In the past fifty years, experimental works based on TEM or grazing incidence X ray diffraction have clearly shown that alloys and ceramics exhibit a nano pattering under irradiation [1, 2, 3]. Many works were devoted to study the nano patterning induced by ion beam mixing in solids [17, 18, 19]. Understanding the nano patterning will provide scientific bases to tailor materials with well-defined microstructures at the nanometric scale. The slowing down of impinging particles in solids leads to a complex distribution of subcascades. Each subcascade will give rise to an athermal diffusion of atoms in the medium. In this work, we focused on this point. Based on the well-known Cahn Hilliard Cook (CHC) equation, we analytically calculate the structure factor describing the nano patterning within the mean field approximation. It has shown that this analytical structure factor mimics the structure factor extracted from direct numerical simulations of the time dependent CHC equation. It appears that this structure factor exhibits a universal feature under irradiation.