# Bragg's law

Bragg's law is the result of experiments into the diffraction of x-rays off crystal surfaces at certain angles, derived by the English physicists Sir W.H. Bragg and his son Sir W.L. Bragg in 1913. Although simple, Bragg's law confirmed the existence of real particles at the atomic scale, as well as providing a powerful new tool for studying crystals in the form of x-ray diffraction. The Braggs were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS, and diamond.

When X-rays hit an atom, they make the electronic cloud move as does any electromagnetic wave. The movement of these charges re-radiate waves with the same frequency (blurred slightly due to a variety of effects); this phenomenon is known as the Rayleigh scattering (or elastic scattering). These re-emitted X-rays interfere, giving constructive or destructive interferences; this is the diffraction phenomenon.

In the following diagram, X-rays are being shined on a crystal, here shown as only four atoms. The top two are shown re-radiating their energy after being hit. The points where the resulting "rings" overlap will be areas of constructive interference, and you can see that there is a definite angle to the resulting radiation, in this example up to the right at about 45 degrees.

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Diffusion_rayleigh_et_diffraction.png

The interference is constructive when the phase shift is proportionnal to 2π; this condition can be expressed by th Bragg's law:

[itex]n\lambda=2d\sin(\theta) \,[itex]

where

• n is an integer,
• λ is the wavelength of x-rays, and moving electrons, protons and neutrons,
• d is the spacing between the planes in the atomic lattice, and
• θ is the angle between the incident ray and the scattering planes

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Loi_de_bragg.png

According to the 2θ deviation, the phase shift causes constructive (left figure) or destructive (right figure) interferences

Note that moving particles, including electrons, protons and neutrons, have an associated wavelength, as determined by Louis de Broglie (see De Broglie wavelength).

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