formulasearchengine - User contributions [en]

Pappus's hexagon theorem

2014-10-26T10:51:10Z

87.219.207.3: /* Proof */

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LCP array

2014-01-22T01:42:32Z

87.219.87.206: /* Efficient Construction Algorithms */

{{Distinguish|Polyhalite}}
'''Polyhalogen ions''' are a group of polyatomic [[cation]]s and [[anion]]s containing [[halogen]]s only. The ions can be classified into two classes, isopolyhalogen ions which contain one type of halogen only, and heteropolyhalogen ions with more than one type of halogen.

==Introduction==

Numerous polyhalogen ions have been found, with their salts isolated in the solid state and structurally characterized. The following tables summarize the species found so far.<ref name="Encyclo">{{cite book
| title = Encyclopedia of Inorganic Chemistry, 2nd edition
| chapter = Chlorine, Bromine, Iodine, & Astatine: Inorganic Chemistry
| author1 = R. Bruce King
| author2 =
| publisher = Wiley
| year = 2005
| isbn = 9780470862100
| page = 747
}}</ref><ref name="InorgChem" /><ref name="Greenwood" /><ref name="AdvInorgChem">{{cite book
| title = Advanced Inorganic Chemistry, 6th Edition
| author1 = F. Albert Cotton
| author2 = Geoffrey Wilkinson
| author3 = Carlos A. Murillo
| author4 = Manfred Bochmann
| publisher = Wiley
| year = 1999
| isbn = 978-0471199571
}}</ref><ref name="wiberg2001">{{Cite book
| title = Inorganic chemistry
| author = Wiberg, Egon; Wiberg, Nils and Holleman, Arnold Frederick
| publisher = Academic Press
| year = 2001
| isbn = 0-12-352651-5
| pages = 419–420
}}</ref>

{| class="wikitable"
! colspan=2|Isopolyhalogen cations
|-
| Diatomic species || *[Cl2]+, [Br2]+, [I2]+
|-
| Triatomic species || [Cl3]+, [Br3]+, [I3]+
|-
| Tetraatomic species || [Cl4]+, [I4]2+
|-
| Pentaatomic species || [Br5]+, [I5]+
|-
| Heptaatomic species || ^[I7]+
|-
| Higher species || [I15]3+
|}
Notes: *[Cl2]+ can only exist as [Cl2O2]2+ at low temperatures, a [[charge-transfer complex]] from O2 to [Cl2]+.<ref name="InorgChem">{{cite book
| title = Inorganic Chemistry, 3rd Edition
| chapter = Chapter 17: The group 17 elements
| author1 = Catherine E. Housecroft
| author2 = Alan G. Sharpe
| publisher = Pearson
| year = 2008
| isbn = 978-0-13-175553-6
| page = 547
}}</ref> Free [Cl2]+ is only known from its electronic band spectrum obtained in a low-pressure discharge tube.<ref name="Greenwood" />
^The existence of [I7]+ is possible but still uncertain.<ref name="Encyclo" />

{| class="wikitable"
! colspan=2|Heteropolyhalogen cations
|-
| Triatomic species || [ClF2]+, [Cl2F]+, [BrF2]+, [IF2]+, [ICl2]+, [IBrCl]+, [IBr2]+, [I2Cl]+, [I2Br]+
|-
| Pentaatomic species || [ClF4]+, [BrF4]+, [IF4]+, [I3Cl2]+
|-
| Heptaatomic species || [ClF6]+, [BrF6]+, [IF6]+
|}

{| class="wikitable"
! colspan=2|Isopolyhalogen anions
|-
| Triatomic species || [Cl3]-, [Br3]-, [I3]-
|-
| Tetraatomic species || [Br4]2-, [I4]2-
|-
| Pentaatomic species || [I5]-
|-
| Heptaatomic species || [I7]-
|-
| Octaatomic species || [Br8]2-, [I8]2-
|-
| Higher species || [I9]-, [I10]2-, [I10]4-, [I11]-, [I12]2-, [I13]3-, [I16]2-, [I22]4-, [I26]3-, [I26]4-, [I28]4-, [I29]3-
|}

