Structure of Al-Li-Cu icosahedral crystals and Penrose tiling

We report synchrotron x-ray powder-diffraction measurements of the Al-Li-Cu icosahedral phase. Our results are found to be in agreement with the computed diffraction intensities of the three-dimensional Penrose tiling when Al and Cu atoms are randomly positioned at the vertices and edge centers of the unit cells. Comparison is also made with a similarly decorated icosahedral structure constructed by dense packing of icosahedra. The agreement is less satisfactory.