Crystal relation between diffraction groups

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

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

Crystal Structure. Diamonds prepared by the direct conversion of well-crystallized graphite, at pressures of about 13 GPa (130 kbar), show certain unusual reflections in the x-ray diffraction patterns (25). They could be explained by assuming a hexagonal diamond stmcture (related to wurtzite) with a = 0.252 and c = 0.412 nm, space group P63 /mmc — Dgj with four atoms per unit cell. The calculated density would be 3.51 g/cm, the same as for ordinary cubic diamond, and the distances between nearest neighbor carbon atoms would be the same in both hexagonal and cubic diamond, 0.154 nm. 

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. 

Shape-symmetry may tell us that a particular crystal has a fourfold axis, but it cannot tell us whether this axis is a simple rotation axis or a screw axis. Nor is it possible by examining the shape of a crystal to distinguish between a reflection plane and a glide plane. But X-ray diffraction patterns do make such distinctions, and in a very straightforward manner just as it is possible to detect compound ( centred ) lattices by noticing the absence of certain types of reflections (p. 233), so also it is possible to detect screw axes and glide planes, for the presence of atoms or groups of atoms related by translations which... 

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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