Calculation of proton conductivity at the Σ3111/11¯0 tilt grain boundary of barium zirconate using density functional theory

• We develop a procedure for proton conductivity calculation.
• The procedure employs space charge layer model and structural disorder model.
• Proton conductivity is calculated at grain boundary of BaZrO3.

We theoretically investigate proton conductivity at the Σ3111/11¯0 tilt grain boundary of barium zirconate using density functional theory. In order to evaluate the space charge layer model and the structural disorder model, segregation energies of a + 1-charged proton and a + 2-charged oxygen vacancy, as well as energy barriers for proton migration, are calculated. The effect of the proton concentration on its segregation is verified and it is found that the segregation energy decreases with increases in the concentration. With consideration of this effect, the segregation energies of the proton and oxygen vacancy are in the range of − 0.35 to − 0.60 and − 0.57 to − 0.65 eV, respectively. Based on the segregation energies, an electrostatic potential of 0.51 V at 600 K is obtained through numerically solving Poisson's equation. An energy barrier range of 0.71–0.95 eV is required for the proton to migrate across the grain boundary core. The proton concentration and mobility that are obtained from the electrostatic potential and energy barrier are used to calculate the proton conductivities in the bulk and at the grain boundary. The calculated proton conductivities are consistent with the experimentally measured proton conductivities in the bulk and at the grain boundaries of barium zirconate.