Origin of Space Charge in Grain Boundaries of Proton-Conducting BaZrO3

Segregation energies of oxygen vacancies and protons near three symmetric tilt grain boundaries (GBs) in BaZrO3 are determined using density functional theory. Two of the GBs have the [$ \overline 1 $10] direction as tilt axis with a (111) or (112) plane as GB plane, while the third has the [001] direction as tilt axis and a (210) plane as GB plane. Both defects are found to segregate to all three GBs, with vacancy segregation energies of 0.5 and 1.5eV and proton segregation energies of about 0.8eV. The effects of the calculated segregation energies on defect concentrations and electrostatic potential in the GB region are investigated using a thermodynamic space charge model. An increased concentration of defects is seen in all GBs, giving electrostatic potential barriers around 0.6V at 400600K. Protons are found to give important contributions to the space charge in all three GBs.