Formation Energy Profiles of Oxygen Vacancies at Grain Boundaries in Perovskite‐Type Electroceramics

Abstract

Oxygen vacancy formation energies play a major role in the electric field‐assisted abnormal grain growth of technologically relevant polycrystalline perovskite phases. The underlying effect on the atomic scale is assumed to be a redistribution of cationic and anionic point defects between grain boundaries (GBs) and the bulk interior regions of the grains due to different defect formation energies in the structurally different regions, accompanied by the formation of space charge zones. Using atomistic calculations based on classical interatomic potentials, optimized structures of the symmetric tilt GBs Σ5(210)[001] and Σ5(310)[001], and of the asymmetric tilt GB (430)[001]||(100)[001] in the electroceramic perovskite materials SrTiO3, BaTiO3, and BaZrO3, are derived and discussed. Profiles of oxygen vacancy formation energies across those GBs are presented and their dependence on composition and GB type is discussed.

How space-charge behaviour at grain boundaries in electroceramic oxides is modified by two restricted equilibria

“…Space-charge layer formation in acceptor-doped SrTiO 3 is assumed 35,116,117 to be due to a difference in the oxygen vacancies' standard chemical potential between the grain-boundary core and the bulk phase (Δ μ ⊖ v < 0), an assumption supported by the results of atomistic simulations. 118–120 This driving energy leads to segregating to the grain-boundary core, and thus, to the buildup of an excess positive core charge. Defect–defect interactions are neglected in our model, and hence, Δ μ ⊖ v is assumed to be independent of the defect concentrations within the core.…”

“…Q c is calculated from formal point-defect concentrations in the core, c c .Previous studies have indicated that the structurally distorted region around the grain-boundary plane is several lattice constants wide, 11,133,134 and only some of the sites in it are energetically more favourable than the bulk sites. 118–120 In our model, we attribute a formal width, w c , to the grain-boundary core, and a formal O-site density, γ c O < γ O , such that the areal core-site density is lower than it would be in a bulk slab of the same width. 35 For convenience, we assume that the number of sites in the Ti sublattice as well as the number of electronic interface states is lowered by the same factor, γ c O / γ O .…”