Module 4 : Solid State Chemistry
Lecture 19 : Indexing Diffraction Patterns
  19.4

The Phase Problem

Everything seemed to be working rather well so far but it would be good to be aware of a major difficulty encountered in the diffraction method and the ways and means of nearly overcoming them. We know that the measured intensity I h k l of diffracted light is proportional to | F h k l | 2 . We need Fh k l in Eq (19.16). How do we know whether to use F h k l or - F h k l or even more generally |F h k l | e i where is the phase of Fh k l. While there are no methods to fully eliminate the problem, a common approach is to use (F h k l )2 in place of F h k l in Eq (19.16). This is called Patterson synthesis.

 

approximate (r) = ( 1 / V ) | F h k l | 2 e - 2 i (h x + k y + l z )

(19.17)
 

The use of Eq (19.17) results in multiple locations of some atoms which have to be corrected by trial and error. Another useful approach is to neglect the scattering functions of light atoms relative to those of the heavy atoms.

 
F = ( ) f heavy ( ) f light (19.20)
 
Since flight values are much smaller than fheavy, the former may be neglected in the first approximation. Other convenient relations like relating the signs of Fa b c and Fd e f to the sign of Fa + d, b + c, c + f are also used in finding partial solutions to the phase problem. Finally, the actual structure of the crystal is obtained by repeatedly refining the results obtained from the diffraction pattern and getting back the diffraction pattern from the estimated electron densities.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1