Surface structure ofi−Al68Pd23Mn

Abstract

A Fibonacci-like terrace structure along a fivefold axis of i-Al 68 Pd 23 Mn 9 monograins has been observed by Schaub et al. with scanning tunneling microscopy. In the planes of the terraces they see patterns of dark pentagonal holes. These holes are well oriented both within and among terraces. In one of 11 planes Schaub et al. 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 Elser 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 polytopes as the only decoration objects, if one believes in their particular stability. We derive a picture of ''geared'' layers of Bergman polytopes from the projection techniques as well as from a huge patch. Under the assumption that no surface reconstruction takes place, this picture explains the Fibonacci sequence of the step heights as well as the related structure in the terraces qualitatively and to a certain extent even quantitatively. Furthermore, this layer picture requires that the polytopes are cut in order to allow for the observed step heights. We conclude that Bergman or Mackay clusters have to be considered as geometric building blocks ͑just the polytopes͒ of the i-Al-Pd-Mn structure rather than as energetically stable entities ͑clusters͒. ͓S0163-1829͑99͒02829-5͔

Fine structure on flat surfaces of quasicrystalline Al-Pd-Mn

“…21 Recently, Papadopolos et al have compared the characteristic distances measured by Schaub et al with arrangements of the Bergman clusters beneath one particular plane. 18,19 The characteristic distances separating Bergman clusters buried beneath this particular plane are shown by the values in brackets in the middle column of Table I. They were calculated from an exact geometrical construction.…”

“…9,10 It has been suggested that these represent specific types of atoms in the surface, e.g., Mn surrounded by Al-Pd pentagons. 17 It has also been suggested 18,19 that these may represent parts of the Bergman cluster, which is a structural unit emphasized in other structural models. 20,21 The present paper elucidates the discussion of the terrace fine structure.…”

Copper adsorption on the fivefoldAl70Pd21Mn9quasicrystal surface

“…3 The surface structure of this material has been identified and determined to be a termination of the bulk structure. [4][5][6][7][8][9][10][11][12] The local atomic configuration ͓see Fig. 1͑a͔͒ is best described with pentagonal dark stars, pentagons and flowers.…”

Local configurations on surfaces of icosahedral quasicrystals

“…Let us briefly recall how the Bergman clusters are used to decorate the tiling T * (2F) [10,14]. In a first step, from the the tiling T * (2F) we locally derive the primitive or Amman-Kramer tiling T (P) .…”