Phason dynamics in decagonal quasicrystals

Abstract

In a spectacular experiment of the year 2000 Edagawa et al. observed white spots in HRTEM images of d-Al-Cu-Co, which formed the vertices of a tiling. On a time scale of seconds to minutes the spots changed positions corresponding to phason flips. To illuminate the origin of the spots, their jump mechanism and frequencies we employ a structure model of Zeger and Trebin of 1996. It consists of quasiperiodic double layers stacked periodically by 4.18 Å. Each double layer contains rings of ten atoms whose centers form the vertices of a Tübingen triangle tiling. Correlated jumps of two atoms in each sublayer cause a simpleton phason flip of the entire ten ring. The stacking of the double layers leads to columns of the ten rings which might be interrupted due to the flips. Columns which contain a critical minimum number of complete ten rings are considered visible as white spots. Simultaneous appearences of vertices and their flipped positions give rise to the pentagonal Penrose pattern as observed by Edagawa et al. and also in other experiments. Postulating microscopic flip rates for the correlated jumps of pairs of atoms in the sublayers we calculate the probabilities for the numbers of complete ten rings in a column and confirm the mesoscopic time scales for the jumps of the white spots.