The Bragg formulation of X-ray diffraction (also referred to as Bragg diffraction) was first proposed by William Lawrence Bragg and William Henry Bragg in 1913 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 in these crystals, for certain specific wavelengths and incident angles, intense peaks of reflected radiation (known as Bragg peaks) were produced. Sir William Lawrence Bragg CH, FRS, (March 31, 1890 - July 1, 1971) was a Australian physicist who won the Nobel Prize in Physics in 1915. ... Sir William Henry Bragg OM, Cantab, OKW (Westward, Cumbria, England July 2, 1862 – March 10, 1942) was an English physicist and chemist, educated at King Williams College, Isle of Man, and Trinity College, Cambridge. ... Crystal (disambiguation) Insulin crystals A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz...

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

1b) Skewed Plane NaCl Crystal.

1a) Normal Plane NaCl Crystal.

Image File history File links BraggDiffraction2. ... Image File history File links BraggDiffraction. ...

Mechanics

As shown in the images on the right, a given crystal (in this case, NaCl) can be decomposed into any number of different Bragg plane configurations, due to the periodicity of the crystal lattice. The incident angle of the incoming wave and its wavelength determines which set of planes is relevant in the calculation. Sodium chloride, also known as common salt, table salt, or halite, is a chemical compound with formula NaCl. ... In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ...

As the wave enters the crystal, some portion of it will be reflected by the first layer, while the rest will continue through to the second layer, where the process continues. By the definition of constructive interference, the separately reflected waves will remain in phase if the difference in the path length of each wave is equal to an integer multiple of the wavelength. Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ... The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ...

In the figure 2 on the right, the path difference is given by , where d denotes the interplanar distance.

2) Diffraction Calculation

This gives the formula for what is known as the Bragg condition or Bragg's law: Image File history File links DiffractionPlanes. ... In physics, Braggs 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. ...

Waves that satisfy this condition interfere constructively and result in a reflected wave of significant intensity.

Equivalence with other formulations

The phenomenon of crystal diffraction can also be formulated in other equivalent ways. One such example is the von Laue formulation of X-ray diffraction. In this model, the crystal is instead seen as a set of identical ions resting at the sites defined by the Bravais lattice, each of which reradiate incident radiation isotropically. The condition for constructive interference in this formulation is given by: In geometry and crystallography, a Bravais lattice is an infinite set of points generated by a set of discrete translation operations. ...

where n is again an integer, is the wave vector describing the incoming wave, is the wave vector describing the outgoing wave, and is any Bravais lattice vector. This can be equivalently stated as A wave vector is a vector that represents two properties of a wave: the magnitude of the vector represents wavenumber (inversely related to wavelength), and the vector points in the direction of wave propagation. ...

or, defining to be a reciprocal lattice vector, and assuming that , In crystallography, the reciprocal lattice of a Bravais lattice is the set of all vectors K such that for all lattice point position vectors R. The reciprocal lattice is itself a Bravais lattice, and the reciprocal of the reciprocal lattice is the original lattice. ...

This final statement can be interpreted as saying that the Laue condition (for constructive interference) is satisfied if and only if the wave vector lies in a plane that is the perpendicular bisector to a reciprocal lattice vector lying at the origin of k-space. These planes are nothing other than the Bragg planes encountered earlier. The set of all Bragg planes in a crystal and the (identical) volumes they enclose define the Brillouin zones of the crystal. Thus the condition for diffraction can be equivalently stated as the requirement that the incoming wavevector (when placed at the origin of k-space) lie on a Bragg plane or on a Brillouin zone. In mathematics and solid state physics, the first Brillouin zone is the primitive cell in the reciprocal lattice in momentum space. ...

To further exemplify the equivalence between these two formulations (the Bragg formulation and the Van Laue formulation), note that the reciprocal lattice vector must have a magnitude which is an integer multiple of 2π / d, where d is again the interplanar distance (this is a consequence of the definition of the reciprocal lattice). Therefore,

Furthermore, from the results of the Van Laue formulation, we know that in the case of constructive interference, we have

where θ is the angle between the incoming wave vector and the plane perpendicular to the reciprocal lattice vector G.

Setting these two equations equal to each other, and recognizing the magnitude of the wave vector is simply equal to 2π / λ, the Bragg condition is retrieved:

Nobel Prize for Bragg diffraction

In 1915, William Henry Bragg and William Lawrence Bragg were awarded the Nobel 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 and Kai Siegbahn, J.J. and George Thomson, and Hans von Euler-Chelpin and Ulf von Euler all having been awarded the prize for separate contributions. Sir William Henry Bragg OM, Cantab, OKW (Westward, Cumbria, England July 2, 1862 – March 10, 1942) was an English physicist and chemist, educated at King Williams College, Isle of Man, and Trinity College, Cambridge. ... Sir William Lawrence Bragg CH, FRS, (March 31, 1890 - July 1, 1971) was a Australian physicist who won the Nobel Prize in Physics in 1915. ... Sir Edward Appletons medal Photographs of Nobel Prize Medals. ... Niels Bohr Niels (Henrik David) Bohr (October 7, 1885 – November 18, 1962) was a Danish physicist who made essential contributions to understanding atomic structure and quantum mechanics // Bohrs contributions to physics Bohrs model The electrons orbital angular momentum is quantized; L=nħ. The theory that electrons travel... Aage Niels Bohr Aage Niels Bohr (born in Copenhagen, Denmark on June 19, 1922) is the son of Margrethe and Niels Bohr. ... Karl Manne Georg Siegbahn (December 3, 1886 - September 26, 1978) was a Swedish physicist, who received the Nobel Prize in Physics in 1924 for his discoveries and research in the field of X-ray spectroscopy. ... Kai Manne Börje Siegbahn (born April 20, 1918) is a Swedish physicist. ... Sir Joseph John Thomson Sir Joseph John Thomson (18 December 1856 – 30 August 1940), often known as J. J. Thomson, was an English physicist, the discoverer of the electron. ... George Paget Thomson (May 3, 1892 – September 10, 1975), British physicist and son of Nobel Prize winning physicist J. J. Thomson. ... Hans Karl August Simon von Euler-Chelpin (1873 - 1964) was a Swedish (German-born) biochemist. ... Ulf von Euler, a Nobel laureat Ulf Svante von Euler (February 7, 1905 – March 9, 1983) was a Swedish physiologist and pharmacologist. ...

W.L. Bragg was 25 years old at the time, making him the youngest Nobel laureate to date.

See also

• Bragg's law
• Diffraction grating
• Diffraction
• Photonic crystal fiber

In physics, Braggs 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. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Photonic-crystal fiber (PCF), also spelled fibre, is a new class of optical fiber based on the properties of photonic crystals. ...

External links

• Nobel Prize in Physics - 1915

References

• Neil W. Ashcroft and N. David Mermin, Solid State Physics (Harcourt: Orlando, 1976).
• http://www.citycollegiate.com/interference_braggs.htm