A new description of Samson's Cd3 Cu4 and a model of icosahedral i-CdCu

Abstract

The structure of Cd3Cu4, solved by S. Samson in 1966, crystallizes with 1124 atoms in a cubic face-centred unit cell with a = 25.871 Å. 568 atoms in the unit cell have icosahedral coordination. Close to this composition quasicrystalline icosahedral i-CdCu exists. A modified description of the structure is presented pointing out icosahedral clustering as found in quasicrystals. The structure is best described as an intergrowth of two networks. The diamond-like network of fused Friauf polyhedra containing only building blocks with tetrahedral or octahedral local symmetry was already discussed by S. Samson. The second network is based on the principles of the I3-cluster concept which was introduced recently. The I3-cluster is a fragment of three vertex connected icosahedra. A cluster to cluster approach enables the construction of larger fragments by scaling symmetry, e.g. the L-unit or the I(2)-unit. The structure of Cd3Cu4 contains a diamond-like network of vertex connected L-units and stuffed I(2)-units. All vertices of the skeleton carry I13-units. These fragments are blocks of 13 icosahedra with local icosahedral symmetry containing the Mackay icosahedron as core cluster. A model for quasicrystalline i-CdCu is constructed along the lines of the “approximan” structure based on a decoration of a zonohedral tiling by Socolar, Steinhardt and Levine. Only six types of topological different coordination polyhedra are present with coordination numbers CN 12, CN 14, CN 15 and CN 16 and a mean coordination number of 13.2. 57.6% of all atoms have icosahedral coordination. The mean atomic volume is 15.8 Å−3, the density 8.92 g cm−3 and the composition 57.6 at% Cu. The structure is best described as τ1 scaled substructure of B-type connected and isolated I13-clusters. The remaining part of the structure is filled mainly by Friauf polyhedra and other Frank-Kasper polyhedra. The relation to quasicrystalline structures of i-AlMnSi, i-AlMgZn and i-AlFeCu class is discussed.