Glide plane table

These include rotation axes of orders two, tliree, four and six and mirror planes. They also include screM/ axes, in which a rotation operation is combined witii a translation parallel to the rotation axis in such a way that repeated application becomes a translation of the lattice, and glide planes, where a mirror reflection is combined with a translation parallel to the plane of half of a lattice translation. Each space group has a general position in which the tln-ee position coordinates, x, y and z, are independent, and most also have special positions, in which one or more coordinates are either fixed or constrained to be linear fimctions of other coordinates. The properties of the space groups are tabulated in the International Tables for Crystallography vol A [21]. 

All tenus in the sum vanish if / is odd, so (00/) reflections will be observed only if / is even. Similar restrictions apply to classes of reflections with two indices equal to zero for other types of screw axis and to classes with one index equal to zero for glide planes. These systematic absences, which are tabulated m the International Tables for Crystallography vol A, may be used to identify the space group, or at least limit die... 

The Burgers vectors, glide plane and ine direction of the dislocations studied in this paper are given in table 1. Included in this table are also the results for the Peierls stresses as calculated here and, for comparison, those determined previously [6] with a different interatomic interaction model [16]. In the following we give for each of the three Burgers vectors under consideration a short description of the results. 

The edge dislocation on the 011 plane is again widely spread on the glide plane w = 2.9 6) and moves with similar ease. In contrast, the edge dislocation on the 001 plane is more compact w = 1.8 6) and significantly more difficult to move (see table 1). Mixed dislocations on the 011 plane have somewhat higher Peierls stresses than either edge or screw dislocations. 

Table 1 Summary of the calculated properties of the various dislocations in NiAl. Dislocations are grouped together for different glide planes. The dislocation character, edge (E), screw (S) or mixed type (M) is indicated together with Burgers vector and line direction. The Peierls stresses for the (111) dislocations on the 211 plane correspond to the asymmetry in twinning and antitwinning sense respectively.

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.

It is seen for this structure that (100) is a reflection plane, (010) a glide plane with translation a/2, and (001) a glide plane with translation a/2 + bj2. The space group is accordingly Y h—Pman. The absent reflections required by V h are (hOl), h odd, and (M0), h- -k odd. Hassel and Luzanski report no reflections of the second class. However, they list (102) in Table V as s.s.schw. This reflection, if real, eliminates this space group and the suggested structure I believe, however, in view of the reasonableness of the structure and the simple and direct way in which it has been derived, as well as of the fact that although thirty reflections of the type (hOl), h even, were observed, only one apparently... 

A glide reflection is one in which S is a reflection in the glide plane followed by a translation w, not necessarily parallel to the reflection plane. The three possible types of translation w are described in Table 16.3. 

The systematic absences due to the various types of lattice centering, screw axes, and glide planes are given in Table 9.4.2, which is used in the deduction of space groups. 

Phase 1 has a two-layer unit cell for the hydroxide component. In the (100) projection (in which the structural calculations were performed) the two idealised hydroxide layers (F in Fig. 5) have a relative rotation of 22° (98°), so that they may be related by an a-glide plane parallel to [010] of the sulphide component and perpendicular to the layers, or by a two-fold axis parallel to [010] of the sulphide component. The ortho-hexagonal subcells of the idealised hydroxide layers can be defined as mutually rotated by 98°, and they will be rotated by 41° and 139° from the component unit cell of the sulphide layers. Thus, the two hydroxide layers have the same orientation to the sulphide component (and to the common modulation), but the cell geometry assumed by Organova et al. makes them non-equivalent (Table 3). The published diffraction pattern suggests that the structure is of the SC type (or perhaps SI), modulated in the b direction. The close relationship with the tochilinites is apparent from the mutual orientation of the adjacent hydroxide and sulphide layers the deviation from that in tochilinites is only 4°. However, in tochilinites successive hydroxide layers are parallel. 

For example, think about the monoclinic point group m in the standard setting, where m is perpendicular to b (Table 1.8). According to Table 1.14, the following Bravais lattices are allowed in the monoclinic crystal system P and C. There is only one finite symmetry element (mirror plane m) to be considered for replacement with glide planes (a, b, c, n and d) ... 

Similar analyses may be performed for other types of glide planes in different orientations and not necessarily traversing the origin of coordinates (as an exercise try to derive the relationships between Miller indices of the systematically absent Bragg peaks for a glide plane, a, perpendicular to Y and Z directions). The relationships between allowed Miller indices for various glide planes in different orientations are shown in Table 2.9. 

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