Orientation relationship of decagonal quasicrystal and tenfold twins in rapidly cooled Al-Fe alloy

We have found that decagonal quasicrystal and 10-fold twins of monoclinic ${\mathrm{Al}}_{13}$ ${\mathrm{Fe}}_4$ coexist in rapidly cooled Al-Fe alloy. The tenfold axis of the decagonal phase is parallel to the pseudotenfold [010] axis of the twins. There is good coincidence between the strong spots of the decagonal twofold diffraction patterns and the corresponding diffraction patterns of ${\mathrm{Al}}_{13}$ ${\mathrm{Fe}}_4$. This orientation relationship is also observed when the decagonal phase transforms into a ${\mathrm{Al}}_{13}$ ${\mathrm{Fe}}_4$ twin on heating in an electron microscope. This shows that the decagonal quasicrystal is not a set of twins although they are closely related in structure.