Twofold surface of the decagonal Al-Cu-Co quasicrystal

We have investigated the atomic structure of the twofold surface of the decagonal Al-Cu-Co quasicrystal using scanning tunneling microscopy and low-energy electron diffraction. We have found that most of the surface features can be interpreted using the bulk-structure model proposed by Deloudi and Steurer (S. Deloudi, Ph.D. thesis, ETH, Zürich, 2008). The surface consists of terraces separated by steps of various heights. Step heights and steps sequences match with the thickness and the stacking sequence of blocks of layers separated by gaps in the model. These blocks of layers define possible surface terminations consisting of periodic atomic rows which are aperiodically stacked. These surface terminations are dense $\left(\sim 10\text{at}\text{.}/{\text{nm}}^2\right)$ and are of three types. The first two types are pure or almost pure Al while the third one contains $30–40\text{at}\text{.}\%$ of transition-metal atoms. Experimentally, we observe three different types of fine structures on terraces, which can be interpreted using the three possible types of bulk terminations. Terraces containing transition metals exhibit a strong bias dependency and present a doubling of the basic 0.42 nm periodicity, in agreement with the 0.84 nm superstructure of the bulk. In addition, a high density of interlayer phason defects is observed on this surface that could contribute to the stabilization of this system through configurational entropy associated with phason disorder.

Figure 1

(Color online) Atomic structure $\left(10\times 10{\text{nm}}^2\right)$ of the $d\text{-Al-Cu-Co}$ quasicrystal in the tenfold plane according to the model by Deloudi and Steurer (Ref. 16). The grid indicates densely spaced atomic rows. These are inclined by $18°$ from the horizontal and correspond to a (10000) orientation. The spacing follows a Fibonacci sequence with $S=0.475\text{nm}$ and $L=\tau S=0.769\text{nm}$. The dark (blue) and bright (orange) dots correspond to Al and TM atoms, respectively. An ideal Penrose tiling is superimposed. The edge of the rhombic tiles is 2.0 nm. The largest decagon decorating the Penrose tiling corresponds to the basic cluster unit.

Figure 2

(Color online) LEED pattern of the twofold $d\text{-AlCu-Co}$ (10000) surface taken at 60 eV electron energy showing a periodic ordering along the [00001] direction and quasiperiodic ordering along the $\left[001\overline{\mathbf{1}}0\right]$ direction.

Figure 3

(Color online) (a) 3D representation of an STM image $\left(285.6\times 285.6{\text{nm}}^2\right)$ of the clean twofold surface of the $d\text{-Al-Cu-Co}$ sample prepared by sputter-annealing (973 K) cycles (−0.8 V and 0.23 nA). (b) Line profile across step edges following the path indicated in (c).

Figure 4

Percentage of the surface area covered by terraces associated with specific step heights. The results are given for the two samples A1 and N1 annealed at 1023 K but for different times (A1 longer than N1). The total surface area investigated is written in brackets in the table.

Figure 5

(Color online) Cross sections of the model oriented along the [10000] direction. The horizontal direction is either the aperiodic $\left[001\overline{\mathbf{1}}0\right]$ direction (left) or the periodic [00001] direction. The dark (blue) and bright (orange) dots correspond to Al and TM atoms, respectively. The position of gaps separating blocks of layers are indicated by arrows. The gap width is 0.13 nm except for the one indicated by a thin arrow (0.10 nm). Most blocks have a thickness of either $S=0.47$ or $L=0.77\text{nm}$ and are stacked according to a Fibonacci sequence.

Figure 6

(Color online) High-resolution STM images $\left(12.8\times 12.8{\text{nm}}^2\right)$ of terraces of (a) type I and (b) type II ($-1\text{V}$ and 0.5 nA). Atomic rows run along the periodic [00001] direction and are spaced by a distance of either $S=0.47$ or $L=0.77\text{nm}$ or a combination of both. The periodicity along the rows is 0.4 nm except for those indicated by white arrows in (b) where a doubling of the periodicity is measured. A section of the atomic structure of a representative bulk termination is superimposed on the image for both types of terraces. The dark (blue) and bright (orange) dots correspond to Al and TM atoms, respectively.

Figure 7

(Color online) High-resolution STM images $\left(15\times 15{\text{nm}}^2\right)$ for terraces of type III acquired at negative bias [occupied states probed in (a), ($-1.2\text{V}$ and 0.5 nA)] or at positive bias [unoccupied states probed in (b), (1.2 V, 0.5 nA)]. Atomic rows running along the periodic [00001] direction have a periodicity of 0.8 nm. Rows with bright contrast in (a) are spaced by distances roughly corresponding to $LS\sim 1.3\text{nm}$ or $LSL\sim 2.1\text{nm}$. The contrast of atomic rows located in between two bright lines spaced by $LSL$ in (a) increases when tunneling into empty states as in (b). The black arrows indicate the position of the same defect in (a) and (b) as a reference point. A section of the atomic structure of representative bulk termination is superimposed on the image for both types of terraces. The dark (blue) and bright (orange) dots correspond to Al and TM atoms, respectively.

Figure 8

(Color online) (a) Interlayer phason defect observed on terrace of type I $\left(7.9\times 7.9{\text{nm}}^2\right)$. (b) and (c) are STM images of the same area $\left(50\times 50{\text{nm}}^2\right)$ and correspond to a terrace of type III recorded at negative bias [(b), ($-1.2\text{V}$ and 0.5 nA)] or at positive bias [(c), (1.2 V and 0.5 nA)]. Dark (blue) sticks in (b) show inversion in the stacking sequence of the bright lines. While most of the surface area is bias dependent, the part of the surface delimited by the bright (yellow) contour is not.