THE DIFFRACTION OF ELECTRONS BY A CRYSTAL 99 



The answer to this question is twofold. In respect of position all 

 the beams which appear will coincide with beams which would issue 

 from a single grating. We get no additional beams by adding extra 

 layers to the lattice. In respect of intensity, however, the results 

 are greatly changed. A given beam may be accentuated or it may 

 be diminished, both absolutely and relatively to the other beams; 

 it may in fact be blotted out completely, or reduced to such an extent 

 that it can no longer be perceived. These are effects of interference 

 among the similar beams proceeding from the various plane gratings 

 that make up the pile. Later we shall consider under what conditions 

 these component beams combine to produce a resultant beam of 

 maximum intensity; for the present, however, I wish only to stress 

 the fact that whenever and wherever a space lattice beam appears 

 its wave-length and colatitude angle 6 will be related to the constant 

 d of the plane grating through the ordinary plane grating formula. 

 We therefore apply this formula to the 54- and 65-volt beams that 

 have been described. The grating constant d has the value 2.15 A., 

 the 54-volt beam occurs at = 50° so that n\ for this beam should 

 have the value 2.15 X sin 50°, or 1.65 A. For the 65-volt beam we 

 obtain for n\ the value 1.50 A. 



We now compare these wave-lengths with the wave-lengths associ- 

 ated with freely moving electrons of these speeds in the theory of 

 wave mechanics. Translated into bombarding potentials, de Broglie's 

 relation 



X = hjmv becomes X = y\-rj- A., 



where V represents the bombarding potential in volts. The length of 

 the phase wave of a "54-volt electron" is (150/54)^/2 = 1.67 A., and 

 for a 65-volt electron 1.52 A. The 54- and 65-volt electron beams do 

 very well indeed as first order phase wave diffraction beams. 



It may be mentioned that beams occur at different voltages in the 

 A- and B-azimuths because the plane gratings that make up the 

 crystal are not piled one immediately above the other. There is a 

 lateral shift from one grating to the next amounting to one third of 

 the grating constant. Because of this shift the phase relation among 

 the elementary beams emerging in the A-azimuth is not the same 

 as that among those emerging in the B-azimuth — and coincidence of 

 phase among these beams occurs at different voltages, or at different 

 wave-lengths, in the two azimuths. 



We next make similar calculations for a beam occurring in the 

 C-azimuth. One such beam attains its maximum development in 



