Allotropes are different forms of the same element. Different bonding arrangements between atoms result in different structures with different chemical and physical properties. Allotropes occur only with certain elements, in Groups 13 through 16 in the Periodic Table. This distribution of allotropic elements is illustrated in Figure 1.
Boron (B), the second hardest element, is the only allotropic element in Group 13. It is second only to carbon (C) in its ability to form element bonded networks. Thus, in addition to amorphous boron, several different allotropes of boron are known, of which three are well characterized. These are red crystalline α -rhombohedral boron, black crystalline β -rhombohedral boron (the most thermodynamically stable allotrope), and black crystalline β -tetragonal boron. All are polymeric and are based on various modes of condensation of the B 12 icosahedron (Figure 2).
In Group 14, only carbon and tin exist as allotropes under normal conditions. For most of recorded history, the only known allotropes of carbon were diamond and graphite. Both are polymeric solids. Diamond forms hard, clear, colorless crystals, and was the first element to have its structure determined by x-ray diffraction. It has the highest melting point and is the hardest of the naturally occurring solids. Graphite, the most thermodynamically stable form of carbon, is a dark gray, waxy solid, used extensively as a lubricant. It also comprises the "lead" in pencils.
The diamond lattice (Figure 3a) contains tetrahedral carbon atoms in an infinite three-dimensional network. Graphite is also an infinite three-dimensional network, but it is made up of planar offset layers of trigonal carbons forming fused hexagonal rings (Figure 3b). The C-C bonds within
a layer are shorter than those of diamond, and are much shorter than the separation between the graphite layers. The weak, nonbonding, interaction between the layers, allowing them to easily slide over each other, accounts for the lubricating properties of graphite.
Diamond and graphite are nonmolecular allotropes of carbon. A range of molecular allotropes of carbon (the fullerenes) has been known since the discovery in 1985 of C 60 (Figure 4). The sixty carbon atoms approximate a sphere of condensed five- and six-membered rings. Although initially found in the laboratory, fullerenes have since been shown to occur in nature at low concentrations. C 60 and C 70 are generally the most abundant and readily isolated fullerenes.
In 1991 carbon nanotubes were discovered. They are more flexible and stronger than commercially available carbon fibers, and can be conductors or semiconductors. Although the mechanism of their formation has not been determined, they can be thought of as the result of "rolling up" a section of a graphite sheet and capping the ends with a hemisphere of C 60 , C 70 , or another molecular allotrope fragment. Five- or seven-membered rings can be incorporated among the six-membered rings, leading to an almost infinite range of helical, toroidal, and corkscrew-shaped tubes, all with different mechanical strengths and conductivities.
Tin is a relatively low melting (232°C) material that exists in two allotropic forms at room temperature and pressure, α -Sn (gray tin) and β -Sn (white tin). α -Sn is the stable form below 13°C and has the diamond structure (Figure 3a). White, or β -Sn is metallic and has a distorted close-packed lattice.
There are two allotropic elements in Group 15, phosphorus and arsenic . Phosphorus exists in several allotropic forms. The main ones (and those from which the others are derived) are white, red, and black (the thermodynamically stable form at room temperature). Only white and red phosphorus are of industrial importance. Phosphorus was first produced as the common white phosphorus, which is the most volatile , most reactive, and most toxic, but the least thermodynamically stable form of phosphorus, α -P 4 . It coverts to a polymorphic form, β -P 4 , at −76.9°C. White phosphorus is a waxy, nonconductor and reacts with air—the phosphorescent reaction of oxygen with the vapor above the solid producing the yellow-green chemiluminescent light, which gives phosphorus its name (after the Greek god, Eosphoros, the morning star, the bringer of light). The phosphorus in commercial use is amorphous red phosphorus, produced by heating white phosphorus in the absence of air at about 300°C. It melts around 600°C and was long thought to contain polymers formed by breaking a P-P bond of each P 4 tetrahedron of white phosphorus then linking the "opened" tetrahedra (Figures 5a and 5b).
A variety of crystalline modifications (tetragonal red, triclinic red, cubic red), possibly with similar polymeric structures can also be prepared by heating amorphous red phosphorus at over 500°C.
The most thermodynamically stable, and least reactive, form of phosphorus is black phosphorus, which exists as three crystalline (orthorhombic-, rhombohedral- and metallic, or cubic) and one amorphous, allotrope. All are polymeric solids and are practically nonflammable. Both orthorhombic and rhombohedral phosphorus appear black and graphitic, consistent with their layered structures.
