Quasicrystalline materials

The report in late 1984 of phases in rapidly cooled aluminium alloys whose electron diffraction patterns exhibit icosahedral symmetry has stimulated intensive research into the structure and properties of quasicrystalline materials. Here I review our current understanding of quasicrystalline materials and quasiperiodic tilings, and in particular I discuss in detail the interpretation of transmission electron microscopy observations of quasicrystalline phases.