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

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.[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).

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.

History

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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

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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).

List of allotropes

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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

[edit]
Element Allotropes
Carbon
Nitrogen
Phosphorus
Oxygen
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.[7]

Metalloids

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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
  • 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) [8]
  • 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[9]
  • Crystalline tellurium – hexagonal crystalline structure (metalloid) (similar chemical properties with selenium)

Metals

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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.[10]
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.[11]
I43d cI16 Forms above 40GPa.[11]
oC88 Forms between 60 and 70 GPa.[12]
oC40 Forms between 70 and 95 GPa.[12]
oC24 Forms above 95 GPa.[12]
Beryllium α-Be P63/mmc hP2 Mg Stable at room temperature and pressure.
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.[13]
I43d cI16 Forms at room temperature, 108GPa.[14]
Pnma oP8 MnP Forms at room temperature, 119GPa.[15]
tI19* A host-guest structure that forms above between 125 and 180 GPa.[12]
hP4 Forms above 180 GPa.[12]
Magnesium P63/mmc hP2 Mg Stable at room temperature and pressure.
Im3m cI2 W Forms above 50 GPa.[16]
Aluminium α-Al Fm3m cF4 Cu Stable at room temperature and pressure.
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.[12]
I4/mcm tI19* A host-guest structure that forms at about 20 GPa.[12]
P63/mmc hP4 NiAs Forms above 25 GPa.[12]
Pnma oP8 MnP Forms above 58GPa.[12]
I41/amd tI4 Forms above 112 GPa.[12]
Cmca oC16 Formas above 112 GPa.[12]
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[17] 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.[12]
oC52 Forms above 13 GPa.[12]
tI19* Forms above 17 GPa.[12]
tI4 Forms above 20 GPa.[12]
oC16 Forms above 48 GPa.[12]
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.[18]
γ'-Sn Immm oI2 MoPt2 Forms above 30 GPa.[18]
σ-Sn, γ"-Sn Im3m cI2 W Forms above 41 GPa.[18] Forms at very high pressure.[19]
δ-Sn P63/mmc hP2 Mg Forms above 157 GPa.[18]
Stanene
Polonium α-Polonium simple cubic
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

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Phase diagram of the actinide elements.

Nanoallotropes

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In 2017, the concept of nanoallotropy was proposed.[21] 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).[22] Such nanoallotropes may help create ultra-small electronic devices and find other industrial applications.[22] The different nanoscale architectures translate into different properties, as was demonstrated for surface-enhanced Raman scattering performed on several different nanoallotropes of gold.[21] A two-step method for generating nanoallotropes was also created.[22]

See also

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Notes

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References

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[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Allotropy

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Allotropy is the property exhibited by certain chemical elements to exist in two or more distinct structural forms, known as allotropes, within the same physical state, such as , , or gas, where the forms differ primarily in the arrangement of atoms and resulting physical properties while sharing the same . These allotropes arise due to variations in bonding and crystal structures, often influenced by environmental factors like and , leading to significant differences in characteristics such as , conductivity, and . A classic example of allotropy is observed in carbon, which manifests as diamond—a rigid, three-dimensional tetrahedral network of sp³-hybridized atoms making it the hardest known natural material and an electrical insulator—and graphite, featuring layered sp²-hybridized sheets with delocalized electrons that confer conductivity and lubricity, as seen in pencils and industrial applications. Other carbon allotropes include fullerenes like C₆₀ buckyballs, carbon nanotubes, and graphene, a single-layer honeycomb structure isolated in 2004, whose exceptional strength and electron mobility earned its discoverers the 2010 Nobel Prize in Physics. In metals, iron demonstrates allotropy through forms such as ferrite (body-centered cubic, stable at room temperature), austenite (face-centered cubic, above 910°C), and high-pressure ε-iron (hexagonal close-packed), which underpin processes like steel heat treatment for enhancing mechanical properties. The phenomenon of allotropy is distinct from polymorphism, which refers to multiple crystal structures in compounds rather than elements, and it plays a pivotal role in by enabling tailored properties for engineering applications, such as improving steel's or developing advanced like for electronics and composites. Understanding allotropy also informs phase diagrams and thermodynamic stability, guiding synthesis methods that mimic natural conditions—e.g., subjecting carbon to extreme heat (2,500°F) and pressure (850,000 psi) to form diamonds. Elements like (white, red, black) and (rhombic, monoclinic) further illustrate this versatility, highlighting allotropy's broad impact across chemistry and technology.

