Phason space analysis and structure modelling of 100 angstrom-scale dodecagonal quasicrystal in Mn-based alloy

摘要

The dodecagonal quasicrystal classified into the five-dimensional space group P12(6)/mmc, recently discovered in a Mn-Cr-Ni-Si alloy, has been analysed using atomic-resolution spherical aberration-corrected electron microscopy, i.e. high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and conventional transmission electron microscopy. By observing along the 12-fold axis, non-periodic tiling consisting of an equilateral triangle and a square has been revealed, of which common edge length is a=4.560 angstrom. These tiles tend to form a network of dodecagons of which size is (2+root 3)a approximate to 17 angstrom in diameter. The tiling was interpreted as an aggregate of 100 angstrom-scale oriented domains of high- and low-quality quasicrystals with small crystallites appearing at their boundaries. The quasicrystal domains exhibited a densely filled circular acceptance region in the phason space. This is the first observation of the acceptance region in an actual dodecagonal quasicrystal. Atomic structure model consistent with the electron microscopy images is a standard Frank-Kasper decoration of the triangle and square tiles that can be inferred from the crystal structures of Zr4Al3 and Cr3Si. Four kinds of layers located at z = 0, +/- 1/4 and 1/2 are stacked periodically along the 12-fold axis, and the atoms at z = 0 and 1/2 form hexagonal anti-prisms consistently with the 12(6)-screw axis. The validity of this structure model was examined by means of powder X-ray diffraction.