An Ultimate Symmetry in Physics? Zorka Papadopolos Peter A.B. Pleasants
Abstract Planes orthogonal to 5-, 3- and 2-fold axes of icosahedral phases We are interested in planes in models of icosahedral quasicrystal that are candidates for surfaces in their physical realizations. Icosahedral quasicrystals are derived from 3 basic modules (or from combinations of them), called by Mermin et al. [Phys. Rev. {\bf B35} 5487 (1987)] "primitive", "face-centered" or "body-centered" and obtained by icosahedral projection of the ZZ^6, D_6 or D*_6 six-dimensional lattices, respectively. The densities of the atomic positions in the 2-fold, 3-fold and 5-fold planes are governed by the underlying module and by the window. When the window is a sphere, or a polytope very close to a sphere, the module is the major influence on the densities of these planes, both in the bulk-model and, if there is no reconstruction, on the surface of an alloy. We give the relative densities of these planes for all three modules and we discuss in particular the model for the icosahedral alloys (i-AlPdMn, i-AlCuFe) defined by three windows. |