Fundamentals

Definition and Overview

Allotropy refers to the existence of a in two or more different structural modifications, known as allotropes, within the same physical state—such as solid, liquid, or gas—due to variations in atomic arrangement or . These forms are chemically identical in composition but often exhibit distinct physical and chemical properties arising from their structural differences. Classic examples illustrate this phenomenon: carbon occurs as , with a tetrahedral lattice of sp³-hybridized atoms, and , featuring layered sp²-hybridized sheets; oxygen exists as dioxygen (O₂), a diatomic gas, and (O₃), a triatomic gas; while manifests as white , a waxy solid with P₄ tetrahedral molecules, and red , an amorphous polymeric solid. These cases highlight how allotropes can coexist under specific conditions, influencing the element's behavior in materials and reactions. Allotropy differs from polymorphism, which involves multiple crystal structures in chemical compounds rather than pure elements, and from isomerism, where compounds share the same molecular formula but differ in atomic connectivity or spatial . From a thermodynamic perspective, allotropes are distinct phases, each characterized by unique curves; the stable allotrope under given temperature and pressure is the one with the lowest free energy.

Types and Causes

Allotropes are classified into monotropic and enantiotropic types based on their thermodynamic stability relationships. In monotropic allotropy, one form is stable under all conditions, while the other is metastable with higher , leading to irreversible transitions; for example, is the stable allotrope of carbon, with being monotropic and thermodynamically unstable at ambient conditions. Enantiotropic allotropy involves two forms that are stable under different or conditions, with reversible transitions at a specific transition point; rhombic and monoclinic exemplify this, where rhombic sulfur is stable below approximately 95.5°C and monoclinic above it. Additionally, allotropes can be categorized as static or dynamic: static allotropy refers to fixed crystal structures differing in atomic arrangement, while dynamic allotropy involves reversible changes over a range without a distinct transition point, often observed in elements like . The existence of allotropes arises primarily from differences in crystal lattice structures and bonding arrangements that minimize under specific conditions. For instance, features a three-dimensional covalent network lattice with tetrahedral coordination, whereas has a layered hexagonal structure with planar sheets; these structural variations lead to distinct stability and properties. Thermodynamically, the stable allotrope at a given and pressure is the one with the lowest , G=H−TSG = H - TS, where phases coexist at boundaries defined by equal chemical potentials. Phase transitions between allotropes follow the Clapeyron , which relates the slope of the transition curve to and changes: dPdT=ΔHTΔV\frac{dP}{dT} = \frac{\Delta H}{T \Delta V} Here, ΔH\Delta H is the enthalpy of transition, TT is temperature, and ΔV\Delta V is the volume change; positive ΔV\Delta V typically results in a positive slope, as seen in solid-solid transitions where denser phases stabilize under pressure. Temperature, pressure, and kinetic factors influence stability, with kinetics often hindering transitions to the global energy minimum, allowing metastable allotropes like diamond to persist. Bonding variations further explain allotropy, particularly through atomic orbital hybridization and intermolecular interactions. In carbon allotropes, diamond exhibits sp3sp^3 hybridization, forming strong sigma bonds in a tetrahedral geometry with bond angles of 109.5°, while graphite uses sp2sp^2 hybridization for trigonal planar sheets with 120° angles and delocalized pi electrons. Intermolecular forces, such as weak van der Waals () interactions, hold graphite layers together, enabling easy sliding and contrasting with the rigid covalent network in . Computational approaches like (DFT) have become essential for predicting new allotropes by calculating total energies, electronic structures, and stabilities of hypothetical lattices. DFT simulations screen vast structural databases, identifying low-energy configurations with mixed hybridizations or novel topologies, such as superhard or semiconducting carbon phases stable under extreme pressures; recent reviews highlight over 1,600 predicted 3D carbon allotropes, guiding experimental synthesis.

