THE X-RAY SPECTROMETER 



13 



When the x-ray beam reaches the crystal it encounters an array of 

 ions (points) symbolized by the open and closed circles. A portion 

 of the incident wave train is reflected from some ion P in the face of 

 the crystal; another portion penetrates deeper and is reflected by an 



o 



• J CI 



O 4 



O ( • ) (o) Na 



Fig. 1-7. This shows, in a schematic way, the location of the Na and CI ions in 

 a sodium chloride crystal and the reflection by the crystal of a monochromatic beam 

 of x-rays incident at glancing angle 9. 



ion at a distance d below P. This latter train travels a longer distance 

 abc, which must be an integral multiple of the wavelength of the x-ray 

 so that on emerging and entering the ionization chamber it reinforces 

 the upper wave train. The geometry of the diagram shows that this 

 path difference is equal to 2d sin 8. For the wave trains to reinforce 

 each other 



7i\ = 2d sin 



where n is a whole number and is called the spectral " order." This 

 relation is known as Bragg's law. 



The value of d may be obtained as follows. There are two ions per 

 molecule, and, as each ion is confined to a volume equal to d 3 , a molecule 

 of NaCl occupies a volume equal to 2d 3 . Since one mole of a substance 

 contains 6.06 X 10 23 molecules, the number of molecules per cubic 

 centimeter is p X 6.06 X 10 23 /M, where p is the density and M is the 

 molecular weight. Hence 



3 M 



2 X p X 6.06 X 10 23 



