How it works : Crystal
CRYSTALS and CRYSTALLOGRAPHY
|Below: magnified view of Epsom salts crystals (MgSO4.7H2O). Although this shows many irregularities and imperfections in the crystal's structure there is a similarity in their general shape.|
All solid materials can be divided into two types-crystalline and amorphous. In crystalline structures the ATOMS or MOLECULES are ideally arranged in a regular ordered way (called a lattice), whereas in amorphous solids there is no recognizable order at all. In reality all materials possess some order although this may not extend for more than a few atoms, and most amorphous solids are in fact a jumble of tiny crystals.
For centuries man has been fascinated by the appearance of crystals, both in the way that they reflect and colour light and their perfectly regular geometric forms. The word 'crystal' is derived from the Greek for clear ice; later it was applied specifically to quartz which was known as 'rock crystal'. It is one of the enigmas of history that the Greeks, with their love of geometry and form, did not study the symmetry of naturally occurring minerals-and thus become the first crystallographers.
Atomic structure of crystals
To the scientist ice and quartz are just two examples of many hundreds of thousands of different types of solids which are recognizable as crystals.
Solids are generally more dense than liquids or gases. The reason for this is that the atoms or molecules are packed more closely together in solids. The distance between atoms in solids is usually comparable to the radii of the atoms and is a few tenths of a nanometre (one nanometre is a thousand millionth-10-9-of a metre).
There are several types of force, or BONDS, holding the atoms together. These include the ionic or electrovalent bond, the covalent bond, and the metallic bond. There is also van der Waal's force-a weak bond between molecules.
It is these bonds which largely determine the shape of the crystal and its physical properties such as colour, refractive index, electrical conductivity and thermal conductivity.
In the ionic bond, electrostatically charged atoms, called IONS, are held together in a regular array with the attractions between opposite charges being balanced by the repulsions between like charges. This arrangement usually leads to a simple structure such as the cubic arrangement of sodium chloride (common salt).
Covalent bonds are characterized by the sharing of electrons between neutral atoms. Because of this, covalent bonded atoms are orientated in preferred directions and these determine the shape of the crystal. For example, the DIAMOND crystal is based on covalent bonded CARBON atoms where each atom has four neighbouring carbon atoms surrounding it in a tetrahedral configuration.
METALS are based on the metallic bond. In this, the lattice of positive metal ions is neutralized by a surrounding cloud of electrons. The electrons are free to move throughout the lattice and give rise to the high optical reflectivity and to the electrical and thermal conductivities characteristic of metals.
Van der Waal's bonding is a weak form of attraction and is the type usually associated with liquids and gases. The bonds are formed between transient dipoles (temporary pairs of opposite charges) resulting from disturbances in the electron clouds surrounding atoms and molecules. This type of bonding is found in some organic crystals.
An interesting example of van der Waal's bonding occurs in graphite, another form of carbon. Covalent bonded sheets (planes) of carbon atoms are loosely held together by van der Waal's forces. These weak bonds allow the planes to slide over each other-hence the good lubricating properties of graphite. Furthermore, the atoms in the sheets are arranged in a close hexagonal structure which allows good electrical conduction along the sheets, but the sheets are too far apart (in atomic terms) to allow conduction in the direction perpendicular to the sheets.
In all crystalline solids the atoms or molecules are not rigidly held hut vibrate in equilibrium with their neighbours. As the temperature of a crystal is raised the vibration increases until it overcomes the cohesive forces, the lattice then breaks up and the crystal melts. In general, the materials with the strongest bonds have the highest melting points. Diamond is the hardest natural crystalline substance known to man and melts at 3700oC (6692oF).
|Above: crystallographers indicate 4-fold rotational axis of symmetry with a square, a 3-fold axis with a triangle and a 2-fold axis with a 'cigar' shape. Common salt is a cubic structure with several of each.||Above: a scanning electron micrograph of a common salt crystal(x800 magnification). Even in small quantities the cubic crystal structure is recognisable and this structure continues down to the atomic level.|
Periodic structures and unit cells
Throughout the universe there are millions of different chemical compounds and yet they are all created from a limited number of basic elements put together in certain arrangements (there are 92 natural and 14 artificial elements that had been produced by 1974). Similarly, although there are a large number of different crystal shapes, they can all be created from 14 elementary groupings of atoms, called unit cells.
