Brownian motion and Edagawa phasons

Abstract

Abstract The so far most direct observation of phasons was reported in the year 2000 by Edagawa et al. In HRTEM images of decagonal Al-Cu-Co they detected white spots which formed vertices of a quasiperiodic tiling. Some spots vanished and reappeared in phason flipped positions within seconds to minutes. Already at ICQ13 we had applied a structure model of Zeger and Trebin of the year 1996 to explain the physical origin of the spots and the time scale of the flips. We found that the spots are columns of ten-rings of atoms which change positions by fluctuations of atomistic phason flips. Thus they resemble Brownian motion of mesoscopic particles, which are pushed by fluctuating knocks of fluid molecules. Whereas Brownian motion is described by a random walk in continuous space, Edagawa phasons can be conceived as a random walk on a quasilattice.