The term 'allotropes' - from the Greek allos, other, and tropos, manner - was coined by Jöns Jakob Berzelius and pertains to different forms of the same element that have different structures whilst being in the same state. Allotropes of the same element give rise to identical chemical compounds. For most allotropes, in each form the atoms are arranged differently in space. However, in the case of iron (see below) the alpha and beta forms differ in the orientation of electronic spin.

Allotropy is a specific form of polymorphism, which is the existence of a substance in more than one crystal form. The different crystal structures are known as polymorphs. The term polymorphism is applied to compounds as well as to elements.

The prevailing crystal structure depends on both the temperature and the external pressure, and perhaps the most familiar example of this occurs with diamond and graphite - both allotropes of carbon. Here, graphite is the stable allotrope at ambient conditions, whereas diamond is formed only at extremely high pressures.

Elements exhibiting allotropy can be found almost anywhere in the Periodic Table , although they are particularly common in Group 4. Thus carbon, the first member of the Group, exists as diamond , graphite, lonsdaleite, C₆₀ (buckminsterfullerene) and the more recently discovered linear acetylenic carbon (LAC). It is of interest to note that, of these allotropes, diamond is the hardest natural substance known to man, whilst graphite is amongst the softest, hence its use in pencils .

The following is not intended to be an exhaustive list of elements and allotropes; it just includes some of the more familiar examples of elements that have allotropes.

Group 4 Elements: Allotropy of Carbon

Diamond and Graphite

Carbon has been known since prehistoric times in the form of charcoal and soot. Indeed, its very name derives from the Latin carbo, for 'charcoal'.

At first sight, diamond and graphite don't appear to be at all similar, and yet both are forms of pure carbon. There are no other elements present. That graphite is pure carbon was discovered by the Swedish chemist, CW Scheele in 1779, while the English chemist, Smithson Tennant, showed that diamond is also a form of carbon in 1796.

The equivalence of diamond and graphite may be proved by burning equal masses of each in excess oxygen, when the same mass of carbon dioxide is formed from each, but there are no other products formed. Interestingly, carbon's position in the periodic table is just above the stepped diagonal line that separates the metals from the non-metals. Elements on either side of this line are semi-conductors and are classed as 'metalloids'. Diamond is often referred to as being a non-conductor but is on the borderline of the arbitrary value that separates insulators from semi-conductors. It is, in fact, a 'wide band-gap' semiconductor¹. Graphite, on the other hand, has no band gap and is a sufficiently good conductor to be considered a 'poor' metal, having a conductivity some 1,000 times lower than copper.

Diamond

In diamond each carbon atom forms a molecular (covalent) bond to four other carbon atoms, which are at the corners of a regular tetrahedron. These four carbon atoms are, in turn, covalently bonded to four other carbon atoms arranged likewise, and so on. This bonding occurs throughout the whole of crystal, so that the whole structure is one giant molecule - called a macromolecule. When all the atoms in a crystal are covalently bonded one to another throughout the whole structure, the solid is called a network solid.

Diamond is a transparent solid, which is a non-conductor of electricity. Because the carbon-to-carbon single bonds in diamond are very strong, diamond is the hardest natural substance known to man, and has a very high melting point (3823K).

Graphite

Graphite is also a network solid, but here the carbon atoms are arranged in flat sheets in which each atom is covalently linked to three other carbon atoms in a trigonal planar arrangement. Hence this is represented as sheets of hexagons of carbon atoms, built up in layers. As the carbon atom has four outer shell electrons, the fourth outer electron of each carbon atom resides between the layers and is mobile (free to move throughout the structure) and so graphite can conduct electricity². This fact was first discovered by Joseph Priestley. The mobile electrons also account for the shiny appearance of graphite, which is comparable to the lustre of metals.

The mobile electrons between the layers are also responsible for weak attractive forces between the layers, called London dispersion forces, which allow the layers to slide over each other easily. Graphite therefore has a slippery feel, has lubricant properties and is therefore often used as an additive in 'penetrating oil' and as the 'lead' in pencils. Soot consists of small particles of graphite.

