Modulated states in Mg–Al alloys and classical Frank–Kasper phases: a high resolution X-ray diffraction study

The Mg–Al system shows for composition in the 50–60 at.% Al range several states, either periodic or quasiperiodic, related to tetrahedral and icosahedral motif structures. The Mg–Al (61 at.%) rapidly solidified alloy shows a cubic quasiperiodic state with inflation symmetry characterized by the algebric number 2−√3. The main question is to know if this state is an example of a new kind of quasicrystal or if this inflation property is only due to a continuous variation of the wavenumber. We report high resolution X-ray diffraction studies of this Mg–Al (61 at.%) metastable state and the related stable Frank–Kasper phase (β-phase). These experiments clearly show fluctuations of the wavenumber. The quasiperiodic Mg–Al (61 at.%) state appears thus to have typical features of incommensurately modulated phases, but with a persisting connection with Frank–Kasper phases.