Atomic scale coexistence of periodic and quasiperiodic order in a 2-fold Al-Ni-Co decagonal quasicrystal surface

Decagonal quasicrystals are made of pairs of atomic planes with pentagonal symmetry periodically stacked along a 10-fold axis. We have investigated the atomic structure of the 2-fold surface of a decagonal Al-Ni-Co quasicrystal using scanning tunneling microscopy. The surface consists of terraces separated by steps of heights 1.9, 4.7, 7.8, and $12.6\mathrm{\AA }$ containing rows of atoms parallel to the 10-fold direction with an internal periodicity of $4\mathrm{\AA }$. The rows are arranged aperiodically, with separations that follow a Fibonacci sequence and inflation symmetry. The results indicate that the surfaces are preferentially Al-terminated and in general agreement with bulk models.

Figure 1

(a) $650\times 650\mathrm{\AA }$ STM image of the 2-fold Al-Ni-Co surface ($V_s=1.0\mathrm{V}$, $I_t=0.1\mathrm{nA}$). Steps and terraces composed of rows of atoms are visible. (b) Line profile showing steps with heights $4.7\mathrm{\AA }$ $\left(S_H\right)$, $7.8\mathrm{\AA }$ $\left(L_H\right)$, and $1.9\mathrm{\AA }$. The ratio of $L_H$ to $S_H$ is approximately equal to the golden mean (1.618), characteristic of aperiodic quasicrystalline structure. The lowest terrace, indicated by the arrow in (b), is a domain where the periodicity along the rows is $8\mathrm{\AA }$. In the other terraces the periodicity along the rows is $4\mathrm{\AA }$.

Figure 2

(a) Collage of STM images $(145\mathrm{\AA }\times 90\mathrm{\AA })$ of two contiguous regions in the 2-fold Al-Ni-Co surface. The terraces are made of rows of periodically arranged atoms $\left(4\mathrm{\AA }\right)$ along the 10-fold direction and separated by distances $L$ and $S$. (b) Expanded view showing the interior in the $L$ and $S$ sections. $L$ contains two atomic rows, separated by $L_2$ and $S_2$ distances. $S$ contains one row, at distances of $L_2$ and $S_2$ from the boundary. (c) The sequence of $L$ and $S$ spacings between rows follows a Fibonacci sequence. The trench in the center of (a) and (c) is due to a missing $L+S$ section. The complete Fibonacci sequence of $LSLSLLSLLS$ is visible in (a).

Figure 3

STM images of the same area acquired at positive and negative bias. (a) $V_s=+1.2\mathrm{V}$, $I=0.1\mathrm{nA}$ (b) $V_s=-1.2\mathrm{V}$, $I=0.1\mathrm{nA}$. (c) Line profiles across the dashed lines in (a) and (b) reveal three electronically different atomic rows, labeled A, B, and C.

Figure 4

(Color online) Atomic model of the 2-fold surface derived from the bulk x-ray diffraction model of Takakura et al. (Ref. 20). The Al is blue and transition metal (Ni, Co) is red. The plane shown here is the one containing only Al atoms, which provides the best fit with the experimental STM images. (a) Top view $(8\mathrm{\AA }\times 90\mathrm{\AA })$. There three levels of color of the Al atoms corresponding to relative distances below the surface ($\text{dark}=\text{top}$; $\text{medium}=-0.5\mathrm{\AA }$, $\text{light}=-2\mathrm{\AA }$). The spacing between Al atoms along the 10-fold direction is $4.1\mathrm{\AA }$, and the sequence along the 2-fold direction shows the same Fibonacci sequence ($LSLSLLSL$ or $S_2{L}_2{L}_2{S}_2{L}_2{S}_2{L}_2{L}_2{S}_2{L}_2{S}_2{L}_2{L}_2{S}_2{L}_2{L}_2{S}_2{L}_2{S}_2{L}_2{L}_2$) as the STM image in Fig. 2c. Dashed arrows mark the positions of local mirror planes. (b) A cross section showing the atomic arrangement perpendicular to the surface (perpendicular to the 10-fold direction). A transition metal rich layer is visible below ($\sim 2.0\mathrm{\AA }$ lower) the topmost Al one. (c) A STM image of section of $L$ and $S$ with the Al sites indicated by blue dots.