15.9 Diffraction of X-ray by Crystals

15.9 Diffraction of X-ray by Crystals

X-rays is a type of electromagnetic radiation of much shorter wavelength, about $10^{-10}\,\mathrm{m}$. In order to observe the effects of diffraction, the grating spacing must be of the order of the wavelength of the radiation used. The regular array of atoms in a crystal forms a natural diffraction grating with spacing that is typically $10^{-10}\,\mathrm{m}$. The scattering of X-rays from the atoms in a crystalline lattice gives rise to diffraction effects very similar to those observed with visible light incident on ordinary grating.

(Fig. 15.18: Diffraction of X-rays by crystal.)

The study of atomic structure of crystals by X-rays was initiated in 1914 by W.H. Bragg and W.L. Bragg with remarkable achievements. They found that a monochromatic beam of X-rays was reflected from a crystal plane as if it acted like mirror. To understand this effect, a series of atomic planes of constant interplanar spacing $d$ parallel to a crystal face are shown by lines $\mathrm{PP'}$, $\mathrm{P'P}_{1}$, $\mathrm{P}_{1}\mathrm{P}'_{1}$, and so on, in Fig. 9.18.

Interesting Application

(Fig. 15.19: Diffraction of radio waves)

Suppose an X-rays beam is incident at an angle $\theta$ on one of the planes. The beam can be reflected from both the upper and the lower planes of atoms. The beam reflected from lower plane travels some extra distance as compared to the beam reflected from the upper plane. The effective path difference between the two reflected beams is $2d \sin\theta$. Therefore, for reinforcement, the path difference should be an integral multiple of the wavelength. Thus,

The value of $n$ is referred to as the order of reflection. The equation 15.8 is known as the Bragg equation. It can be used to determine interplanar spacing between similar parallel planes of a crystal if X-rays of known wavelength are allowed to diffract from the crystal.

X-rays diffraction has been very useful in determining the structure of biologically important molecules such as hemoglobin, which is an important constituent of blood, and double helix structure of DNA.

Interesting Information

lightbulb

The spectrum of white light due to diffraction grating of $100$ slits.

The spectrum of white light due to diffraction grating of $2000$ slits.