# 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 wavefields which are re-emitted interfere with 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 the X-ray wave interface which is called X-ray diffraction (XRD) and proof for the atomic structure of crystals.

Bragg was also awarded 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.

Following is the table explaining the other Physics related laws:

## 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 a 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.

### State if the given statement is true or false: Bragg’s law is not enough to explain the diffraction by crystalline solids.

The given statement is true because the atoms present at the non-corner positions might result in scattering at Bragg angles which is out-of-phase.

### What is the minimum interplanar spacing that is required for Bragg’s diffraction to occur?

$\frac{\lambda }{2}$ is the minimum interplanar spacing which is required for Bragg’s diffraction to occur.

### State if the given statement is true or false: The electronic clouds move when the X-ray is incident on an atom.

The given statement is true. Since X-ray is an electromagnetic wave, it makes the electronic cloud around the atom to move.

### Bragg’s law experiment is based on which scattering of waves?

Bragg’s law experiment is based on the Rayleigh scattering in which the charges are scattered without a change in their wavelength.

### Calculate the wavelength for the first-order spectrum if the angle f incidence is 30 degrees.

From the Bragg’s equation, we know that $n\lambda =2d\;sin\theta$
By substituting the values for
n=1
$sin\theta$=30 degrees = 1/2
We get, $\lambda =d$.