212 



Subsurface Geologic Methods 



Laue's original mathematically complex analysis of this interaction be- 

 tween X-rays and crystalline matter to terms of great simplicity. In 

 figure 91 two such 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 9. 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 

 diff"erence is the distance nop and that no=d sin 6, and op=d sin 9 ; thus 

 nop=2d sin 9=nX, which is the statement of Bragg's law. 



Although this equation is satisfactory for calculating diff"raction 

 eff"ects, it nevertheless reveals little of the actual diff"raction mechanism 



B 



D 



Figure 91. Reflection of X-ray beam from planes in face of crystal. 



involved. A reasonable understanding of this mechanism can be gained 

 from the familiar two-dimensional analogy of the interaction of waves on 

 water. Figure 92 shows in successive steps (1) the generation of a circular 

 set of waves from a series of parallel wave fronts by a post (or other 

 small object) in a quiet body of water; (2) the interaction of these newly 

 generated circular waves from a row of equally spaced posts produced 

 new diffracted wave fronts; (3) the interaction of these generated circular 

 waves from two rows of posts (two planes) under conditions where Bragg's 

 law is not satisfied; and finally (4) the interaction of these waves where 

 the angle 9 has been so chosen that all conditions for the observance of 

 diffraction eff"ects by this particular family of planes have been satisfied. 

 The fact that the diff'racted wave fronts from each row of posts are one- 

 quarter of a wave length out of phase with those diff'racted by the adjacent 

 rows, under the conditions where Bragg's law is not satisfied, immediately 

 shows that we cannot observe any diff'raction from this family of planes 

 under the selected conditions. On the other hand, when the angle 6 has 

 been so adjusted that Bragg's law is satisfied, all of these wave fronts 



