 Solution

For an oxide ion, or an oxygen vacancy measured relative to the ideal lattice, the charge magnitude is $|q|=2e$. The independent-carrier Nernst-Einstein inversion at $1250\mathrm{K}$ givesHere $D$ and $n_{\mathrm{eff}}$ must describe the same carrier convention. If the quoted diffusivity is a mobile-vacancy diffusivity, this is the vacancy density. If it is literally an oxygen-ion tracer diffusivity, it is an effective oxygen-ion density under an uncorrelated model. Vacancy density cannot be substituted for oxygen-ion density while retaining the same diffusivity. This distinction is consequential in the last part.