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Bragg's law
In physics, Bragg's law (or "Wulff -Bragg's condition" in postsoviet countries, a special case of Laue diffraction) gives the angles for coherent and incoherent scattering from a crystal lattice. When X-rays are incident on an atom, they make the electronic cloud move as does any electromagnetic wave. The movement of these charges re-radiates waves with the same frequency, blurred slightly due to a variety of effects; this phenomenon is known as Rayleigh scattering (or elastic scattering). The scattered waves can themselves be scattered but this secondary scattering is assumed to be negligible.
A similar process occurs upon scattering neutron waves from the nuclei or by a coherent spin interaction with an unpaired electron. These re-emitted wave fields interfere with each other either constructively or destructively (overlapping waves either add up together to produce stronger peaks or are subtracted from each other to some degree), producing a diffraction pattern on a detector or film. The resulting wave interference pattern is the basis of diffraction analysis. This analysis is called ''Bragg diffraction''.
== History ==
Bragg diffraction (also referred to as the Bragg formulation of X-ray diffraction) was first proposed by William Lawrence Bragg and William Henry Bragg in 1913〔 (Free access)〕 in response to their discovery that crystalline solids produced surprising patterns of reflected X-rays (in contrast to that of, say, a liquid). They found that these crystals, at certain specific wavelengths and incident angles, produced intense peaks of reflected radiation. The concept of Bragg diffraction applies equally to neutron diffraction and electron diffraction processes.〔John M. Cowley (1975) ''Diffraction physics'' (North-Holland, Amsterdam) ISBN 0-444-10791-6.〕 Both neutron and X-ray wavelengths are comparable with inter-atomic distances (~150 pm) and thus are an excellent probe for this length scale.
William Lawrence Bragg explained this result by modeling the crystal as a set of discrete parallel planes separated by a constant parameter ''d''. It was proposed that the incident X-ray radiation would produce a Bragg peak if their reflections off the various planes interfered constructively. The interference is constructive when the phase shift is a multiple of 2; this condition can be expressed by Bragg's law (see ''Bragg condition'' section below) and was first presented by Sir William Lawrence Bragg on 11 November 1912 to the Cambridge Philosophical Society. 〔See, for example, (this example calculation ) of interatomic spacing with Bragg's law.〕〔There are some sources, like the ''Academic American Encyclopedia'', that attribute the discovery of the law to both W.L Bragg and his father W.H. Bragg, but the (official Nobel Prize site ) and the biographies written about him ("Light Is a Messenger: The Life and Science of William Lawrence Bragg", Graeme K. Hunter, 2004 and “Great Solid State Physicists of the 20th Century", Julio Antonio Gonzalo, Carmen Aragó López) make a clear statement that William Lawrence Bragg alone derived the law.〕 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 and neutron diffraction. William Lawrence Bragg and his father, Sir William Henry Bragg, were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS, and diamond. They are the only father-son team to jointly win. William Lawrence Bragg was 25 years old, making him then, the youngest physics Nobel laureate.
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