The Book of Crystallography

An lattice, and its Fourier Transform:

The grid points (delta functions) are exaggerated for clarity. Note that the Fourier transform of a grid is a grid with reciprocal directions and spacings. This is the origin of the reciprocal lattice.

A crystal, and its Fourier Transform:

Finally, we build up a crystal by convoluting the molecule with the grid. The result is a crystal structure. The Fourier transform of the crystal is thus the product of the molecular transform and the reciprocal lattice. This is the diffraction pattern.

More Fourier transforms. Back to the index.