By C.L. BRIANT and R.P. MESSMER (Eds.)
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Segregation measurements on such samples often showed linear kinetics, in accord with Eq. (21), rather than kinetics in accord with Eqs. (8) or (12). Since the quantity £ Γ^τ,·) was not determined in these studies and was not constant from one experimental run to the next, values of D cannot be obtained from the data. In particular, attempts to determine activation energies for D by plotting the segregation rate measured at each of several temperatures versus reciprocal absolute temperature are not valid.
The equilibrium coverage is then indistinguishable from the saturation coverage and is relatively insensitive to the solute concentration. For the case ch/a« 1, the Langmuir isotherm can be linearized (Fig. 3b): Γ(ί) = Kc(09 0, (6) where Κ = Γ J a. The solution for this case can be found by Laplace transform techniques and is χ χ Dt~] Γ c(x, t) = ch — cb · exp — I · erfc 2(ϋίγϊϊ^ + [_2'~ Κ Κ2] + (Dt)112 Κ (7) The surface coverage follows from (6) and (7): Γ(0 = Γ , [ , - „ ρ ( ^ ) . £ Γ ο ( ^ ) ] , Γ
where T e = Kcb, the equilibrium surface concentration for the bulk concen tration c b.
12). The diffusivities obtained from these data using Eq. (12) exhibit Arrhenius-type behavior. 2. THE EFFECT OF EVAPORATION The expressions derived in the previous section did not consider the possibility of evaporation of solute from the surface. Evaporation does not occur at an electrode in a liquid medium or at an internal grain boundary, but it can occur at a solid-vapor or solid-vacuum interface, and its consequences for the segregation kinetics can be substantial. Lea and Seah (1977) found evaporation to be significant in their Auger study of surface segregation kinetics in the Fe-Sn system.
Auger Electron Spectroscopy by C.L. BRIANT and R.P. MESSMER (Eds.)