arXiv subjects
Publications and source records attributed to Johannes Roth.
The coincidence problem for three-dimensional discrete structures with icosahedral symmetry is reinvestigated. We present a parametric description of the coincidence rotations based on special quaternions, called icosian numbers. In particular, we give a characterization of the possible coincidence indices (Sigma-factors) and present a complete list of the possible rotations with Sigma < 100.
We present a molecular dynamics study on atomic self-diffusion in Frank-Kasper type dodecagonal quasicrystals. It is found that the quasicrystal-specific flip mechanism for atomic diffusion as predicted by Kalugin and Katz, indeed occurs in this system. However, in order to be effective, this mechanism needs to be catalyzed by other defects such as half-vacancies if the structure is truly three-dimensional. For this reason, flip diffusion is difficult to distinguish from standard vacancy diffusion. In a quasi-two-dimensional setup, however, the flips may occur without other defects. Activation energies and flip frequencies are also determined.
A structure model of atoms of two sizes, interacting with Lennard-Jones potentials and simulated by molecular dynamics, was observed to freeze into a decagonal quasicrystal dominated by Frank-Kasper coordination shells and closely related to the Henley-Elser model for icosahedral quasicrystals. Idealized structure models can be described as decorations of triangle-rectangle and rhombus tilings. Equilibrium properties of the idealized model have been determined by molecular dynamics simulations and a high stability of the model and a low jump rate of the atoms have also been observed.