Theory of the formation of quasicrystals

A theoretical model is proposed for the formation of quasicrystalline alloys. The icosahedral phase is known 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 Un modele theorique est propose pour expliquer la formation des alliages quasicristallins. La phase icosaedrique resulte dans ce modele, d'une transition reconstructive de type displacif a partir d'une phase mere cristalline. Le mecanisme de la transition met en jeu deux parametres d'ordre distincts: un champ de deplacements qui transforme certains sous-reseaux cristallins en assemblages icosaedriques, et une onde de densite qui brise de facon incommensurable l'ordre translationnel de la phase mere. Les principaux aspects de la theorie sont introduits a travers l'exemple de AlMnSi