X-RAVS AND ORIENTATION OF QUARTZ CRYSTALS 297 



The United States Bureau of Standards has issued a 28-page booklet 

 entitled "X-Ray Protection" which may be obtained from the Super- 

 intendent of Documents, Washington, D. C. for 10 cents. 



3.4 Diffraction of X-Rays by Crystals 



Following the work of the French crystallographer Haiiy at the end 

 of the eighteenth century the theory that crystals were made up of small 

 identical units in orderly arrangement was widely held by crystallographers. 

 In the late nineteenth century these units were thought of as intersecting 

 planes of atoms. Then, in 1912, the German physicist von Laue conceived 

 the idea that such a lattice of atoms should act as a three-dimensional 

 diffraction grating for electromagnetic waves of wave-length approxi- 

 mating the interplanar spacing of the lattice. If X-rays were, as was 

 suspected, electromagnetic vibrations of short wave-length, they might be 

 of the right order of magnitude to obtain diffraction from crystals. When 

 the experiment was tried it was found that a beam of X-rays (not mono- 

 chromatic) passing through a crystal produced an orderly arrangement of 

 spots on a photographic fihn, the type of photograph now known as a 

 Laue photograph. 



The term reflection may be used in place of diffraction since X-ray dif- 

 fraction is like light reflection in that the entering and leaving beams make 

 equal angles with the reflecting or diffracting atomic planes.- Since this 

 concept is simpler, X-ray diffraction is commonly referred to as reflection. 



Unlike light reflection, X-ray reflection can take place only under the con- 

 ditions given by the following equation which is known as the Bragg law 



nX = 2 J sine (3.1) 



where n = a small whole number, 



o 



X = wave-length of X-rays used (generally stated in Angstrom 



units) 

 (/ = distance between the atomic planes (generally stated in 



Angstrom units). 

 d = angle between the X-rays and the atomic planes ("The Bragg 

 Angle"). 

 That is, the angle of incidence must be such that the path-length of two 

 rays reflected from different atomic planes differs by a whole number of 

 wave-lengths so that the emerging rays will be in phase. If the difference 

 in path-length of the two rays is one wave-length the reflection is called 

 the first-order reflection {n = 1). At some larger d angle the path dif- 

 ference will be exactly 2X and reflection will occur again. This is the second 

 order reflection (n = 2). Monochromatic X-rays are used so that only 



2 Compton, A. H. and Allison, S. K., "X-Rays in Theorj- and Experiment," D. Van 

 Nostrand, New York, 1935, Pages 340-346. 