Historical Development

Early Observations

Ancient civilizations, including those in dating back to the BCE, were familiar with as a hard, transparent , while was utilized in from the for marking and drawing due to its soft, black properties. These materials were regarded as distinct substances with vastly different characteristics, such as 's exceptional and 's , without any recognition of their shared elemental composition. In 1772, French chemist Antoine Lavoisier conducted experiments burning diamonds in oxygen, producing carbon dioxide identical to that from charcoal combustion, thereby establishing diamond as a crystalline form of carbon and hinting at the possibility of multiple forms for the same element. Around the same time, graphite was confirmed to be impure carbon through similar combustion analyses by Lavoisier and others, marking one of the earliest empirical recognitions of what would later be understood as allotropy. In 1774, Joseph Priestley isolated oxygen gas (then called "dephlogisticated air") from heated mercuric oxide, laying the groundwork for identifying its variations; decades later, in 1839, Christian Friedrich Schönbein observed a pungent odor during water electrolysis and slow oxidation of phosphorus, leading to the discovery of ozone as a distinct, more reactive form of oxygen. The 18th century also saw initial isolations of reactive forms of other elements. In 1669, German alchemist obtained white by distilling urine residues, yielding a waxy, spontaneously igniting substance that glowed in the dark, though its elemental nature was not fully appreciated until later. Independently in 1770, Swedish chemist produced white from , but the existence of a more stable form was not observed until 1845, when Austrian chemist Anton von Schrötter heated white out of contact with air, producing a non-toxic, amorphous variety with different and reactivity. For , known since antiquity in its yellow, rhombic crystalline form, the monoclinic variant was first described in 1823 by German chemist Eilhard Mitscherlich, who noted its needle-like crystals forming upon cooling molten above 95.5°C, exhibiting a temporary stability and distinct compared to the rhombic phase. These early observations often led to confusion, with differing forms attributed to impurities, experimental artifacts, or even separate elements, as the prevailing and lack of atomic theory hindered unified explanations. Only with advancing atomic hypotheses in the early , such as those proposed by , did scientists begin to systematically link these variations to inherent structural differences within the same element, paving the way for formal recognition of allotropy.

Key Milestones and Terminology

The term "allotropy" was coined in 1841 by Swedish chemist Jöns Jakob Berzelius in a review of German physicist Moritz Frankenheim's work on the polymorphic forms of mercury(II) iodide and sulfur, where he described it as a third type of isomerism specific to elements, arising from differences in their internal atomic constitution without changes in composition. Berzelius derived the word from the Greek roots allos (other) and tropos (way or manner), emphasizing the varied manners in which elemental atoms could manifest distinct properties. Following the 1860 Karlsruhe Congress, where revived Avogadro's 1811 hypothesis on molecular volumes to establish accurate atomic weights, the concept of allotropy underwent significant refinement by linking crystal forms to atomic arrangements rather than vague compositional ambiguities. This advancement, building on Eilhard Mitscherlich's earlier 1819 of isomorphism—which demonstrated that analogous compounds form similar crystals and aided atomic weight determinations by analogy—allowed chemists to better distinguish allotropic modifications as structural variants of pure elements. By 1888, had further integrated allotropy into atomic theory by attributing it to polyatomic molecular forms, aligning it with Avogadro's principles and solidifying its role in understanding elemental diversity. In the , experimental breakthroughs expanded allotropy through high-pressure techniques. American physicist , starting in the , developed apparatus capable of generating pressures up to several thousand atmospheres, enabling the synthesis and discovery of new allotropic forms; for instance, in his pioneering high-pressure experiments starting in the early , he studied phase transitions in elements such as , identifying denser modifications like Bi II under pressures around 2.5 GPa. Bridgman's innovations, though unsuccessful in directly synthesizing despite repeated attempts, laid the groundwork for later high-pressure allotropy studies. Bridgman's techniques inspired later successes; in December 1954, H. Tracy Hall at achieved the first verified synthesis of crystals from using a high-pressure belt apparatus, producing gem-quality diamonds by 1955 for industrial use. A landmark discovery occurred in 1985 when , , and identified (C60)—a spherical carbon cluster—as a new allotrope of carbon, produced via vaporization of and confirmed through . The terminology surrounding allotropy evolved notably in the early amid advances in . Initially overlapping with "polymorphism"—a broader term for multiple crystal forms—distinctions sharpened as X-ray diffraction revealed that allotropy specifically denoted elemental polymorphs driven by atomic bonding variations, while polymorphism applied to compounds. This formal separation gained traction in the – crystallographic literature, with in 1912 advocating the use of "polymorphism" universally, though the International Union of Pure and Applied Chemistry (IUPAC) retained "allotropy" for its elemental specificity to preserve historical precision.

