The physical space model of the Tsai-type quasicrystal

Abstract

The binary Cd5.7Yb phase representing the Tsai-type category of the icosahedral quasicrystals is solved by the assignment of a unique atomic decoration to rhombohedral units in the Ammann–Kramer–Neri tiling. The unique decoration is found for units with an edge length of 24.1 Å and 3 m internal point symmetry. The structural refinement was carried out for two underlying tilings generated by the projection method for 6D space. The difference lies in the location of the origin point which for one tiling is in the vertex and for the second one in the center of the 6D unit cell. The two tilings exhibit mutual duality. The choice of the tiling has a minor effect on the final structural model as both converge to an R factor of ∼11.5%. The main difference is related to the treatment of the Cd4 tetrahedral motif which is either orientationally ordered and aligned with the threefold axis or disordered and modeled as a partially occupied icosahedron. Both models can be presented as a covering by rhombic triacontahedral clusters with identical positions of clusters within rhombohedral units. The shell structure is Tsai-type in the case of the first tiling and Bergman-type for the other.