Surface structure of i-Al68Pd23Mn9: An analysis based on the T*((2F)) tiling decorated by Bergman polytopes

A Fibonacci-like terrace structure along a fivefold axis of i-Al68Pd23Mn9, monograins has been observed by Schaub et nl. with scanning tunneling micro scopy. In the planes of the terraces they see patterns of dark pentagonal h oles. These holes are well oriented both within and among terraces. In one of 11 planes Schaub et nl. obtain the autocorrelation function of the hole pattern. We interpret these experimental findings in terms of the T*((2F)) tiling decorated by Bergman and Mackay polytopes. Following, the suggestion of EElser that the Bergman polytopes, clusters are the dominant motive of this model, we decorate the tiling T*((2F)) with the Bergman polytopes only . The tiling T*((2f)) allows us to use the powerful tools of the projection techniques. The Bergman polytopes can be easily replaced by the Mackay pol ytopes as the only decoration objects, if one believes in their particular stability. We derive a picture of "geared'' layers of Bergman polytopes fro m the projection techniques as well as from a huge patch. Under the assumpt ion that no surface reconstruction takes place, this picture explains the F ibonacci sequence of the step heights as well as the related structure in t he terraces qualitatively and to a certain extent even quantitatively. Furt hermore, this layer picture requires that the polytopes are cut in order to allow for the observed step heights. We conclude that Bergman or Mackay cl usters have to be considered as geometric building blocks (just the polytop es) of the i-Al-Pd-Mn structure rather than as energetically stable entitie s (clusters). [S0163-1829(99)02829-5].