FIGURE 3. The best-fit candidate model for the atomic decoration of the decagonal quasi-unit cell for Al72Ni20Co8.

From the following article:

Experimental verification of the quasi-unit-cell model of quasicrystal structure

Paul J. Steinhardt, H.-C. Jeong, K. Saitoh, M. Tanaka, E. Abe and A. P. Tsai

Nature 396, 55-57(5 November 1998)

doi:10.1038/23902

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Large circles represent Ni (red) or Co (yellow) and small circles represent Al. The structure has two distinct layers along the periodic c -axis. Solid circles represent c=0 and open circles represent c=1/2. The experimental input used to generate candidate models is: (1) the space group22 is centrosymmetric P 105/mmc based on convergent-beam electron-diffraction methods18; (2) the HAADF image, in which scattering is proportional to the square of the atomic number, highlights the positions of the transition metals relative to the aluminium; and (3), based on X-ray diffraction, the diameter of the decagonal cluster is 2.033 nm and the period along the decagonal c -axis is 0.408 nm, corresponding to two atomic layers per period. To obtain P 105/mmc, different atomic arrangements are placed on the two layers along the c -axis such that two overlapping decagons related by odd-multiple rotations of pi/10 must be shifted by a half-period in order to shore atoms. Thus the covering of the plane can be decomposed into two interpenetrating lattices of decagons, in which the decagon decoration in one set is related by screw symmetry or c -glide symmetry with respect to the other. Using positions of the transition metals inferred from the HAADF images, a sequence of plausible decagon decorations was explored and the best fits to the experimentally measured stoichiometry and density (3.94 g cm-3 plusminus 1%) were found. For each decoration, the constraint had to be imposed that shared atoms at overlapping sites were identical.

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