Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 4.6, p. 623   | 1 | 2 |

Section Twinning and nanodomain structures

W. Steurera* and T. Haibacha

aLaboratory of Crystallography, Department of Materials, ETH Hönggerberg, HCI G 511, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich, Switzerland
Correspondence e-mail: Twinning and nanodomain structures

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High-order approximants of quasicrystals often occur in orientationally twinned form or, on a smaller scale, as oriented nanodomain structures. These structures can be identified by electron microscopy, and, in certain cases, also by high-resolution X-ray diffractometry (Kalning et al., 1994[link]). If the intensity and spatial resolution is sufficient, characteristic reflection splitting and diffuse diffraction phenomena can be observed. It has been demonstrated that for the determination of the local structure (structure-building elements) it does not matter greatly whether one uses a data set for a real quasicrystal or one for a twinned approximant (Estermann et al., 1994[link]). Examples of reciprocal-space images of an approximant, a twinned approximant and the related decagonal phase are shown schematically in Fig.[link] and for real samples in Fig.[link].


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Simulated diffraction patterns of (a) the [\simeq 52\;\hbox{\AA}] single-crystal approximant of decagonal Al–Co–Ni, (b) the fivefold twinned approximant, and (c) the decagonal phase itself (Estermann et al., 1994[link]).


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Zero-layer X-ray diffraction patterns of decaprismatic Al73.5C21.7Ni4.8 crystals taken parallel and perpendicular to the crystal axis on an image-plate scanner (Mar Research) at different temperatures. In (a) and (b), room-temperature (RT) diffraction patterns from a sample quenched after annealing at 1073 K are shown. Reflections from both a crystalline approximant and a decagonal phase are visible. The period along the unique direction in the decagonal phase and the corresponding period in the approximant phase is [\simeq 8\;\hbox{\AA}] (b). At 1520 K, a single-phase decagonal quasicrystal is present with [\simeq 4\;\hbox{\AA}] fundamental structure (c, d). In (e, f), the RT diffraction patterns of the slowly cooled sample indicate a single-phase nanodomain structure with [\simeq 8\;\hbox{\AA}] periodicity along the unique direction.


Estermann, M., Haibach, T. & Steurer, W. (1994). Quasicrystal versus twinned approximant: a quantitative analysis with decagonal Al70Co15Ni15. Philos. Mag. Lett. 70, 379–384.
Kalning, M., Kek, S., Burandt, B., Press, W. & Steurer, W. (1994). Examination of a multiple twinned periodic approximant of the decagonal phase Al70Co15Ni15. J. Phys. Condens. Matter, 6, 6177–6187.

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