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-DELTA-H(m) takes on positive values. For DELTA-H(m) small positive the mixing profile near the interface has the "erfc-like" form alpha(x) = alpha-0(1 - ax(Dt)-1/2 + ...), where alpha(x) is the atomic fraction of a given component, alpha-0 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 DELTA-H(m) large positive the profile is alpha(x) = alpha-0(1 - ax1/2(Dt)-1/4 + ...) with alpha-0 < 1/2. The inequality alpha-0 < 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 DELTA-H(m) the mixing behavior scales accurately as (mixing) infinity (Dt)1/2, showing that there is no steady-state situation. The mixing profile as a whole can be approximated as alpha(x) almost-equal-to a0 erfc{Kx/2(Dt)1/2}, where K depends on the value of DELTA-H(m). An alternative form for the free energy of mixing-DELTA-G(m), 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 DELTA-G(m). was anticipated in work by Martin.