Incommensurate modulated structure in the icosahedral quasicrystalline phase T2 of an Al-Li-Cu alloy

Abstract

Evidence was obtained for an incommensurate modulated phase in an Al-Li-Cu quasicrystal with the icosahedral structure using transmission electron microscopy. The modulated phase exhibits lamellar contrast, but globally shows pseudo icosahedral m35 point group symmetry. The modulation results in a nearly two-dimensional periodic array of the diffraction spots in a reciprocal plane perpendicular to the 2-fold icosahedral axis [0/00/00/2], while quasiperiodic order remains in the third direction. One of the modulation directions is parallel to a pseudo 2-fold axis in between a 3-fold [-1/-20/-10/0] and a 5-fold [-1/00/-10/0] axis, which is approximately 11° away from the [-1/-20/-10/0] axis. Another modulation direction is 5° from a 5-fold axis of [1/00/-10/0]. The amplitudes of the modulation are |a| = 0.38 nm⁻¹ (2.6 nm) and |b| = 0.44 nm⁻¹ (2.2 nm), respectively. The modulation was interpreted on the basis of the cut and projection method of curved atomic hypersurfaces in a high-dimensional hyperspace onto physical space, and in real space this modulation was suggested to correspond to the existence of two different periods for the aluminium and copper atomic positions in the superstructure.