Glide symmetry planes

Planes of symmetry. Planes through which there is reflection to an identical point in the pattern. In a lattice there may be a lateral movement parallel to one or more axes (glide plane). 

Table 6-1. C2(l molecular poinl group. The electronic stales of the flat T6 molecule are classified according lo the lwo-1 old screw axis (C2). inversion (/). and glide plane reflection (o ) symmetry operations. The A and lt excited slates transform like translations Oi along the molecular axes and are optically allowed. The Ag and Bg stales arc isoniorphous with the polarizability tensor components (u), being therefore one-photon forbidden and Iwo-pholon allowed.

When the two vectors are parallel, the crystal planes perpendicular to the line form a helix, and the dislocation is said to be of the screw type. In a nearly isotropic crystal structure, the dislocation is no longer associated with a distinct glide plane. It has nearly cylindrical symmetry, so in the case of the figure it can move either vertically or horizontally with equal ease. 

For the syndiotactic copolymer, highly extended conformations with c values of 7.5-7.6 A can be obtained for a glide plane symmetry when... 

Notice that the symmetry operations of each point group by continued repetition always bring us back to the point from which we started. Considering, however, a space crystalline pattern, additional symmetry operations can be observed. These involve translation and therefore do not occur in point groups (or crystal classes). These additional operations are glide planes which correspond to a simultaneous reflection and translation and screw axis involving simultaneous rotation and translation. With subsequent application of these operations we do not obtain the point from which we started but another, equivalent, point of the lattice. The symbols used for such operations are exemplified as follows ... 

Orthorhombic symmetry mm2 comprises two mirror planes perpendicular to each other, which automatically generates a twofold axis along the line of intersection. This point symmetry applies to all noncentrosymmetric orthorhombic crystals that have mirror or glide planes such as those of space groups Pna2t and Pca2,. 

Microdiffraction is the pertinent method to identify the crystal system, the Bravais lattices and the presence of glide planes [4] (see the chapter on symmetry determination). For the point and space group identifications, CBED and LACBED are the best methods [5]. 

The elements of mirror symmetry d, m, and c can be removed in different ways, resulting in different classes of chiral polymers. Plane d containing the polymer chain is eliminated by the presence, in the main chain, of tertiary carbon atoms —CHR—), or of quaternary atoms with different substituents (—CR R"—), or with equal chiral substituents (—CR R —). Mirror glide plane c does not exist in isotactic structures, nor in syndiotactic ones in which the substituents are chiral and of the same configuration, 75 (33, 263). The perpendicular planes, m, are eliminated by the presence of chiral substituents of the same sign in syndiotactic, 75 (33, 263) or isotactic structures, 76 (263) or if the two directions of the chain are rendered nonreflective. This last condition can be realized in different ways some of which follow (264) ... 

A special position in the crystal is repeated in itself by at least one symmetry element, that is, r = r. According to Eq. (B.2), this means that s must be zero if a symmetry element is to give rise to a special position. It follows that translations, screw operations, and glide planes do not generate special positions. On the other hand, positions located on proper rotation axes or centers of symmetry have lower multiplicity than general positions in the unit cell. 

The stereocenters in all three stereoregular polymers are achirotopic. The polymers are achiral and do not possess optical activity. The diisotactic polymers contain mirror planes perpendicular to the polymer chain axis. The disyndiotactic polymer has a mirror glide plane of symmetry. The latter refers to superposition of the disyndiotactic structure with its mirror image after one performs a glide operation. A glide operation involves movement of one structure relative to the other by sliding one polymer chain axis parallel to the other chain axis. 

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