{| class="wikitable"
! colspan=2|Heteropolyhalogen anions
|-
| Triatomic species || [ClF2]-, [BrF2]-, [BrCl2]-, [IF2]-, [ICl2]-, [IBrF]-, [IBrCl]-, [IBr2]-, [I2Cl]-, [I2Br]-, [AtBrCl]-, [AtBr2]-, [AtICl]-, [AtIBr]-, [AtI2]-
|-
| Pentaatomic species || [ClF4]-, [BrF4]-, [IF4]-, [ICl3F]-, [ICl4]-, [IBrCl3]-, [I2Cl3]-, [I2BrCl2]-, [I2Br2Cl]-, [I2Br3]-,[I4Cl]-, [I4Br]-
|-
| Hexaatomic species || [IF5]2-
|-
| Heptaatomic species || [ClF6]-, [BrF6]-, [IF6]-, [I3Br4]-
|-
| Nonaatomic species || [IF8]-
|}

==Structure==

[[File:Structures of some isopolyhalogen cations.png|center|thumb|650px|Structures of some isopolyhalogen cations.]]

[[File:Solid state structures of the polyhalogen ions (BrF2)+. (ClF2)+, (ICl2)+.png|center|thumb|950px|Solid state structures of the polyhalogen ions [BrF2]+, [ClF2]+, [ICl2]+ in their [SbF6]- salts.]]

[[File:Solid state structure of the (I3Cl2)+ ion.png|right|thumb|300px|Solid state structure of [I3Cl2]+ in [I3Cl2]+[AsCl6]-.]]

[[File:Structure of the (I2F12)- dimer.png|right|thumb|200px|Structure of the [I2F12]- dimer present in [Me4N]+[IF6]-.]]

Most of the structures of the ions have been determined by [[IR spectroscopy]], [[Raman spectroscopy]] and [[X-ray crystallography]]. The polyhalogen ions always have the heaviest and least electronegative halogen present in the ion as the central atom, making the ion asymmetric in some cases. For example, [Cl2F]+ has a structure of [Cl–Cl–F]- but not [Cl–F–Cl]-.

In general, the structures of most heteropolyhalogen ions and lower isopolyhalogen ions were in agreement with the [[VSEPR model]]. However, there were exceptional cases. For example, when the central atom is heavy and has seven [[lone pairs]], such as [BrF6]- and [IF6]-, they have an regular octahedral arrangement of fluoride ligands instead of a distorted one due to the presence of a [[Inert pair effect#Steric activity of the lone pair|stereochemically inert lone pair]]. More deviations from the ideal VSEPR model were found in the solid state structures due to strong cation-anion interactions, which also complicates interpretation of [[vibrational spectroscopy|vibrational spectroscopic]] data. In fact, all known structures of the polyhalogen anion salts, the anions make very close contact, ''via'' halogen bridges, with the counter-cations.<ref name="AdvInorgChem" /> For example, in the solid state, [IF6]- is not regularly octahedral, as solid state structure of [Me4N]+[IF6]- reveals loosely bound [I2F11]2- dimers. Significant cation-anion interactions were also found in [BrF2]+[SbF6]-, [ClF2]+[SbF6]-, [BrF4]+[Sb6F11]-.<ref name="InorgChem" />

{| class="wikitable"
! colspan=2|General structures of selected heteropolyhalogen ions
|-
| Linear (or almost linear) || [ClF2]-, [BrF2]-, [BrCl2]-, [IF2]-, [ICl2]-, [IBr2]-, [I2Cl]-, [I2Br]-
|-
| Bent || [ClF2]+, [Cl2F]+, [BrF2]+, [IF2]+, [ICl2]+, [I2Cl]+, [IBr2]+, [I2Br]+, [IBrCl]+
|-
| Square planar || [ClF4]-, [BrF4]-, [IF4]-, [ICl4]-
|-
| Disphenoidal (or seesaw) || [ClF4]+, [BrF4]+, [IF4]+
|-
| Pentagonal planar || #[IF5]2-
|-
| Octahedral || [ClF6]+, [BrF6]+, [IF6]+, §[ClF6]-, [BrF6]-, [IF6]-
|-
| Square antiprismatic || [IF8]-
|}
Note: #[IF5]2- is one of the two XYn-type species known to have the rare pentagonal planar geometry, the other being [XeF5]-. §[ClF6]- is distorted octahedral as the stereochemical inert pair effect is not significant in the chlorine atom.

The [I3Cl2]+ and [I3Br2]+ ions have a ''trans''-Z-type structure, analogous to that of [I5]+.

