On the determination of the equilibrium surface segregation isotherms form kinetic measurements

Thirty years ago, Lagües and Domange [M. Lagües, J.L. Domange, Surf. Sci. 47 (1975) 77] studying dissolution and segregation kinetics, introduced the surface local equilibrium hypothesis. This hypothesis is based on the idea that the kinetics (diffusion) is faster in the near surface region (selvedge) than in the bulk and thus it can be assumed that the atoms just below the selvedge can be in equilibrium with the atoms of the deposit. Later on numerous articles have dealt with this problem and most of them have confirmed its validity, although the clear meaning of the selvedge and especially its thickness remained unspecified. In this paper, using one dimensional kinetic mean filed (KMF) and three dimensional kinetic Monte Carlo (KMC) models, we show that the local equilibrium can be violated even in simple cases when complex surface phenomena (defects, relaxation, size effects, etc.) are not taking into account. Furthermore we illustrate that, even if the above hypothesis is obeyed, the determination of the surface segregation isotherms from kinetics can lead to uncertain result because of the restricted validity of Fick's first equation on the nanoscale. At the same time we found that the selvedge is typically ends at the first or second subsurface layer.