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 Y_Zr ^' and smaller Al_Zr ^' defects have been explored, proton pathways with Sc_Zr ^', 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 BaSc_0.125Zr_0.875O₃ highlight a trapping region by Sc_Zr ^' and scattered high centrality regions on undoped planes. Connected long-range high centrality regions are found mainly in undoped planes for BaAl_0.125Zr_0.875O₃ and in the dopant planes for BaY_0.125Zr_0.875O₃. The best long-range proton conduction periodic pathways in Al_Zr ^' and Sc_Zr ^' 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 Al_Zr ^', Sc_Zr ^', and Y_Zr ^' 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. BaSc_0.125Zr_0.875O₃ 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.