further studies by other methods when only limited amounts are available. Like- 

 wise for diffraction analysis, microscopic samples weighing no more than 

 several micrograms are sufficient for the analysis. Finally, the diffraction patterns 

 constitute a permanent record which is usually complete regardless of how limited 

 the information desired was at the time the pattern was recorded. 



This discussion is directed principally toward a reading audience which may 

 have only a limited acquaintance with X-ray-diffraction methods. Consequently, 

 a very brief discussion concerning the mechanism of diffraction appears desirable. 

 All crystalline matter is composed of atoms or molecules arranged in definite 

 forms of geometric space packing and in such a manner that they form definite 

 families of planes in various directions through the crystal. By considering 

 primary X-rays to be reflected by these planes within the crystal, the Braggs 

 were able to reduce von Laue's original mathematically complex analysis of this 

 interaction between X-rays and crystalline matter to much simpler terms. In 

 Figure 9-1 two planes, AB and CD, represent one of the many families of planes 

 found in a crystal. Two rays, emf and gnoph, of the defined X-ray beam are 

 shown to be partly reflected from these planes when striking them with an 

 incident and reflected angle of 6. According to the laws of optics these reflected 

 rays must be in phase to be observed as a reflection. Consequently, ray gnoph 

 must be longer than ray emf by an integral value of the wave length A. Inspection 

 reveals that this path difference is the distance nop and the no — d sin 6, and 

 op = d sin 6; thus nop — 2d sin 6 = nX, which is the statement of Bragg's 

 law. 



Although this equation is satisfactory for calculating diffraction effects, it 

 nevertheless reveals little of the actual diffraction mechanism involved. A 

 reasonable understanding of this mechanism can be gained from a familiar 

 two-dimensional analogy of the interaction of waves on water. Figure 9-2 



Figure 9-1. Reflection of X-ray beam from planes in face of crystal. 



150 



