﻿ Diffraction of X-rays

The narrow spaces between the atomic planes in a crystal are suitable for diffraction of x-rays

Simple crystals led to the determination of x-ray wavelengths.

With known values of x-ray wavelengths, more complex crystals were analysed.

The Braggs were the first to successfully interpret x-ray diffraction patterns.

Dots are atoms.
Green lines are planes.
Purple lines are x-rays.

The study of crystals was greatly advanced by x-rays.

Bragg formula

Computers are needed to help analyse diffraction patterns from complex crystals.

Visible light requires very narrow slits for diffraction to occur. The wavelength of x-rays was far shorter than visible light. In 1912 Max von Laue recognised that the wavelength of x-rays was apparently similar to the distances between planes of atoms in crystals and perhaps therefore crystals could act as a diffraction grating for x-rays. Suitable experiments were performed in the next year.

The atoms in a crystal are arranged in a regular lattice as shown. The spacing between planes of atoms is comparable to the wavelength of x-rays.

In 1913 W.L. Bragg successfully interpreted a diffraction pattern obtained when x-rays were directed at a crystal.

The atoms in a crystal may be thought of as defining families of parallel planes (now called Bragg planes). Bragg devised conditions for constructive interference to arise in radiation scattered by crystals.

· The first condition resembles the law of reflection for visible light by a mirror.
· The second condition may be stated as

2d sin= n

where d is the spacing between adjacent Bragg planes in the crystal
and is the wavelength of the x-rays.
The angle between the x-ray beam and the plane of atoms is and n is the order of the image.
(Students will recognise a resemblance to the condition for the diffraction of visible light).

Demonstration of Diffraction (Bragg)

By using crystals with simple structures where d was known, then the wavelength ? of x-rays was accurately determined. Then by directing x-rays of known wavelength at more complex crystals, diffraction patterns were obtained and examined enabling the spacing of the Bragg planes to be determined and so the crystal structure established. Hence x-rays helped the development of crystallography.

The structure of some crystals is so complex that x-ray diffraction patterns take years to analyse. Computers have offered great advantages.

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X-rays played a significant part in the discovery of the helical structure of DNA.