Graph analysis of proton conduction pathways in scandium-doped barium zirconate

Understanding the relationship between the acceptor dopant size and proton conductivity in barium zirconate, BaZrO3, is important for maximizing efficiency in this promising fuel cell material. While proton conduction pathways with larger YZr′ and smaller AlZr′ defects have been explored, proton pathways with ScZr′, a defect of comparable size to the replaced ion, have not been investigated using centrality measures, periodic pathway searches, and kinetic Monte Carlo (KMC). Centrality measures in BaSc0.125Zr0.875O3 highlight a trapping region by ScZr′ and scattered high centrality regions on undoped planes. Connected long-range high centrality regions are found mainly in undoped planes for BaAl0.125Zr0.875O3 and in the dopant planes for BaY0.125Zr0.875O3. The best long-range proton conduction periodic pathways in AlZr′ and ScZr′ systems travel between dopant planes, while those for yttrium-doped BaZrO3 remained on dopant planes. KMC trajectories at 1000 K show long-range proton conduction barriers of 0.86 eV, 0.52 eV, and 0.25 eV for AlZr′, ScZr′, and YZr′ systems, respectively. Long-range periodic conduction highway limiting barrier averages correlate well with the connectivity of the most central regions in each system but ignore diffusion around the dopant and through other high centrality regions. BaSc0.125Zr0.875O3 shows an intermediate overall conduction barrier limited by trapping, which earlier experiments and simulations suggest that it can be mitigated with increased oxygen vacancy concentration.