Thermodynamic and fractal geometric aspects of ion-solid interactions

A thermodynamic approach to atomic diffusion in a thermal spike is reviewed. The approach is based on recent ion mixing experiments which demonstrate the influence of the heat of mixing and the cohesive energy of solids on ion mixing. These thermodynamic effects are assimilated into a phenomenological model of ion mixing. The model is generalized to low-energy ion mixing during sputter depth profiling and is used to elucidate the nature of atomic diffusion in a thermal spike. The onset of radiation-enhanced diffusion in ion mixing is also discussed. A fractal geometry approach to spike formation is presented. An “idealized” collision cascade constructed from the inverse-power potential V(r) ∝ r^−1/m (0 < m ≤ 1) is shown to have a fractal tree structure with a fractal dimension D = 1/2m. The same fractal dimension can also be derived from the Winterbon-Sigmund-Sanders (WSS) theory of atomic collisions in solids. The fractal dimension is shown to increase as an actual collision cascade evolves, because of the change of the effective interaction potentials. The concept of “space-filling” fractals is used to specify spikes. The formation of local spikes, their energy densities, the probability of local spikes overlapping, and the time evolution of a collision cascade are also investigated. It is shown that spikes are not expected to form in a single-component solid consisting of elements with atomic number less than 20; many-body collisions have little effect on the formation of spikes; and, the similarity between high-and low-energy ion mixing is the result of the fractal nature of collision cascades.