Allotropy

Not to be confused with Allotrophy.

Diamond and graphite are two allotropes of carbon: pure forms of the same element that differ in crystalline structure.

Allotropy or allotropism (from Greek ἄλλος (allos), meaning "other", and τρόπος (tropos), meaning "manner, form") is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of these elements. Allotropes are different structural modifications of an element;^[1] the atoms of the element are bonded together in a different manner. For example, the allotropes of carbon include diamond (where the carbon atoms are bonded together in a tetrahedral lattice arrangement), graphite (where the carbon atoms are bonded together in sheets of a hexagonal lattice), graphene (single sheets of graphite), and fullerenes (where the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations). The term allotropy is used for elements only, not for compounds. The more general term, used for any crystalline material, is polymorphism. Allotropy refers only to different forms of an element within the same phase (i.e. different solid, liquid or gas forms); these different states are not, themselves, considered to be examples of allotropy.

For some elements, allotropes have different molecular formulae which can persist in different phases – for example, two allotropes of oxygen (dioxygen, O₂, and ozone, O₃), can both exist in the solid, liquid and gaseous states. Conversely, some elements do not maintain distinct allotropes in different phases – for example phosphorus has numerous solid allotropes, which all revert to the same P₄ form when melted to the liquid state.

History

The concepts of allotropy was originally proposed in 1841 by the Swedish scientist Baron Jöns Jakob Berzelius (1779–1848).^[2] The term is derived from the Greek άλλοτροπἱα (allotropia; variability, changeableness).^[3] After the acceptance of Avogadro's hypothesis in 1860 it was understood that elements could exist as polyatomic molecules, and the two allotropes of oxygen were recognized as O₂ and O₃.^[2] In the early 20th century it was recognized that other cases such as carbon were due to differences in crystal structure.

By 1912, Ostwald noted that the allotropy of elements is just a special case of the phenomenon of polymorphism known for compounds, and proposed that the terms allotrope and allotropy be abandoned and replaced by polymorph and polymorphism.^[2] Although many other chemists have repeated this advice, IUPAC and most chemistry texts still favour the usage of allotrope and allotropy for elements only.^[4]

Differences in properties of an element's allotropes

Allotropes are different structural forms of the same element and can exhibit quite different physical properties and chemical behaviours. The change between allotropic forms is triggered by the same forces that affect other structures, i.e. pressure, light, and temperature. Therefore, the stability of the particular allotropes depends on particular conditions. For instance, iron changes from a body-centered cubic structure (ferrite) to a face-centered cubic structure (austenite) above 906 °C, and tin undergoes a modification known as tin pest from a metallic form to a semiconductor form below 13.2 °C (55.8 °F). As an example of allotropes having different chemical behaviour, ozone (O₃) is a much stronger oxidizing agent than dioxygen (O₂).

List of allotropes

Typically, elements capable of variable coordination number and/or oxidation states tend to exhibit greater numbers of allotropic forms. Another contributing factor is the ability of an element to catenate.

Examples of allotropes include:

Non-metals

Element	Allotropes
Carbon	Diamond – an extremely hard, transparent crystal, with the carbon atoms arranged in a tetrahedral lattice. A poor electrical conductor. An excellent thermal conductor. Lonsdaleite – also called hexagonal diamond. Graphene - is the basic stuctural element of other allotropes, nanotubes, charcoal, and fullerenes. Q-carbon – a ferromagnetic, tough, and brilliant crystal structure that is harder and brighter than diamonds. Graphite – a soft, black, flaky solid, a moderate electrical conductor. The C atoms are bonded in flat hexagonal lattices (graphene), which are then layered in sheets. Linear acetylenic carbon (Carbyne) Amorphous carbon Fullerenes, including Buckminsterfullerene, a.k.a. "buckyballs", such as C₆₀. Carbon nanotubes – allotropes of carbon with a cylindrical nanostructure.
Phosphorus	White phosphorus – crystalline solid P₄ Red phosphorus – polymeric solid Scarlet phosphorus Violet phosphorus Black phosphorus – semiconductor, analogous to graphite Diphosphorus
Oxygen	Dioxygen, O₂ – colorless (faint blue) Ozone, O₃ – blue Tetraoxygen, O₄ – metastable Octaoxygen, O₈ – red
Sulfur	Sulfur has a large number of allotropes, second only to carbon
Selenium	"Red selenium," cyclo-Se₈ Gray selenium, polymeric Se Black selenium, irregular polymeric rings up to 1000 atoms long