[[File:Solid state structure of the (BrF4)+ ion.png|center|thumb|500px|Solid state structure of [BrF4]+ in [BrF4]+[Sb2F11]+.]]

===Higher polyiodides===

{{Main|Polyiodide}}

The [[polyiodide]] ions have much more complicated structures. Discrete polyiodides usually have a linear sequence of iodine atoms and iodide ions, and is described in terms of association between I2, I- and I3- units, which reflects the origin of the polyiodide. In the solid states, the polyiodides can interact with each other to form chains, rings, or even complicated two-dimensional and three-dimensional networks.

==Bonding==

The bonding in polyhalogen ions mostly invoke the predominant use of ''p''-orbitals. Significant ''d''-orbital participation in the bonding is improbable as much promotional energy will be required, while scant ''s''-orbital participation is expected in iodine-containing species due to the [[inert pair effect]], suggested by data from [[Mössbauer spectroscopy]]. However, no bonding model has been capable of reproducing such wide range of bond lengths and angles observed so far.<ref name="Greenwood" />

As expected from the fact that an electron is removed from the [[antibonding orbital]] when X2 is ionized to [X2]+, the bond order as well as the bond strength in [X2]+ gets higher, consequently the interatomic distances in the molecular ion is less than those in X2.

Linear or nearly linear triatomic polyhalides have weaker and longer bonds compared with that in the corresponding diatomic interhalogen or halogen, consistent with the additional repulsion between atoms as the halide ion is added to the neutral molecule. Another model involving the use of [[resonance (chemistry)|resonance theory]] exists, for example, [ICl2]- can be viewed as the [[resonance hybrid]] of the following [[resonance (chemistry)#Use of contributing structures|canonical forms]]:

: [[File:Canonical forms of (ICl2)-.png|none|400px|]]

Evidence supporting this theory comes from the bond lengths (255pm in [ICl2]- and 232pm in [[Iodine monochloride|ICl]](g)) and bond stretching [[wavenumbers]] (267 and 222 cm−1 for symmetric and asymmetric stretching in [ICl2]- compared with 384 cm−1 in ICl), which suggests a bond order of about <math>\tfrac{1}{2}</math> for each I–Cl bonds in [ICl2]-, consistent with the interpretation using the resonance theory. Other triatomic species [XY2]- can be similarly interpreted.<ref name="InorgChem" />

==Synthesis==

The formation of polyhalogen ions can be viewed as the [[molecular autoionization|self-dissociation]] of their parent [[interhalogen]]s or [[halogen]]s:

:* 2 XYn {{eqm}} [XYn-1]+ + [XYn+1]-
:* 3 X2 {{eqm}} [X3]+ + [X3]-
:* 4 X2 {{eqm}} [X5]+ + [X3]-
:* 5 X2 {{eqm}} 2 [X2]+ + 2 [X3]-

===Polyhalogen cations===

There are two general strategies for preparing polyhalogen cations:
* By reacting the appropriate [[interhalogen]] with a [[lewis acid]] (such as the halides of [[Boron|B]], [[Aluminum|Al]], [[Phosphorus|P]], [[Arsenic|As]], [[Antimony|Sb]]) either in an inert or oxidizing solvent (such as anhydrous [[hydrogen fluoride|HF]]) or without one, to give a heteropolyhalogen cation.
: XYn + MYm → [XYn-1]+ + [MYm+1]-
* By an oxidative process, in which the halogen or interhalogen is reacted with an oxidizer and a lewis acid to give the cation:
: Cl2 + ClF + AsF5 → [Cl3]+[AsF6]-
In some cases the lewis acid (the [[fluoride]] acceptor) itself act as an oxidant:
: 3 I2 + 3 [[antimony pentafluoride|SbF5]] → 2 [I3]+[SbF6]- + SbF3

Usually the first method is employed for preparing heteropolyhalogen cations, and the second one is applicable to both. The oxidative process is useful in the preparation of the cations [IBr2]+, [ClF6]+, [BrF6]+, as their parent interhalogens, IBr3, ClF7, BrF7 respectively, has never been isolated:

: Br2 + IOSO2F → [IBr2]+[SO3F]-

: 2 ClF5 + 2 PtF6 → [ClF6]+[PtF6]- + [ClF4]+[PtF6]-

: BrF5 + [KrF]+[AsF6]- → [BrF6]+[AsF6]- + Kr

The preparation of some individual species are briefly summarized in the table below with equations:<ref name="Encyclo" /><ref name="InorgChem" /><ref name="Greenwood" /><ref name="AdvInorgChem" />

