Glide planes symbols

The class symbols can be derived from the space group symbols by deleting the Bravais symbols (P, C, etc.), dropping all subscripts from screw axes (2i, 3i, 4i, etc. -> 2,3,4, etc.) and replacing all glide plane symbols by the mirror plane symbol, m. Thus I4i/acd becomes 4/mmm. A slash means perpendicularity of a rotational element and a reflection element. 

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... 

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 ... 

The onl other symmetry element involving translation which remains to be meniiqued is the glide plane having a translation of one-quarter of a eell-faee diagonal this type of glide, symbolized d, is found only in a few space-groups. 

In a similar way a glide plane normal to the c axis of a crystal having a translation of one-quarter of the ab diagonal (symbolized d) nullifies all hkO reflections except those for which A-j-A is divisible by 4. 

In referring to any particular space-group, the symbols for the symmetry elements are put together in a way similar to that used for the point-groups. First comes a capital letter indicating whether the lattice is simple (P for primitive), body-centred (I for inner), side-centred (A, B, or C), or centred on all faces (F). The rhombohedral lattice is also described by a special letter R. Following the capital letter for the lattice type comes the symbol for the principal axis, and if there is a plane of symmetry or a glide plane perpendicular to it, the two symbols... 

Fig. 148. Lattice side centred on 100 (symbol A) glide plane perpendicular to tho a axis (that is, in tho plane of tho paper).

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. 

Finally, there is a rare type of glide called a diamond glide (plane or operation).-This can occur only for 1 or F lattices where a translation of, for example, a/4 + b/4 can move a corner lattice point to a face centering lattice point (or vice versa). The symbol for a diamond glide is d. 

In the ac projection, the origin and axes are again chosen to conform with a right-handed axis set. The screw axes are now represented by the symbol that shows them to be perpendicular to the projection plane. The glide planes are now shown by the symbol at the upper left, which gives both the elevation (y = i and, by implication, 5) and glide direction (c). 

Figure 11.22. Diagrams showing how three different choices for labeling the axes lead to different symbols for the same space group. At left, where the positions of the glide planes are shown is the standard setting, that is, the conventional, tabulated, choice.

P = 98 92(6)°. The center of inversion is indicated by a dot in the center of the unit cell, and the two two-fold screw axes are perpendicular to the plane of the paper and are marked with the symbol i Two glide planes perpendicular to the screw axes in the. xy plane (parallel with the plane of the paper) are not indicated but are found at distances of one-fourth and three-fourths unit cell depth. Note that a, b, and c do not correspond exactly to x, y, and a because one of the three angles of a monoclinic structure is unequal to 90°. The fluorine atoms have been omitted for clarity. [Modified from Hadj-Baghcri, N. Strickland, D. S., Wilson, S. R. Shapley, J. R. J. Organomet. Chem. 1991,410, 231-239 Courtesy of S. R. Wilson and C. L. Stern.]... 

The combination of reflection and translation gives a glide plane. If the gliding direction is parallel to the a axis, the symbol for the axial glide plane is a and the operation is reflection in the plane followed by translation parallel to the a axis by a/2 . Similar axial glide planes b and c have translation components of b/2 and c/2, respectively. 

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