Allotropy or allotropism (from Ancient Greek ἄλλος (allos) 'other', and τρόπος (tropos) '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 the elements. Allotropes are different structural modifications of an element: the atoms of the element are bonded together in a different manner.[1] For example, the allotropes of carbon include diamond (the carbon atoms are bonded together to form a cubic lattice of tetrahedra), graphite (the carbon atoms are bonded together in sheets of a hexagonal lattice), graphene (single sheets of graphite), and fullerenes (the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations).

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

The term allotropy is used for elements only, not for compounds. The more general term, used for any compound, is polymorphism, although its use is usually restricted to solid materials such as crystals. Allotropy refers only to different forms of an element within the same physical phase (the state of matter, such as a solid, liquid or gas). The differences between these states of matter would not alone constitute examples of allotropy. Allotropes of chemical elements are frequently referred to as polymorphs or as phases of the element.

For some elements, allotropes have different molecular formulae or different crystalline structures, as well as a difference in physical phase; for example, two allotropes of oxygen (dioxygen, O2, and ozone, O3) can both exist in the solid, liquid and gaseous states. Other elements do not maintain distinct allotropes in different physical phases; for example, phosphorus has numerous solid allotropes, which all revert to the same P4 form when melted to the liquid state.


The concept of allotropy was originally proposed in 1840 by the Swedish scientist Baron Jöns Jakob Berzelius (1779–1848).[2][3] The term is derived from Greek άλλοτροπἱα (allotropia) 'variability, changeableness'.[4] After the acceptance of Avogadro's hypothesis in 1860, it was understood that elements could exist as polyatomic molecules, and two allotropes of oxygen were recognized as O2 and O3.[3] 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.[5][3] Although many other chemists have repeated this advice, IUPAC and most chemistry texts still favour the usage of allotrope and allotropy for elements only.[6]

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:


Element Allotropes
  • 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 structural 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, also known as "buckyballs", such as C60.
  • Carbon nanotubes – allotropes having a cylindrical nanostructure.
  • Schwarzites
  • Cyclocarbon
  • Glassy carbon
  • Superdense carbon allotropes – proposed allotropes
  • Cyclo-Pentasulfur, Cyclo-S5
  • Cyclo-Hexasulfur, Cyclo-S6
  • Cyclo-Heptasulfur, Cyclo-S7
  • Cyclo-Octasulfur, Cyclo-S8
  • "Red selenium," cyclo-Se8
  • Gray selenium, polymeric Se
  • Black selenium, irregular polymeric rings up to 1000 atoms long
  • Monoclinic selenium, dark red transparent crystals


Element Allotropes
  • 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
  • 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
  • Yellow arsenic – molecular non-metallic As4, with the same structure as white phosphorus
  • Gray arsenic, polymeric As (metalloid)
  • Black arsenic – molecular and non-metallic, with the same structure as red phosphorus
  • blue-white antimony – stable form (metalloid), with the same structure as gray arsenic
  • yellow antimony (non-metallic)
  • black antimony (non-metallic)
  • explosive antimony
  • amorphous tellurium – gray-black or brown powder[7]
  • crystalline tellurium – hexagonal crystalline structure (metalloid)


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 Phase name(s) Space group Pearson symbol Structure type Description
Lithium R3m hR9 α-Samarium structure Forms below 70 K.[8]
Im3m cI2 Body-centered cubic Stable at room temperature and pressure.
cF4 Face centered cubic Forms above 7GPa
hR1 An intermediate phase formed ~40GPa.
cI16 Forms above 40GPa.
Beryllium P63/mmc hP2 Hexagonal close packed Stable at room temperature and pressure.
Im3m cI2 Body centered cubic Forms above 1255 °C.
Sodium R3m hR9 α-Samarium structure Forms below 20 K.
Im3m cI2 Body centered cubic Stable at room temperature and pressure.
Fm3m cF4 Face centered cubic Forms at room temperature above 65 GPa.[9]
I43d cI16 Forms at room temperature, 108GPa.[10]
Pnma oP8 Forms at room temperature, 119GPa.[11]
Magnesium P63/mmc hP2 hexagonal close packed Stable at room temperature and pressure.
Im3m cI2 Body centered cubic Forms above 50 GPa.[12]
Tin α-tin, gray tin, tin pest Fd3m cF8 Diamond cubic Stable below 13.2 °C.
β-tin, white tin I41/amd tI4 β-Tin structure Stable at room temperature and pressure.
γ-tin, rhombic tin I4/mmm Body-centered tetragonal
σ-Sn Body-centered cubic Forms at very high pressure.[13]
Iron α-Fe, ferrite Im3m cI2 Body-centered cubic Stable at room temperature and pressure. Ferromagnetic at T<770 °C, paramagnetic from T=770–912 °C.
γ-iron, austenite Fm3m cF4 Face-centered cubic Stable from 912 to 1,394 °C.
δ-iron Im3m cI2 Body-centered cubic Stable from 1,394 – 1,538 °C, same structure as α-Fe.
ε-iron, Hexaferrum P63/mmc hP2 Hexagonal close-packed Stable at high pressures.
Cobalt α-Cobalt simple cubic Forms above 417 °C.
β-Cobalt hexagonal close packed Forms below 417 °C.
Polonium α-Polonium simple cubic
β-Polonium rhombohedral