{| class="wikitable"
! colspan=3|Synthesis of some polyhalogen cations
|-
! Species !! Relevant chemical equation !! Additional conditions required
|-
| [Cl2]+ (as [Cl2O2]+) || Cl2 + [O2]+[SbF6]- → [Cl2O2]+[SbF6]- || in anhydrous HF at low temperatures
|-
| [Br2]+ || Br2 (in BrSO3F) + 3 SbF5 → [Br2]+[Sb3F16]- (not balanced) || at room temperature
|-
| [I2]+ || 2 I2 + S2O6F2 → 2 [I2]+[SO3F]- || in [[fluorosulfuric acid|HSO3F]]
|-
| [Cl3]+ || Cl2 + ClF + AsF5 → [Cl3]+[AsF6]- || at a temperature of 195K
|-
| [Br3]+ || 3 Br2 + 2 [O2]+[AsF6]- → 2 [Br3]+[AsF6]- + 2 O2 ||
|-
| [I3]+ || 3 I2 + S2O6F2 → 2 [I3]+[SO3F]- ||
|-
| [Cl4]+ || 2 Cl2 + IrF6 → [Cl4]+[IrF6]- || in anhydrous HF, at a temperature of <193K
|-
| [I4]2+ || 2 I2 + 3 AsF5 → [I4]2+[AsF6-]2 + AsF3 || in liquid SO2
|-
| [Br5]+ || 8 Br2 + 3 [XeF]+[AsF6]- → 3 [Br5]+[AsF6]- + 3 Xe + BrF3 ||
|-
| [I5]+ || 2 I2 + ICl + AlCl3 → [I5]+[AlCl4]- ||
|-
| [I7]+ || 7 I2 + S2O6F2 → 2 I7SO3F ||
|-
| [ClF2]+ || ClF3 + AsF5 → [ClF2]+[AsF6]- ||
|-
| [Cl2F]+ || 2 ClF + AsF5 → [Cl2F]+[AsF6]- || at a temperature of <197K
|-
| [BrF2]+ || 5 BrF3 + 2 Au → 3 BrF + 2 [BrF2]+[AuF4]- || with excess BrF3 required
|-
| [IF2]+ || IF3 + AsF5 → [IF2]+[AsF6]- ||
|-
| [ICl2]+ || ICl3 + SbCl5 → [ICl2]+[SbCl6]- ||
|-
| [IBr2]+ || Br2 + IOSO2F → [IBr2]+[SO3F]- ||
|-
| [ClF4]+ || ClF5 + SbF5 → [ClF4]+[SbF6]- ||
|-
| [BrF4]+ || BrF5 + AsF5 → [BrF4]+[AsF6]- ||
|-
| [IF4]+ || IF5 + 2 SbF5 → [IF4]+[Sb2F11]- ||
|-
| [ClF6]+ || ‡Cs2NiF6 + 5 AsF5 + ClF5 → [ClF6]+[AsF6]- + Ni[AsF6]2 + 2 CsAsF6 ||
|-
| [BrF6]+ || [KrF]+[AsF6]- + BrF5 → [BrF6]+[AsF6]- + Kr ||
|-
| [IF6]+ || IF7 + BrF3 → [IF6]+[BrF4]- ||
|}
‡In this reaction, the active oxidizing species is [NiF3]+, which is formed ''in situ'' in the Cs2NiF6/AsF5/HF system. It is an even more powerful oxidizing and fluorinating agent than [[platinum hexafluoride|PtF6]].

===Polyhalogen anions===

For polyhalogen anions, there are two general preparation strategies as well:
* By reacting an interhalogen or halogen with a [[lewis base]], most likely a fluoride:

: [Et4N]+Y- + XYn → [Et4N]+[XYn+1]-

: X2 + X- → X3-

* By oxidation of simple [[halide]]s:

: KI + Cl2 → K+[ICl2]-

The preparation of some individual species are briefly summarized in the table below with equations:<ref name="Encyclo" /><ref name="InorgChem" /><ref name="Greenwood" /><ref name="AdvInorgChem" />

