96 METHODS FOR DETERMINING MOLECULAR SIZE AND SHAPE 



some of the line intensities. It should not be difficult to construct the 

 argument leading to the conclusion that other lines could actually be 

 enhanced. 



Now imagine that these extra atoms are moved so that they touch the 

 original crystal atoms; the result will still be increases and decreases in 

 the intensities of some of the lines. When two atoms are close together 

 at a crystal position, the situation is entirely equivalent to having a 

 diatomic molecule at that position. Accordingly, we have deduced that 

 the effect of making a crystal out of diatomic molecules is to produce a 

 pattern of lines that is the same as that of a single atom crystal, but 

 with a different set of intensities. Continuing in this vein, we argue that 

 if we place polyatomic molecules at the crystal positions, once again the 

 basic pattern of lines is obtained, but the intensities will differ in a very 

 complicated fashion. From the lines and their intensities, it should be 

 possible to make deductions about the structures of the polyatomic 

 molecules. 



To say this more directly, if we make crystals of enzymes (or any 

 other polyatomic molecules), we obtain patterns of lines and intensities 

 which apparently can be used to deduce the three-dimensional structure 

 of the molecules. We say apparently because in practice the difficulty 

 increases enormously as the number of atoms in the molecules increases. 

 For biologically important molecules, the unraveling of the structures is 

 presently a matter of years, even utilizing the fastest of modern com- 

 puters for the mathematical work and using some important new devices 

 developed for such studies. 



It is not always possible, even theoretically, to deduce the structures of 

 molecules from the intensities. The theoretical difficulty stems from the 

 so-called phase problem, which we shall now attempt to picture for you. 



Consider part (a) of Fig. 48. We have indicated that the scattering 

 from the two black atoms is such that crests are leaving them at the 

 particular instant at which a trough is leaving the uncolored atom, which 

 we will use as the reference atom. In part (b) the black atoms have been 

 moved so that they are emitting troughs, but you will notice that at their 

 old positions, indicated by the dotted circles, crests are present. Therefore 

 the blackening on the film will be the same in both instances. Thus we 

 have indicated that a given blackening can be produced by two (and of 

 course there are many other possibilities) different configurations of the 

 atoms within the molecule. If we knew the relative phases of the scatter- 

 ing (whether crests or troughs arc being emitted when the reference atom 

 is emitting a trough) we could deduce the structure directly. But since 

 we don't know the phases, we can't know the positions of the atoms. 



In parts (c) and (d) of the figure we show a way of getting around 

 this difficulty. The molecule will be part of many different planes and, 



