On the application of Darken analysis to ion-beam mixing

There is some indication (Cheng et al., Appl. Phys. Lett. 45 (1984) 185; Peiner and Kopitzki, Nucl. Instr. and Meth. B34 (1988) 173) that ion-beam mixing correlates with DELTA-H(m), the heat of mixing, in spite of being basically a ballistic process. Using Darken's expression for the chemically guided part of the overall diffusion flux, we set up and evaluate the corresponding continuity equation: partial alpha-i/partial t = D(i)b(1 + p){partial 2-alpha-i/partial x2 - q(1 - 2-alpha-i)(partial alpha-i/partial x)2 - q-alpha-i(1- alpha-i)partial 2-alpha-i/partial x2}, where alpha-i is the atom fraction of component i, D(i)b is the combined diffusion coefficient for ballistic motion and for nonguided point defects, D(i)g = pD(i)b is the diffusion coefficient for chemically guided point defects, and q is a composition-independent parameter proportional to the heat of mixing. For DELTA-H(m) < 0 the diffusion profile is found to be more penetrating than in the absence of chemical effects. For DELTA-H(m) > 0 the profile is less penetrating, while for all DELTA-H(m) the two scalings are confirmed, (mixing) proportional t1/2 and (mixing)2 proportional \DELTA-H(m)\.