Property Variations

Physical Differences

Allotropes of the same element can exhibit striking differences in physical properties due to variations in atomic arrangement, leading to diverse applications in materials science. For instance, the carbon allotropes graphite and diamond differ significantly in density, with graphite at 2.26 g/cm³ and diamond at 3.51 g/cm³, reflecting graphite's layered structure versus diamond's compact tetrahedral lattice. These density variations influence mechanical behavior, as seen in hardness: diamond achieves a Mohs scale value of 10, making it the hardest known natural material, while graphite scores only 1–2, enabling its use as a lubricant. Electrical and thermal conductivity also diverge markedly; graphite conducts electricity anisotropically due to delocalized π electrons in its planar layers, whereas diamond is an electrical insulator but excels in thermal conductivity, up to 2200 W/m·K along certain directions, owing to its rigid sp³-bonded framework. Optical properties further highlight allotropic distinctions, often tied to electronic structure and light interaction. Diamond's high of 2.42 contributes to its exceptional brilliance and dispersion, responsible for the "fire" in gem-quality stones, while graphite appears opaque and dull. Color variations are evident in allotropes, where white phosphorus displays a waxy, translucent white-to-yellow hue, contrasting with the amorphous red phosphorus's reddish-brown appearance, both arising from different molecular packings. Thermal stability among allotropes is governed by phase transition temperatures, affecting practical usability. In tin, gray tin (α-Sn) is stable below 13.2°C, transitioning to the metallic white tin (β-Sn) above this point, a change known as "tin pest" that can cause structural degradation in cold environments. Such transitions underscore the sensitivity of allotropes to , with implications for material design in varying conditions. External factors like profoundly alter physical properties by favoring denser phases. For carbon, compression of glassy carbon above 40 GPa yields amorphous diamond, a superhard allotrope with fully sp³-bonded structure and diamond-like density, demonstrating enhanced mechanical strength under extreme conditions.

Chemical and Structural Differences

Allotropy manifests in distinct atomic arrangements and bonding configurations that profoundly influence the chemical behavior of elements. In carbon, for instance, diamond adopts a with the Fd-3m, where each carbon atom is tetrahedrally coordinated to four others, forming a three-dimensional network of sp³ hybridized bonds with a uniform of approximately 1.54 . In contrast, features a hexagonal with layers of sp² hybridized carbon atoms arranged in a planar lattice, where each atom has a of three within the plane and bond lengths of about 1.42 , connected by weaker van der Waals forces between layers. These structural differences dictate the overall rigidity and interlayer mobility, directly impacting chemical accessibility. Chemical reactivity among allotropes varies markedly due to these structural motifs. White consists of discrete P₄ tetrahedral molecules with strained P-P bonds, rendering it highly reactive and prone to spontaneous ignition in air, necessitating storage under to prevent oxidation. Red , however, forms an amorphous polymeric network of linked P₄ units with more stable covalent bonds, exhibiting lower reactivity and stability in air without ignition. Such variations arise because the molecular isolation in white facilitates easier bond cleavage and oxidation to phosphorus oxides like P₄O₁₀, whereas the extended structure in red hinders initial attack, influencing the effective oxidation pathways despite the elemental remaining zero in the pure forms. Stability differences further highlight allotropic distinctions, with some forms being thermodynamically favored while others persist due to kinetic barriers. is the thermodynamically stable allotrope of carbon at standard conditions, whereas is metastable, maintained by high activation energies that prevent spontaneous conversion despite 's lower free energy. Transitions between allotropes can be catalyzed; for example, iron, a Group VIII metal, facilitates the conversion of to under high-pressure, high-temperature conditions by dissolving carbon and lowering the energy barrier for , enabling sp² to sp³ bond rearrangement. Spectroscopic techniques exploit these structural variances for allotrope identification. reveals diamond through a sharp peak at 1332 cm⁻¹, corresponding to the triply degenerate vibration of its sp³ C-C bonds in the cubic lattice. , conversely, displays characteristic G-band at 1582 cm⁻¹ from in-plane sp² vibrations and a D-band around 1350 cm⁻¹ indicating disorder, allowing differentiation from diamond even in mixed samples. complements this by probing bond symmetries, though Raman's sensitivity to carbon's vibrational modes makes it particularly effective for non-destructive analysis.

