Glide translation vector

There are parallels between the two-and three-dimensional cases. Naturally, mirror lines in two dimensions become mirror planes, and glide lines in two dimensions become glide planes. The glide translation vector, t, is constrained to be equal to half of the relevant lattice vector, T, for the same reason that the two-dimensional glide vector is half of a lattice translation (Chapter 3). 

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.

Accordingly, glide planes are those planes which have the shortest b vectors a/2 <110> for fee, a/2 <111> for bcc, and a/3 <211.0) for hep lattices. Dislocations can split into so-called Shockley partials b = bx +b2, if b2>b +b. Since b and b2 are not translational vectors of the crystal lattice, they induce a stacking fault. The partial dislocation therefore bounds the stacking fault. 

Symmetry plane or symmetry line Graphic symbol Glide vector in units of lattice translation vectors parallel and normal to the projection plane Printed symbol... 

Fixed-Point-Free Motions. These include translations, screw rotations, and glide reflections. Because the primitive translation vector, Eq. 1.2, joins any two lattice points, an equivalent statement is that Eq. 1.2 represents the operation of translational symmetry bringing one lattice point into coincidence with another. However, we must choose the basis vectors (a, b, c) so as to include all lattice points, thus defining a... 

Infinite symmetry elements interact with one another and produce new symmetry elements, just as finite symmetry elements do. Moreover, the presence of the symmetry element with a translational component (screw axis or glide plane) assumes the presence of the full translation vector as seen in Figure 1.28 and Figure 1.29. Unlike finite symmetry, symmetry elements in a continuous space (lattice) do not have to cross in one point, although they may have a common point or a line. For example, two planes can be parallel to one another. In this case, the resulting third symmetry element is a translation vector perpendicular to the planes with translation (t) twice the length of the interplanar distance d) as illustrated in Figure 1.30. 

The translation vector associated with a glide plane is ... 

Fig. 5.1. a is the unit translational vector. The motif suffers a reflection on the mirror plane and undergoes a translation half the way. g the mirror perpendicular to the diagram and is known as the glide plane... 

Atoms and molecules in solids arranged in a lattice can be related by four crystallographic symmetry operations - rotation, inversion, mirror, and translation - that give rise to symmetry elements. Symmetry elements include rotation axis, inversion center, mirror plane, translation vector, improper rotation axis, screw axis, and glide plane. The reader interested in symmetry and solving crystal stmctures from diffraction data is encouraged to refer to other sources (7-... 

The symbols for plane groups, the Hermann-Mauguin symbol, have been the standard in crystallography. The first place indicates the type of lattice, p indicates primitive, and c indicates centered. The second place indicates the axial symmetry, which has only 5 possible vales, 1-, 2-, 3-, 4-, and 6-fold. For the rest, the letter m indicates a symmetry under a mirror reflection, and the letter g indicates a symmetry with respect to a glide line, that is, one-half of the unit vector translation followed by a mirror reflection. For example, the plane group pAmm means that the surface has fourfold symmetry as well as mirror reflection symmetries through both x and y axes. 

Fig. 229. Left When a crystal has a plane of symmetry normal to b, the distances of atoms from this plane are given by maxima along the line OyO of the vector cell. Right When there is a glide plane perpendicular to b, with translation c/2, the distances oi atoms from this plane are given by maxima along the line OyJ of the vector cell.

It turns out that three types of glide plane can be differentiated. In the first type, the translation is in the direction of a principal lattice vector, that is, it is given by one of the vectors a/2, b/2, or c/2. For each of these, the plane must be parallel to the plane defined by the translation direction and one of the other two principal directions. Thus, if we have a glide plane parallel to the plane of a and c, the glide component may be either a/2 or c/2. Planes of this type are called axial glide planes and are symbolized a, b> or c, according to the direction of the glide. 

In eq. (1), v is not necessarily a lattice translation t, since w may be either the null vector 0 or the particular non-lattice translation associated with some screw axis or glide plane. If v C a VR, then there are no screw axes or glide planes among the symmetry elements... 

It is noteworthy to point out that two sequential screw-axis or glide-plane operations will yield the original object that has been translated along one of the unit cell vectors. For example, a 63 axis yields an identical orientation of the molecule only after 6 repeated applications - 4.5 unit cells away (i.e., 6 x 3/4 = 4.5). However, since glide planes feature a mirror plane prior to translation, the first operation will... 

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