A generalization of the nernst-Einstein equation for self-diffusion in high defect concentration solids

We show that the Nernst-Einstein equation can be generalized for a high defect concentration solids solid to relate the mobility or conductivity to the self-diffusion coefficient in the standard form: λaDa = qakBT, where λa is the mobility of the charge carriers, qa is their charge, and Da is the self-diffusion coefficient; kB and T are Boltzmann's constant and the temperature. We derive this relationship assuming that the diffusing particles interact strongly and that the mobility is concentration-dependent. We derive this relationship for interstitial disordered structures, but it is perfectly general to any mechanism of self diffusion as long as diffusion in a pure system is considered.