Allotropes by Element Category

Non-metals

Non-metal elements exhibit a rich variety of allotropes due to their ability to form diverse covalent networks and molecular structures, leading to stark differences in physical and chemical properties. Carbon, a quintessential non-metal, displays multiple allotropes that highlight this diversity. consists of a three-dimensional tetrahedral network of sp³-hybridized carbon atoms, resulting in exceptional (Mohs scale 10) and thermal conductivity, making it an ideal abrasive and material. In contrast, features planar layers of sp²-hybridized carbon atoms arranged in hexagonal rings, held together by weak van der Waals forces, which imparts lubricity, electrical conductivity along the planes, and softness ( 1-2). Fullerenes, such as (C60_{60}), form closed-cage structures with 60 carbon atoms in a truncated icosahedral , exhibiting high and stability due to delocalized π-electrons, with properties including solubility in organic solvents and potential for when doped. Carbon nanotubes, cylindrical extensions of sheets, can be single-walled or multi-walled with helical arrangements of hexagonal carbon rings, diameters ranging from 1 to tens of nanometers, and exceptional tensile strength (up to 100 GPa) alongside electrical conductivity that varies from metallic to semiconducting based on . Oxygen, another key non-metal, exists primarily as dioxygen (O2_2), a with a that is paramagnetic and colorless in the gas phase but takes on a pale blue hue in the liquid state due to its electronic transitions. (O3_3), a triatomic bent molecule, is a diamagnetic gas with a pungent odor and pale blue color, highly reactive as an oxidant, and less stable than O2_2 owing to its higher energy structure. Under (8-96 GPa), oxygen forms the ε-phase, a red polymeric solid composed of O8_8 molecular units in a rhombohedral lattice, exhibiting a loss of , intense infrared absorption, and a darker with increasing due to narrowing. Sulfur demonstrates temperature-dependent allotropes centered on S8_8 rings. Rhombic sulfur (α-sulfur), the most stable form below 95.5°C, crystallizes in an orthorhombic lattice with puckered crown-shaped S8_8 molecules, appearing as crystals that are insoluble in water but soluble in . Monoclinic sulfur (β-sulfur), stable between 95.5°C and 119°C, features a similar S8_8 ring but in a needle-like monoclinic packing, with slightly lower and solubility properties akin to the rhombic form. Plastic sulfur, an amorphous formed by rapid quenching of molten sulfur, consists of long entangled chains that confer viscoelastic behavior, allowing it to stretch like rubber when warm before reverting to a brittle solid upon cooling. Phosphorus allotropes vary dramatically in reactivity and . White comprises discrete P4_4 tetrahedral molecules, a waxy white solid that is highly toxic, glows in the dark via , and ignites spontaneously in air at approximately 30°C due to its strained bonds. Red phosphorus is an amorphous network of linked phosphorus atoms, less reactive and non-toxic compared to the white form, with an ignition temperature around 240°C, making it suitable for safety matches. Black phosphorus adopts a layered orthorhombic analogous to , with puckered sheets of phosphorus atoms forming a with a direct of about 0.3 eV, exhibiting high carrier mobility and anisotropic properties. Other non-metals like show polymorphic forms. Gray , the stable hexagonal allotrope, features helical chains of atoms in a metallic-gray crystalline lattice, behaving as a photoconductor with electrical resistivity decreasing under exposure. Red is a monoclinic crystalline form with discrete Sen_n rings (n=6-8), appearing brick-red and amorphous in powder, while vitreous is a , glassy formed by rapid cooling, all less stable than the gray form and convertible to it upon heating.

