Equilibrium segregation of sulfur to the free surface of single crystalline titanium

Equilibrium segregation of sulfur to the free surface of single crystalline titanium from 560 deg. C to 800 deg. C was investigated using Auger electron spectroscopy (AES) measurements. To describe the concentration evolution in the sulfur overlayer, Fick's first law was modified by adding a local function df(x)/dx, to the concentration gradient to drive the segregation starting from an initially homogeneous distribution. The diffusion equation thus derived was solved for the case f(x)=asexp (-x/ds). It was found that the solution leads to an AES intensity evolution for segregants, IS(t)=IS∞ (1-eα erfc((α)1/2)), α=Dt/ds2, which fits the experimental results extremely well. An exponentially decaying distribution of sulfur beneath the titanium surface at equilibrium was revealed by sputter depth profiling, which in turn justifies our modification to Fick's first law. Without referring to the detailed kinetics, an activation energy Ea =718 meV/atom was determined by comparing the sulfur concentration evolution at different temperatures. (author)