SEPT. 19, 1921 WYCKOFF: WAVE LENGTHS OF X-RAYS 



367 



regular and orderly repetition of a certain grouping of atoms through- 

 out space (as seems entirely permissible) , and if we assume the correct- 

 ness of the Laue theory^ that the atoms in this crystal act as diffracting 

 centers of a three-dimensional diffraction grating, then it follows that 

 the wave length of the X-rays diffracted by this crystal, the "spacing 

 between like planes" in the direction of the diffraction, and the angle 

 of the diffraction effect are connected by the familiar expression 



fi\ = 2d sin d (1) 



Fig. 1. 



where n is the "order" of the reflection, 



X is the wave length of the diffracted X-rays, 



d is the "spacing," that is, the distance between like 



planes in the chosen direction, and 



6 is the angle of the diffraction. 



In figure 1 ADEFCGBO represents the unit cell which is repeated 



along the axes of coordinates in a cubic crystal. The length of the 



side of this unit cube, AO, is (iioo, the "spacing" against the cube face. 



The volume of this unit is then 



mM 

 V = (J.oo)^ = — (2) 



P 



where M is the weight of one chemical molecule of the substance, 

 »M. Laue. Ann. Phys. 41: 971. 1913. 



