Chemical Self-Organization During Crystal Growth : a new kind of toy model

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. Two one-dimensional models are considered. The first one is a lattice-gas model with short-range decreasing and convex chemical interactions. It is proved that the growing structures are the so-called uniform structures where the atoms are arranged as regularly as possible and which are known to be the ground state equilibrium structures of the same model. The second model uses an electronic tight-binding hamiltonian for which the growth of uniform structures is also observed. In spite of its original simplicity, this toy model for growth shows unexpected results.