STRUCTURE OF CRYSTALS WYCKOFF. 207 



distant from the slit. This fact is of utmost importance in designing 

 an X-ray spectrograph. If a photographic film is curved to the arc 

 of a circle of a radius equal to the distance from the crystal to the slit, 

 and whose center is at the crystal face, then a focused image of a 

 small range of wave lengths will appear upon the film. Furthermore, 

 if the crystal is but rotated continuously back and forth, all of the 

 different wave lengths in the original beam will be reflected at some 

 angle of the rotating crystal. A photographic image of the entire 

 X-ray spectrum can thus be obtained. Figure 13 shows a spectro- 

 graph designed for obtaining such reflections. Figure 15 (pi. 6) 

 gives the X-ray spectrum of tungsten obtained in the manner just 

 outlined. 



Spectrometer data. — The principal use of the photographic X-ray 

 spectrometer (spectrograph) in studying the structure of crystals 

 lies in determining the absolute distances apart of like planes in some 

 one direction in the crystal. This information, furnishing a knowl- 

 edge of the number of molecules to be associated with the unit of 

 structure, is the first piece of experimental data that is required in 

 studying the structure of a crystal. It can be obtained much more 

 readily by photographic means than by searching about looking for 

 a reflection, as must be done if the spectrometer itself is employed to 

 give the same information. 



The following is an outline of the nature of the data which the 

 spectrometer and the spectrograph can be expected to yield. It has 

 just been stated that the number of chemical molecules associated 

 with the unit of structure can be deduced from a knowledge of the 

 position of the reflection from a single face of a crystal. The pro- 

 cedure required to give this information is quite the same as that 

 already used in getting the wave lengths of X rays. Equation (1), 



tiK 



n\=2d sin6 can be written : d= —-. . It has been indicated that 



2 sinG 



F=— • (2) 



p 



v=c(d 100 y (3) 



where d 100 is the spacing in the direction of the side of the unit prism 

 and c is a constant whose value is determined by the symmetry of the 

 crystal (and is obviously equal to unity in the case of a cubic crystal). 



c(d ) 3 p 

 By combining (2) and (3) : m= ^ ; substituting the value of d 



obtained by equation (1), there results: 



m _ c\ 3 p 

 n 3 ~8 sin 3 dM' 

 Besides telling the absolute distances apart of the planes of atoms 

 in the crystal, spectrometer measurements give some indication of 