Metalloids

Metalloids exhibit allotropy that bridges non-metallic covalent bonding and metallic conductivity, often resulting in behaviors critical for and . These elements, including , , , and , display diverse structures ranging from crystalline frameworks to amorphous and molecular forms, influencing their electrical, optical, and thermal properties. Silicon, a cornerstone of , primarily exists in a crystalline structure at ambient conditions, where each atom bonds tetrahedrally to four others in a face-centered cubic lattice with Fd̅3m and lattice parameter a = 5.44 , yielding an indirect bandgap of approximately 1.1 eV that enables efficient transport in devices like transistors. , lacking long-range order, features a continuous random network of Si-Si bonds with a higher optical bandgap around 1.7-1.8 eV, though it suffers from lower (about 1 cm²/V·s) due to defect states, making it suitable for thin-film solar cells and displays where flexibility is prioritized over performance. Silicon clathrates represent open-framework allotropes, such as type I (Si₄₆) and type II (Si₁₃₆) structures, composed of polyhedral cages hosting guest atoms like sodium; these exhibit or quasi-direct bandgaps (1.4-2.4 eV), enhancing light absorption for photovoltaic applications compared to the indirect bandgap of . In 2023, Q-silicon was discovered through laser melting and quenching of , forming a high-density phase (60% denser than ) with sp³ bonding and random packing of diamond tetrahedra subunits, which introduces ( >400 K) absent in standard , potentially revolutionizing spintronic devices. Germanium shares structural similarities with but displays greater phase diversity under pressure, starting with the stable allotrope ( Fd̅3m), a with a narrower indirect bandgap of 0.66 eV that supports high-speed due to superior mobility (1900 cm²/V·s). The white metallic allotrope adopts a body-centered tetragonal β-tin under (above ~10 GPa), transitioning from semiconducting to metallic behavior with increased conductivity, though it is metastable at ambient conditions and reverts upon decompression. Layered germanium forms, such as puckered hexagonal sheets analogous to , exhibit tunable bandgaps (0.5-1.5 eV) depending on stacking, enabling potential use in 2D , while high-pressure hexagonal phases (e.g., simple hexagonal at ~100 GPa) further diversify its structural motifs with metallic properties. Boron allotropes are characterized by complex icosahedral clusters (B₁₂ units) that dictate their semiconductor properties, with amorphous boron consisting of a disordered network of these clusters linked by three-center two-electron bonds, resulting in a wide bandgap (~2 eV) and high hardness suitable for abrasives. The α-rhombohedral form features a primitive lattice of isolated B₁₂ icosahedra with weak inter-icosahedral bonding, yielding semiconducting behavior with anisotropic conductivity and a bandgap of 1.5-2 eV, while the β-tetragonal allotrope incorporates linked icosahedra in chains, enhancing stability and electrical resistivity up to 10¹⁰ Ω·cm. These icosahedral-based structures underscore boron's structural diversity, where cluster packing variations lead to varying degrees of covalent-metallic hybridization, influencing applications in neutron detectors and high-temperature ceramics. Arsenic demonstrates pronounced allotropy tied to its nature, with the gray allotrope forming stable layered sheets in a rhombohedral lattice ( R̅3m), behaving as a with overlapping (small ) that confer anisotropic semiconductor-like transport properties for thermoelectric devices. Yellow arsenic comprises discrete tetrahedral As₄ molecules, akin to white , with a molecular bandgap exceeding 2.5 eV and high reactivity due to weak van der Waals interactions, limiting it to low-temperature studies but highlighting covalent molecular diversity. The black polymeric allotrope, synthesized under (>0.7 GPa), adopts a puckered layered structure similar to black , featuring a direct bandgap (~0.3 eV) and higher stability below 300°C, though it irreversibly converts to gray arsenic upon heating or decompression, illustrating pressure-induced structural transitions in metalloids. Antimony's allotropes reflect its semimetallic character, dominated by the stable metallic rhombohedral form ( R̅3m) with puckered layers and a small bandgap (~0.15 eV), enabling moderate electrical conductivity (comparable to ) and applications in alloys for enhanced thermoelectric efficiency through Seebeck coefficients up to 50 μV/. The explosive form, an ill-defined amorphous variant produced by in acidic media, exists in a strained, highly disordered state with expanded interatomic distances, detonating upon shock due to rapid recombination of chains, though it is not a thermodynamically distinct phase. This form's instability contrasts with the metallic allotrope's robustness, underscoring antimony's potential in energy conversion where structural sensitivity tunes thermal and electrical responses.

