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A rule due to Bravais of wide validity for crystals is that their surfaces correspond to the densest planes of atoms in the bulk of the material. Comparing a theoretical model of i-AlPdMn with experimental results, we find that this correspondence breaks down and that surfaces parallel to the densest planes in the bulk are not the most stable, i.e. they are not so-called bulk terminations. The correspondence can be restored by recognizing that there is a contribution to the surface not just from one geometrical plane but from a layer of stacked atoms, possibly containing more than one plane. We find that not only does the stability of high-symmetry surfaces match the density of the corresponding layer-like bulk terminations but the exact spacings between surface terraces and their degree of pittedness may be determined by a simple analysis of the density of layers predicted by the bulk geometric model., Comment: 8 pages of ps-file, 3 Figs (jpg)

The structure of the Al_{70}Pd_{21}Mn_{9} surface has been investigated using high resolution scanning tunnelling microscopy (STM). From two large five-fold terraces on the surface in a short decorated Fibonacci sequence, atomically resolved surface images have been obtained. One of these terraces carries a rare local configuration in a form of a ring. The location of the corresponding sequence of terminations in the bulk model M of icosahedral i-AlPdMn based on the three-dimensional tiling T*(2F) of an F-phase has been estimated using this ring configuration and the requirement from the LEED work of Gierer et al. that the average atomic density of the terminations is 0.136 atoms per A^2. A termination contains two atomic plane layers separated by a vertical distance of 0.48 A. The position of the bulk terminations is fixed within the layers of Bergman polytopes in the model M: they are 4.08 A in the direction of the bulk from a surface of the most dense Bergman layers. From the coding windows of the top planes in terminations in M we conclude that a Penrose (P1) tiling is possible on almost all five-fold terraces. The shortest edge of the tiling P1, is either 4.8 A or 7.8 A. The experimentally derived tiling of the surface with the ring configuration has an edge-length of 8.0 +- 0.3 A and hence matches the minimal edge-length expected from the model., Comment: 11 pages LaTeX file (withowt figures), 16 figures; changed content: new results on new STM data, old results valid and included

The nature of the five-fold surface of Al(70)Pd(21)Mn(9) has been investigated using scanning tunneling microscopy. From high resolution images of the terraces, a tiling of the surface has been constructed using pentagonal prototiles. This tiling matches the bulk model of Boudard et. al. (J. Phys.: Cond. Matter 4, 10149, (1992)), which allows us to elucidate the atomic nature of the surface. Furthermore, it is consistent with a Penrose tiling T^*((P1)r) obtained from the geometric model based on the three-dimensional tiling T^*(2F). The results provide direct confirmation that the five-fold surface of i-Al-Pd-Mn is a termination of the bulk structure., Comment: 4 pages, 4 figures

A Fibonacci-like terrace structure along a 5fold axis of i-Al(68)Pd(23)Mn(9) monograins has been observed by T.M. Schaub et al. with scanning tunnelling microscopy (STM). 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 Katz-Gratias-de Boisseu-Elser model. Following the suggestion of Elser that the Bergman clusters are the dominant motive of this model, we decorate the tiling T*(2F) by 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 decoration objects. 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 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 of the i-AlPdMn structure rather than as energetically stable entities.