Experimental Observation of Quasicrystal Growth

The growth of an Al-Ni-Co decagonal quasicrystal was observed by in situ, high-temperature, high-resolution transmission electron microscopy. The tiling patterns extracted from a series of high-resolution transmission electron microscopy images were analyzed on the basis of the high-dimensional description of quasicrystalline structures. The analyses indicated that the growth proceeded with frequent error-and-repair processes. The final, grown structure showed nearly perfect quasicrystalline order. Our observations suggest that the repair process by phason relaxation, rather than local growth rule, plays an essential role in the construction of ideal quasicrystalline order in real materials.

Figure 1

(a) An example of a HRTEM image taken at 1183 K, in which two grains, designated as $A$ and $B$, are separated by the grain boundary indicated by the red curve. The growth direction of grain $A$ is indicated by the arrow. For details of the image processing, see the Supplemental Material [14]. (b) The tiling pattern constructed by connecting the white spots in image (a) using the basis vectors ${\mathbf{p}}_i$ ($i=0,\mathrm{...},4$). (c) The perp-space point distribution deduced from the tiling pattern in (b). The decagon indicates the domain for the pentagonal Penrose tiling.

Figure 2

(a)–(d) The HRTEM images at $t=2.1$, 4.9, 11.3, and 13.6 s, respectively, where the time was measured from the moment at which the image in Fig. 1 was taken. The positions of the growth front at $t=0$, 2.1, 4.9, 11.3, and 13.6 s are indicated by red curves in the figures.

Figure 3

An example of an error-and-repair process. In the left column, the vertices of the tilings extracted from the images at $t=4.9$ (a), 6.1 (b), and 6.6 s (c) are presented, and the lattice planes parallel to ${\mathbf{p}}_1$ are drawn. The lattice planes on which many vertices lie consist mostly of two different lattice spacings, $L$ and $S$. In the right column, 2D maps of the lattice planes are shown (see text).

Figure 4

(a) Time dependence of the degree of order in the lattice plane arrangement, where $\mathrm{\Delta }=0$ corresponds to the ideal order. We find that $\mathrm{\Delta }$ departs from and returns to zero, which corresponds to an error-and-repair event. Six such events are identifiable in the shaded time regions. (b)–(d) 2D maps of the lattice planes and perp-space point distributions at $t=0$, 6.4, and 14.9 s, respectively, showing that the overall growth proceeds while maintaining a nearly perfect quasicrystalline order.