98 



BELL SYSTEM TECHNICAL JOURNAL 



interference among elements of the incident beam scattered by the 

 atoms of the crystal. With this picture in mind we try next to 

 calculate wave-lengths of this electron radiation from the data of 

 these beams and from the geometry and scale of the crystal. 



To begin with, we shall need to look more closely into our crystal. 

 The atoms in the triangular face of the crystal may be regarded as 

 arranged in lines or files at right angles to the plane of the A- and 

 B-azimuths. If a beam of radiation were scattered by this single 

 layer of atoms, these lines of atoms would function as the lines of an 

 ordinary line grating. In particular, if the beam met the plane of 

 atoms at normal incidence, diffraction beams would appear in the A- 

 and B-azimuths, and the wave-lengths and inclinations of these 

 beams would be related to one another and to the grating constant d 

 by the well-known formula, n\ = d sin 6, as illustrated at the top of 

 the figure. 



.% \{n\=dsine)/ #, 

 ^ \ V ° s 



Fig. 5 — Showing n\ = d sin 6 relation in the A-, B- and C-azimuths 



In the actual experiments the diffracting system is not quite so 

 simple. It comprises not a single layer of atoms, but many layers; 

 it is equivalent not to a single line grating, but to many line gratings 

 piled one above the other, as shown graphically at the bottom of the 

 figure. What diffraction beams will issue from this pile of similar 

 and similarly oriented plane gratings? 



