Interactive Tutorial about Diffraction
Interactive example: Phase angles IV

Phase problem
Shift in real space
Centrosymmetric vs. Acentric

Interactive examples
Single atom
Pair of atoms
One atom in unit cell
Two atoms in unit cell


In this interactive example you should investigate the effect of the atom position on the amplitude and phase angle of a single Bragg reflection.

The controls on the right allow you to create two electrons, Si or Pb atoms located within a unit cell. The unit cell represents a cubic crystal of 10 Angstroem lattice constants. The position of the atoms/electrons is given in fractional coordinates.
Four diagrams will be plotted. The first displays the position of the atoms, the second (the lower left diagram) displays the position of the Bragg reflection in reciprocal space. The third diagram (upper right) shows the real and imaginary part of the Bragg reflection in the complex plane. The x-axis reflects the real part, the y-axis the imaginary part of the structure factor. The angle between the positive x-axis and the structure factor represents the phase angle. The three different colors represent the contributions of atom 1 and atom 2 and the total structure factor. The final diagram displays the corresponding numerical values.

Start exploring and try to answer the questions below:

  • Work out the relationship between the individual contributions and the total structure factor.
  • What is the effect, if you choose two different atoms?
  • For an H0 reflection, can you place two identical atoms such that the amplitude of the structure factor is zero?
  • Which coordinates are relevant for this placement x and/or y ?

  • Use a general HK reflection. Again try to place two atoms such that the total structure factor amplitude is zero.
  • Find relative placements of the two atoms such that all H0 reflections with H odd have zero amplitude.
  • Find relative placements of the two atoms such that all HK reflections with (H+K) odd have zero amplitude.
Once you are done, click here to verify your answers.
© Th. Proffen and R.B. Neder, 2003