Limit of Electron Microscopy 135 



a fair approximation to the elastic scattering of all atoms of the 

 periodic system, particularly the heavier ones. The results are 

 summed up in figure 47. It can be seen that practically all scat- 

 tered electrons are confined inside a cone for which the parameter 



_ 



\/V.sin-J i_ 



assumes a value roughly between 3 and 4. If we .fix the limit, 



somewhat arbitrarily, at 3.7, and repeat the same calculation as 



in the case of the hydrogen atom, w^e obtain an apparent atom 



0.82 

 diameter dz = i, . As the estimate is rather rough it is 



preferable to say that even in the most perfect electron micro- 

 scope an atom will appear as a rather blurred disk with a 

 diameter 



dz«:^Z-3A (57) 



Thus heavier atoms appear smaller than lighter ones. The 

 heaviest, uranium, will be about 0.22 A. As the scattering cross 



2 



section increases with Z and the apparent area decreases with Z'^ 



5 



the contrast will increase with Z^, i.e., it will be about nineteen 

 hundred times better for uranium than for hydrogen. Thus it 

 ought to be rather easy to identify atoms of dififerent kinds. 



It is evident from this discussion that, although it may be 

 possible to resolve atomic lattices, the detail visible in them would 

 be much inferior to the wonderful electron density diagrams 

 obtained by W. L. Bragg's indirect methods of structure anal- 

 ysis "^ of which figure 48 gives an example. Without going into 

 details, it can be said that these diagrams have been obtained 

 by the interference of difi^racted beams from millions of unit 

 cells.* The reason for this inferiority is not the electron micro- 



* G. P. Thomson and W. Cochrane suggest the useful word inter frac- 

 tion for phenomena of this sort, as opposed to diffraction which ought to 

 be reserved for what goes under this name in optical treatises. 



