Allotropes of sulfur

The allotrope of the element, sulfur, most prevalent in nature, cyclo-octasulfur (cyclo-S₈).

The allotropes of sulfur refers to the many allotropes of the element sulfur. In terms of large number of allotropes, sulfur is second only to carbon. In addition to the allotropes, each allotrope often exists in polymorphs, delineated by Greek prefixes (α, β, etc.).

Furthermore, because elemental sulfur has been an item of commerce for centuries, its various forms are given traditional names. Early workers identified some forms that have later proved to be single or mixtures of allotropes. Some forms have been named for their appearance, e.g. "mother of pearl sulfur", or alternatively named for a chemist who was pre-eminent in identifying them, e.g. "Muthmann's sulfur I" or "Engel's sulfur".

The most commonly encountered form of sulfur is the orthorhombic polymorph of S
₈, which adopts a puckered ring – or "crown" – structure. Two other polymorphs are known, also with nearly identical molecular structures. In addition to S₈, sulfur rings of 6, 7, 9–15, 18 and 20 atoms are known. At least five allotropes are uniquely formed at high pressures, two of which are metallic.

The number of sulfur allotropes reflects the relatively strong S−S bond of 265 kJ/mol. Furthermore, unlike most elements, the allotropes of sulfur can be manipulated in solutions of organic solvents and is amenable to analysis by HPLC.

Phase diagram for sulfur

A historic phase diagram of sulfur. A phase diagram from 1975, presenting data through 1970. The ordinate is pressure in kilobars (kbar). and the abscissa is temperature in Kelvin (K). (The temperatures 200, 400, 600, and 800 K correspond to the approximate temperatures of −73, 127, 327, and 527 °C, respectively.) The Roman numerals I-XII refer to known solid phases identified by "volumetric, optical, and electrical resistance techniques," and letters A-E to putative distinct liquid "phases" identified by differential thermal analysis. Phase information is based on the work of G. C. Vezzoli, et. al, as reviewed by David Young; as Young notes, "The literature on the allotropy of sulfur presents the most complex and confused situation of all the elements." Phase information, while complete to this date, are incomplete as of 2015, since limited to ≤50 kbar and thus omitting metallic phases.

The pressure-temperature (P-T) phase diagram for sulfur is complex (see image). The region labeled I (a solid region), is α-sulfur. See the legend for further identifications and information, and see the section on high pressure forms for information on these phases.

High pressure solid allotropes

In a high-pressure study at ambient temperatures, four new solid forms, termed II, III, IV, V have been characterized, where α-sulfur is form I. Solid forms II and III are polymeric, while IV and V are metallic (and are superconductive below 10 K and 17 K, respectively). Laser irradiation of solid samples produces three sulfur forms below 200–300 kbar (20–30 GPa).

Solid cyclo allotrope preparation

Two methods exist for the preparation of the cyclo-sulfur allotropes. One of the methods, which is most famous for preparing hexasulfur, is to react hydrogen polysulfides with polysulfur dichloride:

H₂S_x + S_yCl₂ → cyclo-S_x+y + 2 HCl

A second strategy uses titanocene pentasulfide as a source of the S₅²⁻ unit. This complex is easily made from polysulfide solutions:

[NH₄]₂[S₅] + (C₅H₅)₂TiCl₂ → (C₅H₅)₂TiS₅ + 2 NH₄Cl

Then the resulting pentasulfur-titanocene complex is allowed to react with polysulfur dichloride to give the desired cyclo-sulfur in the series:

(C₅H₅)₂TiS₅ + S_yCl₂ → cyclo-S_y+5 + (C₅H₅)₂TiCl₂

Solid cyclo-sulfur allotropes

Cyclo-Pentasulfur, cyclo-S₅

This has not been isolated, but has been detected in the vapour phase.

