STRUCTURE OF CRYSTALS — WYCKOFF. 



213 



cleaved, parallel to the cube, (100), face. 21 In figure 1 (p. 200) the 

 pinhole beam of X rays strikes this thin section of the crystal mounted 

 at C; most of it passes directly through the crystal and forms an 

 undiffracted image of the pinholes at ; the rest of the rays are 

 " reflected " by the various planes of atoms in the crystal and produce 

 a group of images, each one corresponding to a crystal plane, ar- 

 ranged about this central spot. (Fig. 20.) 



The relative positions of the reflections from the different planes 

 are conditioned only by the kind of symmetry which the crystal 

 exhibits; the absolute positions of these spots upon the plate depend 

 on the distance from the crystal section to the photographic plate. 

 The patterns from different cubic crystals, or from two other crystals 

 which have the same axial ratios and belong to the same system of 

 crystal symmetry, differ from each other then simply in the relative 

 intensities of the re- 

 flections from the 

 various planes ; this, 

 of course, depends 

 upon the arrange- 

 ment of the atoms 

 within the crystal 

 and upon their rela- 

 t i v e " reflecting " 

 powers. Consider 

 the reflection from 

 the plane contain- 

 ing the line OP and 

 parallel to the Y 

 axis of a cubic 

 crystal. (Fig. 21.) 

 The intercepts of 

 this plane upon the Z and X axes are in the proportion of 1:2; the 

 Y intercept is infinity. Since the ratio of the intercepts of the plane 

 are thus 2:a> : 1, its indices must by definition be 102 (y 2 , 0, 1). 

 If the angle between this plane and the incident rays is 0, the re- 

 flection will be along CR, where the angle RCO=2Q. In a similar 

 fashion the position of the reflection from any plane can be deter- 

 mined from the characteristics of symmetry of the diffracting 

 crystal. Conversely, it is possible to get such characteristics as the 

 axial ratio of a costal from a study of the Laue photographs. 



'This purely geometrical problem of identifying the reflections that 

 are obtained upon the photographic plate with those planes that may 

 be thought of as producing them can be easily solved with the aid of 



Fig. 21. 



21 Ralph W. G. Wyckoff, Am. J. Sci., 1, 138, 1921. 



