X-RAY DIFFRACTION 



93 



To detector 



Figure 44 



Figure 45 



farther than the first ray by the amount indicated by the heavy line. A 

 detector (such as a photographic film) into which these rays go will yield 

 one of three possible results: 



(a) If the extra distance is just equal to a whole wave, then the two 

 rays arrive at the detector in the same phase of their motion (that 

 is, crests are with crests, and troughs with troughs). They add up 

 to give an intensity greater than that from a single ray. 



(b) If the extra distance is just equal to half a wave, then the two 

 rays arrive at the detector exactly out of phase (the crest of ray 

 I would be superposed on the trough from ray II) and the rays 

 cancel, giving zero intensity. 



(c) If the extra distance is neither of these two alternatives there will 

 also be a cancellation, because in actuality the detector receives 

 many rays, not just two, and except for the two cases presented 

 the rays will be at all phases of the motion with respect to each 

 other and there will be an over-all cancellation. 



For any spacing between planes, there will be precisely one angle 6 

 which causes the rays to be exactly one wave apart, so that they reinforce 

 each other; at any other angle general cancellation will occur. 



Bragg was the first to point out that arrays of atoms in a crystal could 

 be thought of as forming planes in the way shown. This is clearly an 

 approximation, but the exact treatment of the problem by advanced 

 methods yields precisely the same criterion for reinforcement as Bragg 

 obtained from his simple model. 



The relation for the condition of reinforcement is 



X = 2d sin 0, 



where X is the wavelength of the x-rays used and d is the spacing between 

 planes. As will be indicated below, X and are usually measured, which 

 permits the computation of d. 