Cyclo-hexasulfur, cyclo-S₆

Main article: Hexasulfur

File:Hexasulfur 3D.png

Cyclo-hexasulfur, cyclo-S₆

This was first prepared by M. R. Engel in 1891 by reacting HCl with thiosulfate, HS₂O₃⁻. Cyclo-S₆ is orange-red and forms a rhombohedral crystal. It is called ρ-sulfur, ε-sulfur, Engel's sulfur and Aten's sulfur. Another method of preparation involves reacting a polysulfane with sulfur monochloride:

H₂S₄ + S₂Cl₂ → cyclo-S₆ + 2 HCl (dilute solution in diethyl ether)

The sulfur ring in cyclo-S₆ has a "chair" conformation, reminiscent of the chair form of cyclohexane. All of the sulfur atoms are equivalent.

Cyclo-heptasulfur, cyclo-S₇

It is a bright yellow solid. Four (α-, β-, γ-, δ-) forms of cyclo-heptasulfur are known. Two forms (γ-, δ-)have been characterized. The cyclo-S₇ ring has an unusual range of bond lengths of 199.3–218.1 pm. It is said to be the least stable of all of the sulfur allotropes.

Cyclo-octasulfur, cyclo-S₈

Main article: Octasulfur

α-Sulfur

α-Sulfur, see image, is the form most commonly found in nature. When pure it has a greenish-yellow colour (traces of cyclo-S₇ in commercially available samples make it appear yellower). It is practically insoluble in water and is a good electrical insulator with poor thermal conductivity. It is quite soluble in carbon disulfide: 35.5 g/100 g solvent at 25 °C. It has a rhombohedral crystal structure. This is the predominant form found in "flowers of sulfur", "roll sulfur" and "milk of sulfur". It contains S₈ puckered rings, alternatively called a crown shape. The S-S bond lengths are all 203.7 pm and the S-S-S angles are 107.8° with a dihedral angle of 98°. At 95.3 °C, α-sulfur converts to β-sulfur.

β-Sulfur

This is a yellow solid with a monoclinic crystal form and is less dense than α-sulfur. Like the α- form it contains puckered S₈ rings and only differs from it in the way the rings are packed in the crystal. It is unusual because it is only stable above 95.3 °C, below this it converts to α-sulfur.It can be prepared by crystallising at 100 °C and cooling rapidly to slow down formation of α-sulfur. It has a melting point variously quoted as 119.6 °C and 119.8 °C but as it decomposes to other forms at around this temperature the observed melting point can vary from this. The 119 °C melting point has been termed the "ideal melting point" and the typical lower value (114.5 °C) when decomposition occurs, the "natural melting point".

γ-Sulfur

This form, first prepared by F.W. Muthmann in 1890, is sometimes called "nacreous sulfur" or "mother of pearl sulfur" because of its appearance. It crystallises in pale yellow monoclinic needles. It contains puckered S₈ rings like α-sulfur and β-sulfur and only differs from them in the way that these rings are packed. It is the densest form of the three. It can be prepared by slowly cooling molten sulfur that has been heated above 150 °C or by chilling solutions of sulfur in carbon disulfide, ethyl alcohol or hydrocarbons. It is found in nature as the mineral rosickyite.

Cyclo-S_n (n = 9–15, 18, 20)

Cyclo-dodecasulfur, cyclo-S₁₂

These allotropes have been synthesised by various methods for example, reacting titanocene pentasulfide and a dichlorosulfane of suitable sulfur chain length, S_n−5Cl₂:

(η⁵-C₅H₅)₂TiS₅ + S_n−5Cl₂ → cyclo-S_n

or alternatively reacting a dichlorosulfane, S_n−mCl₂ and a polysulfane, H₂S_m:

S_n−mCl₂ + H₂S_m → cyclo-S_n

S₁₂, S₁₈ and S₂₀ can also be prepared from S₈. With the exception of cyclo-S₁₂, the rings contain S-S bond lengths and S-S-S bond angle that differ one from another.

Cyclo-S₁₂ is the most stable cyclo-allotrope. Its structure can be visualised as having sulfur atoms in three parallel planes, 3 in the top, 6 in the middle and three in the bottom.

Two forms (α-, β-) of cyclo-S₉ are known, one of which has been characterized.

