Tiling theory applied to the surface structure of icosahedral AlPdMn quasicrystals

Abstract

Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model due to Elser which incorporates many experimental data. The model has dodecahedral Bergman clusters within an icosahedral tiling T^*(2F) and is projected from the 6D face-centered hypercubic lattice. We derive the occurrence and Fibonacci spacing of atomic planes perpendicular to any 5fold axis, compute the variation of planar atomic densities, and determine the (auto-) correlation functions. Upon interpreting the planes as terraces at the surface we find quantitative agreement with the STM experiments.