Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.2, pp. 740-741

Section Optical activity

H. Klappera and Th. Hahna Optical activity

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The symmetry information obtained from optical activity is quite different from that given by optical refraction. Optical activity is in principle confined to the 21 noncentrosymmetric classes but it can occur in only 15 of them (Table[link]). In the 11 enantiomorphism classes, a single crystal is either right- or left-handed. In the four non-enantiomorphous classes [m,\ mm2,\ \overline{4}] and [\overline{4}2m], optical activity may also occur; here directions of both right- and left-handed rotations of the plane of polarization exist in the same crystal. In the other six noncentrosymmetric classes, [3m], [4mm, \overline{6}, 6mm, \overline{6}2m, \overline{4}3m], optical activity is not possible.

In the two cubic enantiomorphous classes 23 and 432, the optical activity is isotropic and can be observed along any direction.23 For the other optically active crystals, the rotation of the plane of polarization can, in practice, be detected only in directions parallel (or approximately parallel) to the optic axes. This is because of the dominating effect of double refraction. No optical activity, however, is present along an inversion axis or along a direction parallel or perpendicular to a mirror plane. Thus, no activity occurs along the optic axis in crystal classes [\overline{4}] and [\overline{4}2m]. In classes m and mm2, no activity can be present along the two optic axes if these axes lie in m. If they are not parallel to m, they show optical rotation(s) of opposite sense.

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