Approximants of icosahedral quasicrystals: Atomic structure, inherent defects, and superstructural ordering

The structural features of approximants of icosahedral and decagonal quasicrystals and new unusual approximants (rhombohedral AlPd and cubic Al₆₈Pd₂₀Ru₁₂) are considered. It is shown that most approximants can be described in terms of universal local ordering of atoms, in which the nearest neighbors of each atom occupy the vertices of an almost ideal dodecahedron: the so-called dodecahedral local ordering. A set of general atomic motifs in the approximants of different orders is found for quasicrystals of different types. It is shown that the dodecahedral local ordering can be easily described by the project method, in which the basis vectors directed along icosahedral threefold axes are used. Different types of defects inherent in dodecahedral local ordering are analyzed.