Allotropy

Allotropy, or allotropism, describes how certain chemical elements can appear in multiple distinct forms while remaining in the same state of matter. These forms are called allotropes, and they result from different ways the element's atoms are bonded together structurally. For instance, carbon's allotropes include diamond, where atoms form a cubic lattice of tetrahedra; graphite, with atoms arranged in hexagonal sheets; graphene, which is a single sheet of graphite; and fullerenes, where atoms form spherical, tubular, or ellipsoidal shapes.

The term "allotropy" applies only to elements, not compounds. The broader term for compounds is polymorphism, though it is mostly used for solid crystals. Allotropy specifically concerns different forms within the same physical phase—solid, liquid, gas, or plasma—so simply changing between these states does not count as allotropy. Allotropes are sometimes called polymorphs or phases of an element.

Some elements have allotropes with different molecular formulas or crystal structures, and these can exist in multiple physical phases. Oxygen, for example, has two allotropes: dioxygen (O₂) and ozone (O₃), both of which can be solid, liquid, or gas. Other elements, like phosphorus, have many solid allotropes but revert to a single P₄ form when melted into a liquid.

The concept of allotropy was first proposed in 1840 by Swedish scientist Jöns Jakob Berzelius. After Avogadro's hypothesis was accepted in 1860, it became clear that elements could form polyatomic molecules, leading to the recognition of oxygen's two allotropes. By the early 1900s, cases like carbon were understood as differences in crystal structure. In 1912, Wilhelm Ostwald argued that allotropy is just a special case of polymorphism and suggested dropping the terms "allotrope" and "allotropy" in favor of "polymorph" and "polymorphism." Though many chemists have agreed, IUPAC and most chemistry texts still use the original terms for elements only.

Allotropes of the same element can have very different physical properties and chemical behaviors. Transitions between allotropic forms are driven by pressure, light, or temperature, so the stability of a given allotrope depends on conditions. For example, iron shifts from a body-centered cubic structure (ferrite) to a face-centered cubic structure (austenite) above 906 °C, and tin changes from a metallic to a semimetallic form below 13.2 °C in a process called tin pest. Chemically, ozone is a much stronger oxidizing agent than dioxygen.

Elements that can vary their coordination number or oxidation state, or that readily form chains (catenate), tend to have more allotropes. Examples span non-metals, metalloids, and metals. Among the 56 naturally occurring metallic elements (up to uranium, excluding technetium and promethium), 27 are allotropic at ambient pressure: lithium, beryllium, sodium, calcium, titanium, manganese, iron, cobalt, strontium, yttrium, zirconium, tin, lanthanum, cerium, praseodymium, neodymium, samarium, gadolinium, terbium, dysprosium, ytterbium, hafnium, thallium, thorium, protactinium, and uranium. Key phase transitions for technologically important metals include titanium at 882 °C, iron at 912 °C and 1,394 °C, cobalt at 422 °C, zirconium at 863 °C, tin at 13 °C, and uranium at 668 °C and 776 °C.

Among the lanthanides and actinides, cerium, samarium, dysprosium, and ytterbium each have three allotropes. Praseodymium, neodymium, gadolinium, and terbium have two. Plutonium has six distinct solid allotropes at normal pressures, with densities varying by about 4:3, complicating casting, machining, and storage; a seventh allotrope exists at very high pressures. Neptunium, americium, and curium are also allotropic, while promethium, americium, berkelium, and californium each have three allotropes.

In 2017, the concept of nanoallotropy was introduced. Nanoallotropes are nanoporous materials with the same chemical composition (such as gold) but different architectures at the nanoscale—roughly 10 to 100 times the size of individual atoms. These different architectures lead to different properties, as shown in surface-enhanced Raman scattering experiments on various gold nanoallotropes. A two-step method for creating nanoallotropes has also been developed.