{| class="wikitable"
! colspan=3|Synthesis of some polyhalogen anions
|-
! Species !! Relevant chemical equation !! Additional conditions required
|-
| [Cl3]-, [Br3]-, [I3]- || X2 + X- → [X3]- (X = Cl, Br, I) ||
|-
| [Br3]- || Br2 + [nBu4N]+Br- → [nBu4N]+[Br3]- || in [[1,2-dichloroethane]] or liquid sulfur dioxide. [Br3]- does not exist in solution and is only formed when the salt crystallizes out.
|-
| [Br5]- || 2 Br2 + [nBu4N]+Br- → [nBu4N]+[Br5]- || in 1,2-dichloroethane or liquid sulfur dioxide, with excess Br2
|-
| [ClF2]- || ClF + CsF → Cs+[ClF2]- ||
|-
| [BrCl2]-<ref>"Cesium dichlorobromide" in Handbook of Preparative Inorganic Chemistry, 2nd Ed. Edited by G. Brauer, Academic Press, 1963, NY. Vol. 1. p. 294.</ref> || Br2 + Cl2 + 2 CsCl → 2 Cs+[BrCl2]- ||
|-
| [ICl2]-<ref>"Potassium dichloroiodide" in Handbook of Preparative Inorganic Chemistry, 2nd Ed. Edited by G. Brauer, Academic Press, 1963, NY. Vol. 1. p. 295.</ref> || KI + Cl2 → K+[ICl2]- ||
|-
| [IBr2]-<ref>"Cesium dibromoiodide" in Handbook of Preparative Inorganic Chemistry, 2nd Ed. Edited by G. Brauer, Academic Press, 1963, NY. Vol. 1. p. 297.</ref> || CsI + Br2 → Cs+[IBr2]- ||
|-
| [AtBr2]-, [AtICl]-, [AtIBr]-, [AtI2]- || [[Astatine|At]]Y + X- → [AtXY]- (X = I, Br, Cl; Y = I, Br) ||
|-
| [ClF4]- || NOF + ClF3 → [NO]+[ClF4]- ||
|-
| [BrF4]- || 6 KCl + 8 BrF3 → 6 K+[BrF4]- + 3 Cl2 + Br2 || excess BrF5 needed
|-
| [IF4]- || 2 XeF2 + [Me4N]+I- → [Me4N]+[IF4]- + 2 Xe || the reactants were mixed at 242K, then warmed to 298K for the reaction to proceed
|-
| [ICl4]-<ref>"Potassium tetrachloroiodide" in Handbook of Preparative Inorganic Chemistry, 2nd Ed. Edited by G. Brauer, Academic Press, 1963, NY. Vol. 1. p. 298.</ref> || KI + ICl3 → K+[ICl4]- ||
|-
| [IF5]2- || IF3 + 2 [Me4N]+F- → [Me4N+]2[IF5]2- ||
|-
| [IF6]- || IF5 + CsF → Cs+[IF6]- ||
|-
| [I3Br4]- || [PPh4]+Br- + 3 IBr → [PPh4]+[I3Br4]- ||
|-
| [IF8]- || IF7 + [Me4N]+F- → [Me4N]+[IF8]- || in [[acetonitrile]]
|}

The higher polyiodides were formed upon crystallization of solutions containing various concentrations of I- and I2. For instance, the monohydrate of KI3 crystallizes when a saturated solution containing appropriate amounts of I2 and [[potassium iodide|KI]] is cooled.<ref>"Potassium triiodide" in Handbook of Preparative Inorganic Chemistry, 2nd Ed. Edited by G. Brauer, Academic Press, 1963, NY. Vol. 1. p. 294.</ref>

==Properties==

===Stability===

In general, a large counter cation or anion (such as [[Cesium|Cs]]+, [SbF6]-) can help stabilize the polyhalogen ions formed in the solid state from [[lattice energy]] considerations, as the packing efficiency was increased.

The polyhalogen cations are strong oxidizing agents, as indicated by the fact that they can only be prepared in oxidative liquids as a solvent, such as [[oleum]]. The most oxidizing and therefore most unstable ones are the species [X2]+ and [XF6]+ (X = Cl, Br), followed by [X3]+ and [IF6]+.

