A previously reported formalism for ion-beam mixing is extended to include the formation of an intermediate phase as required by the binary phase diagram. It is shown that the general requirements of the phase diagram can be established simply by introducing discontinuities in the diffusion parameters, effectively in the kinetics. Specifically, a self-consistent argument was developed with a system of five domains corresponding to the two terminal solid solutions, two transition regions, and an intermediate phase. The domains are justified in terms of the free energy of mixing DELTAG(m). A numerical solution of the problem for a bilayer geometry reproduces the experimental laws : the phase thickness increases as (dose)1/2, and total amount of mixing also increases as (dose)1/2.