# Ion-beam mixing with chemical guidance II: Analysis for positive heats of mixing

## Abstract

We consider both numerical and analytical results for the problem of ion-beam mixing of a binary system when the motion is in part ballistic and in part chemically guided and when the heat of mixing ΔHm takes on positive values. For ΔHm small positive the mixing profile near the interface has the " erfc-like" form α(x)=α0(1-aα(Dt) -1 2+⋯, where α(x) is the atomic fraction fraction of a given component, α0 is 1 2, a is a known constant, and D is the combined ballistic and chemically guided diffusion coefficient. There is no miscibility gap. For ΔHm large positive the profile is α(x)=α0(1-ax 1 2(Dt) -1 4+⋯) with α0 < 1 2. The inequality α0< 1 2 corresponds to the existence of a miscibility gap, but we note that what solubility occurs greatly exceeds the equilibrium value. However, for all values of ΔHm the mixing behavior scales accurately as (mixing) ∞ (Dt) 1 2, showing that there is no steady-state situation. The mixing profile as a whole can be approximated as α(x)≈a0 erfc {Kx/2(Dt) 1 2} where K depends on the value of ΔHm. An alternative form for the free energy of mixing ΔGm, valid for systems subject to both ballistic and chemically guided motion, can be constructed which correctly reproduces both the miscibility gap and the diffusion flux. Such a modification of ΔGm was anticipated in work by Martin. © 1992.