**CHEMICAL ORDERING IN**** ****Al**_{72}Ni_{20}Co_{8}** ****DECAGONAL QUASICRYSTALS**^{1}

*Y. Yan,*^{1}* S. J. Pennycook*^{2}

*Nature*, **403**, 266 (2000),

*Phys. Rev. Lett*., **86**, 1542 (2001)

The ability of Z-contrast microscopy to locate and distinguish Al atom sites from transition metal sites has allowed a new, reliable structure to be determined for the high-perfection Al_{72}Ni_{20}Co_{8} decagonal quasicrystal. The structure reveals that the central ring of the 2-nm clusters dominating the structure have broken symmetry. Given this broken symmetry, clusters can only overlap in two specific ways, which restricts the possible overlaps and enforces the perfect quasiperiodic tiling that is observed. However, the underlying reason for the broken symmetry in the central ring cannot be established by imaging alone.

To explore the driving force for the broken symmetry we performed first-principles total energy calculations on a cluster with and without broken symmetry in the central ring. From the Z-contrast image it was seen that five of the ten columns in the central ring were transition metal. Since the image could not distinguish Co from Ni we performed calculations for each separately. Both gave similar results. Models were selected as shown in Fig. 1, with (a) ten alloy columns each comprising 50% Al and 50% Ni, (b) five pure Al and five pure Ni columns in a symmetric arrangement, and (c) five pure Al and five pure Ni columns now arranged with broken symmetry. All models contain the same numbers of atoms so the total energies can be directly compared. The energy differences were surprisingly large. The ordered structure (b) is about 7 eV lower in energy than the disordered structure (a), and the ordered structure with broken symmetry (c) is a further 5 eV lower in energy than the symmetric structure (b). The final relaxed structure from the starting model (c) is shown in Fig. 1(d) superimposed on the Z-contrast image. Three of the Al columns in the central ring (arrowed) have moved inwards to relieve the stress, and the fit with the Z-contrast image is excellent.

The availability of good structure data from real space images is very effective in the field of quasicrystals. Total energy calculations have revealed a strong driving force towards the broken symmetry that is the origin of quasiperiodic ordering. Further theoretical studies can reveal sites of phason flips and the energy barriers, while atomic resolution electron energy loss spectroscopy may reveal local electronic structure anomalies.

Figure 1:
(a-c) Starting models for total energy calculations with different arrangements of Ni and Al atoms in the central ring. The large circles denote Ni, small circles Al, shaded circles alloy columns. (d) Lowest energy structure superimposed on the Z-contrast image.

1. National Renewable Energy Laboratory, Golden, CO.

2. Solid State Division, ORNL