Quasiperiodicity in decagonal phases forced by inclined net planes?

Abstract

It is generally assumed that decagonal quasicrystals show periodically arranged atomic layers only on net planes perpendicular to the tenfold axis and quasiperiodically arranged ones parallel to it. However, there also do exist only slightly puckered atomic layers that are periodically arranged and inclined to the tenfold axis. They coincide with the net planes of the periodic average structures of the decagonal phase and are related to the strongest Bragg re¯ections. Since they link quasiperiodic and periodic directions, inclined net planes may play a crucial role for growth and stabilization of decagonal quasicrystals. In fact, it is shown how ideal quasiperiodic long-range order and in¯ation symmetry allow for the existence of inclined net planes with small corrugation and reinforce the relation with the periodic average structures.

Reflections on symmetry and formation of axial quasicrystals

“…For the growth of DQC, they can play an important role in guiding the growth in the quasiperiodic direction. Some of them have been observed as growth facets (Steurer, Cervellino, 2001;Gille et al, 2005). In Fig.…”

“…6). In DQCs, there also exist special sets of net planes, the so called 'inclined net planes', connecting both the periodic and quasiperiodic directions (Steurer, Cervellino, 2001) (Fig. 7).…”

X-ray standing wave study of Si clusters on a decagonal Al-Co-Ni quasicrystal surface

“…In order to maximize the signal we chose the planes, which have the second-highest scattering amplitudes for Al-Co-Ni, after the (00004) planes [47]. For the quasicrystal, there are 5 reflections that are symmetrically identical to those from the planes, all tilted 60.4° from (00004) planes and having an interlayer spacing of 2.02 Å (see Table 1) [42,47]. This is the there is no true periodicity in this structure, the atoms are arranged such as to reflect an average 2.03 Å periodicity for these planes, as is seen rather clearly in Figure 4b.…”

Czochralski growth and X-ray topographic characterization of decagonal AlCoNi quasicrystals

“…On each of the crystals small facets are to be seen that reveal their single-crystalline nature. Measuring the inclination of all observed facets [8], that well correspond to net planes with the strongest structure amplitudes [9], allows the construction of the idealized decagonal quasicrystal shape that is shown in figure 1c.…”

“…Email: gille@lmu.de. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 9 Ni 19 seed crystals in the desired orientation were cut from former single crystals using a wire saw. The Czochralski growth apparatus has been modified during the series of experiments.…”