Reliability of the diffusion approximation for the ballistic relocation function in atomic mixing by ion beams

A simple idealized ballistic relocation function is considered for the case of a single marker layer. Material collectively displaced by recoiling atoms is represented by a Kirkendall drift velocity. The mixing equations are solved numerically both in the diffusion approximation and with the exact relocation function. For small mean relocation distance it is shown that the diffusion approximation gives very good agreement with the exact solution, but for larger mean relocations the diffusion approximation gives solutions with qualitatively wrong features, in some cases reversing the direction of motion of the peak of the marker layer.