32 research outputs found
Thick atomic layers of maximum density as bulk terminations of quasicrystals
The clean surfaces of quasicrystals, orthogonal to the directions of the main
symmetry axes, have a terrace-like appearance. We extend the Bravais' rule for
crystals to quasicrystals, allowing that instead of a single atomic plane a
layer of atomic planes may form a bulk termination.Comment: 4 pages, 4 figure
A maximum density rule for surfaces of quasicrystals
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
Tiling of the five-fold surface of Al(70)Pd(21)Mn(9)
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 figure
Tiling theory applied to the surface structure of icosahedral AlPdMn quasicrystals
Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show
atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model
due to Elser which incorporates many experimental data. The model has
dodecahedral Bergman clusters within an icosahedral tiling T^*(2F) and is
projected from the 6D face-centered hypercubic lattice. We derive the
occurrence and Fibonacci spacing of atomic planes perpendicular to any 5fold
axis, compute the variation of planar atomic densities, and determine the
(auto-) correlation functions. Upon interpreting the planes as terraces at the
surface we find quantitative agreement with the STM experiments.Comment: 30 pages, see also http://homepages.uni-tuebingen.de/peter.kramer/ to
be published in J.Phys.
Surface structure of i-Al(68)Pd(23)Mn(9): An analysis based on the T*(2F) tiling decorated by Bergman polytopes
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
A molecular overlayer with the Fibonacci square grid structure
Quasicrystals differ from conventional crystals and amorphous materials in that they possess long-range order without periodicity. They exhibit orders of rotational symmetry which are forbidden in periodic crystals, such as five-, ten-, and twelve-fold, and their structures can be described with complex aperiodic tilings such as Penrose tilings and Stampfli-Gaehler tilings. Previous theoretical work explored the structure and properties of a hypothetical four-fold symmetric quasicrystal-the so-called Fibonacci square grid. Here, we show an experimental realisation of the Fibonacci square grid structure in a molecular overlayer. Scanning tunnelling microscopy reveals that fullerenes (C ) deposited on the two-fold surface of an icosahedral Al-Pd-Mn quasicrystal selectively adsorb atop Mn atoms, forming a Fibonacci square grid. The site-specific adsorption behaviour offers the potential to generate relatively simple quasicrystalline overlayer structures with tunable physical properties and demonstrates the use of molecules as a surface chemical probe to identify atomic species on similar metallic alloy surfaces