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 atomic surfaces between QC and IC. This has been pointed out by many authors, and turns the subject into a really subtle issue. Generally spoken, the atomic surfaces in QC are not continuous. Based on these studies it was anticipated that "phasons" in QC would not be collective propagating modes as in IC but rather atomic jumps, that can be visualized by configuration flips within Penrose-like tiling models. Ensuing experimental studies confirmed this picture. In our current understanding an atomic jump is a stochastic single-particle process. The phonon heat bath produces a fluctuating environment that from time to time will open a low-energy gateway that is prosperous for a jump. Starting from this conceptual image that thrives on disorder, it is hard to imagine an orderly concerted choreography of simultaneous jumps of two or more atoms. This only stresses the fact that, although they are both materialized by a sliding of the cut in superspace, phasons in QC and IC should correspond to very different, antipodal types of dynamics. Nevertheless, this poses a number of small problems in QC. First of all, the (anomalous) temperature dependence of the (quasielastic) neutron-scattering signal that reveals the existence of the hopping does not tally with the description we gave above of the jump process in terms of a phonon bath. Secondly, tile flips in real, i.e. not mono-atomic structural models entail in general several simultaneous atomic jumps. It was therefore inferred that the elementary phason building brick would rather be the atomic jump than the tile flip. In triple-axis neutron-scattering experiments on a large single-grain sample of the icosahedral phase Al-Mn-Pd, we came across some evidence that seems to challenge this common-sense based paradigm. In fact, we found a Q-dependence of the quasielastic signal that we are only able to explain by assuming that two (or more) atoms jump simultaneously keeping their separation vector fixed.