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

International Tables for Crystallography (2006). Vol. D. ch. 3.3, p. 405

Table 3.3.6.4 

Th. Hahna* and H. Klapperb

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 3.3.6.4 | top | pdf |
The four different variants of Japanese twins according to Frondel (1962[link])

Handedness of twin partners Azimuthal difference (°) Twin element = twin law Label in Fig. 65 of Frondel (1962[link])
L–L or R–R 0 Irrational twofold twin axis normal to plane [(11{\bar 2}2)] I(R), I(L)
180 Rational twofold twin axis [[11{\bar 1}]\equiv[11{\bar 2}{\bar 3}]] parallel to plane [(11{\bar 2}2)] II(R), II(L)
L–R or R–L 0 Rational twin mirror plane [(11{\bar 2}2)] III
180 Irrational twin mirror plane normal to direction [[11{\bar 1}]\equiv[11{\bar 2}{\bar 3}]] IV
The line [[11{\bar 1}]\equiv[11{\bar 2}{\bar 3}]] is the edge between the faces [z(01{\bar 1}1)] and [r(10{\bar 1}1)] and is parallel to the composition plane [(11{\bar 2}2)]. It is parallel or normal to the four twin elements. Transformation formulae between the three-index and the four-index direction symbols, UVW and uvtw, are given by Barrett & Massalski (1966[link], p. 13).