Metals

Metallic elements exhibit allotropy through phase transitions driven by temperature, pressure, or composition, resulting in distinct crystal structures that influence mechanical properties such as and strength. These transformations are particularly significant in metals used for structural applications, where the stability of phases determines performance. For instance, many transition metals display body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal close-packed (HCP) lattices, with transitions occurring at specific critical temperatures. Iron demonstrates classic allotropy with three primary phases at : alpha-iron (ferrite), which adopts a BCC structure and is ferromagnetic up to the of 770°C; gamma-iron (), an FCC structure stable between approximately 912°C and 1394°C; and delta-iron, another BCC form existing from 1394°C to the at 1538°C. In steels, rapid cooling from the phase produces , a supersaturated BCC variant distorted to body-centered tetragonal due to trapped carbon, enhancing hardness but reducing . These phase changes underpin processes in production. Tin exists in two allotropes at ambient conditions: white tin (beta-tin), a metallic tetragonal stable above 13.2°C with of 7.31 g/cm³, and gray tin (alpha-tin), a non-metallic that forms below this temperature, leading to the brittle "tin pest" degradation where objects crumble due to the 27% volume expansion. This transformation is autocatalytic and historically affected tin alloys in cold environments, such as organ pipes in cathedrals. Titanium undergoes an allotropic transformation at 882°C, shifting from the low-temperature phase with HCP structure to the high-temperature beta phase with BCC structure, enabling the design of , and alloys with tailored properties. Under , titanium can form the phase, a hexagonal structure that appears in pure titanium or alloys subjected to gigapascal stresses, altering electronic properties and hardness. Among lanthanides and actinides, exhibits remarkable complexity with seven allotropic forms under varying conditions, including the low-temperature alpha phase (monoclinic) and the ductile delta phase (FCC), stabilized at by small additions of elements like for nuclear applications. These phases arise from the delocalized 5f electrons, leading to anomalous properties like in delta-, which impacts handling, machining, and safety in cycles due to . Uranium similarly shows three allotropes: alpha-uranium (orthorhombic, stable up to 668°C), beta-uranium (tetragonal, 668–776°C), and gamma-uranium (BCC, above 776°C to melting at 1132°C), with the alpha phase's causing dimensional instability in components. These transformations affect uranium's reactivity and mechanical integrity, critical for fabrication and storage. Other metals like sodium reveal allotropy under , transitioning from ambient BCC through FCC, complex structures such as cI16 (at ~100 GPa), oP8, and tI19, with these phases linked to an anomalous melting curve minimum around 120 GPa due to electronic restructuring. Such high-pressure forms provide insights into planetary interiors but are not stable at ambient conditions.

