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∗(2F) decorated by Bergman and Mackay polytopes. Using information stemming from the inflation properties of the tiling T∗(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 106 atoms) public.