Exceptionally large areas of local tenfold symmetry in decagonal Al59Cr21Fe10Si10

Highlights: • We found a 5.2 nm decagon possessing local tenfold symmetry. • Largest area with tenfold symmetry in decagonal quasicrystal was observed. • We showed how the local tenfold symmetry of DQCs is expanded. • The self-similarity of decagonal quasicrystals was displayed. The decagonal diffraction symmetry of a decagonal quasicrystal (DQC) results from its particular autocorrelation (Patterson) function. Structural subunits ('clusters') with decagonal symmetry may exist but do not need to exist. By atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), we observed the so far largest tenfold symmetric structural subunits in decagonal Al₅₉Cr₂₁Fe₁₀Si₁₀ scaling up to 5.2 nm. This amazing result provides direct experimental evidence how the local tenfold symmetry of DQCs is expanded to a larger size.