  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.
