Table 3.3.9.1

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. 425

Table 3.3.9.1

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 3.3.9.1 | top | pdf |
Staurolite, 60° and 90° twins

Comparison of the twin operations with the `symmetry operations' of the primitive pseudo-cube with respect to obliquity $[\omega]$ and lattice index [[j]] , referred both to the pseudo-cubic axes, $[{\bf a}'_c]$ , $[{\bf b}'_c]$ , $[{\bf c}'_c]$ , and the monoclinic (metrically orthorhombic) axes, $[{\bf a}_m]$ , $[{\bf b}_m]$ , $[{\bf c}_m]$ . The calculations were performed with the program OBLIQUE by Le Page (1999, 2002).

(a) 90° cross (eight twin operations).

Twin operations referred to		Obliquity $[\omega]$ $[[^\circ]]$	Lattice index [j] referred to		Remarks
$[{\bf a}'_c, {\bf b}'_c, {\bf c}'_c]$	$[{\bf a}_m, {\bf b}_m, {\bf c}_m]$	Obliquity $[\omega]$ $[[^\circ]]$	$[{\bf a}'_c, {\bf b}'_c, {\bf c}'_c]$	$[{\bf a}_m, {\bf b}_m, {\bf c}_m]$	Remarks
		0	1	1	Four collinear twin operations , , $[{\bar 4}{^1}]$ , $[{\bar 4}{^3}]$
		1.19	1	6	Four `diagonal' (with respect to the monoclinic unit cell) twin operations intersecting in
		1.19	1	6
	$[2[0{\bar 1}3]_m]$	1.19	1	6
	$[m(0{\bar 3}1)_m]$	1.19	1	6

(b) 60° cross.

Twin operations referred to		Obliquity $[\omega]$ $[[^\circ]]$	Lattice index [j] referred to		Equivalent directions
$[{\bf a}'_c, {\bf b}'_c, {\bf c}'_c]$	$[{\bf a}_m, {\bf b}_m, {\bf c}_m]$	Obliquity $[\omega]$ $[[^\circ]]$	$[{\bf a}'_c, {\bf b}'_c, {\bf c}'_c]$	$[{\bf a}_m, {\bf b}_m, {\bf c}_m]$	Equivalent directions
( $[\pm120^\circ]$ )		0.87	3	3	$[[11{\bar 1}]_c = [{\bar 1}02]_m ]$
$[3[{\bar 1}11]_c]$ ( $[\pm120^\circ]$ )		0.25	3	9	$[[1{\bar 1}1]_c = [3{\bar 2}0]_m ]$
( $[\pm 90^\circ]$ )		1.19	1	6	$[[010]_c = [0{\bar 1}3]_m ]$
		1.19	1	6
		0.90	1	12	$[[011]_c = [3{\bar 1}3]_m ]$
		0.90	1	12	$[[10{\bar 1}]_c = [{\bar 3}13]_m ]$
					$[[01{\bar 1}]_c = [31{\bar 3}]_m ]$