Proton conducting oxide ceramics have shown potential for use in fuel cell technologies. Understanding the energy pathways for proton conduction could help us design more efficient fuel cell materials. This paper describes how octahedral tilting affects the relative energies of proton binding sites, transition states, and conduction pathways in cubic and pseudo-cubic perovskites. First, the structure for cubic and pseudo-cubic forms of BaTiO3, BaZrO3, CaTiO3, and CaZrO3, is found. Even when cubic symmetry is enforced, CaTiO3, and CaZrO3 exhibit octahedral tilting distortions characteristic of orthorhombic phases while BaTiO3 and BaZrO3 remain undistorted. Octahedral tilting gives rise to proton binding sites facilitating inter- and intra-octahedral proton transfer while the proton binding sites of undistorted perovskites facilitate only intra-octahedral proton transfer. The nudged elastic band method is used to find minimum energy paths between the proton binding sites. As distortions increase, inter-octahedral proton transfer barriers decrease while intra-octahedral proton transfer barriers increase. Concurrently, rotational barriers from oxygens facilitating inter-octahedral proton transfer increase while rotational barriers from oxygens facilitating intra-octahedral proton transfer decrease. Intra-octahedral transfer is the rate-limiting step to the lowest energy extended proton conduction pathway in all the perovskites considered.

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 BaZr0.875Y0.125O3. 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.

Y-doped BaZrO₃ is a promising proton conductor for intermediate temperature solid oxide fuel cells. In this work, a combination of static DFT calculations and DFT based molecular dynamics (DFT-MD) was used to study proton conduction in this material. Geometry optimizations of 100 structures with a 12.5% dopant concentration allowed us to identify a clear correlation between the bending of the metal–oxygen–metal angle and the energies of the simulated cells. Depending on the type of bending, two configurations, designated as inward bending and outward bending, were defined. The results demonstrate that a larger bending decreases the energy and that the lowest energies are observed for structures combining inward bending with protons being close to the dopant atoms. These lowest energy structures are the ones with the strongest hydrogen bonds. DFT-MD simulations in cells with different yttrium distributions provide complementary microscopic information on proton diffusion as they capture the dynamic distortions of the lattice caused by thermal motion. A careful analysis of the proton jumps between different environments confirmed that the inward and outward bending states are relevant for the understanding of proton diffusion. Indeed, intra-octahedral jumps were shown to only occur starting from an outward configuration while the inward configuration seems to favor rotations around the oxygen. On average, in the DFT-MD simulations, the hydrogen bond lengths are shorter for the outward configuration which facilitates the intra-octahedral jumps. Diffusion coefficients and activation energies were also determined and compared to previous theoretical and experimental data, showing a good agreement with previous data measuring local proton motion.