The atomic structure of the decagonal phase and its approximants as random coincidence networks

Abstract

It is shown that the decahedral recursive model (DRM) explains at atomic level the structure of the decagonal (D) phase and associated approximant structures as random coincidence networks (RCNS), random packings of clusters satisfying DRM energy minimizing rules. RCNS are degenerate random tilings that become quasiperiodic when entropic disorder is maximized at high temperature through phason flips requiring small atomic movements. Such phason flips can change the relative ratio and geometry of tiles, making transformations between systems using different tile sets possible. Electron microscopic observations for AlCuCoSi, AlCuFeCr, AlCoCu and AlPdMn systems are reproduced, including the observed Fibonacci sequenced lines in the former.