One-Dimensional Quasicrystal in Rapidly Solidified Alloys

A 1D quasicrystal derived from the 2D decagonal quasicrystal has been found in rapidly solidified ${\mathrm{Al}}_{80}$ ${\mathrm{Ni}}_{14}$ ${\mathrm{Si}}_6$, ${\mathrm{Al}}_{65}$ ${\mathrm{Cu}}_{20}$ ${\mathrm{Mn}}_{15}$, and ${\mathrm{Al}}_{65}$ ${\mathrm{Cu}}_{20}$ ${\mathrm{Co}}_{15}$ alloys. They inherit periodicity along the tenfold axis and have, in addition, translation periodicity in one of the twofold axes of the decagonal phase. Crystalline phases based on ordering of vacancies in (111) layers of the CsCl-type structure with a layer sequence of 5, 8, 13, and 21, respectively, have also been found. The important role played by the Fibonacci sequence in these aperiodic and periodic structures is discussed.