Abstract
A centrality measure based on the time of first returns rather than the number of steps is developed and applied to finding proton traps and access points to proton highways in the doped perovskite oxides: AZr(0.875)D(0.125)O3, where A is Ba or Sr and the dopant D is Y or Al. The high centrality region near the dopant is wider in the SrZrO3 systems than the BaZrO3 systems. In the aluminum-doped systems, a region of intermediate centrality (secondary region) is found in a plane away from the dopant. Kinetic Monte Carlo (kMC) trajectories show that this secondary region is an entry to fast conduction planes in the aluminum-doped systems in contrast to the highest centrality area near the dopant trap. The yttrium-doped systems do not show this secondary region because the fast conduction routes are in the same plane as the dopant and hence already in the high centrality trapped area. This centrality measure complements kMC by highlighting key areas in trajectories. The limiting activation barriers found via kMC are in very good agreement with experiments and related to the barriers to escape dopant traps.
Highlights
Graph theory has long been used to study a variety of networks, including social, telecommunications, ecological, cellular signaling, and citation networks
Kinetic Monte Carlo trajectories show that this secondary region is an entry to fast conduction planes in the aluminum-doped systems in contrast to the highest centrality area near the dopant trap
Centrality measures based on time rather than number of steps at 1000 K have been used to assess proton movement in AZr0.875D0.125O3 perovskites, where A is Ba or Sr and the dopant D is Y or Al
Summary
Graph theory has long been used to study a variety of networks, including social, telecommunications, ecological, cellular signaling, and citation networks. The difference between the average number of steps connecting any two vertices when connecting paths must pass through a vertex i versus not passing through vertex i may be calculated. The inverse of this difference is another measure of centrality of i. The needed theorems are proven in the Appendix Using these theorems, centrality measures based on time rather than number of steps are calculated.
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