Icosahedral density waves

A theoretical model is proposed for the formation of quasicrystalline alloys. The icosahedral phase is shown to result from a reconstructive transition of the displacive type from a parent crystalline structure. Two order parameters are involved in the transition mechanism: a displacement field which transforms a number of sublattices into icosahedral clusters, and an icosahedral density wave which breaks incommensurately the initial translational order. The main features of the model are introduced through the illustrative example of AlMnSi.