Lonsdaleite

A lesser-known allotrope of carbon is lonsdaleite, also known as 'hexagonal diamond'. It is transparent and brownish-yellow in colour, and is believed to be formed when meteoritic graphite falls to Earth. The intense heat and stress of the impact is believed to transform the graphite into diamond, whilst retaining graphite's hexagonal crystal lattice. Lonsdaleite was first identified from 'Meteor Crater' in Arizona in 1967; but has also been identified in other meteorites, including the Allan Hills A77283 meteorite from Antarctica and the Tunguska impact site, Russia. Lonsdaleite has a Moh's hardness of 7-8, compared to 10 for diamond.

Linear Acetylenic Carbon (LAC)

Chemists in the USA have recently reported (ca 1995) an allotrope of carbon consisting of long chains of carbon atoms where the alternate carbon-carbon bonds are of different lengths; and consist of C-C bonds and C≡C bonds.

Carbon Nanoclusters - The Buckminsterfullerenes

Unlike diamond and graphite, which have been known for centuries, buckminsterfullerene was only discovered in 1985. This allotrope has the molecular formula C₆₀.

The structure of buckminsterfullerene resembles the geodesic dome designed by the American architect Buckminster Fuller, for Expo 67 in Montreal, hence its name. The carbon atoms are arranged into pentagons and hexagons, there being 20 hexagons and 12 pentagons arranged as are the panels in the modern football. This has given rise to the popular name of 'bucky balls'.

Buckminsterfullerene is a dark solid at ambient temperatures and dissolves in organic solvents such as benzene, where it gives a reddish brown solution, and chlorobenzene, where the colour of the solution is purple.

It is possible to fuse two or more molecules of C₆₀ to form closed cylindrical structures known as nanotubes. It is further possible to open these tubes and fill them with a variety of atoms, ions and molecules, including biological molecules; and thus perform chemical reactions within them. Such structures are known as nano test-tubes. It has also been found that nanotube structures have remarkable absorptive and catalytic properties, and that they can be used as components of fuel cells.

Since the discovery of buckminsterfullerene and nanotubes, there has been much research into their properties, including potential applications in the fields of lubrication, electric cells, semi- and superconductors and biosensors.

The three discoverers of buckminsterfullerene, Harry Kroto, Richard Smalley and Robert Curl were jointly awarded the Nobel Prize for Chemistry in 1996.

Group 4 Elements: Tin

Tin exists in three crystalline (allotropic) forms known as grey tin (alpha-tin), white tin (beta tin), which is the ordinary form of tin and rhombic (gamma) tin, which is also metallic.

Grey tin is stable below 13°C, has a Relative Density of 5.75 and a diamond-like lattice.

White tin, the familiar form of tin, is stable between 13°C and 161°C, has a Relative Density of 7.28 and a tetragonal lattice. White tin is a soft, silvery-white metal. When one bends pure white tin, its crystalline structure is ruptured, making it give out a noise known as 'tin cry'.

Rhombic (or gamma) tin is stable between 161 and 232°C, at which temperature it melts. This has a density of 6.56 and a rhombic lattice.

Below 13°C, tin metal slowly changes to the powdery alpha allotrope, and so the metal crumbles, the phenomenon being known as 'tin disease' or 'tin pest'.

Group 5 Elements: Phosphorus

Phosphorus is an excellent example of an element that exhibits allotropy, as its various allotropes have strikingly different properties.

The two most common allotropes are white phosphorus and 'red' phosphorus³. A third form, scarlet phosphorus, is obtained by allowing a solution of white phosphorus in carbon disulphide to evaporate in sunlight. A fourth allotrope, black phosphorus, is obtained by heating white phosphorus under very high pressures (12,000 atmospheres) In appearance, properties and structure it is very like graphite, being black and flaky, a conductor of electricity and has puckered sheets of linked atoms.

