What is Bragg's Diffraction

Fulfillment of the Bragg condition on polycrystalline graphite

The graphite platelet is a polycrystalline structure. This means that the graphite platelet consists of a large number of small individual or microcrystals that are randomly arranged in space. And due to the structure of very many individual crystals, there are \ (\ lambda \) crystals for electrons of any wavelength, which are so in space that they meet the Bragg condition for this wavelength \ (\ lambda \). In the graphic, electrons fall at different speeds and therefore different wavelengths (e.g. \ (\ lambda_1 \), \ (\ lambda_2 \) and \ (\ lambda_3 \)) on the graphite plate. For each wavelength there are different crystals that are oriented in such a way that the Bragg condition is met.

In the experiment, the graphite plate is usually bombarded with electrons of the same speed, since all electrons in an electron gun are accelerated to the same speed \ (v_0 \). Therefore the electrons here all have the same wavelength \ (\ lambda \). The waves diffracted (reflected) on the appropriately oriented crystal now reinforce each other (constructive interference) and ensure an interference maximum. The interference maximum is visible on the fluorescent screen as a bright circle. The angle between the incident electron beam and the reflected beam that fulfills the Bragg condition is just twice as large as the angle of incidence \ (\ theta \) for which the Bragg condition is fulfilled, i.e. \ (2 \ theta \) ( see grafic).
The reason for the circular shape is that all crystals are randomly oriented in space. Some crystals are positioned in such a way that they ensure an interference maximum "above" in relation to the beam direction of the electrons, others in turn so that they ensure an interference maximum on the left, right, below or somewhere in between. The result is a circle at the angle \ (2 \ theta \).

  • What is the wavelength \ (\ lambda \) of the electron beam?
  • What is the grid spacing \ (d \) of graphite?
  • Why are there two diffraction rings on the screen?