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Allotropy

Property of some chemical elements to exist in two or more different forms

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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 different manners. 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).

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, i.e. plasmas, gases, liquids, or solids). 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.

Comparison of Isomerism, Allotropy, and Polymorphism
Feature	Isomerism (Isomers)	Allotropy (Allotropes)	Polymorphism (Polymorphs)
Core Concept	Molecules with identical molecular formulas but distinct structural arrangements or spatial orientations.	Distinct structural modifications of a single element within the same physical state.	The capacity of a solid compound or element to manifest in multiple distinct crystal lattices.
Scope of Applicability	Compounds and molecules (organic and inorganic).	Elements exclusively.	Crystalline solids (elements, ionic salts, or molecular solids).
Structural Variation	Variations in chemical bonding, atom connectivity, or three-dimensional spatial geometry.	Variations in bonding patterns, molecular formulas, or crystal structures of an element.	Variations in the packing arrangements or space groups of atoms or molecules in a solid.
Chemical Properties	Significant variances in reactivity and functionality (e.g., ethanol versus dimethyl ether).	Marked divergence in chemical reactivity (e.g., the inertness of diamond versus the reactivity of graphite).	Identity in liquid or gaseous phases; minor variations in solid-state surface reactivity.
Physical Properties	Variances in boiling points, melting points, and densities.	Radical divergence in characteristics (e.g., the transparency and hardness of diamond versus the opacity and softness of graphite).	Distinct variations in solubility, hardness, density, and melting points.
Physical State	Gas, liquid, and solid phases.	Predominantly solid phases, with occurrences in liquid and gas phases (e.g., dioxygen versus ozone gas).	Crystalline solids exclusively.
Primary Mechanism	Alternative modes of atomic linkage, functional group placement, or molecular rotation.	Alternative modes of homonuclear bonding and molecular aggregation.	Thermodynamic variations in temperature and pressure during the process of crystallization.
Examples	Butane and isobutane Ethanol and dimethyl ether	Carbon allotropes: Diamond, graphite, graphene, and fullerenes Oxygen allotropes: Dioxygen and ozone	Calcium carbonate forms: Calcite and aragonite Titanium dioxide forms: Rutile, anatase, and brookite Carbon systems: Diamond and graphite (classified concurrently as allotropes and polymorphs)

01History

The concept of allotropy was originally proposed in 1840 by the Swedish scientist Baron Jöns Jakob Berzelius (Swedish: [jœ̌ns ˈjɑ̂ːkɔb bæˈʂěːlɪɵs]; 1779-1848). The term is derived from Greek άλλοτροπἱα (allotropia) 'variability, changeableness'. 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. 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. Although many other chemists have repeated this advice, IUPAC and most chemistry texts still favour the usage of allotrope and allotropy for elements only.

02Differences 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 semimetallic 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).

03List 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 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 semimetallic, soft, black, flaky solid, a good 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
Nitrogen	Dinitrogen, by far the most common and stable form of nitrogen, found in the air. Hexazine Hexanitrogen Octaazacubane Tetranitrogen Trinitrogen Solid nitrogen
Phosphorus	White phosphorus, crystalline solid of tetraphosphorus (P₄) molecules Red phosphorus, amorphous polymeric solid Scarlet phosphorus Violet phosphorus with monoclinic crystalline structure Black phosphorus, semiconductor, analogous to graphite Diphosphorus, gaseous form composed of P₂ molecules, stable between 1200 °C and 2000 °C; created e.g. by dissociation of P₄ molecules of white phosphorus at around 827 °C
Oxygen	Dioxygen, O₂, colorless (faint blue liquid and solid) Ozone, O₃, blue Tetraoxygen, O₄, metastable Octaoxygen, O₈, red
Sulfur	Cyclo-Pentasulfur, Cyclo-S₅ Cyclo-Hexasulfur, Cyclo-S₆ Cyclo-Heptasulfur, Cyclo-S₇ Cyclo-Octasulfur, Cyclo-S₈
Selenium	"Red selenium", cyclo-Se₈ Gray selenium, polymeric Se Black selenium, irregular polymeric rings up to 1000 atoms long Monoclinic selenium, dark red transparent crystals
Spin isomers of hydrogen	Orthohydrogen, H₂ with nuclear spins aligned parallel Parahydrogen, H₂ with nuclear spins aligned antiparallel These nuclear spin isomers have sometimes been described as allotropes, notably by the committee which awarded the 1932 Nobel prize to Werner Heisenberg for quantum mechanics and singled out the "allotropic forms of hydrogen" as its most notable application.

