Lattice-Distortion-Mediated Proton Pairing and Trapping in Solid State Oxides

Abstract

Experiments have evidenced proton pairing in Y-doped BaZrO3. However, the nature of proton pairing and its impact on conduction remain insufficiently understood theoretically. Here, through quantitative computational analysis of proton-proton interactions in Y-doped BaZrO3, we identify lattice-distortion-mediated elastic interaction as the key factor determining whether two protons form a stable pair or exhibit net repulsion. When a proton resides at an inward-bending distortion site induced by another proton, the resulting net repulsive interaction leads to an unstable configuration. In contrast, the proton tends to be trapped at a nearby outward-bending site that favors the formation of a stable proton pair. Moreover, the site where the two protons form the lowest-energy configuration also corresponds to a proton trapping site. By calculating the long-range diffusion pathways accessible to protons under different local environments in both single- and two-proton cases, we find that the range of rate-limiting barriers is 0.24-0.45 eV for two-proton conduction and 0.19-0.39 eV for single-proton conduction. The higher and more experimentally consistent barriers in the two-proton pathways indicate that the proton trapping effect induced by pairing hinders proton conduction. Our study elucidates the multi-proton diffusion mechanism, providing a theoretical foundation for the experimental design of electrolytes with enhanced proton conductivity.

Figures (12)

• Figure 1: Lattice distortions induced by a proton in the (a) bc, (b) ba, and (c) ac planes. Cyan-blue, gray-green, and pink spheres represent Zr, Y, and O atoms, respectively, while the black sphere denotes the first fixed proton.
• Figure 2: (a,c) Schematic illustration of two-proton configurations with proton 1 fixed at the Y-adjacent oxygen site along the b-axis (a) and c-axis (c). The black sphere represents the fixed proton 1, and the white sphere represents proton 2 at different positions. (b,d) Proton-proton interaction energy $E_{int}$, and electrostatic repulsion energy $E_{elec}$ (blue line of insert) and elastic interaction energy $E_{elas}$ (pink line of insert) for the configurations in (a) and (c), respectively.
• Figure 3: (a) Lattice distortion in the plane induced by a proton at the nearest-neighbor site of Y along the b-axis (top), and the modified distortion when a second proton is added at the repulsive site 6 (bottom). (b) Similar distortions for a proton at the Y-adjacent site along the c-axis (top), and with an additional proton at repulsive site 10 (bottom).
• Figure 4: (a) Schematic of the minimum energy pathway for two-proton migration under uniform Y doping. (b) Energy barrier along the pathway shown in (a); the inset illustrates the rate-limiting step(red line). (c) Single-proton diffusion pathway (inset) and energy barrier corresponding to (a), with the red line indicating the rate-limiting step.
• Figure 5: (a) Schematic of the two-proton diffusion pathway in the low-density, non-uniform Y-doped region. (b) Energy barrier along the pathway shown in (a); the inset illustrates the rate-limiting step (red line). (c) Single-proton diffusion pathway (inset) and energy barrier corresponding to (a), with the red line indicating the rate-limiting step. (d-f) Two-proton and single-proton diffusion in the high-density, non-uniform Y-doped region.