By C.L. BRIANT and R.P. MESSMER (Eds.)
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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). Note that in Eq. (17) α and d no longer occur simply as a product. We shall return to this point shortly. In Eq. (17) the evaporation rate is proportional to c(0, t), allowing the continued use of Laplace transform techniques in obtaining solutions. Computed curves for the time dependence of the surface coverage for various values of the parameter are shown in Fig.
Of course, the definition of the dimensionless parameter V does not affect the mathematical correctness of the curves shown in Fig. 6 as solutions to the diffusion equation for the stated boundary conditions. The definition affects only the way in which the curves can be applied as universal curves in treating differing alloy systems. The use of Eq. (18) rather than (19) is consistent with the physical model that Lea and Seah assume for the evaporation process. They take the solute 36 GREGORY L U C K M A N evaporation to be occurring from the matrix just below the surface rather than from the surface layer itself.
For the present, we assume a uniform bulk concentration ch as an initial condition: c = c 5, a constant, for t = 0, and χ > 0. (4) We also assume the boundary condition c -+ch for χ -> oo and t > 0, (5) to insure that c(x, t) remains bounded for all x. 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.
Auger Electron Spectroscopy by C.L. BRIANT and R.P. MESSMER (Eds.)