Multiple quasicrystal approximants with the same lattice parameters in Al-Cr-Fe-Si alloys

By means of atomic-resolution high-angle annular dark-field scanning transmission electron microscopy, we found three types of giant approximants of decagonal quasicrystal in Al-Cr-Fe-Si alloys, where each type contains several structural variants possessing the same lattice parameters but different crystal structures. The projected structures of these approximants along the pseudo-tenfold direction were described using substructural blocks. Furthermore, the structural relationship and the plane crystallographic groups in the (a, c) plan of these structural variants was also discussed. The diversity of quasicrystal approximants with the same lattice parameters was shown to be closely related to the variety of shield-like tiles and their tiling patterns.

Occupation Waves the Way You Have Never Seen Them: the Orthorhombic Quasicrystal Approximants RE13Zn58+δ (RE = Ho, Er, Tm, and Lu)

A series of binary quasicrystal approximants RE13Zn58+delta (RE = Ho, Er, Tm, and Lu) have been prepared, and structural studies were performed by means of single-crystal X-ray diffraction. All four compounds crystallize in the orthorhombic system, but while the Ho-containing compound crystallizes in space group Pcmn, the rest of the compounds crystallize in Pc21n. This work is a continuation of the structural studies on RE13Zn approximately 58 (RE = Ce, Pr, Nd, Sm, Gd, Tb, and Dy), which all belong to the hexagonal system. The sequence of RE13Zn58+delta compounds exhibits a large variability in local ordering and composition, and therefore the crystal structures are generally rather more complex than those previously reported and exhibit a number of different ordering modes. These four compounds are structurally closely related to each other.