International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. D. ch. 3.3, p. 404
Section 3.3.6.3.1. Dauphiné twins
a
Institut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and bMineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany |
This twinning is commonly described by a twofold twin rotation around the threefold symmetry axis [001]. The two orientation states are of equal handedness but their polar axes are reversed (`electrical twins'). Dauphiné twins can be transformation or growth or mechanical (ferrobielastic) twins. The composite symmetry is , the point group of high-temperature quartz (-quartz). The coset decomposition of with respect to the eigensymmetry (index [2]) contains the operations listed in Table 3.3.6.3.
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The left coset constitutes the twin law. Note that this coset contains four twofold rotations of which the first one, , is the standard description of Dauphiné twinning. In addition, the coset contains two sixfold rotations, and . The black–white symmetry symbol of the composite symmetry is (supergroup of index [2] of the eigensymmetry group ).
This coset decomposition was first listed and applied to quartz by Janovec (1972, p. 993).
References
Janovec, V. (1972). Group analysis of domains and domain pairs. Czech. J. Phys. B, 22, 974–994.Google Scholar