Xray diffraction

In certain situations we may use other sorts of 'light' to illuminate objects. X-rays have wavelengths of the order of 1000 times shorter than visible light, making it possible in principle to resolve much smaller objects.

Crystals as diffraction gratings

The German physicist Max Von Laue (1879-1960) was a very versatile scientist whose work and interests ranged over a wide field. In February 1912, his research student P.P. Ewald approached him for advice about crystal optics: 'But during the conversation I was suddenly struck by the obvious question of the behaviour of waves which are short by comparison with the lattice-constants of the space lattice. And it was at that point that my intuition for optics suddenly gave me the answer: lattice spectra would have to ensue. The fact that the lattice constant in a crystal is of an order of 10— cm was sufficiently known The order of X-ray wavelengths was estimated by Wien and Sommerfeld at 10~9 cm. Thus the ratio of wavelengths and lattice constants was extremely favourable if X-rays were to be transmitted through a crystal. I immediately told Ewald that I anticipated the occurrence of interference phenomena with X-rays'.

Von Laue continues his account: '.acknowledged masters of our science, Wilhem Wien and Arnold Sommerfeld, were sceptical. A certain amount of diplomacy was necessary before Walter Friedrich (1883-1968) and Paul Knipping (1883-1935) were finally permitted to carry out the experiment according to my plan, using very simple equipment at the outset/

The plan was successful beyond all expectations. The two research students observed interference patterns, just as Von Laue had predicted. It was now possible to see crystal structures using X-rays or light of wavelength comparable to the size of the molecules themselves. The 'seeing' is in terms of interference patterns which came directly as a result of reflections from individual atoms and molecules. For conceiving this groundbreaking work in X-ray crystallography, Von Laue was awarded the Nobel Prize for Physics in 1914.

* W. Friedrich and K. Knipping, research students.

X-ray diffraction pattern of a protein crystal. Courtesy of NASA-MSFC.

X-ray diffraction pattern of a protein crystal. Courtesy of NASA-MSFC.

A crystal is a diffraction grating with a difference. It is a three-dimensional arrangement of vast numbers of atoms, unlike the more traditional gratings used to diffract light. Each atom scatters incoming X-rays, giving complex diffraction patterns. Rock salt was the first crystal structure to be fully determined.

A crystal can be visualised as a stack of identical unit cells, something like a honeycomb. The basic atomic arrangement is duplicated in each cell and symmetries in the diffraction pattern reflect symmetries in the arrangement of atoms in the cell. No two crystals have exactly the same diffraction Unit cell. pattern; each has its own 'fingerprint' in the same way as a light-emitting atom.

The Laue pattern of spots was explained theoretically by the English physicist William Henry Bragg (1862-1942). He and his son Lawrence Bragg (1890-1971) jointly received the 1915 Nobel Prize for Physics for the use of X-rays to determine crystal structure. Lawrence, aged 25 at the time, is the youngest-ever Nobel laureate. The Braggs developed X-ray diffraction as a tool to systematically investigate crystal structures. They analysed reflections of X-rays from each one of the numerous atomic surfaces in crystals and were able to determine the internal structure with some precision.

Bragg's law

Bragg's law simplifies the mathematics of crystal diffraction by considering different sets of parallel planes of atoms and writing down the condition for constructive interference between X-rays reflected from them. The arrangement of atoms in each plane in Figure 8.16 looks similar to the arrangement of slits in an optical diffraction grating.

Path difference between the incoming and outgoing rays = AC + CB = 2d sin 0.

For constructive interference: 2d sin d = nX (similar to the condition for light).

Figure 8.16 Bragg's law.

The investigation of crystal structure using Bragg's law is by no means as straightforward as it might seem at first glance. The condition for constructive interference is simple enough but we have essentially replaced each slit by a unit cell and there may be many sets of parallel planes of atoms at different angles.

X-rays in medical science

X-rays were discovered by the German physicist Wilhelm Conrad Röntgen (1845-1923) in 1896. The very first Nobel

Prize for Physics was awarded to Röntgen in 1901 for the discovery of X-rays. He was the first person to use X-rays as a medical imaging tool. The stamp shows an X-ray image of his wife's hand, with a clear impression of a ring on the third finger. X-ray images of this kind are still extensively used for viewing bone structure.

X-ray diffraction techniques were used to disentangle the structure of the complex molecule deoxyribonucleic acid (DNA). The British postgraduate student Francis Harry Compton Röntgen Commemoration. Crick (1916-2004) and the American Courtesy of Egyptian Post. postdoctoral fellow in zoology James

Dewey Watson (1928-) believed DNA to be the primary factor in heredity. To establish this they needed to know how the molecule was able to replicate itself, store genetic information and mutate. Maurice Frederick Wilkins (1916-2004), a British bio-physicist, was the son of a physician, originally from Dublin. He worked in the biophysics unit at King's College, London. His X-ray diffraction studies of DNA were crucial to the determination of its molecular structure by Watson and Crick. For this work the three scientists were jointly awarded the Nobel Prize for Medicine in 1962.

Rosalind Elsie Franklin (1920-1958), a molecular biologist, made a vital contribution to the identification of DNA. She and Wilkins worked in the biophysics unit at King's College, London, and her X-ray diffraction photographs were key data. She died of cancer four years before the award of the Nobel Prize.

8.10.2 Electron diffraction

Optical microscopes are severely limited by diffraction and can only magnify up to about 2,000 times, at best. Electron with energies of 120 keV have a wavelength about 100,000 times smaller than the wavelength of red light so an electron microscope has much higher magnification than its optical counterpart.

Electron microscopes

To prevent the scattering of the electrons by air molecules, the microscope is enclosed in a metal cylinder maintained at a high vacum. The electron beam is focused by magnetic, rather than

James Dewey Watson. Courtesy of US National Library of Mecicine.

object c

Figure 8.17 Magnetic lens.

optical, lenses. A magnetic lens consists of a coil of copper wires mounted inside iron pole pieces. A current passing through the wires creates a magnetic field between the pole pieces (see Chapter 10).

The magnetic field is weakest along the axis as illustrated in Figure 8.17 so electrons close to the axis are less strongly deflected than those far from the axis. The overall effect is that a beam of parallel electrons is focused into a spot. The electrons in magnetic lenses are much less well behaved than light in optical lenses; they spiral in the magnetic field, so the image is rotated with respect to the object.

Transmission microscopes. Electrons penetrate even transparent materials to a very limited extent. Specimens used in transmission electron microscopy must be thin (between 10 and 200 nm) to be transparent to electrons and carefully prepared to withstand the high vaccum.

Reflection microscopes. The surface of a solid can be used to diffract electrons; it behaves rather like an optical reflection grating. The energies and intensities of the diffracted electrons reflect the atomic arrangement on the surface.

Electron microscope were first used in Material Science to examine structures at almost atomic levels. They are used extensively in Biological and Medical Sciences for the study of cells.

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