PRINCIPLES OF STRUCTURE 



33 



b. Structural Chemistry 



After the discovery of stereoisomery^ structural chemistry learnt to 

 distinguish between different positions of the substituents to the 

 carbon atom. At first, the results of this interesting science (Werner, 

 1904; Freudenberg, 1933) were little more than qualitative and re- 

 ferred mainly to the directions radiating from the C-atom. Quantitative 

 determinations of distances along these directions were not yet possible. 

 The results of crystal structure, however, determine not only qualita- 

 tively but also quantitatively the relative positions of the atoms in space. 



The starting point for the new development in structural chemistry 

 was the crystal lattice of diamond, which crystallizes in the cubic 



Fig. 30. Diamond lattice, a) Unit cell, h) projection. 



system. Its unit cell is a cube containing 8 C-atoms, 4 of which belong 

 to a face-centred cube as in the case of gold, while the four remaining 

 atoms are situated on the body diagonals halfway between the corners 

 of the cube and its centre (Fig. 50a). Thus the unit cell contains, as it 

 were, 4 central atoms surrounded by 4 neighbouring atoms at the 

 corners of a tetrahedron, in conformity with their co-ordination num- 

 ber (Fig. 29). If this three-dimensional lattice is projected on to its 

 base. Fig. 50b is obtained, which shows the arrangement of valency 

 lines commonly used in organic chemistry ! Thus the usual scheme of 

 the quadrivalent carbon (Fig. 24, p. 25) is morphologically correct if it 

 is considered as the projection of a tetrahedron. 



According to X-ray analysis, the lattice period of diamond, i.e., the edge 

 of the cube, measures 3.55 A. It follows that the distance between the lattice 

 points on the face diagonal is 1-3.55 -Vz = 2.51 A; the shortest distance 

 between two C-atoms on the body diagonal is 5-3.55 -^3 = 1.54 A. It is 

 in this simple way that the C — C-distance corresponding to the sphere of 

 action of a C-atom in an aliphatic bond has been calculated (Table III, p. 31). 



