THE DIFFRACTION OF ELECTRONS BY A CRYSTAL 



103 



where they do. The most we have been able to do is to relate their 

 occurrences with those of the Laue beams that would issue from the 

 same crystal if the incident beam were a beam of x-rays. 



In Fig. 7 we indicate by crossed circles in 

 a (X, sin Q) diagram the x-ray diffraction 

 beams that would be observed in the B-azi- 

 muth. We show also again the electron 

 beams as actually observed. It is obvious 

 that the law of occurrence of electron beams 

 is not the same as the law of occurrence of 

 Laue beams, and yet we see that the occur- 

 rences of the two sets of beams have certain 

 features in common. The dots representing 

 electron beams occur along the plane grating 

 lines at about the same intervals as the 

 crossed circles representing the Laue beams. 

 Other points of similarity are found with 

 further study of the data and one is led 

 finally to the conviction that each electron 

 beam is the analogue of a particular Laue 

 beam. The electron beam represented by a 

 given dot appears to be the analogue of the 

 Laue beam of the same order represented by 

 the crossed circle occurring next above it in the diagram, 

 sociation of beams is indicated in the figure. 



The occurrences of the Laue beams are determined in part by the 

 separation between the atomic plane gratings that make up the 

 crystal. If the separation between adjacent planes were increased 

 the crossed circles representing the Laue beams would be moved 

 upward along the plane grating lines; if the separation were decreased 

 the crossed circles would be moved downward. Merely as a mode of 

 description, then, we may say that a given electron beam has the 

 wave-length and position that its Laue beam analogue would have if 

 the separation between planes were decreased by a certain factor. 



We have calculated this spacing factor for each of the 21 beams 

 and the values found are plotted in the upper part of Fig. 8 against 

 the voltages of the beams. The points form a very bad curve. They 

 do indicate, however, that the factor increases with the speed of the 

 electron, and there is the suggestion that it approaches unity as a 

 limiting value. There is the suggestion, that is, that at high voltages 

 the law of occurrence of electron beams is the same as the law of 

 occurrence of Laue beams. 



Fig. 7 — X sin d diagram for 

 B-azimuth 



Thi 



is as- 



