Microscopic Symmetry Elements in Crystals

So far we have discussed the macroscopic symmetry elements that are manifested by the external shape of the three-dimensional patterns, that is, crystals. They can be studied by investigating the symmetry present in the faces of the crystals. In addition to these symmetry elements there are two more symmetry elements that are related to the detailed arrangements of motifs (atoms or molecules in actual crystals). These symmetry elements are known as microscopic symmetry elements, as they can only be identified by the study of internal arrangement of the motifs. As X-ray or electron diffraction can reveal the internal structures, these symmetry arrangements can only be identified by X-ray, Electro or Neutron diffraction. Obviously, they are not revealed in the external shape of the pattern. These symmetry elements are classified as microscopic symmetry elements. There are two such types of synunetry elements (i) glide plane of symmetry and (ii) screw axis of synunetry. 

The translation associated with the glide plane may be one of the following (Fig. 5.3)  

Hermann-Mauguin symbol of glide plane of symmetry  

Reflection - - translation a/2 symbol = a Reflection - - translation b/2 symbol = b Reflection - - translation c/2 symbol = c Reflection - -1/2 face diagonal symbol = n Reflection - -1/4 face diagonal symbol = d 

There are plenty of natural examples The stacking sequence of the close-packed planes, that is, 111 sets of planes in face-centered lattice (fee) are 

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Microscopic Symmetry Elements in Crystals Stacking sequence of Billiard balls... 

Microscopic Symmetry Elements in Crystals 39 Table 5.1. Eleven different types of screw axes of symmetries... 

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