Real-space observation of quasicrystalline Sn monolayer formed on the fivefold surface of icosahedral $\mathrm{Al}\mathrm{Cu}\mathrm{Fe}$ quasicrystal

We investigate a thin Sn film grown at elevated temperatures on the fivefold surface of an icosahedral $\mathrm{Al}\mathrm{Cu}\mathrm{Fe}$ quasicrystal by scanning tunneling microscopy (STM). At about one monolayer coverage, the deposited Sn is found to form a smooth film of height consistent with one-half of the lattice constant of the bulk Sn. Analysis based on the Fourier transform and autocorrelation function derived from high-resolution STM images reveals that Sn grows pseudomorphically and hence exhibits a quasicrystalline structure.

Figure 1

(a) High-resolution image on a terrace of the clean fivefold $i\text{‐}\mathrm{Al}\mathrm{Cu}\mathrm{Fe}$ surface (area $A=16\times 16{\mathrm{nm}}^2$; bias voltage $V_B=1.1\mathrm{V}$; and tunneling current $I_T=0.25\mathrm{nA}$). (b) Description of the marked area in terms of atom sites (Ref. 17). Small solid circles mark sites which can be occupied by an atom or empty, depending on locations.

Figure 2

STM images of the Sn-covered fivefold $i\text{‐}\mathrm{Al}\mathrm{Cu}\mathrm{Fe}$ surface for about 1 ML coverage. Arrows point to steps associated with Sn film. ($V_B=2.8\mathrm{V}$ and $I_T=0.2\mathrm{nA}$.) (a) Image is presented in derivative form to highlight steps ($A=300\times 300{\mathrm{nm}}^2$). (b) 3D view of framed area of image (a).

Figure 3

(a) High-resolution image of Sn film for about 1 ML coverage ($A=35\times 24{\mathrm{nm}}^2$, ${\mathrm{V}}_B=1.2\mathrm{V}$, and $I_T=0.2\mathrm{nA}$). Representatives of repeating motifs are marked by circles of different colors and squares. Arrow points to the step associated with Sn film. (b) Fourier transform derived from image (a). Arrow marks about $3.0{\mathrm{nm}}^{-1}$. The successive maxima are marked by circles as a guide for eyes. (c) Autocorrelation function derived from image (a) ($A=33\times 24{\mathrm{nm}}^2$). (d) Height profile along the line pointed by arrows in autocorrelation function (c). Peaks indicated by arrows correspond to maxima marked by circles in autocorrelation function (c). Peaks are located at $\tau$-scaling distance. (e) Depiction of possible location of dotlike protrusions observed on the film, marked by circles in image (a). Gray and black solid circles represent the location of Sn protrusions and the substrate atom sites, respectively.

Figure 4

(a) A portion of image in Fig. 3a after height filtering ($A=31\times 24{\mathrm{nm}}^2$). (b) Fourier transform of the filtered image. Arrow marks about $3.0{\mathrm{nm}}^{-1}$. (c) Autocorrelation function of the filtered image ($A=31\times 24{\mathrm{nm}}^2$).