Oxygen vacancy formation energy is an important quantity for enabling fast oxygen diffusion and oxygen catalysis in technologies like solid oxide fuel cells. Both previous literature in various systems and our calculations in LaMnO3, La0.75Sr0.25MnO3, LaFeO3, and La0.75Sr0.25FeO3, show mixed results for the direction and magnitude of the change in vacancy formation energy with strain. This paper develops a model to make sense of the different trend shapes in vacancy formation energy versus strain. We model strain effects using a set of consistent ab initio calculations, and demonstrate that our calculated results may be simply explained in terms of vacancy formation volume and changes in elastic constants between the bulk and defected states. A positive vacancy formation volume contributes to decreased vacancy formation energy under tensile strain, and an increase in elastic constants contributes to increases in vacancy formation energy with compressive and tensile strains, and vice versa. The vacancy formation volume dominates the linear portion of the vacancy formation energy strain response, while its curvature is governed by the vacancy-induced change in elastic constants. We show results sensitive to B-site cation, A-site doping, tilt system, and vacancy placement, which contributions may be averaged under thermally averaged conditions. In general, vacancy formation energies for most systems calculated here decreased with tensile strain, with about a 30-100 meV/% strain decrease with biaxial strain for those systems which showed a decrease in vacancy formation energy. Experimental verification is necessary to confirm the model outside of calculation.
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