# Bragg's Law

## Bragg’s Law Statement

Bragg’s law is a special case of Laue diffraction which determines the angles of coherent and incoherent scattering from a crystal lattice. When X-rays are incident on a particular atom, they make an electronic cloud move just like an electromagnetic wave. The movement of these charges radiates waves again with similar frequency, slightly blurred due to different effects and this phenomenon is known as Rayleigh scattering.

The same process takes place upon scattering neutron waves via nuclei or by a coherent spin interaction with an isolated electron. These wave fields which are re-emitted interfere among each other either destructively or constructively creating a diffraction pattern on a film or detector. The basis of diffraction analysis is the resulting wave interference and this analysis is known as Bragg diffraction.

### Bragg Equation

According to Bragg Equation:

nλ = 2d sinΘ

Therefore, according to the derivation of Bragg’s Law:

• The equation explains why the faces of crystals reflect X-ray beams at particular angles of incidence (Θ, λ).
• The variable d indicates the distance between the atomic layers and the variable Lambda specifies the wavelength of the incident X-ray beam.
• n as an integer.

This observation illustrates X-ray wave interface which is called as X-ray diffraction (XRD) and proof for the atomic structure of crystals.

Braggs was also awarded with Nobel Prize in Physics in identifying crystal structures starting with NaCl, ZnS and diamond. Diffraction has been developed to understand the structure of every state of matter by any beam e.g, ions, protons, electrons, neutrons with a wavelength similar to the length between the molecular structures.

## Applications of Bragg’s Law

There numerous Bragg’s law applications in the field of science. Some common applications are given in the points below.

• In the case of XRF (X-ray fluorescence spectroscopy) or WDS (wavelength dispersive spectrometry), crystals of known d-spacings are used as analyzing crystals in the spectrometer.
• In XRD (X-ray diffraction) the interplanar spacing or d-spacing of a crystal is used for characterization and identification purposes.

### Bragg’s diffraction

Bragg’s diffraction was first proposed by William Henry Bragg and William Lawrence Bragg, in 1913. Bragg’s diffraction occurs when subatomic particle or electromagnetic radiation, waves have wavelengths that are comparable to atomic spacing in a crystal lattice.

## Bragg’s law Conclusion

The concluding ideas from Bragg’s law are:

• The diffraction has three parameters i.e, the wavelength of X rays,λ
• The crystal orientation defined by the angle θ
• The spacing of the crystal planes, d.

The diffraction can be conspired to occur for a given wavelength and set of planes. For instance, changing the orientation continuously i.e, changing theta until Bragg’s Law is satisfied.