A family of hexagonal and orthorhombic (Al,Si)4Cr approximants of quasicrystals

By means of transmission electron microscopy, four crystalline phases with compositions close to (Al,Si)4Cr have been found in Al–Cr–Si alloys. The hexagonal μ′-(Al,Si)4Cr has the same space group P63/mmc as μ-(Al,Si)4Cr, but its c parameter is only one half of cμ. On the other hand, the orthorhombic ɛ-Al4Cr, ɛ′- and ɛ″-(Al,Si)4Cr have about the same lattice parameters but different space groups: Bbmm (or Cmcm), Pbnm and P212121, respectively. The lattice parameters of these phases are closely related: aɛ,ɛ′,ɛ″ = 3aμ,μ′ ≅ 3.46 nm; bɛ,ɛ′,ɛ″ = aμ,μ′ ≅ 2.00 nm; cɛ,ɛ′,ɛ″ = 1/2cμ = cμ′ ≅ 1.24 nm. The symmetry of space group decreases from μ(μ′), ɛ, ɛ′ to ɛ″ and the space groups of any two neighboring phases have the minimal supergroup and the maximal subgroup relationship. Strong diffraction spots of all these phases exhibit pseudo icosahedral symmetry. In the (0 0 1) plane, icodahedra are linked by mutual penetration along the five-fold axis forming icosahedral chains in three directions at 120° apart. These four (Al,Si)4Cr phases together with the ɛ-Al4Cr are not only structurally close related, but also are approximants of quasicrystals.