Symmetry analysis of the modulated icosahedral phase in AlCuFe

(Received 5 April 1994, accepted 26 May 1994)

Abstract
The symmetry of the modulated icosahedral structure recently observed in Al _63.5Cu ₂₄Fe _12.5 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 (F m, P m). Within the frame of a generalized Landau theory, the irreducible representation associated with the order parameter describing the distortion is determined. 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 internai comportent of the modulation vectors, being undetermined by experiment, can be chosen along the corresponding 5-fold directions in the internat 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 deformations of the atomic hypersurfaces is chosen for the modulation.