Modulated quasicrystals : a mechanism induced by 6D shears

Modulated quasicrystals have been recently observed as possible intermediate states in structural transformations between an icosahedral phase and a periodic rhombohedral one in the AlFeCu system. We propose a mechanism based on “fractional” shears in 6D which yields modulated quasiperiodic structures. These fractional shears are bounded and locally linear mappings which transform the 6D cubic lattice into lattices for which the 3D physical space is rational. In particular, the 6D nodes associated to quasiperiodic structures undergo small displacements which give rise to modulated structures after projection. These structures show characteristic planar defects parallel to the facets of the primitive rhombohedral cell and their Fourier transforms show satellite peaks shifted in the 5-fold directions as experimentally observed.