# Bragg Diffraction

Bragg diffraction was proposed by William Lawrence Bragg and William Henry Bragg in 1912. Diffraction occurs when electromagnetic radiation encounters an obstacle and must scatter in various directions. Bragg’s law allows for the angles at which the beam of electromagnetic radiation is scattered when the beam strikes a solid crystalline surface to be known. Bragg diffraction utilizes Bragg’s law to study the diffraction patterns for crystalline solids. X-ray radiation is typically used when studying diffraction. Bragg’s law is used in X-ray diffraction to study the structure of crystalline solids[1].

## What is Diffraction?

Diffraction occurs when a wave runs into an obstacle and must avoid the obstacle. Therefore, diffraction describes the apparent bending of waves around objects and the spreading of waves when passing through a small hole. The pattern in which diffraction occurs is due to constructive and destructive wave interference which leads to either a larger or smaller amplitude wave respectively. Diffraction patterns can yield information about the arrangement of the lattice points where diffraction occurs.

## Bragg’s law

Bragg’s law is mathematically defined as

$n\lambda=2d\sin\theta,\!$

where λ is the wavelength of the incident electromagnetic radiation wave, n is an integer, d is the spacing between the planes of the lattice and θ is the angle between the incident wave and the scattering planes[1]. Bragg’s law can be derived by examining a simple image of lattice planes[2] from the following link

X-ray diffraction of a crystal [link is broken]

A monochromatic incident wave strikes the lattice point Y at an angle θ and both reflects at angle θ and also continues to pass through the lattice. A distance of d separates neighboring lattice points. If the distance XY + YZ = then the radiation wave will be in phase at along the black line from the lattice point above point Y to Z. The distances XY and YZ are equal to $d\sin\theta,\!$ and therefore,

$n\lambda=2d\sin\theta,\!$

must be true for constructive interference to occur. At all other angles destructive interference is observed. This equation is called the Bragg equation and is fundamentally important in understanding at which angles constructive and destructive interference occurs respectively[1].

## X-ray Diffraction

The use of X-rays for the study of crystalline solids is due to the fact that the wavelength of an X-ray is on the same order of the distance between lattice planes. Therefore, X-rays will diffract in a crystalline solids. The requirements for X-ray diffraction are that the spacing between the lattice layers must be the same as the wavelength of the source radiation and that the lattice centers must be highly ordered to produce constructive and destructive interference. Constructive interference causes the scattering radiation to be reflected from the crystal lattice, and destructive interference causes the scattering radiation to be destroyed. Therefore, only at lattice points where constructive interference takes place is scattered radiation detected. The constructive and destructive interference that results from the diffraction of highly ordered diffraction planes causes highly ordered diffraction patterns that can be used to identify the pattern of the diffraction planes[1].

## References

1. Skoog, Douglas A., F. James Holler, and Stanley R Crouch. “Diffraction of X-rays” Principles of Instrumental Analysis. Belmont: Thomson Brooks/Cole, 2007. 309-310., additional text.
2. [“Introduction,” Centre for Diffraction Studies, The University of Aderbeen. <http://www.abdn.ac.uk/~che241/cdiff/indexx.htm>.], additional text.