves for selected x_Ca. The DMT model was used to interpret these experimental data, creating green fit lines. c Statistics of the values of Young’s modulus obtained by repeating the force-distance measurement at many different places on the surface. The lines represent Gaussian fittings of the observed distributions. d The measured Young’s modulus versus x_Ca. The error bar is defined as the standard deviation of distributions.