Abstract
Polycrystalline aggregates with overall icosahedral symmetry have been found in rapidly solidified Al—Mn—Fe—Si alloys. The orientation relationship between crystals is such that icosahedral motifs in all the crystals are parallel. Although the cubic axes undergo fivefold rotation about irrational ⟨1, τ, 0⟩ axes, only five orientations occur among hundreds of crystals. This is a special orientation relationship, but there is neither a coincidence nor a twin lattice (S = σ = ∞). The concepts of twinning and special grain boundaries are re-examined, and a new definition of special orientations (hypertwins) based on the reduction of the number of arithmetically independent lattice vectors is proposed. It includes both old and new special orientations and can be easily interpreted in terms of quasilattices.