Table 3.3.10.1

Hahn, Th.; Klapper, H.

doi:10.1107/97809553602060000644

International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

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International Tables for Crystallography (2006). Vol. D. ch. 3.3, p. 430

Table 3.3.10.1

Th. Hahn^a ^* and H. Klapper^b

^a Institut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and ^bMineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany
Correspondence e-mail: hahn@xtal.rwth-aachen.de

Table 3.3.10.1 | top | pdf |
Examples of permissible twin boundaries for higher-order merohedral twins ([j]> 1)

	$[\Sigma 3]$ growth and deformation twins of cubic crystals, twin mirror plane (111) (spinel law)	$[\Sigma 5]$ growth twins of tetragonal rare-earth sulfides (SmS_1.9), twin mirror plane (120)	$[\Sigma 33]$ deformation twins of cubic galena (PbS), twin mirror plane (441)^†
Eigensymmetry $[{\cal H}]$	$[4/m{\bar 3}2/m]$	$[4/m\,2/m\,2/m]$	$[4/m{\bar 3}2/m]$
Intersection symmetry $[{\cal H}^\ast]$ ^‡	$[{\bar 3}2/m]$ parallel to [111]	parallel to [001]	parallel to $[[1{\bar 1}0]]$
Reduced composite symmetry $[{\cal K}^\ast]$ ^‡	$[6'/m'_1({\bar 3})2/m\,2'/m'_3]$	$[4/m\,2'/m'_1\,2'/m'_2]$	$[2'/m'_1\,2/m\,2'/m'_2]$
Permissible twin boundaries	Three pairs of perpendicular planes	Two pairs of perpendicular planes	One pair of permissible planes
	& $[m_3 = (11{\bar 2})]$	& $[({\bar 2}10)]$	$[m_1 \,= \,(441)]$ & $[m_2 \,= \,(11{\bar 8})]$
	& $[m_3 = ({\bar 2}11)]$	& $[({\bar 1}30)]$
	& $[m_3 = (1{\bar 2}1)]$
Reference system	Cubic axes	Tetragonal axes	Cubic axes

^† The existence of this deformation twin is still in doubt (cf. Seifert, 1928

).
^‡The intersection symmetry $[{\cal H}^\ast]$ and the permissible boundaries are referred to the coordinate system of the eigensymmetry; the reduced composite symmetries $[{\cal K}^\ast]$ are based on their own conventional coordinate system derived from the intersection symmetry $[{\cal H}^\ast]$ plus the twin law (cf. Section 3.3.4