The effects of carrier–carrier interaction on the proton diffusivity in a proton-conducting perovskite, Y-doped BaZrO3, have theoretically been investigated in a first-principles manner. The proton diffusivity with the proton–proton interaction was estimated by solving the master equation under the single-particle approximation. The correlation effect between successive jumps was also taken into account to estimate the proton diffusivity with more accuracy. As a result, the proton–proton interaction has two competitive effects on the proton diffusivity, i.e., the negative effect of carrier blocking and the positive effect of trap-site filling. In BaZr1–x Y x O3−δ at the typical doping level (x = 0.2), the trap-site filling effect is dominant, resulting in higher proton diffusivity than that estimated without proton–proton interaction. This positive effect suggests a possible strategy for improving the proton mobility, i.e., trap-site-killer doping, which has a function to fill, annihilate, and/or destabilize the trap sites.

The effect of dopant configurations on the proton diffusivity in yttrium-doped barium zirconate (BZY).

We propose a machine-learning-based (ML-based) method for efficiently predicting atomic diffusivity in crystals, in which the potential energy surface (PES) of a diffusion carrier is partially evaluated by first-principles calculations. To preferentially evaluate the region of interest governing the atomic diffusivity, a statistical PES model based on a Gaussian process (GP-PES) is constructed and updated iteratively from known information on already-computed potential energies (PEs). In the proposed method, all local energy minima (stable & metastable sites) and elementary processes of atomic diffusion (atomic jumps) are explored on the predictive mean of the GP-PES. The uncertainty of jump frequency in each elementary process is then estimated on the basis of the variance of the GP-PES. The acquisition function determining the next grid point to be computed is designed to reflect the impacts of the uncertainties of jump frequencies on the uncertainty of the macroscopic atomic diffusivity. The numerical solution of the master equation is here employed to readily estimate the atomic diffusivity, which enables us to design the acquisition function reflecting the centrality of each elementary process.