Lanthanides and actinides

Phase diagram of the actinide elements.


In 2017, the concept of nanoallotropy was proposed by Prof. Rafal Klajn of the Organic Chemistry Department of the Weizmann Institute of Science.[15] Nanoallotropes, or allotropes of nanomaterials, are nanoporous materials that have the same chemical composition (e.g., Au), but differ in their architecture at the nanoscale (that is, on a scale 10 to 100 times the dimensions of individual atoms).[16] Such nanoallotropes may help create ultra-small electronic devices and find other industrial applications.[16] The different nanoscale architectures translate into different properties, as was demonstrated for surface-enhanced Raman scattering performed on several different nanoallotropes of gold.[15] A two-step method for generating nanoallotropes was also created.[16]

See also


  1. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006) "Allotrope". doi:10.1351/goldbook.A00243
  2. See:
    • Berzelius, Jac. (1841). Årsberättelse om Framstegen i Fysik och Kemi afgifven den 31 Mars 1840. Första delen [Annual Report on Progress in Physics and Chemistry submitted March 31, 1840. First part.] (in Swedish). Stockholm, Sweden: P.A. Norstedt & Söner. p. 14. From p. 14: "Om det ock passar väl för att uttrycka förhållandet emellan myrsyrad ethyloxid och ättiksyrad methyloxid, så är det icke passande för de olika tillstånd hos de enkla kropparne, hvari dessa blifva af skiljaktiga egenskaper, och torde för dem böra ersättas af en bättre vald benämning, t. ex. Allotropi (af αλλότροπος, som betyder: af olika beskaffenhet) eller allotropiskt tillstånd." (If it [i.e., the word isomer] is also well suited to express the relation between formic acid ethyl oxide [i.e., ethyl formate] and acetic acid methyloxide [i.e., methyl acetate], then it [i.e., the word isomers] is not suitable for different conditions of simple substances, where these [substances] transform to have different properties, and [therefore the word isomers] should be replaced, in their case, by a better chosen name; for example, Allotropy (from αλλότροπος, which means: of different nature) or allotropic condition.)
    • Republished in German: Berzelius, Jacob; Wöhler, F., trans. (1841). "Jahres-Bericht über die Fortschritte der physischen Wissenschaften" [Annual Report on Progress of the Physical Sciences]. Jahres Bericht Über die Fortschritte der Physischen Wissenschaften (in German). Tübingen, (Germany): Laupp'schen Buchhandlung. 20: 13. From p. 13: "Wenn es sich auch noch gut eignet, um das Verhältniss zwischen ameisensaurem Äthyloxyd und essigsaurem Methyloxyd auszudrücken, so ist es nicht passend für ungleiche Zustände bei Körpern, in welchen diese verschiedene Eigenschaften annehmen, und dürfte für diese durch eine besser gewählte Benennung zu ersetzen sein, z. B. durch Allotropie (von αλλότροπος, welches bedeutet: von ungleicher Beschaffenheit), oder durch allotropischen Zustand." (Even if it [i.e., the word isomer] is still well suited to express the relation between ethyl formate and methyl acetate, then it is not appropriate for the distinct conditions in the case of substances where these [substances] assume different properties, and for these, [the word isomer] may be replaced with a better chosen designation, e.g., with Allotropy (from αλλότροπος, which means: of distinct character), or with allotropic condition.)
    • Merriam-Webster online dictionary: Allotropy
