# X-ray diffraction and Bragg’s Law

X-ray Diffraction

When x-ray is passed through very thin slits, it is called x-ray diffraction. The nature and arrangement of molecule in a crystals is studied through x-ray diffraction. In 1913, W. Laue showed the  diffraction of X-ray through a crystal. The arrangement for the diffraction is shown below:

X-ray diffraction through crystals

The apparatus consists of x-ray source, two slits, a ZnS crystal and a photographic plate placed straight to one another. When X-ray is passed though two slits and ZnS crystals for a hour, a faint regular spot were formed in the photographic plate. These spots are known as Laue spot. From this experiment, it was concluded that X-ray is electromagnetic wave and atoms of crystals are arranged in three dimensional lattice.

Bragg’s law

Bragg studied the diffraction of x-ray in detail and introduced a method for determining the wavelength of X-rays.

Let us suppose a crystal with lattice spacing d. when X-rays are passed to the crystals at a glancing angle, there raises a path difference between various rays in the screen due to the reflection of X-rays from different planes. This gives rise to formation of diffraction pattern on screen. Bragg studied these patterns and found a relation called Bragg’s law.

In the above figure the rays PQR and P’Q’R’ are diffracted from two successive planes of a crystal. The path difference is given by

Path difference = MQ’ + NQ’

= dsinθ + dsinθ

= 2dsinθ

If the path difference is integral multiple of λ then bright fringe is obtained. So,

2dsinθ = nλ

The above equation is known as Bragg’s Law.

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