Bragg condition ↩

Metadata

aliases: [Bragg's law, Wulff–Bragg's condition, Laue-Bragg interference]
shorthands: {}
created: 2022-01-20 18:16:21
modified: 2022-01-20 18:55:05

The Bragg condition applies when waves are being diffracted on a crystal and the wavelength of the wave is comparable to the atomic spacings. This results in scattering in a specular fashion, aka mirror-like reflection by the atoms of the crystal. This phenomenon is called Bragg diffraction and is a special case of Laue diffraction.

It states that the condition for constructive interference when a wave is Bragg-diffracted is:

Where is a natural number, is the wavelength of the wave, is the distance between the lattice planes and is the angle of the incoming wavefronts.

In simple terms, this states that: for reflection, the difference of the paths taken must be an integer multiple of the wavelength in order to have constructive interference. The condition is easy to derive using simple trigonometry.

Application

When we know the atomic spacing of a crystal, we can measure the wavelength of a wave by finding the angles by which it gets reflected and then use the Bragg condition
The fact that according to quantum mechanics, every particle is a wave was verified using the Bragg condition and scattering on crystals. The results lined up with the de Broglie wavelength for the electron.