Atom clusters in a 2/1 cubic approximant phase for understanding the structures of icosahedral phases

Two types of atom clusters found in the beta-(AlPdMnSi) cubic phase, referred to as a 2/1 crystalline approximant, with a composition of approximately Al,,Pd,,Mn,Si, which is near to the composition Al72Pd20Mn8 of the icosahedral phase, are discussed in detail for understanding the structure of the AI-Pd-Mn icosahedral phase. A large dodecahedral atom cluster located at the body-centered position can be divided into 19 atom shells with approximately icosahedral symmetry, and a dodecahedron of the 12th shell internally touches the surface of the cubic unit cell with a lattice constant of 2.0211 nm. At each vertex of the dodecahedron, a small icosahedral atom cluster consisting of 12 Al atoms surrounding a central Pd atom is located. The dodecahedron is connected to each other by edge-sharing, namely by sharing two small icosahedral atom clusters, along the twofold rotational direction, and forms a simple-cubic packing of the atom cluster in the beta-(AlPdMnSi) cubic phase. Another atom cluster located at the origin fills up gaps of the simple-cubic packing of the large dodecahedral atom cluster. By using the dodecahedral and bridging atom clusters, the structure of the Al-Pd-Mn icosahedral quasicrystal is discussed.