CORRELATED SIMULTANEOUS PHASON JUMPS IN AN ICOSAHEDRAL Al-Mn-Pd QUASICRYSTAL

The relationships between quasicrystals and other incommensurately modulated crystals (IC) have many interesting theoretical aspects. An obvious link is that both can be derived from a common description based on an embedding in a higher-dimensional superspace that contains a periodic lattice of so-called atomic surfaces. The superspace cut-and-projection algorithm permits a group-theoretical classification of all possible structures. Hyperspace crystallography leads also to the possibility of an attractive analogy within the realm of lattice dynamics based on the introduction of the notion of " phasons " in addition to the usual phonons. Here we stumble onto a first real difficulty. Once we go beyond one-dimensional structures, there are very important differences in the topology of the atomi