Chemical self-organization during crystal growth

A chemical growth model for binary alloys is presented. At each step, using a simple energetic criterion, an A or a B atom is aggregated to the growing cluster. For short-range decreasing and convex chemical interactions, it is proved that, in one dimension, the growing structures are the so-called uniform structures where the atoms an arranged as regularly as possible. When they are not convex other ordered structures can grow for appropriate initial conditions.