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Order, regularity and symmetry attract
admiration in art, architecture and in the natural world. Of course,
disorder and chaos characterise many types of physical entities; and the
second law of thermodynamics formulates in precise and quantitative terms
the evolution of all systems towards states of increasing disorder. But
many natural objects are ordered and symmetric. Crystals have long been
an object of fascination to the layman and to the scientist (especially
so when rarity adds value, as in gemstones). Typical real crystals
are characterised by regular shapes, smooth
faces and sharp, well defined angles between the faces. We are also often
interested and intrigued by the optical properties of crystals - their
colour (or, as in diamond, their high refractive index which causes light
to be reflected internally and results in the special glitter and brilliance
of the stone); and mechanical behaviour, like the exceptional hardness
of diamond, are another stimulant to our curiosity. The starting point
of our enquiry in this section is, however, their special geometrical properties
of regularity and symmetry. In particular, we will enquire whether the
regularity of the external appearance of crystals is reflected in their atomic
architectures.
The structure of diamond.
The first clue to this puzzle comes from
the experiment of Davidson. We recall how the wave-like
properties of the electron were apparent from the results of shining a
beam of electrons on a thin metal foil. The electron beam was 'diffracted'
on passing through the foil, thereby showing both that the beam was behaving
like a wave and that the arrangements of atoms in the foil was regular.
Electrons interact strongly with matter; they can pass through, forexample,
very thin films, but cannot penetrate into the bulk of normal crystals.
In contrast, another form of radiation, X-rays, (discovered , we will remember,
by Röntgen in 1895 and which we now know is simply a form of electromagnetic
radiation, like light but with a much shorter wavelength) will penetrate
below the surfaces of solids. And the science of crystallography - the
determination of the arrangements of atoms in crystals - was founded in
1912 by Lawrence Bragg, who discovered that crystals diffract X-rays.
The only interpretation of this observation is that crystals consist of
regular ordered arrangements of atoms which act as a diffraction grating;
and by analysing the diffraction pattern, we can learn about the atomic
arrangements in the crystal.
Metal crystal structures.
A crystal structure consists essentially
of a 'pattern' of atoms (often referred to as the unit cell) which is repeated
regularly and indefinitely in three dimensions, as shown in the images on
the left.
The pattern may be extremely simple, and in the limiting case may comprise
just one atom, as in the crystal structures of many metals; structures
in which the repeat pattern contains two atoms
include sodium chloride (rocksalt) also shown on the left.
The structure of sodium chloride or rocksalt.
The pattern of atoms in magnesium oxide, MgO, which adopts the same structure as rocksalt
The other extremes are the crystals of viruses where the repeat unit
is the whole virus containing hundreds of thousands of atoms. Yet, in one
of the most remarkable achievements of recent crystallography, the crystal
structures of viruses have been determined. The image on the left
shows the structure of the 'foot and mouth disease' virus
determined by David Stuart and coworkers.
So for these, the simplest of living things, we now know
to a reasonable degree of accuracy the positions of all the atoms
in their outer coats. This knowledge allows the design of
anti-viral molecules which interact with the virus and interfere
with the machinery of its protein armour.
The structure of a virus.
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