Metalloids

Element	Allotropes
Boron	Amorphous boron – brown powder – B₁₂ regular icosahedra α-rhombohedral boron β-rhombohedral boron γ-orthorhombic boron α-tetragonal boron β-tetragonal boron High-pressure superconducting phase
Silicon	Amorphous silicon crystalline silicon, Diamond cubic structure Silicene, buckled planar single layer Silicon, similar to graphene
Arsenic	Yellow arsenic – molecular non-metallic As₄, with the same structure as white phopshorus Gray arsenic, polymeric As (metalloid) Black arsenic – molecular and non-metallic, with the same structure as red phosphorus
Germanium	α-germanium – semimetallic, with the same structure as diamond β-germanium – metallic, with the same structure as beta-tin Germanene - Buckled planar Germanium, similar to graphene
Antimony	blue-white antimony – stable form (metalloid), with the same structure as gray arsenic yellow antimony (non-metallic) black antimony (non-metallic) explosive antimony
Tellurium	amorphous tellurium - gray-black or brown powder^[5] crystalline tellurium - hexagonal crystalline structure (metalloid)

Metals

Among the metallic elements that occur in nature in significant quantities (56 up to U, without Tc and Pm), almost half (27) are allotropic at ambient pressure: Li, Be, Na, Ca, Ti, Mn, Fe, Co, Sr, Y, Zr, Sn, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Yb, Hf, Tl, Th, Pa and U. Some phase transitions between allotropic forms of technologically relevant metals are those of Ti at 882 °C, Fe at 912 °C and 1394 °C, Co at 422 °C, Zr at 863 °C, Sn at 13 °C and U at 668 °C and 776 °C.

Element	Allotropes
Tin	grey tin (alpha tin, Tin pest) white tin (beta tin) rhombic tin (gamma tin) sigma tin (forms at very high pressure)^[6]
Iron	ferrite (α-iron): the ferromagnetic form at T < 770 °C (the Curie point, T_C); BCC crystal structure β-iron: T = 770 – 912 °C; the paramagnetic form of α-iron; same structure as α austenite (γ-iron): 912 – 1,394 °C; FCC crystal structure δ-iron: 1,394 – 1,538 °C; forms from cooling down molten iron; same structure as α ε-iron (also called hexaferrum): forms at high pressures; HCP crystal structure
Cobalt	α-cobalt – forms above 417 °C simple cubic (metallic) β-cobalt – forms below 417 °C hexagonal close packed (hcp) (metallic)
Polonium	α-polonium – simple cubic (metallic) β-polonium – rhombohedral (metallic)

Lanthanides and actinides

Phase diagram of the actinide elements.

Cerium, samarium, dysprosium and ytterbium have three allotropes.
Praseodymium, neodymium, gadolinium and terbium have two allotropes.
Plutonium has six distinct solid allotropes under "normal" pressures. Their densities vary within a ratio of some 4:3, which vastly complicates all kinds of work with the metal (particularly casting, machining, and storage). A seventh plutonium allotrope exists at very high pressures. The transuranium metals Np, Am, and Cm are also allotropic.
Promethium, americium, berkelium and californium have three allotropes each.^[7]

Notes

↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Allotrope".
1 2 3 Jensen, W. B. (2006), "The Origin of the Term Allotrope", J. Chem. Educ., 83 (6): 838–39, Bibcode:2006JChEd..83..838J, doi:10.1021/ed083p838 .
↑ "allotropy", A New English Dictionary on Historical Principles, 1, Oxford University Press, 1888, p. 238 .
↑ Jensen 2006, citing Addison, W. E. The Allotropy of the Elements (Elsevier 1964) that many have repeated this advice.
↑ https://books.google.co.uk/books?id=0uwDTrxyaB8C&pg=PA1327&lpg=PA1327&dq=tellurium+allotrope+amorphous+powder&source=bl&ots=yDVTfXiKKs&sig=zm-XatQQhaC1rBtAo7N2JwXuv9c&hl=en&sa=X&ved=0CEsQ6AEwBmoVChMI77Puq7ySxgIViDsUCh10cQBq#v=onepage&q=tellurium%20allotrope%20amorphous%20powder&f=false
↑ Molodets, A. M.; Nabatov, S. S. (2000). "Thermodynamic Potentials, Diagram of State, and Phase Transitions of Tin on Shock Compression". High Temperature. 38 (5): 715–721. doi:10.1007/BF02755923.
↑ http://www.iop.org/EJ/article/0305-4608/15/2/002/jfv15i2pL29.pdf?request-id=AFlRqDDL3BGhbarg2wi7Kg

References

Chisholm, Hugh, ed. (1911). "Allotropy". Encyclopædia Britannica (11th ed.). Cambridge University Press.

External links

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