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In the Al-Co-Cu alloy system, both the decagonal quasicrystal with the spacegroup of $P\overline{10}m2$ and its approximant Al$_{13}$Co$_4$ phase withmonoclinic $Cm$ symmetry are present around 20 at.% Co-10 at.% Cu. In thisstudy, we examined the crystallographic features of prepared Al-(30-x) at.%Co-x at.% Cu samples mainly by transmission electron microscopy in order tomake clear the crystallographic relation between the decagonal quasicrystal andthe monoclinic Al$_{13}$Co$_4$ structure. The results revealed a coexistencestate consisting of decagonal quasicrystal and approximant Al$_{13}$Co$_4$regions in Al-20 at.% Co-10 at.% Cu alloy samples. With the help of thecoexistence state, the orientation relationship was established between themonoclinic Al$_{13}$Co$_4$ structure and the decagonal quasicrystal. In thedetermined relationship, the crystallographic axis in the quasicrystal wasfound to be parallel to the normal direction of the (010)$_{\rm m}$ plane inthe Al$_{13}$Co$_4$ structure, where the subscript m denotes the monoclinicsystem. Based on data obtained experimentally, the state stability of thedecagonal quasicrystal was also examined in terms of the Hume-Rothery (HR)mechanism on the basis of the nearly-free-electron approximation. It was foundthat a model based on the HR mechanism could explain the crystallographicfeatures such as electron diffraction patterns and atomic arrangements found inthe decagonal quasicrystal. In other words, the HR mechanism is most likelyappropriate for the stability of the decagonal quasicrystal in the Al-Co-Cualloy system.

Crystallographic features and state stability of the decagonal quasicrystal in the Al-Co-Cu alloy system