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

Abstract

The dodecagonal quasicrystal classified into the five-dimensional space group P12₆/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 Å. These tiles tend to form a network of dodecagons of which size is a ≈ 17 Å in diameter. The tiling was interpreted as an aggregate of 100 Å-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 12₆-screw axis. The validity of this structure model was examined by means of powder X-ray diffraction.

Keywords:

• quasicrystal
• dodecagonal
• Mn-based alloy
• Cs-corrected TEM

Acknowledgements

The authors thank Hayato Iga and Yuya Tanaka for their cooperation to this research project. They also thank Marc de Boissieu for valuable discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

A part of this work was supported by “Nanotechnology Platform” Program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. MM was supported by Slovak [grant number VEGA 2/0189/14], [grant number APVV-0076-11].