Interactive Tutorial about Diffraction
Modification II: Shift atom
In this example one of the atoms has been moved to a slightly different
site within the unit cell. The example demonstrates the sensitivity
of the Fourier transform to atomic positions.
The oxygen (I) is moved from 0.25 0.25 0.25 to the
new position 0.30 0.30 0.30. The unit cell size is left unchanged.
A simple projection of the structure along  is shown in the following
image (one unit cell). The grid gives 0.25 intervalls in fractional
coordinates. The origin of the unit cell is at the lower left corner, the
horizontal axis is , the vertical axis . Click on the picture
to get a full screen version of it.
The left image shows the original Fourier transform of the unit cell, the right image the Fourier transform of the modified unit cell. The overall intensity distribution is similar, the intensity in the range h= 4 to 6 has changed considerably. Both pictures show the hk0 layer of reciprocal space. The image corresponds to the Fourier transform of a single unit cell. The intensity distributions of the crystal are shown as blue dots marking the Bragg reflections.
The identical one-dimensional cuts as in the previous example demonstrate the intensity change even more clearly. The blue curves give the intensity distribution of the original cell, the red curves those of the modified cell. The Fourier transform of the crystal based on the modified unit cell is displayed as a green line. Note that the relative intensity change varies considerably through reciprocal space. Again, the vertical scale has been cut off at approximately 40% of the intensity at 0,0,0. Click on the pictures to get a full screen image.
The students can learn the following based on the observations made so far:
|© Th. Proffen and R.B. Neder, 2003|