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Additional info for Auger Electron Spectroscopy
1), one for each segregating element. These equations are coupled, but only through the adsorption isotherms that serve as boundary conditions. The studies that have been reported so far have been motivated by grain boundary segregation and consequent embrittlement effects in alloy steels. Treatments of temper embrittlement kinetics and related treatments of surface segregation kinetics in multicomponent systems have employed isotherms based on Guttmann's (1975) theory of cosegregation. These isotherms are multicomponent analogues of the Fowler-Guggenheim mean field isotherm: The free energy of segregation for each of two solutes consists of a constant term plus a term proportional to the surface concentration of the other segregating solute.
For simplicity, we also assume that there is no initial segregation: Γ(0) = 0, although this is not essential, and the necessary modifications for nonzero initial surface coverage are straightforward. Let us now consider two limiting cases of the general problem posed by Eqs. (1) through (5): cja«l and ch/a»\. Simplified isotherms appropriate for these two limits are shown in Fig. 3b and c, respectively. Each limiting case represents a situation that an experimenter might expect to encounter in would be Auger studies of surface segregation kinetics.
15) These equations are equivalent to Eqs. (2) and (8), respectively. Consequent ly, it is as expected that α and d appear only as a product. The parameter d may be important in describing the details of the solute distribution at the boundary, but α · d is still the only length scale needed to describe the process of segregation. After obtaining Eqs. (14) and (15), Lea and Seah examined the conse quences of adding an evaporative loss term to Eq. (14): d— ^ = D dt \ dx - evaporation rate. (16) They assumed an evaporation rate R of the form R =y ^ = y ) , ) where Κ is a dimensionless parameter (following the terminology of Lea and Molinari, 1984).