Two forms of cyclo-S₁₈ are known where the conformation of the ring is different. To differentiate these structures, rather than using the normal crystallographic convention of α-, β-, etc., which in other cyclo-S_n compounds refer to different packings of essentially the same conformer, these two conformers have been termed endo- and exo-.

Cyclo-S₆.cyclo-S₁₀ adduct

This is produced from a solution of cyclo-S₆ and cyclo-S₁₀ in CS₂. It has a density midway between cyclo-S₆ and cyclo-S₁₀. The crystal consists of alternate layers of cyclo-S₆ and cyclo-S₁₀. For all the elements this may be the only allotrope which contains molecules of different sizes.

Solid catena allotropes

Two parallel monatomic sulfur chains grown inside a single-wall carbon nanotube (CNT, a). Zig-zag (b) and straight (c) S chains inside double-wall CNTs.

The production of pure forms of catena-sulfur has proved to be extremely difficult. Complicating factors include the purity of the starting material and the thermal history of the sample.

ψ-Sulfur

This form, also called fibrous sulfur or ω1-sulfur, has been well characterized. It has a density of 2.01 g·cm⁻³ (α-sulfur 2.069 g·cm⁻³) and decomposes around its melting point of 104 °C. It consists of parallel helical sulfur chains. These chains have both left and right-handed "twists" and a radius of 95 pm. The S-S bond length is 206.6 pm, the S-S-S bond angle is 106° and the dihedral angle is 85.3°, (comparable figures for α-sulfur are 203.7 pm, 107.8° and 98.3°).

Lamina sulfur

This has not been well characterized but is believed to consist of criss-crossed helices. It is also called χ-sulfur or ω2-sulfur.

Catena sulfur forms

The naming of the different forms is very confusing and care has to be taken to determine what is being described as the same names are used interchangeably.

Amorphous sulfur

This is the quenched product of sulfur melts above 160 °C (at this point the properties of the liquid melt change remarkably, e.g. large increase in viscosity). Its form changes from an initial plastic form gradually to a glassy form, hence its other names of plastic, glassy or vitreous sulfur. It is also called χ-sulfur. It contains a complex mixture of catena-sulfur forms mixed with cyclo-forms.

Insoluble sulfur

This is obtained by washing quenched liquid sulfur with CS₂. It is sometimes called polymeric sulfur, μ-S or ω-S.

Fibrous (φ-) sulfur

This is a mixture of the allotropic ψ- form and γ-cycloS₈.

ω-Sulfur

This is a commercially available product prepared from amorphous sulfur that has not been stretched prior to extraction of soluble forms with CS₂. It sometimes called "white sulfur of Das" or supersublimated sulfur. It is a mixture of ψ-sulfur and lamina sulfur. The composition depends on the exact method of production and the samples history. One well known commercial form is "Crystex". ω-sulfur is used in the vulcanization of rubber.

λ-Sulfur

This name is given to the molten sulfur immediately after melting, cooling this gives predominantly β-sulfur.

μ-Sulfur

This name is applied to solid insoluble sulfur and the melt prior to quenching.

π-Sulfur

Dark-coloured liquid formed when λ-sulfur is left to stay molten. Contains mixture of S_n rings.

Biradical catena (S_∞) chains

This term is applied to biradical catena- chains in sulfur melts or the chains in the solid.

List of allotropes and forms

Allotropes are in Bold.

