Effective carrier convention in the Nernst-Einstein relation

The density and diffusivity in $\sigma =n{q}^{2}D/(k_{B}T)$ must refer to the same carrier species and correlation convention. Oxygen vacancy diffusivity belongs with vacancy density; tracer diffusion of oxygen atoms is not automatically the vacancy diffusivity. A transport inversion may determine an effective density without uniquely determining a chemical defect concentration.