  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.
  4. "allotropy", A New English Dictionary on Historical Principles, vol. 1, Oxford University Press, 1888, p. 238.
  5. Ostwald, Wilhelm; Taylor, W.W., trans. (1912). Outlines of General Chemistry (3rd ed.). London, England: Macmillan and Co., Ltd. p. 104. From p. 104: "Substances are known which exist not only in two, but even in three, four or five different solid forms; no limitation to the number is known to exist. Such substances are called polymorphous. The name allotropy is commonly employed in the same connexion, especially when the substance is an element. There is no real reason for making this distinction, and it is preferable to allow the second less common name to die out."
  6. Jensen 2006, citing Addison, W. E. The Allotropy of the Elements (Elsevier 1964) that many have repeated this advice.
  7. Raj, G. Advanced Inorganic Chemistry Vol-1. Krishna Prakashan. p. 1327. ISBN 9788187224037. Retrieved January 6, 2017.
  8. Overhauser, A. W. (1984-07-02). "Crystal Structure of Lithium at 4.2 K". Physical Review Letters. American Physical Society (APS). 53 (1): 64–65. Bibcode:1984PhRvL..53...64O. doi:10.1103/physrevlett.53.64. ISSN 0031-9007.
  9. Hanfland, M.; Loa, I.; Syassen, K. (2002-05-13). "Sodium under pressure: bcc to fcc structural transition and pressure-volume relation to 100 GPa". Physical Review B. American Physical Society (APS). 65 (18): 184109. Bibcode:2002PhRvB..65r4109H. doi:10.1103/physrevb.65.184109. ISSN 0163-1829.
  10. McMahon, M. I.; Gregoryanz, E.; Lundegaard, L. F.; Loa, I.; Guillaume, C.; Nelmes, R. J.; Kleppe, A. K.; Amboage, M.; Wilhelm, H.; Jephcoat, A. P. (2007-10-18). "Structure of sodium above 100 GPa by single-crystal x-ray diffraction". Proceedings of the National Academy of Sciences. 104 (44): 17297–17299. Bibcode:2007PNAS..10417297M. doi:10.1073/pnas.0709309104. ISSN 0027-8424. PMC 2077250. PMID 17947379.
  11. Gregoryanz, E.; Lundegaard, L. F.; McMahon, M. I.; Guillaume, C.; Nelmes, R. J.; Mezouar, M. (2008-05-23). "Structural Diversity of Sodium". Science. American Association for the Advancement of Science (AAAS). 320 (5879): 1054–1057. Bibcode:2008Sci...320.1054G. doi:10.1126/science.1155715. ISSN 0036-8075. PMID 18497293. S2CID 29596632.
  12. Olijnyk, H.; Holzapfel, W. B. (1985-04-01). "High-pressure structural phase transition in Mg". Physical Review B. American Physical Society (APS). 31 (7): 4682–4683. Bibcode:1985PhRvB..31.4682O. doi:10.1103/physrevb.31.4682. ISSN 0163-1829. PMID 9936412.
  13. 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. S2CID 120417927.
  14. Benedict, U.; Haire, R. G.; Peterson, J. R.; Itie, J. P. (1985). "Delocalisation of 5f electrons in curium metal under high pressure". Journal of Physics F: Metal Physics. 15 (2): L29–L35. Bibcode:1985JPhF...15L..29B. doi:10.1088/0305-4608/15/2/002.
  15. Udayabhaskararao, Thumu; Altantzis, Thomas; Houben, Lothar; Coronado-Puchau, Marc; Langer, Judith; Popovitz-Biro, Ronit; Liz-Marzán, Luis M.; Vuković, Lela; Král, Petr (2017-10-27). "Tunable porous nanoallotropes prepared by post-assembly etching of binary nanoparticle superlattices". Science. 358 (6362): 514–518. Bibcode:2017Sci...358..514U. doi:10.1126/science.aan6046. ISSN 0036-8075. PMID 29074773.
  16. "Materials That Don't Exist in Nature Might Lead to New Fabrication Techniques". Archived from the original on 2017-12-09. Retrieved 2017-12-08.


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