The effect of yttrium dopant on the proton conduction pathways of BaZrO₃, a cubic perovskite

When BaZrO₃ is doped with Y in 12.5% of Zr sites, density functional theory with the PBE functional predicts octahedral distortions within a cubic phase yielding a greater variety of proton binding sites than undoped BaZrO₃. Proton binding sites, transition states, and normal modes are found and used to calculate transition state theory rate constants. The binding sites are used to represent vertices in a graph. The rate constants connecting binding sites are used to provide weights for graph edges. Vertex and color coding are used to find proton conduction pathways in BaZr0.875 Y0.125 O ₃. Many similarly probable proton conduction pathways which can be periodically replicated to yield long range proton conduction are found. The average limiting barriers at 600 K for seven step and eight step periodic pathways are 0.29 and 0.30 eV, respectively. Inclusion of a lattice reorganization barrier raises these to 0.42 and 0.33 eV, respectively. The majority of the seven step pathways have an interoctahedral rate limiting step while the majority of the eight step pathways have an intraoctahedral rate limiting step. While the average limiting barrier of the seven step periodic pathway including a lattice reorganization barrier is closer to experiment, how to appropriately weight different length periodic pathways is not clear. Likely, conduction is influenced by combinations of different length pathways. Vertex and color coding provide useful ways of finding the wide variety of long range proton conduction pathways that contribute to long range proton conduction. They complement more traditional serial methods such as molecular dynamics and kinetic Monte Carlo.