Interactive Tutorial about Diffraction
Interactive example: Solutions

Interactive examples
Electron density
Relation H and 2H


Example 1:
  • A single reflection contributes to the electron density in form of a plane wave. The wave front stands normal to the reciprocal vector h,k,l.
  • The electron density distribution created by a single reflection is periodic and has a wave length inversely proportional to the length of the reciprocal vector. Thus, reflections with low indices h,k,l define the broad general crystal structure features, while reflections with high indices define the accurate atomic positions. Keep in mind that the structure factor of higher order reflections is generally smaller due to the decrease of the atomic form factor. Thus the contibution of the inner reflections defines the main parts of the crystal structure.
  • Since a single reflection creates a plane wave electron density distribution it defines atomic position only along the normal to the wave front. No information is given about the atomic position within the plane.
  • Each reflection contributes as much positive as negative electron density. The total electron density is the sum of all individual contributions.
  • The amplitude is directly proportional to the resulting electron density. Strong reflections define most of the electron density distribution, while weak reflections create the smaller details.
  • The phase angle does not affect the amplitude of the electron density distribution, but shifts the location of the maximum density along the wave vector. Thus, it is the phase angle that determines were you will place the atoms within the unit cell. Its correct determination is the crucial part of the crystal structure determination process.
  • The 0,0,0 reflection does not cause a wave like electron distribution, but a constant electron distribution equal to the average electron density. remember that F(0,0,0) is equal to the number of electrons per unit cell! Since the integral over the electron density contribution of all other reflections is zero, the other reflections do not change the average electron density, but shift it around within the unit cell. This shifting will eventually create the distinct maxima at the atomic positions.
© Th. Proffen and R.B. Neder, 2003