A violet crystalline allotrope, monoclinic phosphorus, or Hittorf's phosphorus, after its discoverer, can be produced by a complicated thermal and electrolytic procedure. The structure is very complex, consisting of tubes of
pentagonal cross section joined in pairs to form double layers, which are repeated through the crystal. The tubes are formed from cagelike P 8 and P 9 groups, linked by P 2 units.
At least six forms of solid arsenic have been reported, of which three are amorphous. The most stable and most common form of arsenic at room temperature is a brittle, steel-gray solid ( α -As) with a structure analogous to that of rhombohedral black phosphorus. Arsenic vapor contains tetrahedral As 4 molecules, which are thought to be present in the yellow unstable arsenic formed by condensation of the vapor. Arsenic occurs naturally as α -As and also as the mineral arsenolamprite, which may have the same structure as orthorhombic black phosphorus.
There are only three allotropic elements in Group 16, oxygen, sulfur, and selenium. Only two oxygen allotropes are known—dinuclear "oxygen" (dioxygen, O 2 ) and trinuclear ozone (O 3 ) (Figure 6). Both are gases at room temperature and pressure. Dioxygen exists as a diradical (contains two unpaired electrons) and is the only allotrope of any element with unpaired electrons. Liquid and solid dioxygen are both pale blue because the absorption of light excites the molecule to a higher energy (and much more reactive) electronic state in which all electrons are paired ("singlet" oxygen). Gaseous dioxygen is probably also blue, but the low concentration of the species in the gas phase makes it difficult to observe.
Ozone is a V-shaped, triatomic dark blue gaseous molecule with a bond order of 1½. It is usually prepared from dioxygen by electric discharge (e.g., lightning) and can be detected by its characteristic "sharp" smell—from which it gets its name (after the Greek ozein : to smell). Ozone is thermodynamically unstable and reverts spontaneously to dioxygen.
The dark blue color of O 3 is important because it arises from the intense absorption of red and ultraviolet (UV) light. This is the mechanism by which ozone in the atmosphere (the ozone layer) protects Earth from the Sun's UV radiation. After F 2 , ozone is the most powerful oxidant of all the elements.
Sulfur (S) is second only to carbon in the number of known allotropes formed. The existence of at least twenty-two sulfur allotropes has been demonstrated. The simplest allotrope of sulfur is the violet disulfur molecule, S 2 , analogous to the dioxygen molecule. Unlike O 2 , however, S 2 does not occur naturally at room temperature and pressure. It is commonly generated in the vapor generated from sulfur at temperatures above 700°C. It has been detected by the Hubble Space Telescope in volcanic eruptions on Jupiter's satellite, Io.
The most thermodynamically stable of all of the sulfur allotropes and the form in which sulfur ordinarily exists is orthorhombic sulfur, α -S 8 , cyclooctasulfur, which contains puckered eight-membered rings, in which each sulfur atom is two-coordinate (Figure 7).
The second allotrope of sulfur to be discovered was cyclohexasulfur (sometimes called rhombohedral sulfur), first reported in 1891. It is the densest of the sulfur allotropes and forms air-sensitive orange-red crystals containing chair-shaped, six-membered rings. Sulfur forms an extensive series of generally yellow crystalline allotropes, S n (where species with n up to 30 have been identified). The color of liquid sulfur changes from pale yellow to orange, then red and finally to black, near the boiling point (445°C). At about 159°C, the viscosity increases as polymeric sulfur is formed. The liquid is thought to contain chains of sulfur atoms, wound into helices.
Selenium (Se) also exists in several allotropic forms—gray (trigonal) selenium (containing Se n helical chain polymers), rhombohedral selenium (containing Se 6 molecules), three deep-red monoclinic forms— α -, β -, and γ -selenium (containing Se 8 molecules), amorphous red selenium, and black vitreous selenium, the form in industrial usage. The most thermodynamically stable and the densest form is gray (trigonal) selenium, which contains infinite helical chains of selenium atoms. All other forms revert to gray selenium on warming. In keeping with its density, gray selenium is regarded as metallic, and it is the only form of selenium that conducts electricity. A slight distortion of the helical structure would produce a cubic metallic lattice.
The trend from nonmetallic to metallic character upon going down the group is exemplified by the conductivities of these elements. Sulfur is an insulator, selenium and tellurium are semiconductors, while the conductivity of polonium is typical of a true metal . In addition, the conductivities of sulfur, selenium, and tellurium increase with increasing temperature, behavior typical of nonmetals, whereas that of polonium increases at lower temperatures, typical of metals.
SEE ALSO Arsenic ; Boron ; Carbon ; Fullerenes ; Oxygen ; Ozone ; Phosphorus ; Selenium ; Sulfur ; Tin .
Anthony F. Masters
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