Relation H and 2H
- 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
- 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.