SYMMETRY ANALYSIS OF THE MODULATED ICOSAHEDRAL PHASE IN ALCUFE

The symmetry of the modulated icosahedral structure recently observed in Al63.5Cu24Fe12.5 is analyzed. The 12D superspace group associated w ith the structure is described by a pair of 6D icosahedral superspace groups, which can be identified as (F5BAR3BARm, P5BAR3BAR(m)). Within the frame of a generalized Landau theory, the irreducible representati on associated with the order parameter describing the distortion is de termined. The possible form of the modulation is strongly symmetry res tricted, so that some modulation parameters introduced in previous lit erature can be a priori set to zero. Ambiguities on the description of the modulated distortion when done in 6D superspace are stressed. It is demonstrated that the internal component of the modulation vectors, being undetermined by experiment, can be chosen along the correspondi ng 5-fold directions in the internal subspace; but, in contrast to pre vious assumptions, their modulus is not predetermined, and should be f itted to the diffraction intensity data once a model without deformati ons of the atomic hypersurfaces is chosen for the modulation.