The effect of dopant at the Zr site on the proton conduction pathways of SrZrO3: an orthorhombic perovskite.

Doping orthorhombic SrZrO(3) at 12.5% of the Zr sites with Al(3+) leads to a local squaring of the lattice, while doping with larger Y(3+) increases local octahedral distortions. Proton activation energy barriers and transition state theory prefactors are calculated. The wide range of intra-, inter-, and rotational barriers suggest that a comprehensive pathway analysis is needed to find the limiting conduction barriers. Simple seven to ten step periodic pathways leading to system wide conduction are enumerated using vertex coding. At 900-1300 K, the average limiting barriers to long range conduction are 0.6 and 0.4 eV in Al/SrZrO(3) and Y/SrZrO(3), respectively, in reasonable agreement with the experiment. Path analysis gives the added insight that conduction pathways in Al/SrZrO(3) avoid doped regions, while conduction pathways in Y/SrZrO(3) traverse them.

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

When BaZrO(3) 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 BaZrO(3). 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 BaZr(0.875)Y(0.125)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.

Comparison of proton conduction in KTaO3 and SrZrO3.

In the present paper, the authors focus on proton conduction pathways in a cubic perovskite KTaO(3) and an orthorhombic perovskite SrZrO(3). Density functional theory with a generalized gradient approximation is used to find proton binding sites. The nudged elastic band method is used to find transition states between minima. With this potential energy map of binding and transition states, adjacency matrices and their analogs identify four types of conduction paths in KTaO(3). Distortions from these paths are seen in SrZrO(3). In both cases, the lowest energy path has an intraoctahedral transfer rate-limiting barrier. A Fourier analysis of the OH stretch in ab initio molecular dynamics simulations revealed a strongly redshifted OH stretch in SrZrO(3) relative to KTaO(3). Hence, an orthorhombic system with a lowest energy conduction path limited by an intraoctahedral barrier can exhibit a redshifted OH stretch.