Interactive Tutorial about Diffraction
Interactive example: Phase angles III

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 simulation window allow you to create a single electron a single Si or a single Pb atom located within a unit cell. The unit cell represents a cubic crystal of 10 Angstroem lattice constants. The position of the atom/electron is given in fractional coordinates. You can also select whether to calculate X-ray or neutron intensities. Four diagrams will be plotted. The first displays the position of the atom, 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 final diagram displays the corresponding numerical values.

Start exploring and try to answer the questions below:

  • What is the effect of the position on the amplitude, the real part, the imaginary part and the phase angle of the diffraction pattern ?
  • For an H0 reflection, what is the difference between a shift in the positive and the negative x-direction ?
  • For an H0 reflection, what is the difference between a shift in the x-direction and y-direction, respectively?
  • What is the difference that identical shifts have on different H0 reflections ?
  • Use a general HK reflection. Compare the effect of a shift to that of an H0 reflection.
    Along which direction do you have to shift the atom to obtain equivalent results, which a shift along the x-direction and along the y direction has on the H0 reflection ?
  • What is the influence of the electron/atom type on the X-ray amplitude/phase angle ?
  • Describe the difference between X-ray and neutron diffraction results.
  • Try to work out the relationship between the magnitude of the shift and the phase angle ?
  • Why does the phase angle change periodically, although the other features of the diffraction pattern do not ?
Once you are done, click here to verify your answers.
© Th. Proffen and R.B. Neder, 2003