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one value of d will satisfy the equation for each order reflection. Thus, 

 with a monochromatic X-ray beam one may not obtain reflection from the 

 planes at all angles as with visible light, but only at such specific angles 

 as satisfy the Bragg law. Further, even with optimum conditions for 

 reflection the ratio of the intensity of the reflected X-ray beam to that of 

 the incident beam is of the order of 1 : 10,000. The Bragg angle d is highly 

 critical and the reflection of X-rays from atomic planes therefore serves 

 as a precise method of crystal orientation. 



Figure 3.3 is a diagrammatic representation of the relation n\ = 2d sin d. 

 On such a diagram the following laws of X-ray reflection become obvious: 



(1) X must be smaller than 2d, that is, the wave-length of X-rays used 

 must be less than twice the inter-planar spacing of the atomic planes to 

 be X-rayed. 



(2) The number of different orders of reflection n obtainable from atomic 

 planes with interplanar spacing d is fixed by the expression n\ < 2d. In 



Fig. 3.3 — A diagrammatic representation of Bragg's law, n\ = 2d sin 



other words, since sin 6 cannot be greater than 1 the value of X must be 



9/7 



less than — . The distance between the atomic planes parallel to the 

 n 



O o 



hexagonal prism of quartz is 4.2466 A and the wave-length of the Kai 

 radiation from a copper target is 1.5374 A. Hence no reflection higher 

 than the 5th order could be obtained from this set of planes using a copper 

 target. 



On the other hand, a target metal whose characteristic wave-length is 

 very much shorter than 2d is undesirable since it gives so many orders of 

 reflection from each set of atomic planes that the multitude of closely 

 spaced reflections leads to confusion. 



(3) Higher orders of reflection occur at larger 6 angles. 



(4) The relation of to X is not linear but sinusoidal. 



The reflected beam can only lie in a plane containing the normal to the 

 atomic plane and the incident beam. Conditions are unchanged by ro- 

 tating the crystal about the normal to the atomic plane being used. 



3R. B. Sosman, "The Properties of Silica," Chemical Catalogue Co.. New York 1927. 



