## Diffraction | X-Rays and the Braggs

Paul explains about Diffraction | X-Rays and the Braggs.

• ## Elemental Spectra

We are familiar with shadows cast on a wall by an object and know that the shadow has the same shape as the object. However, if we look carefully, we will see that the edges of the shadow are a little fuzzy, that is, they are no perfectly sharp. This lack of sharply defined edges on the shadow is due to the phenomenon of diffraction. Diffraction refers to the spreading out of light waves around the edge of an object to when light passes through a small aperture.

Young’s double slit experiment showed that light does not travel past an object in straight lines, but spreads out around the object’s edges as waves. These waves can interfere with each other as they spread out. This spreading out of light that occurs around an object or when light is passing through a small aperture is called diffraction. It is pronounced when the waves have to travel different paths to a point some distance from the source and in doing so travel paths that have differences in length that approach either multiples of half or full wavelengths. A diffraction pattern is shown in the following figure.

• ## X-Ray Diffraction

Diffraction is a property of all waves, including electromagnetic radiation. Diffraction effects increase as the physical dimension of the aperture approaches the wavelength of the waves. Diffraction of waves results in interference that produces dark and bright rings or spots. The precise nature of these effects is dependent on the geometry of the object causing the diffraction.

X-rays were discovered by Rontgen towards the end of the nineteenth century. A study of their nature revealed they were electromagnetic waves. Although similar to light and radio waves, X-rays were determined by experiment to have a wavelength much shorter than that of visible light, in the order of m. Within a short period, scientists studying these new electromagnetic waves were able to reliably produce X-rays of a specific frequency.

A diffraction grating for visible light is a device for producing interference effects such as spectra. A grating consists of a large number of equidistant parallel lines engraved on a glass or metal surface. The distance between the lines is of the same order as the wavelength of the light. Note that the larger the number of slits on a grating, the sharper the image obtained. This is why a diffraction grating produces a well-separated pattern of narrow peaks.

• ## X-rays are electromagnetic radiation

X-rays are electromagnetic radiation with a wavelength of the order of m. Compare this with a wavelength of  m for green light in the middle of the visible spectrum. A standard optical diffraction grating cannot be used to discriminate between different wavelengths in the X-ray wavelength range as it can in the visible spectral range. An optical grating can split visible light up into a series of spectral lines or the rainbow of colours you are probably familiar with from earlier learning. The discrimination of different wavelengths in the X-ray range requires an instrument capable of measuring an angle of less than required for their diffraction.

In 1912, the German physicist Max Von Laue (1879-1960) proposed that the regular spacing of a crystal, such as sodium chloride, might form a natural three-dimensional ‘diffraction grating’ for X-rays. A crystal is a naturally occurring solid with a regular polyhedral shape. All crystals of the same substance grow so that they have the same angles between their faces. The atoms that make up the crystal have a regular arrangement called crystal lattice. This experiment was carried out by his colleagues, W. Friedrich and P. Knipping, who bombarded a crystal of zinc sulphide. They obtained a diffraction pattern on photographic film.

• ## The Braggs

British physicist Sir William Henry Bragg (1862-1942) and his Australian-born son Sir William Lawrence Bragg (1890-1971) developed an X-ray spectrometer to systematically study diffraction of X-rays from crystal surfaces. They proposed that X-rays, because of their short wavelength (in the order of the size of the atom,  m), could penetrate the surface of matter and ‘reflect’ from the atomic lattice planes within the crystals. When X-rays enter a crystal such as sodium chloride see the following figure, they are scattered (absorbed and re-emitted) in all directions.

• ## X-ray reflecting

In some directions the scattered waves undergo destructive interference, resulting in an intensity minimum; in other directions, the interference is constructive, resulting in an intensity maximum. This process of scattering and interference is a form of diffraction. The Braggs observed that the maxima occurred in specific directions. They concluded that the X-rays were reflected from the regularly spaced parallel planes of the crystal that were formed by the arrangement of atoms in the crystal lattice. This effect is shown in the following figure. For the first time, thanks to the work of the Braggs, it was possible to look at the arrangement of the atoms in a solid material.

• ## X-ray Diffraction

The work of W. L. Bragg provided a mathematical analysis of their experiments, deriving the relationship between the spacing of the crystal planes, the wavelength of the radiation and the angle of reflection. X-ray diffraction provides a tool for studying both X-ray spectra and the arrangement of atoms in a crystal.

To study spectra, a crystal is chosen with a known interplanar spacing, d. A detector is mounted on a device called a goniometer and can be rotated through a range of angles to measure the crystal rotation angles at which the maxima occur. A chart recorder produces a trace of X-ray intensity against rotation angle.