Twin obliquity

Fig. 12.4. Plan-view image of a (103) film. The domains or grains are elongated along [010]. (110) twins are ob rved within the grains on the erystallographically equivalent (110) and (110) planes whieh are oblique to the film plane.

Only the two-fold rotation about c of the twin lattice is a correct twin operation, in the sense that it restores the lattice, or a sublattice, of the individuals. If however twin operation. The rotations about c give simply the (approximate) relative rotations between pairs of twinned mica individuals, but are not true twin operations. Similar considerations apply also to the rotoinversion operations, s depends upon the obliquity of the twin but, at least in Li-poor trioctahedral micas, is sufficiently small to be neglected for practical purposes (Donnay et al. 1964 Nespolo et al. 1997a,b, 2000a). 

Selection of optically pure crystals can be accomplished with the aid of a polariscope in which the thin plates of quartz are examined between crossed Nicol prisms in polarized light. These plates are sawed perpendicular to the optical axis of well formed natural crystals. Brasilian twins exhibiting bright interference patterns in crossed Nicol prisms must be broken out. Only optically pure areas are selected for further use, for example, for asymmetric adsorption and for asymmetric catalysis. Piezoquartz as plates of an oblique cut, called the "Cut of Curie", are used in radio electronics and can be identified by the sign of their optically rotation according to the method of Lemmlein According to this method, the etched plate of piezoquartz is... 

FEED pattern shows directly the size and orientation of the surface unit cell. Flowever, the symmetry of the unit cell is not necessarily identical to the experimentally observed symmetry in LEED including spot intensities. The properties of symmetries such as rotation axes or mirror planes affect the intensities of the spots. The distinction between the structural symmetries of the surface and symmetries observed among spot intensities in LEED can be performed by changing the direction of the incident electron beam. At oblique incidence only mirror planes can be observed when the incident beam is parallel to the symmetry plane, otherwise the diffraction pattern exhibits no symmetry. In cases where the surface is not well ordered one may obtain additional symmetry information from the diffused LEED spots. The characteristic distribution of diffuse intensity in reciprocal space indicates the existence of short-range ordered antiphase domains or twin domains. 

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