Diffraction relation between crystal point groups

The relation between the diffraction groups and the crystal point groups can be seen in Table 3. 

Table 3. Relation between diffraction groups and crystal point groups (from Buxton et al [17])...

In the orthorhombic point group mm2 there is an ambiguity in the sense of the polar axis c. Conventional X-ray diffraction does not allow one to differentiate, with respect to a chosen coordinate system, between the mm2 structures of Schemes 15a and b (these two structures are, in fact, related by a rotation of 180° about the a or c axis) and therefore to fix the orientation and chirality of the enantiomers with respect to the crystal faces. Nevertheless, by determining which polar end of a given crystal (e.g., face hkl or hkl) is affected by an appropriate additive, it is possible to fix the absolute sense of the polar c axis and so the absolute structure with respect to this axis. Subsequently, the absolute configuration of a chiral resolved additive may be assigned depending on which faces of the enantiotopic pair [e.g., (hkl) and (hkl) or (hkl) and (hkl)] are affected. 

The nature of the relation which exists between the symmetry of diffraction effects and that of the crystal may be gathered by consideration of the hkO intensities of two simple tetragonal crystals—urea (0---C(NH2)2), whose point-group symmetry is 42m, and penta-erythritol (C(CH2OH)4), belonging to class 4. For urea (see Fig. 144), the intensity of 310 is the same as that of 310, as is obvious from the relation of the molecules to the traces of these planes the equality... 

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