On the Validity of the Einstein’s Relation and the Fick I Law on the Nanoscale

The classical Einstein’s relation for the Brownian migration has a mesoscopic character and it deteriorates when e.g. diffusion in solids is considered in the nanoscale (i.e. if the diffusion distance is comparable with the atomic spacing). This behaviour is strongly related to the well-known diffusion paradox, predicting infinitely fast diffusion kinetics at short times (distances). Indeed, according to the Fick I law the gradient is infinite if there is a discontinuity in the density at the beginning (which is the case in typical interdiffusion measurements). In this paper these questions and a possible resolution of the above paradox will be discussed on the basis of results obtained in our Laboratory.