A family of hexagonal and orthorhombic (Al,Si)_4Cr approximants of quasicrystals

摘要

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 mu'-(Al,Si_)_4Cr has the same space group P6_3/mmc as mu-(Al,Si)_4Cr, but its c parameter is only one half of c_(mu). On the other hand, the orthorhombic elpsilon-Al_4Cr, epsilon'- and epsilon"-(Al,Si)_4Cr have about the same lattice parameters but different space groups: Bbmm (or Cmcrn), Pbnm and P2_12_12_1, respectively. The lattice parameters of these phases are closely related: a_(epsilon,epsilon',epsilon'') =3a_(mu,mu')~(1/2) ident to 3.46nm; b_(epsilon,epsilon',epsilon'') =a_(mu,mu') ident to 2.00nm; c_(epsilon,epsilon',epsilon'') = 1/2c_(mu) = C_(mu') ident to 1.24 nm. The symmetry of space group decreases from MU(MU'), epsilon, epsilon' to epsilon" 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 (001) plane, icodahedra are linked by mutual penetration along the five-fold axis forming icosahedral chains in three directions at 120 deg apart. These four (Al,Si)_4Cr phases together with the epsilon-Al_4Cr are not only structurally close related, but also are approximants of quasicrystals.