Fivefold surfaces

On a large scale (>100 nm), the fivefold surfaces (orthogonal to the fivefold symmetry axis) present sequences of flat terraces with characteristic terrace step heights... 

Apart from the fivefold surfaces, the twofold surfaces were imaged. These surfaces also exhibit terraces, visible in Figures 12-14, 12-15, but the fivefold surfaces are the most stable, followed by the twofold surfaces, whereas the threefold surfaces become faceted, i.e. are breaking into islands that tend to orientate themselves differently [13]. 

Visible in Figure 12-10, the typical heights of terrace steps on the fivefold surface are 4.08 A and 6.60 A. From Figures 12-14 and 12-15 of the twofold surfaces the common heights are circa 6.3 A and 10.2 A. The typical heights on surfaces of both kinds are considerably larger than the minimum interplane distance in the corresponding directions, as listed in Table 12-3. Two questions arise. What are the structures in terms of atomic planes of the terraces Which atomic plane terminates a fivefold or a twofold surface ... 

In Ref [23] we sought to determine a criterion for an appearance of a fivefold surface. At that time it was generally expected [17] that the smaller, Bergman poly-hedra in the model are energetically stable clusters. In our investigations... 

Figure 12-10. An STM image of a fivefold surface, size 1750 x 1750 nm, of i-AlPdMn. This image is taken from Ref. [9] (rotated by 180°), produced by J. Ledieu. In Ref. [26] a Fibonacci sequence of the step heights (circa) m = 4.08 A and / = 6.60 A was measured on the surface. We fix a marked subsequence of steps /, /, m, /, m from left-right, downwards, corresponding to a subsequence of the g fefeg -terminations in Ad(T ) from Figure 12-12 bottom). Numbers 193, 196 and 198 label the tiling fivefold planes in the model...

Boudard model. Not only have we shown that the atomic decorations in a shape of Bergman and Mackay polyhedra can not be stable clusters but also we have drawn the appearance of the cut polyhedra on the surfaces that matches the image of the real material on the fivefold surface. 

Figure 8.1 Binding and hydroxylation energies (kcal/mol H20) for water at threefold (corner), fourfold (edge) and fivefold (surface) coordinated defect sites on the MgO(lOO) surface (Scamehorn et al., 1994).

Figure 18.4 Examples of step height histograms on fivefold surfaces of icosahedral QCs. (a) Frequency of step heights on i-AI-Cu-Fe [127]. The ideal values, based on the bulk structure and the surface structure determination, are 2.40, 3.99, and...

Another powerful approach is to use simple analyses based on the superposition of appropriate geometric features. Figure 18.7a shows a high-resolution scan of the fivefold surface of i-Al-Pd-Mn, over a 100 x 100 A region. This scan is at the best resolution that can be achieved on this surface. Although the surface is not periodic, there are certain striking arrangements of motifs, which recur at... 

Krajci and Hafner [161] used both a Penrose PI tiling (as in Figure 18.7c) and a decagon-hexagon-boat-star tiling to describe the fivefold surface of i-Al-Pd-Mn, and showed how these tilings are structurally related. (Both tilings are illustrated and... 

Figure 18.9 Radial distributions calculated (upper curve) from the autocorrelation pattern of a high-resolution STM image of the fivefold surface of i-AI-Pd-Mn and (lower curve) from the autocorrelation pattern of a specific plane in a bulk...

Figure 18.11 The LEED pattern of the clean fivefold surface of i-AI-Pd-Mn at normal incidence and with 88 eV kinetic energy [92]. http //prl.aps.org/abstract/PRL/v78/i3/p467 1. (Copyright (1997) by the American Physical Society.)...

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