Determination of the crystal structure of icosahedral Al-Cu-Li

The x-ray diffraction of a single crystal of the icosahedral phase of Al-Cu-Li has been measured on a diffractometer. Only 37 symmetrically inequivalent reflections were found with nonzero intensity. The structures considered, decorations of the Penrose packing with edge length 0.5039 nm, were refined to match the intensity data. An excellent agreement ($R_F$=7.0%) is obtained for Cu or Al occupying vertex and edge-center positions of both rhombohedra and Li or Al occupying two body-diagonal sites of the prolate rhombohedron. The icosahedral and cubic structure are compared.