Phase-induced atomic permutations in icosahedral quasicrystals : a model for self-diffusion

Abstract

The process of phase-induced self-diffusion has been investigated for the three-dimensional Ammann-Kramer-Penrose tiling. This happens along the lines of Kalugin and Katz (1993) for the octagonal planar tiling. It is found that for any permutation within two subsets of the ten vertices in a triacontahedral cage there is a corresponding loop in phase space. There are other loops by which vertices are exchanged between interlocked triacontahedral cages. Along chains of such triacontahedral cages, percolative diffusion is possible. This self-diffusion, however, occurs along two separated sublattices. Thus it is a two-component diffusion.