# Bragg diffraction

**Bragg diffraction**(also referred to as the**Bragg formulation of X-ray diffraction**) was first proposed byWilliam Lawrence Bragg andWilliam Henry Bragg in 1913 in response to their discovery thatcrystal line solids produced surprising patterns of reflectedX-rays (in contrast to that of, say, a liquid). They found that in these crystals, for certain specific wavelengths and incident angles, intense peaks of reflected radiation (known as "Bragg peaks") were produced. The concept of "Bragg diffraction" applies equally toneutron diffraction andelectron diffraction processes [*John M. Cowley (1975) "Diffraction physcis" (North-Holland, Amsterdam) ISBN 0 444 10791 6*] .W. L. 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 Bragg Condition**Bragg diffraction occurs when electromagnetic radiation or subatomic particle waves with wavelength comparable to atomic spacings, are incident upon a crystalline sample, scattered by the atoms in the system and undergo constructive interference in accordance to Bragg's law. For a crystalline solid, the waves are scattered from lattice planes separated by the interplanar distance "d". Where the scattered waves interfere constructively they remain in phase since the path length of each wave is equal to an

integer multiple of the wavelength. The path difference between two waves undergoing constructive interference is given by $2dsin\; heta$, where θ is the scattering angle. This leads toBragg's law which describes the condition for constructive interference from successivecrystallographic planes ("h,k,l") [*citation|title=Introductory Solid State Physics|author=H.P.Myers|publisher=Taylor & Francis|year=2002|isbn=0-7484-0660-3*] of the crystalline lattice::$2\; dsin\; heta\; =\; nlambda\; .$ [

*citation|url=http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/bragg.html|title=Bragg's Law|author=Carl.R. Nave|publisher=HyperPhysics, Georgia State University|accessdate=2008-07-19*]A diffraction pattern is obtained by measuring the intensity of scattered waves as a function of scattering angle. Very strong intensities known as Bragg peaks are obtained in the diffraction pattern when scattered waves satisfy the Bragg condition.

**Reciprocal space**More elegant is the description in

reciprocal space . Reciprocal lattice vectors describe the set of lattice planes as a normal vector to this plane with length $G\; =\; 2pi\; /\; d\; .$ Then Bragg's law is simply expressed by the conservation ofmomentum transfer $(G\; =\; k\_f\; -\; k\_i)$ with incident and final wave vectors k_{i}and k_{f}of identical length. The precedent relation is also calledLaue diffraction and not only gives the absolute value, but a full vectorial description of the phenomenon. The scanning variable can be the length or the direction of the incident or exit wave vectors relating to energy- and angle-dispersive setups. The simple relationship between diffraction angle and Q-space is then:$Q\; =\; frac\; \{4\; pi\; sin\; left\; (\; heta\; ight\; )\}\{lambda\}\; .$**Selection rules and practical crystallography**Bragg's law, as stated above, can be used to obtain the lattice spacing of a particular

cubic system through the following relation:: $d\; =\; frac\{a\}\{\; sqrt\{h^2\; +\; k^2\; +\; l^2$

where $a$ is the lattice spacing of the

cubic crystal , and $h$, $k$, and $l$ are theMiller indices of the Bragg plane. Combining this relation with Bragg's law:: $left(\; frac\{\; lambda\; \}\{\; 2a\; \}\; ight)^2\; =\; frac\{\; sin\; ^2\; heta\; \}\{\; h^2\; +\; k^2\; +\; l^2\; \}.$

One can derive selection rules for the

Miller indices for different cubicBravais lattices ; here, selection rules for several will be given as is.These selection rules can be used for any crystal with the given crystal structure. Selection rules for other structures can be referenced elsewhere, or derived.

**Nobel Prize for Bragg diffraction**In 1915,

William Henry Bragg andWilliam Lawrence Bragg were awarded theNobel Prize for their contributions to crystal structure analysis. They were the first and (so far) the only father-son team to have jointly won the prize. Other father/son laureates include Niels and Aage Bohr, Manne andKai Siegbahn ,J. J. Thomson and George Thomson, Hans von Euler-Chelpin andUlf von Euler , and Arthur andRoger Kornberg , who were all awarded the prize for separate contributions.W. L. Bragg was 25 years old at the time, making him the youngest Nobel laureate to date.

**See also***

Bragg's law

*Diffraction

**Diffraction grating

*Distributed Bragg reflector

**Fiber Bragg grating

*Photonic crystal fiber

*Powder diffraction

*X-ray crystallography **References****Further reading*** Neil W. Ashcroft and N. David Mermin, "Solid State Physics" (Harcourt: Orlando, 1976).

**External links*** [

*http://nobelprize.org/physics/laureates/1915/index.html Nobel Prize in Physics - 1915*]

* http://www.citycollegiate.com/interference_braggs.htm

* http://srs.dl.ac.uk/station/9.4/diffraction-selection-rules.htm

* http://www.physics.uoguelph.ca/~detong/phys3510_4500/xray.pdf

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### Look at other dictionaries:

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