X-Ray Crystallography of Biological Macromolecules 



Figure 2. Structure of stilbene 

 projected on plane normal to 

 b axis. The asymmetric unit 

 is marked by dotted lines. 

 {Reproduced from Bunn 6 .) 



An example is shown in Figure 2, which is the b projection of the 

 monoclinic cell of stilbene (in other words a projection on to the plane 

 perpendicular to the b axis). The cell contains four molecules (some 

 fall partly in adjoining cells, but the total per cell is 4), and the asym- 

 metric unit is shown surrounded by a dotted line — here it consists of 

 half of one molecule and half of another. In projection the asymmetric 

 units are related by a diad axis passing through the centre of the pro- 

 jected cell and normal to the plane of the paper. 



THE REFLEXION OF X-RAYS FROM CRYSTALS 



The distances between the atoms in a crystal are of the same order as 

 the wave-length of x-rays (wave-length of Ka line in x-radiation from 

 copper = 1-54 Angstrom units. 1 A = 10 -8 cm), and it can be shown 

 that a set of parallel and equidistant ' net planes ' through the crystal 

 (that is to say, planes drawn so as to contain a large number of lattice 

 points) diffracts a beam of x-rays just as an optical grating diffracts 

 visible light. A very large number of such sets of planes can be drawn 

 through a given lattice, and each of these may give rise to a diffracted 

 x-ray beam {Figure 3 is a crystal lattice showing a few types of planes). 

 We are dealing, however, with a three-dimensional array in the 

 crystal, and unlike the two-dimensional grating which diffracts visible 

 light for all angles of incidence, mutual interference between the 

 crystal planes of a set suppresses the diffracted beams except at certain 

 angles of incidence given by the Bragg Law 



n\ = 2d. sin 6 



where X is the wave-length of the x-rays, 6 is the angle of incidence 

 (which is also equal to the angle of diffraction), dis the spacing between 

 planes, and n is an integer. Thus as a crystal is rotated in a mono- 



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