Allotropy

Allotropy or allotropism 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, graphite, graphene, and fullerenes.
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 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 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.

History

The concept of allotropy was originally proposed in 1840 by the Swedish scientist Baron Jöns Jakob Berzelius. The term is derived. 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.

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 to a face-centered cubic structure above 906 °C, and tin undergoes a modification known as tin pest from a metallic form to a semimetallic form below 13.2 °C. As an example of allotropes having different chemical behaviour, ozone is a much stronger oxidizing agent than dioxygen.

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

Metalloids

Metals

Among the metallic elements that occur in nature in significant quantities, almost half 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	Space group	Pearson symbol	Structure type	Description
Lithium	α-Li	Rm	hR9	α-Sm	Forms below 70 K.
Lithium	β-Li	Imm	cI2	W	Stable at room temperature and pressure.
Lithium		Fmm	cF4	Cu	Forms above 7GPa
Lithium		Rm	hR1	α-Hg	An intermediate phase formed ~40GPa.
Lithium		I3d	cI16		Forms above 40GPa.
Lithium			oC88		Forms between 60 and 70 GPa.
Lithium			oC40		Forms between 70 and 95 GPa.
Lithium			oC24		Forms above 95 GPa.
Beryllium	α-Be	P6₃/mmc	hP2	Mg	Stable at room temperature and pressure.
Beryllium	β-Be	Imm	cI2	W	Forms above 1255 °C.
Sodium	α-Na	Rm	hR9	α-Sm	Forms below 20 K.
Sodium	β-Na	Imm	cI2	W	Stable at room temperature and pressure.
Sodium		Fmm	cF4	Cu	Forms at room temperature above 65 GPa.
Sodium		I3d	cI16		Forms at room temperature, 108GPa.
Sodium		Pnma	oP8	MnP	Forms at room temperature, 119GPa.
Sodium			tI19*		A host-guest structure that forms above between 125 and 180 GPa.
Sodium			hP4		Forms above 180 GPa.
Magnesium		P6₃/mmc	hP2	Mg	Stable at room temperature and pressure.
Magnesium		Imm	cI2	W	Forms above 50 GPa.
Aluminium	α-Al	Fmm	cF4	Cu	Stable at room temperature and pressure.
Aluminium	β-Al	P6₃/mmc	hP2	Mg	Forms above 20.5 GPa.
Potassium		Imm	cI2	W	Stable at room temperature and pressure.
Potassium		Fmm	cF4	Cu	Forms above 11.7 GPa.
Potassium		I4/mcm	tI19*		A host-guest structure that forms at about 20 GPa.
Potassium		P6₃/mmc	hP4	NiAs	Forms above 25 GPa.
Potassium		Pnma	oP8	MnP	Forms above 58GPa.
Potassium		I4₁/amd	tI4		Forms above 112 GPa.
Potassium		Cmca	oC16		Formas above 112 GPa.
Iron	α-Fe, ferrite	Imm	cI2	Body-centered cubic	Stable at room temperature and pressure. Ferromagnetic at T<770 °C, paramagnetic from T=770–912 °C.
Iron	γ-iron, austenite	Fmm	cF4	Face-centered cubic	Stable from 912 to 1,394 °C.
Iron	δ-iron	Imm	cI2	Body-centered cubic	Stable from 1,394 – 1,538 °C, same structure as α-Fe.
Iron	ε-iron, Hexaferrum	P6₃/mmc	hP2	Hexagonal close-packed	Stable at high pressures.
Cobalt	α-Cobalt			hexagonal-close packed	Forms below 450 °C.
Cobalt	β-Cobalt			face centered cubic	Forms above 450 °C.
Cobalt	ε-Cobalt	P4₁32		primitive cubic	Forms from thermal decomposition of . Nanoallotrope.
Rubidium	α-Rb	Imm	cI2	W	Stable at room temperature and pressure.
Rubidium			cF4		Forms above 7 GPa.
Rubidium			oC52		Forms above 13 GPa.
Rubidium			tI19*		Forms above 17 GPa.
Rubidium			tI4		Forms above 20 GPa.
Rubidium			oC16		Forms above 48 GPa.
Tin	α-tin, gray tin, tin pest	Fdm	cF8	d-C	Stable below 13.2 °C.
Tin	β-tin, white tin	I4₁/amd	tI4	β-Sn	Stable at room temperature and pressure.
Tin	γ-tin, rhombic tin	I4/mmm	tI2	In	Forms above 10 GPa.
Tin	γ'-Sn	Immm	oI2	MoPt₂	Forms above 30 GPa.
Tin	σ-Sn, γ"-Sn	Imm	cI2	W	Forms above 41 GPa. Forms at very high pressure.
Tin	δ-Sn	P6₃/mmc	hP2	Mg	Forms above 157 GPa.
Tin	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. 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.