The structure of an Al–Rh–Cu decagonal quasicrystal studied by spherical aberration (Cs)-corrected scanning transmission electron microscopy

Abstract

The structure of an Al–Rh–Cu decagonal quasicrystal formed with two quasiperiodic planes along the periodic axis in an Al₆₃Rh_18.5Cu_18.5 alloy has been studied by spherical aberration (Cs)-corrected high-angle annular detector dark-field (HAADF)- and annular bright-field (ABF)-scanning transmission electron microscopy (STEM). Heavy atoms of Rh and mixed sites (MSs) of Al and Cu atoms projected along the periodic axis can be clearly represented as separate bright dots in observed HAADF-STEM images, and consequently arrangements of Rh atoms and MSs on the two quasiperiodic planes can be directly determined from those of bright dots in the observed HAADF-STEM image. The Rh atoms are arranged in pentagonal tiling formed with pentagonal and star-shaped pentagonal tiles with an edge-length of 0.76 nm, and also MSs with a pentagonal arrangement are located in the pentagonal tiles with definite orientations. The star-shaped pentagonal tiles in the pentagonal tiling are arranged in τ²(τ: golden ratio)-inflated pentagonal tiling with a bond-length of 2 nm. From arrangements of Rh atoms placed in pentagonal tilings with a bond-length of 2 nm, which are generated by the projection of a five-dimensional hyper-cubic lattice, occupation domains in the perpendicular space are derived. Al atoms as well as Rh atoms and MSs are represented as dark dots in an observed ABF-STEM image, and arrangements of Al atoms in well-symmetric regions are discussed.

Keywords:

• quasicrystal
• decagonal quasicrystal
• aluminium–rhodium–copper
• structure
• scanning transmission electron microscopy
• STEM
• HAADF-STEM
• ABF-STEM

Acknowledgements

We are grateful to Dr FJ Lincoln, the University of Western Australia, for critical reading of the manuscript and his valuable advice.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

A part of this work was financially supported by the Grant-in-Aid for Scientific Research (B), [grant number 24360284] from the Ministry of Education, Culture, Sports, Science and Technology, Japan.