INCOMMENSURATE MODULATED STRUCTURE IN THE ICOSAHEDRAL QUASI-CRYSTALLINE PHASE T2 OF AN AL-LI-CU ALLOY

Evidence was obtained for an incommensurate modulated phase in an Al-L i-Cu quasicrystal with the icosahedral structure using transmission el ectron microscopy. The modulated phase exhibits lamellar contrast, but globally shows pseudo icosahedral <m(35)over bar> point group symmetr y. The modulation results in a nearly two-dimensional periodic array o f the diffraction spots in a reciprocal plane perpendicular to the 2-f old 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 degrees away from the [-1 /-20/-10/0] axis. Another modulation direction is 5 degrees from a 5-f old 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 meth od of curved atomic hypersurfaces in a high-dimensional hyperspace ont o physical space, and in real space this modulation was suggested to c orrespond to the existence of two different periods for the aluminium and copper atomic positions in the superstructure.