Quasicrystal and approximant structures in the Al-Cu-Fe system

We present an extensive study of the approximant phases present in the Al-Cu-Fe phase diagram in the vicinity of the icosahedral phase. In addition to the rhombohedral and the two pentagonal phases previously observed, a new orthorhombic approximant has been identified. The identification of these structures, via x-ray diffraction and TEM, is based on both symmetry considerations and the 'shear' description in the perpendicular space. These simple geometric tools give very satisfactory and accurate crystallographic results. This suggests that these phases derive from the parent icosahedral phase both via systematic introduction of atomic jumps preserving most of the atomic local environments and via long-range atomic diffusion.