Formula/name	Common name	Other names	Notes
S2	disulfur		A diatomic gas with a triplet ground state like dioxygen.
S3	trisulfur		A cherry red triatomic gas with a bent ozone-like structure.
S4	tetrasulfur		Structure not determined but calculations indicate it to be cyclo-S4.
cyclo-S5	cyclo-pentasulfur		Not yet isolated, only detected in sulfur vapour.
cyclo-S6	ρ-sulfur	cyclo-hexasulfur, "ε-sulfur", "Engel's" sulfur, "Aten's sulfur"	The ring adopts a chair form in the solid.
cyclo-S6/cyclo-S10 adduct			A mixed crystal with alternating layers of cyclo-S6 and cyclo-S10.
cyclo-S7	α-, β-, γ-, δ- cycloheptasulfur		Four forms known, two(γ-, δ- ) characterized.
cyclo-S8	α-sulfur	"orthorhombic sulfur" "rhombic sulfur", "flowers of sulfur", "roll sulfur" "milk of sulfur", "Muthmann's sulfur I"	Yellow solid consisting of S8 puckered rings. The thermodynamically stable form at ordinary temperatures.
cyclo-S8	β-sulfur	"monoclinic sulfur" "prismatic sulfur" "Muthmann's sulfur II"	Yellow crystalline solid, consisting of S8 puckered rings. Only stable above 95.3 °C, it reverts to α-sulfur at room temperature.
cyclo-S8	γ-sulfur	"nacreous sulfur" "mother of pearl sulfur" "Gernez’s sulfur" or "Muthmann's sulfur III".	Light yellow solid, crystal monoclinic, consisting of S8 puckered rings. Found in nature as the rare mineral rosickyite.
cyclo-Sn n = 9–15, 18, 20	cyclo-(nona; deca; undeca; dodeca; trideca; tetradeca; pentadeca; octadeca; eicosa)sulfur		Pure forms all allotropes, cyclo-S9 has four forms, cyclo-S18 has two forms. Generally synthesised rather than obtained by treatment of another form of elemental sulfur.
catena-Sx	fibrous (ψ) sulfur		Well characterized, contains parallel helical sulfur chains and is difficult to obtain pure.
catena-Sx	lamina sulfur		Not well characterized, contains helical chains partially crossed.
	amorphous sulfur		Quenched molten sulfur plastic sulfur at first crystallises to amorphous or glassy sulfur. Consists of a mixture of catena sulfur and cyclo sulfur.
	insoluble sulfur		Quenched liquid sulfur with soluble species extracted with CS2. Sometimes called polymeric sulfur, μ-S or ω-S.
	φ-sulfur		A mixture of allotropic ψ-sulfur and cyclo forms mainly γ-cyclo-S8.
	ω-sulfur	insoluble sulfur	A mixture of chains with a minimum of soluble species.
	λ-sulfur		Light yellow mobile liquid formed when β-sulfur first melts at 119.6 °C. Consists of S8 rings.
	μ-sulfur		The dark-coloured viscous liquid formed when π-sulfur is heated and the solid when cooled. Contains a mixture of polymeric chains.
	π-sulfur		Dark-coloured liquid that develops as λ-sulfur is left molten. Contains mixture of Sn rings.
High-pressure forms of α-sulfur	S-II, S-III, S-IV, S-V and others		Four high-pressure phases (at ambient temperature) including two that are metallic and become superconducting at low temperature and some additional phases photo-induced below 20–30 GPa.

High-temperature gaseous allotropes

Disulfur, S₂

Main article: Disulfur

Disulfur, S₂, is the predominant species in sulfur vapour above 720 °C (a temperature above that shown in the phase diagram); at low pressure (1 mmHg) at 530 °C, it comprises 99% of the vapor. It is a triplet diradical (like dioxygen and sulfur monoxide), with an S-S bond length of 188.7 pm. The blue colour of burning sulfur is due to the emission of light by the S₂ molecule produced in the flame.

The S₂ molecule has been trapped in the compound [S₂I₄][EF₆]₂ (E = As, Sb) for crystallographic measurements, produced by reacting elemental sulfur with excess iodine in liquid sulfur dioxide. The [S₂I₄]²⁺ cation has an "open-book" structure, in which each [I₂]⁺ ion donates the unpaired electron in the π^* molecular orbital to an vacant orbital of the S₂ molecule.

Trisulfur, S₃

Main article: Trisulfur

S₃ is found in sulfur vapour, comprising 10% of vapour species at 440 °C and 10 mmHg. It is cherry red in colour, with a bent structure, similar to ozone, O₃.

Tetrasulfur, S₄

This has been detected in the vapour phase but has not been fully characterized; various forms, (e.g. chains, branched chains and rings) have been proposed. A primary research result based on theoretical calculations suggests that it has a ring structure.