Interactive Tutorial about Diffraction
Interactive example: Finite size effect

Reciprocal space
Square lattice
Rectangular lattice
Oblique lattice
Translation of lattice
Rotation lattice

Interactive examples
2D crystal builder
Planes and HKL's
Finite size effect


When calculating intensities based on a structural model, the crystal should extend to infinity, otherwise the Fourier transform is truncated, resulting in ripples. This is also referred to as size effect. However, by choosing the correct grid in reciprocal space, these ripples can be avoided by choosing a grid coinciding with the nodes of the "ripples". This examples allows one to explore this concept.

The controls in the simulator allow you to specify the size of a model crystal and the range and grid in reciprocal space (hk-plane) that will be calculated. Since the simulated crystals have a finite size the scattering pattern will in general contain contributions cause by the limited size of the crystal. A detailed discussion is given the DISCUS Users Guide.

A simple recipe for selecting a suitable grid in reciprocal space is given below:

  • Select your grid size for the calculation of the scattering pattern as dh = n/Nx, where dh is the grid size in h-direction, Nx is the number of unit cells in x-direction and n is a integer value (n=1,2,..). This rule assumes that the reciprocal space units are reciprocal lattice parameters !

  • One advantage of reciprocal lattice parameter units is the fact, that Bragg peaks appear at integer values of (h,k,l), e.g. the (210) in our plane is at h=2 and k=1. Since Bragg peaks are sharp features, one needs to make sure that the selected grid contains the Bragg positions. A small offset and the Bragg peaks seem to have disappeared.

© Th. Proffen and R.B. Neder, 2003