# Bragg diffraction

 Contents

## History

Bragg diffraction was first proposed by William Lawrence Bragg in 1912 as a means of analyzing the structure of crystals. Bragg and his father William Henry Bragg collimated x-rays to diffract off of different crystal planes. The x-rays were then collected in an ionization chamber and the level of ionization was measured as a function of the incident angle of the x-rays.

Using this method, the Braggs were able to determine the crystalline spacing for a number of substances.

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BraggDiffraction2.png
1b) Skewed Plane NaCl Crystal
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BraggDiffraction.png
1a) Normal Plane NaCl Crystal

## Mechanics

The image on the right depicts a salt crystal (NaCl) in two different Bragg plane configurations. The incident angle of the diffracting wave determines which plane is calculated in the diffraction.

As the wave enters the crystal, some portion of it will be reflected by the first layer, while some will continue through to the second layer before being reflected. The separated waves will remain in phase if the path length of each wave is equal to an integer multiple of the wavelength.

If, given an arbitrary origin [itex]\vec O[itex], some place in the crystal lattice. Then there must be an integer number of Bragg planes beween the origin and any position vector [itex]\vec R[itex]. If when drawing a line connecting connecting [itex]\vec O[itex] and [itex]\vec R[itex], one does not cross any Bragg planes, then the position [itex]\vec R[itex] is said to be in the first Brillouin zone. In general, a point in a crystal lattice is in the [itex]n^{th}[itex] Brillouin zone if one crosses [itex]n-1[itex] Bragg planes.

In the figure 2 on the right, the path difference is given by [itex]\begin{matrix}d\sin\theta\end{matrix}\,[itex], where d denotes the crystal spacing.
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DiffractionPlanes.png
2) Diffraction Calculation
This gives the formula for what is known as the Bragg Condition or Bragg's law:
[itex]2 d\sin\theta = m\lambda\,[itex]

Waves that satisfy this condition interfere constructively and have the same apparent strength as reflection. Thus, by varying the wavelength λ and the incident angle θ, the Braggs were able to calculate the spacing.

## Nobel Prize

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.

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

## References

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

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