The concept of crystalline approximants for decagonal and icosahedral quasicrystals

The concept of crystalline approximants is reviewed for icosahedral and decagonal quasicrystalline phases. A systematic study of the local order at short- and medium-range distances in these compounds leads to the classification of most of the known icosahedral and decagonal phases into two groups. The first group is related to the Mackay-type atomic local environment based on the Mackay icosahedral cluster. The structure of these compounds is formed by a dense stacking of tetrahedra and octahedra, with as first neighbours ideal coordination polyhedra, the icosahedron and the pentagonal prism with two additional atoms in front of the two pentagonal faces. This group contains phases such as the icosahedral Al-Pd-transition metals (TM) (TM = Mn or Re), Al-Cu-TM (TM = Fe, Ru or Os) and Ti-TM-Si (TM = V, Cr, Mn or Fe) alloys and all the known decagonal phases. The second group is related to the Bergman type (or Frank-Kasper-type) local environment based on the Bergman cluster. The structures belonging to this group can be constructed as a dense stacking of tetrahedra, with as first neighbours ideal coordination polyhedra, the icosahedron and the Friauf polyhedron. This group contains phases such as icosahedral Al-Li-Cu and Zn-Mg-RE (RE = rare earth). Using these local criteria, several other complex crystalline phases are shown to be valuable approximants, leading to the possible occurrence of new icosahedral or decagonal phases (at least metastable) in miscellaneous systems.