Symmetry analysis of the modulated icosahedral phase in AlCuFe

-The symmetry of the modulated icosahedral structure recently observed m Al~,~cu~~fej~~ is analyzed. The 12D superspace group associated with the structure is described by a pair of 6D icosahedral superspace groups, which can be identified as jF53m, P53m). Within the frame of a generalized Landau theory, the irreducible representation associated with the order parameter describing the distortion is deterrnined. The possible form of the modulation is strongly symmetry restricted, so that some modulation parameters introduced in previous literature 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 intemal component of the modulation vectors, being undeterrnined by experiment, can be chosen along the corresponding 5-fold directions in the infernal subspace ; but, in contrast to previous assumptions, their modulus is not predetermined, and should be fitted to the diffraction intensity data once a model without deforrnations of the atomic hypersurfaces is chosen for the modulation.