Equilibrium Segregation to Free Surface:Kinet ics and Experiment

Fick's first law is modified with an additional term df(x)/dx to describe the segregation phenomenon, f(x) is a local, analytical function related to the depth profile at equilibrium. It thus can be determined experimentally by depth profiling technique. Segregation starting in an initially homogeneous solid is described by an inhomogeneous diffusion equation on the half-infinite domain. Segregation with and without formation of overlayer suggests different boundary conditions. The solution for the Ansatz f(x) = a_s exp(-x/d_s) is in perfect agreement with experimental results on sulphur segregation to the surface of titanium. Independent from the detailed kinetics, activation energy can be inferred from the surface concentration evolution under different temperatures. For sulphur segregation in titanium, E_act = 718 meV/atom.