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What is Bragg’s law?

Introduction

W. L. Bragg gave a simple explanation for the study of crystal structure by using the phenomenon of diffraction and name it is as Bragg’s law. He gave a simple and convincing derivation of diffraction by crystal.

Thus it is possible to study the structure of the crystal  through the diffraction of electrons, photons and neutrons. However the phenomenon of diffraction depends on the structure of crystal structure and also on the wavelength.

The visible light rays then pass through a sharp edge of an object and can form some bright regions inside the geometrical shadow of the object. This is due to the bending nature of light. This bending of light is diffraction. Diffraction can only occur whenever Bragg’s law is satisfied.

Derivation

Consider Bragg’s planes. Where Bragg’s planes are a set of parallel planes. Each atom in the crystal is behaving as a scattering center. The reflected beam at certain angles will have maximum intensity. The intensity is maximum when two waves  are reflected from adjacent planes and have path difference equal to the integral multiple of λ.

Let us consider ‘d’ be the separation between two adjacent planes. Wavelength of incident X-rays is  ‘λ’ and the glancing angle is  ‘θ’.

From the above figure it is clear that the the rays reflected at A & B  have path difference

= CB +BD = dsinθ + dsinθ = 2dsinθ

If the two consecutive planes scatter waves in phase with each other, then the path difference must be an integral multiple of the wavelength.

= nλ

The intensity is maximum when two reflected wave have path difference equal to

nλ= 2dsinθ

Where ‘n’ is the order of scattering.

This is Bragg’s law.

According to the law, X-rays diffracted from different parallel planes of a crystal interfere constructively when the path difference is integral multiples of wavelength of X-rays.

From Bragg’s law nλ = 2d sin θ, since the maximum possible value for sin θ is 1,

nλ/2d ≤ 1 or λ ≤ 2d.

This sets the limitation on the wavelength. Thus to obtain the diffraction pattern by a crystal, the wavelength of X-rays should be less than twice the interplanar spacing.

Importance of Bragg’s law

1. Bragg’s law is the essential condition to be satisfied by crystal planes in order to get a diffraction pattern from a crystal.
2. It is useful in calculating interplanar spacing. Lattice parameters can be determined by knowing the values of interplanar spacing.

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