Model for the transformation of an icosahedral phase into a B2 crystalline phase

A model for the transformation of an Al-Cu-Fe icosahedral quasicrystal into a crystal with a B2-type phase is proposed. The model is based on two assumptions: (1) the main building block for the quasicrystal structure is a hierarchical dodecahedron composed of two icosahedral clusters, coinciding with two different sections of the {3, 3, 5} polytope; (2) the transformation of the quasicrystal into a B2-type crystal phase can be described as the transition between 3D sections of two polytopes, namely {3, 3, 5} and {3, 4, 3}. In the framework of the proposed model, two experimental facts gain plausible explanations: the transformation of the Al-Cu-Fe quasicrystal into the BCC phase specifically and the orientational relationships observed between this BCC phase and the initial icosahedral quasicrystal.