5. Perspectives and challenges

Almost forty years after their discovery in 1984, quasicrystals remain an active field of research. New intermetallic phases are regularly discovered in phase diagrams. This is hardly surprising when you consider the dizzying number of possible combinations that can be made from the 80 or so metallic elements (around 3,000 binaries, 80,000 ternaries, etc.). As each of these systems may contain several phases, it is estimated that less than 50% of binary phases, less than 5% of ternary phases and probably less than 1% of quaternary phases have been discovered. It's an extremely rich field, and a vast area of exploration for the discovery of new materials, and undoubtedly new quasicrystalline phases. On the other hand, quasiperiodicity is also found in other classes of materials such as the recently discovered two-dimensional oxides, and new similar systems are currently being investigated....