Advanced Topics

Nanoallotropes

Nanoallotropes refer to structural variants of elements at the nanoscale, typically below 100 nm, that exhibit distinct properties from their bulk counterparts due to quantum confinement, high surface-to-volume ratios, and altered bonding configurations. These forms often display unique electronic, optical, mechanical, or catalytic behaviors not observed in macroscopic allotropes. The concept of nanoallotropy was formally proposed in to describe composed of the same elemental nanoparticles but arranged in different architectures, analogous to traditional allotropy but confined to nanoscale dimensions. A prominent example is found in carbon nanoallotropes, which extend beyond bulk forms like and into low-dimensional structures. , a single layer of sp²-hybridized carbon atoms in a 2D lattice, possesses exceptional mechanical strength, with a tensile strength approximately 200 times that of and a of about 1 TPa. Carbon nanotubes, representing 1D rolled-up sheets, exhibit high electrical conductivity and tensile strength up to 100 GPa, depending on . Fullerenes, such as C₆₀ in 0D buckyball form, feature curved sp² networks with unique electronic properties enabling in doped variants. These carbon nanoallotropes demonstrate how alters charge transport and reactivity compared to bulk carbon. For other elements, silicon nanoallotropes like nanowires contrast sharply with bulk 's brittleness. Silicon nanowires, with diameters of 20–100 nm, show enhanced and can undergo reversible deformation under bending, achieving strains up to 10% without , due to surface-mediated activity. In metals, nanoparticles illustrate size-dependent phases; for instance, arrays of 10–15 nm particles can form non-close-packed structures such as tetrahedral clusters (vac₁Au₅) or layered quartets and septets (vac₁Au₁₁), which enhance surface-enhanced (SERS) signals by factors of 10³–10⁴ compared to close-packed bulk films, owing to tunable nanoscale gaps. Synthesis of nanoallotropes commonly employs methods like (CVD) for and nanowires, where precursors decompose on substrates at 800–1000°C to grow aligned structures. Arc discharge, used for carbon nanotubes and fullerenes, involves vaporizing electrodes in to produce 1–10 nm diameter tubes or clusters. For metallic nanoallotropes, post-assembly of binary superlattices—such as selectively removing from gold-iron oxide arrays with HCl—yields stable porous architectures. However, nanoallotropes face stability challenges, including aggregation driven by high surface energies (up to 1–10 J/m²) and phase instability under ambient conditions, often requiring passivation layers or low-temperature processing to prevent coalescence into bulk-like forms.

Recent and Emerging Forms

In 2023, Q-silicon emerged as a novel allotrope synthesized through nanosecond melting of ion-implanted followed by rapid from an undercooled state. This process yields a composed of randomly packed tetrahedra in amorphous variants (Q1, Q2, Q3) and a crystalline phase with subunit cells of higher atomic density—60% greater than that of —arranged along <110> directions with alternating voids. Q-silicon demonstrates robust at , with a blocking temperature exceeding 400 K and a above 600 K, alongside enhanced and metallic conductivity derived from delocalized electrons during the molten . Recent investigations into tin's high-pressure phases, detailed in a 2022 combining X-ray diffraction, calculations, and Gibbs energy modeling, have confirmed multiple allotropes beyond the familiar α-Sn () and β-Sn (body-centered tetragonal). These include γ-Sn (body-centered tetragonal, stable above ~10 GPa), γ'-Sn (body-centered cubic, above 45 GPa), σ-Sn (a complex phase at intermediate pressures), and δ-Sn (body-centered cubic form at over 120 GPa, potentially transitioning to hexagonal close-packed). Such phases exhibit metallic behavior and hold promise as high-temperature superconductors, with critical temperatures potentially reaching 10-20 K under compression. High-pressure studies have also uncovered advanced allotropes of black , including a body-centered cubic phase identified as a cI16 derived from simple cubic black , stable above 260 GPa. This form, explored through experimental synthesis and theoretical modeling, contrasts with the orthorhombic of ambient black and enables tunable electronic properties for extreme-condition applications. Ongoing theoretical research continues to predict low-dimensional metallic phases of , such as 2D configurations, which could exhibit and serve as lightweight energy carriers if stabilized at accessible pressures. Computational advancements in , including Bayesian interatomic potentials, have accelerated the discovery of stable elemental allotropes like those of (α-B, β-B, γ-B), by evaluating thermodynamic stability and spectra to prioritize synthesizable candidates over exhaustive searches. These emerging forms fill critical gaps in , such as spintronic devices from ferromagnetic Q-silicon and high-pressure superconductors from tin and phases, expanding allotropy's role in next-generation technologies.

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