These unit cells 'are the indivisible units, or 'building blocks', from which all crystals can be constructed. Furthermore, by grouping these unit cells into larger units, certain repetitive or periodic arrangements are possible. It is the periodic structures of crystals which give rise to their characteristic geometrical shapes, and in particular, properties of symmetry.
Some crystals tend to break along well defined planes to form beautifully flat surfaces called cleavage faces. These correspond to prominent planes of atoms within the crystal structure. Other crystalline materials, however, neither break along cleavage planes nor show any outward signs of symmetry. Metals, for example, are crystalline and so are most forms of stone, cement and brick. Many plastics, especially those which make good fibres, are also crystalline. Natural polymers-bone, muscle, hair and tendons-contain regular (periodic) arrangements of molecules and are correspondingly crystalline, although they do not show the same degree of symmetry as, say, certain minerals.
It is rare for perfect crystals to exist naturally: they are normally found in a mass of small imperfect shapes and each crystal contains internal defects such as impurities and 'dislocations' or faults in the crystal lattice. Those crystals which do exist in near perfection, such as diamonds, must be cut to show the crystal faces of the gems to their full effect.
The science of crystallography developed in the last century and stemmed from the study of external shapes of minerals and crystals which were classified on the basis of their symmetry.
Symmetry is a property which enables a crystal to be rotated or reflected in a certain way but then still appear exactly as it did before. Common salt crystals, for example, can be seen under a microscope to be small cubes, and several symmetry elements or components can be identified on a cube.
The three axes which pass through the centres of its faces are examples of four-fold rotation axes of symmetry, or tetrads for short. The cube appears unchanged in orientation after any rotation of 90o about one of these axes. Similarly, there are 4 three-fold axes (triads) emerging from the corners of the cube and 6 two-fold axes (diads) from the centres of the edges.
It is also possible to recognize planes, as well as axes, of symmetry in a crystal. These are imaginary surfaces dividing the crystal into two parts, each the mirror image of the other. With a cube, there are three such planes parallel to each pair of opposite cube faces and six further symmetry planes which divide the cube diagonally.
In the example of the cube all the rotation axes and mirror planes have one point common to all-at the centre of the cube-and together these are known as a point group of symmetry elements. A cubic crystal of common salt, because it contains so many symmetry elements, is said to have high symmetry. Other types of crystal are not so well endowed. Tartaric acid, for example, has only one diad (two-fold axis), whereas copper sulphate has neither rotation axis nor mirror planes.
There are 32 different classes of crystal symmetry or point groups. These point groups define all the ways in which different elements of crystallographic symmetry can be distributed about a single point in space. These 32 classes are divided into seven crystal systems, each characterized by their geometrical shapes, dictated by the angles between the sides of the unit cell and the relative lengths of the sides. For each of these seven systems there is one simple, or primitive, unit cell which describes the basic shape of that system. These primitive cells consist of only 8 atoms-one at each corner of the unit cell. There are seven other unit cells, which make up the total of 4 possible types of unit cell (building blocks). These are based on the primitive cells but with extra atoms in the faces of the cell (face centred) or in the centre of the cell (body centred).
This rather theoretical description of crystal shapes, using unit cells, axes and planes of symmetry, point groups or classes and crystal systems, has been found to be extremely helpful in determining the atomic structure of a substance under investigation.
