Interactive Tutorial about Diffraction
Interactive example: Direct methods I

Interactive examples
Electron density
Fourier analysis
Relation H and 2H
Triplet phases
Intensity Statistics
Origin choice

Solving a structure


In these interactive examples you should investigate the effect of the amplitude and phase of one or two reflections on the electron density distribution within a unit cell.

The controls in the simulator window allow you to choose one or two reflection, their amplitude and phase angle. All calculations are based on a unit cell with lattice constants 10 Angstroem and 90 degrees, and use the reflection H,K and its Friedel pair -H,-K.

The first calculation uses only the reflection H,K and -H,-K. The reflection 0,0 has been omitted.

In the second calculation, however, the reflection 0,0 has been included with an amplitude of 1000. In many of your choices for the respective amplitudes and phases of the two reflections this inclusion means that you will get an electron density that is larger than zero.

Three diagrams will be plotted. The first displays the electron density distribution within the unit cell (the upper right diagram). The second and third diagrams display the electron density along two lines through the unit cell (parallel x at y=0 and parallel y at x=0, respectively). Start exploring and try to answer the questions below:

  • How does a reflection contribute to the electron density ?
  • What are the respective effects of the indices H,K, the amplitude, and the phase angle on the electron density distribution ?
  • What effect does the reflection 0,0 have ?

  • Why are the phase angles for structures with a center of symmetry at the origin limited to phase angles of 0 or 180 degrees ?
Once you are done, click here to verify your findings.
© Th. Proffen and R.B. Neder, 2003