. This yields the ∆µ O range over which a given material is stable, i.e., its grand energy above the hull, ϕ H , equals zero. Figure shows a strong correlation between the minimum value of the stability range, min(∆µ ϕ H =0 O ), vs. the minimum vacancy formation energy in a given material, with an approximate lower bound of min(∆µ ϕ H =0 O ) ≈ -1 eV -min (∆H V ). This trade-off constrains the space in which materials with desired host and defect stability can be designed. Meanwhile, neither criteria strongly correlates with the diffusivity λ1500 , which can be tuned more independently.