Ion-beam mixing with chemical guidance .1. The bilayer problem

It has been suggested by Cheng et al. that the square of the extent of ion-beam mixing scales with the heat of mixing, DELTA-H(m), when the latter is negative. Peiner and Kopitzki, and later Traverse et al., found greatly reduced extents of mixing when DELTA-H(m) is positive, with both types of result suggesting a role for chemical guidance in ion-beam mixing. Beginning with Darken's expression for a diffusion flux subject to chemical guidance, we set up a more general flux equation which allows for ballistic motion: flux = -D(i)b(1 + p)[1 - alpha(i)(1 - alpha(i)q](partial derivative-alpha(i)/partial derivative-x), where alpha(i) is the atom fraction of component i, D(i)b is the combined diffusion coefficient for ballistic motion and for non-guided point defects, D(i)g = pD(i)b is the diffusion coefficient for chemically guided point defects, and q = 2h(m)p/RT (1 + p) is a parameter proportional to the heat of mixing (contained in the quantity h(m)). We also set up the corresponding continuity equation and solve it numerically for a bilayer geometry. The results fall into three basic groups. (a) For q < 0, corresponding to DELTA-H(m) < 0, the profile is significantly more penetrating than in the absence of chemical effects. Also, much of what is found can be related, with greater or lesser precision, to an effective diffusion coefficient of the form D(i)eff = D(i)b(1 + p)(1 - q/4). (b) For 0 < q < 4, corresponding to DELTA-H(m) being small positive, the profile is less penetrating than in the absence of chemical effects but D(eff) is still useful. (c) For q > 4, corresponding to DELTA-H(m) being large positive, new effects set in, including a composition discontinuity at the interface, a complete failure of D(eff), and an indication (which we fail to understand) of a role for the spinodal rather than equilibrium solubility.