MODEL OF GROWTH FOR LONG-RANGE CHEMICALLY ORDERED COMPOUNDS - APPLICATION TO QUASI-CRYSTALS

We propose an electronic model for the growth of long-range chemically ordered binary compounds. By varying one parameter, we show that a specific concentration can be dynamically selected and the associated chemical order propagated during a rapid solidification. The basic assumptions of the model are: 1) the diffusion inside the growing structure is frozen out, and 2) the << chemical >> reconstruction at its surface remains free to occur. In a first step, we study two one-dimensional models and show that both periodic and quasi-periodic structures can be built-up one atom at a time, using an energetic rule of growth. The first model is phenomenological and includes classical interactions between the atoms, the second is a tight-binding model including quantum effects. We next discuss the possible application to quasicrystals and argue - with energetical considerations - that one possibility for favoring systematically quasi-periodic structures is a growth mechanism which uses clusters preexisting in the liquid phase as building blocks of the solid phase.