Determining crystal structure
Distinguishing between crystals is often difficult as their external structure may be irregular, belying the internal symmetry. To probe deeper into the crystal a crystallographer will often use X-ray techniques.
|Above: X-ray diffraction photograph of common salt looking directly at one cube face. The 4-fold rotation symmetry shown by the pattern of spots indicates that the atoms are also packed in a cubic arrangement.|
In 1912 von Laue first suggested that the interference pattern (see WAVE MOTION) produced by a beam of light passing through a screen containing a regular pattern of holes is an analogous phenomenon to the diffraction of X-rays by the atoms of a solid. When an electron in an atom is subjected to a beam of X-rays,which have a wavelength comparable to the interatomic distance, it is forced to vibrate at the same frequency as the beam. This produces an acceleration in the electron's motion, which in turn gives rise to radiation of the same wavelength as the initial X-ray beam (see ELECTRO MAGNETIC RADIATION). All the electrons in any one atom will be contributing radiation in this fashion, thereby creating a series of wavelets from the single initial wave. These wavelets will in general be out of phase with each other, creating an interference pattern.
W L Bragg in later years treated the problem not by diffraction but by reflection from successive planes in the crystal. Considering two planes of the crystal, the incident beam reflected from the deeper layer in the crystal will have to travel further than a beam reflected from the layer nearer the surface. If this additional distance is equal to either an integral (whole number: 1, 2, 3 and so on) or half-integral (1½,2½ and so on) number of wavelengths, then the beams will reinforce or cancel each other respectively, again creating an interference pattern.
|Left: model showing the positions of atom centres in
a zinc crystal. This is called a hexagonal close packed(HCP) structure.
Right: from the external shape, symmetry and X-ray diffraction of common salt crystals, an atomic model can be constructed. In an actual crystal the sodium and chlorine ions are like close packed spheres.
These interference patterns are recorded on photographic film and angles of scattering are calculated. From these the distance between lattice planes may be determined and the crystal identified. There is an inherent uncertainty in this and often models of structures will be built to see whether it is physically possible to arrange atoms in a particular way.
Crystallization occurs from a solution, molten salt or vapour. The crystal grows by the addition of new material until an equilibrium is reached when the rate of deposition of material equals the rate at which the crystal is dissolved into the surrounding medium. Crystallization normally takes place when a concentrated solution or melt is cooled. In some cases it is necessary to 'seed' the solution with a minute particle of the solid. This particle forms the nucleus around which crystals grow. It is possible to seed crystal formation with a seed of another material: for example, silver iodide (AgI) is used to seed the formation of ice in clouds to promote rain.
Industrial crystallization for the production of crystals such as those of washing soda is carried out in a multistage process. A hot concentrated solution is cooled and purified through a layer of seed crystals which grow and reduce the concentration of the solution. The depleted solution is recycled until maximum crystallization has occurred, and the crystals are removed when they are large enough. In the case of the sugar industry, sugar syrup is heated under vacuum until it becomes supersaturated and deposits crystals around seeds. Heating under vacuum reduces the operating temperature and minimizes discoloration due to decomposition of the sugar syrup.
There is a demand for large single crystals of certain materials. These can be made by slow cooling of a crucible full of molten material. Another method widely used for the production of materials for electronic and optical applications is crystal pulling. In this process a small seed crystal is dipped into melted material and is then withdrawn slowly into a cool zone. The solid grows as a long thin single crystal. One advantage of this method is that impurities tend to stay behind in the melt. Further purification can be achieved by zone refining in this process a molten zone is moved along the specimen taking with it many of the impurities which can be isolated at one end of the single crystal.
|Above: iron pyrites is a naturally occurring ore containing iron sulphide crystals. The regular crystal shapes can be easily seen.|
It is possible for a material to exist in more than one crystal shape: for example, gypsum (CaSO4.2H2O) exists in a wide variety of shapes including plates and rods; it is the interlocking of gypsum rods which give strength to plaster and plaster of Paris. The crystal shape depends upon the temperature at which the crystals were formed and upon the speed of their formation. Impurities can also change crystal shapes and colours: for example, alumina (Al2O3) is white but alumina with traces of chromium and iron oxides becomes the deep red gemstone ruby; traces of titania (TiO2) give the blue gemstone sapphire. Alumina, ruby and sapphire are, apart from the impurities, the same chemically but different in colour and shape.
It is usually considered that fluids have no ordered structure; however, certain liquids known as LIQUID CRYSTALS do exhibit alignment of the molecules under certain conditions. These are used in a number of applications including digital displays in electronic calculators.
Reproduced from HOW IT WORKS p684