Three-dimensional space-groups unit cell

The same species (atom, ion, or molecule) may also be present in other locations about the unit cell, and they may reside at differing distances and angles depending on the dimension. CsCl, for example, has a very simple unit cell that can be illustrated as a cubic structure other compounds are not so simply described. It can be shown that there are only 14 ways of describing how similar species (like the Cs or Cl ions) will be arranged in three-dimensional space. These 14 structures can be grouped into seven systems depending on their symmetry elements within each system, there can be variations in the appearance of atoms/ions/molecules at certain positions within the unit cell. 

Symmetry axes can only have the multiplicities 1,2,3,4 or 6 when translational symmetry is present in three dimensions. If, for example, fivefold axes were present in one direction, the unit cell would have to be a pentagonal prism space cannot be filled, free of voids, with prisms of this kind. Due to the restriction to certain multiplicities, symmetry operations can only be combined in a finite number of ways in the presence of three-dimensional translational symmetry. The 230 possibilities are called space-group types (often, not quite correctly, called the 230 space groups). 

Fig. 7.33 (el Unit cell of the 1-2-3 superconductor, orthorhombic, space group Pmtnm. Qne-dirnensional CuOi chains run along the b axis, and two-dimensional CuO, layers lie in the ab plane, (b) The cubic stricture of perovskite. SrTiO,. Three unit cells are shown sleeked vertically, (c) The unit cell of the 1-2-3 superconductor in the context of the surrounding crystal. Copper atoms are surrounded either by five oxygen atoms in a square pyramid or four oxygen atoms in a square plane. (From Holland. C. F. Stacy, A. M. Ace. Chem. Res. 1988,21, 8-15. Reproduced with permission.]... 

Phenazine (39) is found in two crystalline modifications, a- and jS-(Herbstein and Schmidt, 1955a). The a-form (space group P2ja, with two molecules in the unit cell) has been studied at room temperature (Herbstein and Schmidt, 1955a, b) and at about 90°K (Hirshfeld and Schmidt, 1957). The more accurate low-temperature analysis using partial three-dimensional data indicates that the deviations from the expected mmm molecular symmetry only exceed the estimated experimental accuracy ( + 0-003 A) in a direction normal to the mean molecular plane, the maximum deviation being 0-010 A. This slight non-planarity of the molecule is ascribed to the action of intermolecular forces. 

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