Gliding 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). 

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]. 

If the space group contains screw axes or glide planes, the Patterson fiinction can be particularly revealing. Suppose, for example, that parallel to the c axis of the crystal there is a 2 screw axis, one that combines a 180° rotation with... 

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 core structure of the (100) screw dislocation is planar and widely spread w = 2.66) on the 011 plane. In consequence, the screw dislocation only moves on the 011 glide plane and does so at a low Peierls stress of about 60 MPa. 

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... 

Fig. 13—Normalized o>/b as function of tglb, cta/b is the critical shear stress to move a dislocation from the B layer into the A layer, Q=(G -Gb)/(G +Gg), G and Gg are the shear moduli of A and B, b is the Burgers vector, fg is the thickness of one single B layer, and e is the angle between the A/B interfaces and the dislocation glide plane.

Top left perspective illustration of a glide plane. Other images printed and graphical symbols for glide planes perpendicular to a and c with different glide directions. z = height of the point in the unit cell... 

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. 

Figure 4.1 Schematic dislocation line a simple cubic crystal structure. The line enters the crystal at the center of the left-front face. It emerges at the center of the right-front face. The shortest translation vector of the structure is the Burgers Vector, b. The line bounds the glided area of the glide plane (100) from the unglided area.

Figure 4.2 Quasi-hexagonal dislocation loop lying on the (111) glide plane of the diamond crystal structure. The <110> Burgers vector is indicated. A segment, displaced by one atomic plane, with a pair of kinks, is shown a the right-hand screw orientation of the loop. As the kinks move apart along the screw dislocation, more of it moves to the right.

When there are no distinct bonds crossing a glide plane, there are no distinct kinks. This is the case for pure simple metals, for pure ionic crystals, and for molecular crystals. However, the local region of a dislocation s core still controls the mobility in a pure material because this is where the deformation rate is greatest (Gilman, 1968). 

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