Lattice distortion mediated proton pairing and trapping in solid state oxides

Experiments have evidenced proton pairing in Y-doped ${\mathrm{BaZrO}}_{3}$. 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 ${\mathrm{BaZrO}}_{3}$, 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 multiproton diffusion mechanism, providing a theoretical foundation for the experimental design of electrolytes with enhanced proton conductivity.