Energy barriers for proton migration in yttrium-doped barium zirconate super cell with Σ5 (310)/[001] tilt grain boundary

The energy barriers for proton migration in polycrystalline yttrium-doped barium zirconate were investigated using density functional theory. The Σ5 (310)/[001] tilt grain boundary was constructed by attaching two (310) planes along the [001] direction, and replacing a Zr ion with an Y ion. In the thus-prepared super cell, the energy barriers for the transfer of the proton across the grain boundary were calculated. The energy barriers for proton migration up to the grain boundary within a single grain, which is the combination of the transfer and rotation of the proton, were also calculated. The most plausible pathway for proton migration from one grain to an adjacent grain across the Σ5 (310)/[001] tilt grain boundary required an energy barrier of 0.72 eV.