electron microscopy



Bragg's Law of Diffraction

The scattering of electrons, X-rays and neutrons by crystals can be described as a reflection of the beams at planes of atoms (lattice planes), independent of the actual physical reason causing the diffraction event.

If the incident plane wave hits the crystal at an arbitrary angle, the interference of the reflected waves can be either destructive or constructive.

Destructive interference of reflected waves (in the two reflected waves, maximum and minimum of the respective wave amplitude are superimposed).

Constructive Interference of reflected waves (reflected waves in phase, i.e., maxima are superimposed).

To obtain constructive interference, the path difference between the two incident and the scattered waves, which is 2dsinΘ, has to be a multiple of the wavelength λ. For this case, the Bragg equation gives the relation between interplanar distance d and diffraction angle Θ:

nλ = 2dsinΘ



ED-Basics | Ewald sphere | ED vs. XRD | Examples


ETH Zürich | ETH chemistry department | ETH inorganic chemistry

modified: 6 February, 2015 by F. Krumeich | © ETH Zürich and the authors