15:4/ X-ray Analyses of Proteins and Nucleic Acids 



283 



Figure 7 shows several planes in a cubic crystal, each with a number 

 of atoms per plane. These planes are numbered by Miller indices 

 (hkl) which are described in Figure 8. In Figure 7, one may notice that 

 the planes are spaced at varying distances. By and large, as the Miller 



(110) 

 c/= 1.20 A 



(110) 

 Diffraction 

 Maximum 



n = \ 



(120) 

 rf = 0.77A 



(100) 

 d=\.7QA 



a Incident X-ray 

 I A/o Mnximn 



X-ray 



(100) 

 Diffraction 

 Maximum 



n=2 



0=50° 



X-ray 

 (010) Plane Gives Same Value of<$> 



Figure 7. Diffraction of an X-ray beam. In working out 

 angles, it is assumed that the X-ray wavelength A is 1.52 A 

 and that the crystal had cubic symmetry with a lattice con- 

 stant of 1.70 A. 



indices go up, the spacing d between adjacent planes decreases, and the 

 number of maxima likewise decreases. For the example shown, there 

 are two angles corresponding to n = 1 and n = 2 for the (010) and (100) 

 planes. The (110) and (120) planes each have only one diffraction 

 maximum corresponding to n = 1. The maximum for the (120) plane 

 essentially reflects the incident beam back on itself and could not be 

 observed. None of the higher planes will exhibit diffraction maxima. 

 However, planes not perpendicular to the xy plane, such as (101) and 

 (011), will give maxima whose diffracted beams will not lie in the plane 

 of the paper. Thus, the maxima will form a two-dimensional pattern 

 such as that shown in Figure 5. To show all the planes with mono- 

 chromatic X rays, a number of different schemes have been developed 

 which lead to an easier interpretation of the Miller indices of the planes 

 giving rise to a given reflection. For complex molecules, such as 



