Allotropes of sulfur

There are a large number of allotropes of sulfur. In this respect, sulfur is second only to carbon. The most common form found in nature is yellow orthorhombic α-sulfur, which contains puckered rings of S
₈. Chemistry students may have seen "plastic sulfur", this is not an allotrope but is a mixture that contains long chain polymeric sulfur, two forms of which have been identified as allotropes. In addition to these there are other solid forms that contain sulfur rings of 6, 7, 9-15, 18 and 20 atoms. There are also gases, S₂, S₃; some species only detected in the vapour phase, S₄ and S₅ and perhaps five or more high pressure forms, two of which are metallic.

The range of molecular allotropes possessed by sulfur can in part be ascribed to the wide range of bond lengths (180pm -260pm) and inter bond angles(90° - 120°) exhibited by the S-S bond and its strength, (the unrestrained S-S single bond has a high bond energy of 265 kJmol^-1 ).

Early workers identified some forms that have later proved to be allotropes i.e. pure forms, whilst others have proved to be mixtures. 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". A commonly used naming system uses Greek suffixes (α, β etc.) however this system predates the discovery of the new forms that have been synthesised rather than prepared from elemental sulfur.

List of allotropes and forms

Allotropes are bold.

Formula	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	cyclo-hexasulfur, ρ-sulfur "ε-sulfur", "Engel's" sulfur, "Aten's sulfur"	The ring adopts a chair form in the solid.
cyclo-S6.cyclo-S10 adduct		An usual mixed crystal with alternating layers of cyclo-S6 and cyclo-S10.
cyclo-S7	α-, β-, γ-, δ- cycloheptasulfur	Four forms known, two(γ-, δ- ) characterised.
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 solid, consisting of S8 puckered rings. Only stable above 95°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 characterised, contains parallel helical sulfur chains and is difficult to obtain pure.
catena-Sx	lamina sulfur	Not well characterised, 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	4 high pressure phases (at ambient temperature) including two that are metallic and become superconducting at low temperature and some additional phases photo-induced below 20-30GPa..

Gaseous allotropes

S₂, disulfur

S₂ is the predominant species in sulfur vapour above 720°C. at low pressure (1mm Hg) at 530°C it comprises 99% of vapour species. It is a singlet diradical like dioxygen with an S-S bond length of 188.7 pm. The blue colour of burning sulfur is due to emission of light by the S₂ molecule produced in the flame.

S₃, trisulfur

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

S₄, tetrasulfur

This has been detected in the vapour phase but has not been fully characterised. Various forms, (e.g chains, branched chains and rings) have been proposed. The latest view, based on theoretical calculations is that it has a ring structure.

Solid cyclo-sulfur allotropes

cyclo-S₅, pentasulfur

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

S₆, cyclo-hexasulfur

This was first prepared by M.R. Engel in 1891 by reacting concentrated 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 +2HCl (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 essentially equivalent.

cyclo-hexasulfur

cyclo-hexasulfur, cyclo-S6

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.

S₇,cyclo-heptasulfur

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

Cyclo-S₈

α-sulfur

α-sulfur 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 35.5g/100g 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 206pm and the S-S-S angles are 108° 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 ca. 119°C melting point has been termed the "ideal melting point" and the typical lower value (114.5°) when decomposition occurs, the "natural melting point".

γ-sulfur

This form was first prepared by F.W Muthmann in 1890, 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)

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_xCl₂ and a polysulfane, H₂S_y:

S_n−mCl₂ + H₂S_m → cyclo-S_n

S₁₂, S₁₈ and S₂₀ can alternatively 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-dodecasulfur

cyclo-dodecasulfur, cyclo-S12

Cyclo-S₁₂ is the second most stable cyclo- allotrope after cyclo-S₈. 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 characterised.
Two forms of cyclo-S₁₈ are known where the conformation of the ring is different. To differentiate these structures rather than use 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-.

Solid catena sulfur allotropes

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 (confusingly) fibrous sulfur or ω1-sulfur, has been well characterised. It has a density of 2.01g cm^-3 (α-sulfur 2.069g 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 95pm. The S-S bond length is 206.6pm, the S-S-S bond angle is 106° and the dihedral angle is 85.3°, (comparable figures for α-sulfur are 203.7pm, 107.8° and 98.3°).

lamina sulfur

This has not been well characterised 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 remakably 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.

φ-sulfur, fibrous 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 .

S_∞

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

High pressure forms

The P-T phase diagram of sulfur is complex. Some researchers have used laser illumination of samples and found that perhaps 3 forms can be photo-induced below 20-30 GPa. In a high pressure study at ambient temperatures, four forms, termed S-II, S-III, S-IV, S-V have been characterised (α-sulfur being S-I) . S-II and S-III are polymeric forms, S-IV and S-V are metallic and are superconductors below 10 K and 17 K respectively.