Crystallography and Crystal Defects. Anthony Kelly

Figure 2.23 Screw axes 3₁ and 3₂: these are screw axes of opposite hand, as shown by the symbols at the top

      2.12.2 Glide Planes

The operation of glide plane repetition is shown in Figure 2.22c. Again, the magnitude of the translation will be of the order of the lattice parameters. Macroscopically, the glide plane in Figure 2.22c would show itself as a mirror plane.

      Glide planes are described as axial glide planes if the translation parallel to the mirror is parallel to a single axis of the unit cell and equal to one‐half of the lattice parameter in that direction. Such glide planes are given the symbols a, b, or c, corresponding to the directions of the glide translations. A diagonal glide plane involves a translation of one‐half of a face diagonal or one‐half of a body diagonal (the latter in the tetragonal and cubic systems), and is given the symbol n. A diamond glide plane, given the symbol d, can only occur in orthorhombic F, tetragonal I, and cubic I and F lattices. In orthorhombic F lattices, this involves a translation of one‐quarter of a face diagonal, whereas in the tetragonal and cubic lattices this involves a translation of one-quarter of a body diagonal.

      2.12.3 Combinations of Symmetry Operations to Form Space Groups

      When we combine the operations of rotation with translation and look for the possible consistent combinations we can start with the point group and associate its symmetry elements with each lattice point of the lattices consistent with it. From the number of Bravais lattices and number of point groups detailed in Figures 1.19 and 2.6 it might be expected that 66 space groups could be obtained (2 triclinic, 6 monoclinic, 12 orthorhombic, 14 tetragonal, 5 trigonal with a rhombohedral lattice, 5 trigonal with a hexagonal lattice, 7 hexagonal, and 15 cubic). Seven additional ones arise because of cases in which the glide planes or screw axes automatically arising are different for different orientations of the point group with respect to the lattice; for example, in the tetragonal system and are distinct space groups. The 14 space groups for which this consideration is relevant are Cmm2, Amm2 (≡ C2mm), P2m,

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