High activation energy for proton migration at ∑3111/11¯0 tilt grain boundary in barium zirconate

The behavior of a proton at a ∑3111/11¯0 tilt grain boundary in barium zirconate was investigated in order to explain proton migration at grain boundaries by using density functional theory. The space charge layer model and the structural disorder model have been proposed in the literature to explain the high activation energies for proton migration at grain boundaries as compared with those at the bulk. The space charge layer model was evaluated by calculating the segregation of an oxygen vacancy at the grain boundary core. The segregation of the oxygen vacancy at the grain boundary core developed a Schottky barrier height and generated a space charge layer at both sides of the core by expelling positively charged mobile protons. Since the activation energy for proton migration was affected by the decreased proton concentration in the space charge layer, the formation energy of the proton was considered in explaining the high activation energy at grain boundaries. The structural disorder model was evaluated by calculating the energy barriers for proton migration at the grain boundary core. High energy barriers for proton migration, in the range of 0.61 ~ 0.64 eV, were required at the grain boundary core, while relatively low energy barriers, in the range of 0.18 ~ 0.24 eV, were required near it. This high energy barrier for proton migration due to the structural disorder at the grain boundary core can also explain the high activation energy. Therefore, both the effect of the Schottky barrier height and the structural disorder at the grain boundary core should be considered in explaining the high activation energy for proton migration at the grain boundary in barium zirconate.