White Phosphorus

White phosphorus is a soft, white wax-like solid, with an appreciable vapour pressure at ordinary temperatures. The vapour density indicates that the vapour is composed of P₄ molecules up to about 800°C. Above that temperature, dissociation into P₂ molecules occurs. The P₄ molecule is tetrahedral, with each phosphorus atom being at the apices of the tetrahedron.

It ignites spontaneously at about 50°C, and at much lower temperatures if finely divided. White phosphorus is only slightly soluble in water and, indeed, it can be stored under water. However, it is soluble in benzene, oils, carbon disulphide and sulphur monochloride. The Relative Molecular Mass in solution corresponds to that expected for P₄ molecules.

White phosphorus is chemically very reactive, and will spontaneously ignite in an abundant supply of air to give phosphorus (V) oxide:

P₄ + 5O₂ > P₄O₁₀

Red Phosphorus

This is much less reactive than white phosphorus, as evidenced by:

P _white > P _violetΔ H = -16.8J

It does not ignite in air until heated to 300°C, and it is insoluble in water, alkali and carbon disulphide. It does not react so readily with the halogens, but can be oxidised by nitric acid to phosphoric acid.

If it is heated in an atmosphere of inert gas, for example nitrogen or carbon dioxide, it sublimes and the vapour condenses as white phosphorus. If, however, it is heated in a vacuum and the vapour condensed rapidly, violet phosphorus is obtained. It would appear that violet phosphorus is a polymer of high Relative Molecular Mass, which on heating breaks down into P₂ molecules. On cooling, these would normally dimerize to give P₄ molecules (i.e. white phosphorus) but, in vacuo, they link up again to form the polymeric violet allotrope.

Group 5 Elements: Arsenic

Like phosphorus, arsenic exists in several allotropic modifications. The ordinary form is grey arsenic, which is a solid with a metallic lustre, is brittle and exhibits some electrical conductivity. On heating it sublimes at 600°C, giving a yellow vapour consisting of As₄ molecules. Above 800°C it begins to break down into diatomic As₂ molecules. Rapid cooling of the vapour produces yellow arsenic, a wax-like solid of much lower density than the grey form.. Yellow arsenic is soluble in carbon disulphide and is easily oxidised. When burned in oxygen, it luminesces similarly to white phosphorus. On warming, yellow arsenic is easily re-converted to grey arsenic, although an intermediate form, black arsenic is sometimes observed.

Group 6 Elements: Oxygen

Oxygen can exist either as diatomic molecules in oxygen gas, O₂ ('di-oxygen') or as the triatomic ozone, O₃.

Oxygen itself is a colourless gas with a boiling point of -183°C. It can be condensed out of air by cooling with liquid nitrogen, which has a boiling point of -196°C. Liquid oxygen is pale blue in colour, and is quite markedly paramagnetic : liquid oxygen contained in a flask suspended by a string is attracted to a magnet.

Ozone is a pale blue gas condensable to a dark blue liquid. It is formed whenever air is subjected to an electrical discharge, and has the characteristic pungent odour of new-mown hay, or for those living in urban environments, of sub-ways - the so-called 'electrical odour'.

Electrical discharges cause di-oxygen to split into oxygen radicals. Most of these recombine to form di-oxygen, but a few react with di-oxygen to give ozone:

O₂ + O. > O₃

The ozone molecules themselves can also react with oxygen free radicals, to reform di-oxygen, and so the actual concentration of atmospheric ozone is quite small. It is believed that ozone is formed in the upper atmosphere by the photo-dissociation of di-oxygen by the intense ultra-violet radiation from the Sun. This light energy is thus absorbed, otherwise it would reach the Earth and destroy all life forms quite rapidly. Ozone is a greenhouse gas and, as such, would contribute to global warming if present in the lower atmosphere.

