Atomic decoration of Katz-Gratias-de Boissieu-Elser model applied to the surface structure of i-Al-Pd-Mn

The Katz-Gratias-de Boissieu-Elser (KGdeBE) model for icosahedral quasicrystals is studied in order to provide an atomic bulk model for i-Al-Pd-Mn and i-Al-Cu-Fe. We interpret the KGdeBE model as the tiling T exp *2(F) decorated by Bergman and Mackay polytopes. Using information stemming from the inflation properties of the tiling T exp *(2F) (arrows on the edges of the tiles), we propose rules to make a unique choice between split positions and derive the corresponding vertex-windows. The resulting bulk model is used to provide atomic models of the five-, three-, and twofold surfaces of i-Al-Pd-Mn, as well as the terrace structure found in these materials. In order to stimulate new LEED calculations for these surfaces, we make the data sets (ranging up to some 10 exp 6 atoms) public.