Bragg's law

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In physics, Bragg's law is the result of experiments into the diffraction of x-rays off crystal surfaces at certain angles, derived by physicists Sir W.H. Bragg and his son Sir W.L. Bragg in 1912, and first presented on 1912-11-11 to the Cambridge Philosophical Society. 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.

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

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

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

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).

References

W.L. Bragg, "The Diffraction of Short Electromagnetic Waves by a Crystal", Proceedings of the Cambridge Philosophical Society, 17 (1912), 43–57.

Bragg's law

References

See also