A fourth allotrope of oxygen, tetraoxygen (O₄) , whose existence had been suspected since the early 1900's when it was known as oxozone , was identified in 2001 by a team led by F.Cacace at the University of Rome. It is a deep red solid and is formed by pressurizing O₂ to around 20 GPa. Its properties are being investigated for potential use in rocket fuels , as it is a much more powerful oxidising agent than either O₂ or O₃. Liquid di-oxygen , known as LOX, is already used in rocket fuels as it reacts energetically with fuels such as hydrogen and hydrocarbons; and O₄ is likely to be even more energy-dense.

Cacace's team think that O₄ probably consists of two dumbbell-like O₂ molecules that are loosely associated together.

Group 6 Elements: Sulphur

Sulphur exists in several allotropic forms. The familiar stable yellow form that exists at ordinary temperature (ie below 370K) is rhombic sulphur, also known as α- sulphur. This exists as crown-shaped S₈ rings, which are able to stack up on top of each other. Rhombic sulphur is soluble in carbon disulphide and has a density of 2.06.

If this is melted gently, partly allowed to solidify, and the mother liquor poured off, there remain long, needle-like crystals of monoclinic (or β)-sulphur, where the crystals are almost colourless. This also consists of S₈ rings but has a density of 1.96. This is stable between 370 and 395K.

S_α↔ S_β (Transition temperature = 370K)

Enantiotropism

The existence of a substance in two physical forms, one being stable below a certain temperature (the transition temperature), the other above it.

When α-sulphur is melted at 388K, the viscosity and the colour changes as the temperature is raised. This is because, firstly the rings separate one from another, to give an orange colour, the form of sulphur being known as S-lambda. Above 433K the rings open to form spiral chains of S-mu, which are able to slide over one another. These chains then link up to make longer chains containing about 100,000 sulphur atoms and, at this stage, the colour is a deeper red. The polymeric nature of molten sulphur may be recognised if molten sulphur is poured in a thin stream into cold water, when a plastic rubbery product is obtained, known as plastic sulphur or S-mu.

Plastic sulphur has a helical structure with eight atoms per spiral. It is only slightly soluble in carbon disulphide but, on standing it rapidly loses its plasticity and reverts to the soluble rhombic sulphur.

Transition Elements: Iron

Iron represents perhaps the best-known example for allotropy.

There are four allotropic forms of iron, known as alpha, beta, gamma, and delta. As molten iron cools down it crystallises at 1535°C into its delta allotrope, which has a body-centred cubic (BCC) crystal structure. As it cools further its crystal structure changes to face centred cubic (FCC) at 1401°C, when it is known as gamma-iron, or austenite. At 912°C the crystal structure again becomes BCC as beta-iron⁴ is formed, and at 770°C (the Curie point, T_c ) the iron becomes magnetic as alpha-iron, also known as ferrite, which is also BCC, is formed. Thus there is no change in crystalline structure, but there is a change in 'domain structure', where each domain contains iron atoms with a particular electronic spin. In unmagnetised iron, all the electronic spins of the atoms within one domain are in the same direction. However, in neighbouring domains they point in various directions and thus cancel out. In magnetised iron, the electronic spins of all the domains are all aligned, so that the magnetic effects of neighbouring domains reinforce each other. Although each domain contains billions of atoms, they are very small, about one thousandth of a centimetre across.

Iron, of course, is of most importance when mixed with certain other metals and with carbon to form steels. There are many types of steels, all with different properties; and an understanding of the properties of the allotropes of iron is key to the manufacture of good quality steels.

Alpha iron, also known as ferrite, is the most stable form of iron at normal temperatures. It is a fairly soft metal that can dissolve only a small concentration of carbon (no more than 0.021% by mass at 910 °C).

Above 912°C and up to 1401°C alpha iron undergoes a phase transition from body-centred cubic to the face-centred cubic configuration of gamma iron, also called austenite. This is similarly soft and metallic but can dissolve considerably more carbon (as much as 2.04% by mass at 1146°C). This form of iron is used in the type of stainless steel used for making cutlery, and hospital and food-service equipment.