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 Cubic boron High-pressure superconducting phase Borophene Borospherene, B₄₀
Silicon	Amorphous silicon α-silicon, a semiconductor, diamond cubic structure β-silicon - metallic, with the BCC similar to molybdenum and beta-tin (High Pressure Phase) Q-Silicon - a ferromagnetic (Similar to Q-Carbon) and highly conductive phase of silicon (similar to graphite) Silicene, buckled planar single layer Silicon, similar to Graphene
Germanium	Amorphous germanium α-germanium, semimetallic element or semiconductor, with the same structure as diamond (similar chemical properties with sulfur and silicon) β-germanium, metallic, with the same structure as beta-tin Germanene, Buckled planar Germanium, similar to graphene
Arsenic	Yellow arsenic, molecular non-metallic As₄, with the same structure as white phosphorus (Similar chemical properties with nitrogen and phosphorus) Gray arsenic, polymeric As (metallic, though heavily anisotropic) (similar to aluminum and antimony in chemical properties) Black arsenic, molecular and non-metallic, with the same structure as red phosphorus
Antimony	Blue-white antimony, stable form (metallic), with the same structure as gray arsenic (similar to arsenic in chemical properties) Black antimony (non-metallic and amorphous, only stable as a thin layer)
Tellurium	Amorphous tellurium, gray-black or brown powder Crystalline tellurium, hexagonal crystalline structure (metalloid) (similar chemical properties with selenium)

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 1,394 °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	α-Li	R3m	hR9	α-Sm	Forms below 70 K.
	β-Li	Im3m	cI2	W	Stable at room temperature and pressure.
		Fm3m	cF4	Cu	Forms above 7GPa
		R3m	hR1	α-Hg	An intermediate phase formed ~40GPa.
		I43d	cI16		Forms above 40GPa.
			oC88		Forms between 60 and 70 GPa.
			oC40		Forms between 70 and 95 GPa.
			oC24		Forms above 95 GPa.
Beryllium	α-Be	P6₃/mmc	hP2	Mg	Stable at room temperature and pressure.
Beryllium	β-Be	Im3m	cI2	W	Forms above 1255 °C.
Sodium	α-Na	R3m	hR9	α-Sm	Forms below 20 K.
	β-Na	Im3m	cI2	W	Stable at room temperature and pressure.
		Fm3m	cF4	Cu	Forms at room temperature above 65 GPa.
		I43d	cI16		Forms at room temperature, 108GPa.
		Pnma	oP8	MnP	Forms at room temperature, 119GPa.
			tI19*		A host-guest structure that forms above between 125 and 180 GPa.
			hP4		Forms above 180 GPa.
Magnesium		P6₃/mmc	hP2	Mg	Stable at room temperature and pressure.
Magnesium		Im3m	cI2	W	Forms above 50 GPa.
Aluminium	α-Al	Fm3m	cF4	Cu	Stable at room temperature and pressure.
Aluminium	β-Al	P6₃/mmc	hP2	Mg	Forms above 20.5 GPa.
Potassium		Im3m	cI2	W	Stable at room temperature and pressure.
		Fm3m	cF4	Cu	Forms above 11.7 GPa.
		I4/mcm	tI19*		A host-guest structure that forms at about 20 GPa.
		P6₃/mmc	hP4	NiAs	Forms above 25 GPa.
		Pnma	oP8	MnP	Forms above 58GPa.
		I4₁/amd	tI4		Forms above 112 GPa.
		Cmca	oC16		Formas above 112 GPa.
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			hexagonal-close packed	Forms below 450 °C.
	β-Cobalt			face centered cubic	Forms above 450 °C.
	ε-Cobalt	P4₁32		primitive cubic	Forms from thermal decomposition of [Co₂CO₈]. Nanoallotrope.
Rubidium	α-Rb	Im3m	cI2	W	Stable at room temperature and pressure.
			cF4		Forms above 7 GPa.
			oC52		Forms above 13 GPa.
			tI19*		Forms above 17 GPa.
			tI4		Forms above 20 GPa.
			oC16		Forms above 48 GPa.
Tin	α-tin, gray tin, tin pest	Fd3m	cF8	d-C	Stable below 13.2 °C.
	β-tin, white tin	I4₁/amd	tI4	β-Sn	Stable at room temperature and pressure.
	γ-tin, rhombic tin	I4/mmm	tI2	In	Forms above 10 GPa.
	γ'-Sn	Immm	oI2	MoPt₂	Forms above 30 GPa.
	σ-Sn, γ"-Sn	Im3m	cI2	W	Forms above 41 GPa. Forms at very high pressure.
	δ-Sn	P6₃/mmc	hP2	Mg	Forms above 157 GPa.
	Stanene
Polonium	α-Polonium			simple cubic
Polonium	β-Polonium			rhombohedral

Most stable structure under standard conditions.
Structures stable below room temperature.
Structures stable above room temperature.
Structures stable above atmospheric pressure.

Lanthanides and actinides

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.

04Nanoallotropes

In 2017, the concept of nanoallotropy was proposed. 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). Such nanoallotropes may help create ultra-small electronic devices and find other industrial applications. The different nanoscale architectures translate into different properties, as was demonstrated for surface-enhanced Raman scattering performed on several different nanoallotropes of gold. A two-step method for generating nanoallotropes was also created.

Watch videos about AllotropyExplainers and documentaries on YouTube (opens in a new tab)

Sources and credits

This article is adapted from the Wikipedia article “Allotropy”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

Images, from Wikimedia Commons:

Diamond and graphite.jpg by User:Itub, CC BY-SA 3.0
Jöns Jacob Berzelius.png by Olof Johan Södermark (1790-1848). Print Artist: Charles W. Sharpe, d. 1875(76). Per [2], Public domain
Actinide phases.svg by James L. Smith, LANL., Public domain

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