The stability of the [X2]+ salts (X = Br, I) are thermodynamically quite stable. However, their stability in solution depends on the [[superacid]] solvent. For example, [I2]+ is stable in HF of highest highest acidity (HF with 0.2''N'' SbF5, [[Hammett acidity function|H0]] = -20.65), but disproportionates to [I3]+, [I5]+ and I2 as acidity is decreased by adding different amounts of [[Niobium pentafluoride|NbF5]], [[Tantalum pentafluoride|TaF5]] or [[sodium fluoride|NaF]].<ref name="AdvInorgChem" />

: 14 [I2]+ + 5 F- → 9 [I3]+ + IF5

For polyhalogen anions with the same cation, the more stable ones are those with a heavier halogen at the center, symmetric ions are also more stable than asymmetric ones. therefore the stability of the anions decrease in the order:

: [I3]- > [IBr2]- > [ICl2]- > [I2Br]- > [Br3]- > [BrCl2]- > [Br2Cl]-

Heteropolyhalogen ions with a coordination number larger than or equal to four can only exist with fluoride ligands.

===Color===

Most polyhalogen ions are intensely colored, with deepened color as the atomic weight of the constituent element increases. The well-known [[starch]]-iodine complex has a deep blue color due to the linear [I5]- ions present in the [[amylose]] helix.<ref name="AdvInorgChem" /> Some colors of the common species were listed below:<ref name="Greenwood">{{Greenwood&Earnshaw2nd|page=835}}</ref>
:* fluorocations tend to be colorless or pale yellow, other heteropolyhalogen ions are orange, red or deep purple<ref name="AdvInorgChem" />
:* compounds of [ICl2]+ are wine red to bright orange; while that of [I2Cl]+ are dark brown to purplish black
:* [Cl3]+ is yellow
:* [Cl4]+ is blue<ref name="InorgChem" />
:* [Br2]+ is cherry red
:* [Br3]+ is brown
:* [Br5]+ is dark brown
:* [I2]+ is bright blue
:* [I3]+ is dark brown to black
:* [I4]2+ is red to brown
:* [I5]+ is green or black, the salt [I5]+[AlCl4]- exists as greenish-black needles, but appears brown-red in thin sections
:* [I7]+ is black, if its existence in the compound I7SO3F has been firmly established
:* [I15]3+ is black<ref name="wiberg2001" />
:* [ICl4]- is golden-yellow
:* polyiodides have very dark colors, either dark brown or dark blue

===Chemical properties===

The heteropolyhalogen cations are explosively reactive oxidants, and the cations often have higher reactivity than their parent interhalogens and decompose by reductive pathways. As expected from the highest oxidation state of +7 in [ClF6]+, [BrF6]+ and [IF6]+, these species are extremely strong oxidizing agents, demonstrated by the reactions shown below:

: 2 O2 + 2 [BrF6]+[AsF6]- →2 [[dioxygenyl|[O2]+]][AsF6]- + 2 BrF5 + F2
: [[Radon|Rn]] + [IF6]+[SbF6]- →[RnF]+[SbF6]- + IF5

Polyhalogen cations with lower oxidation states tend to [[disproportionation|disproportionate]]. For example, [Cl2F]+ is unstable in solution and disproportionate completely in [[fluoroantimonic acid|HF/SbF5]] even at 197K:

: 2 [Cl2F]+ → [ClF2]+ + [Cl3]+

[I2]+ reversibly dimerizes at 193K, and is observed as the blue color of [[paramagnetic]] [I2]+ dramatically shifts to the red-brown color of [[diamagnetic]] [I2]+, together with a drop in [[magnetochemistry#Magnetic susceptibility|paramagnetic susceptibility]] and [[electrical conductivity]] when the solution is cooled to below 193K:<ref name="InorgChem" />

: 2 [I2]+ {{eqm}} [I4]2+

The dimerization can be attributed to the overlapping of the half-filled π* orbitals in two [I2]+.

[Cl4]+ in [Cl4]+[IrF6]- is structurally analogous to [I4]2+, but decomposes at 195K to give salts of [Cl3]+ instead of [Cl2]+ and Cl2.<ref name="InorgChem" />

Attempts to prepare ClF7 and BrF7 by fluorinating [ClF6]+ and [BrF6]+ using [[nitrosyl fluoride|NOF]] have met with failure, instead the following reactions occurred:<ref name="Greenwood" />

: [ClF6]+[PtF6]- + NOF →[NO]+[PtF6]- + ClF5 + F2

: [BrF6]+[AsF6]- + 2 NOF →[NO]+[AsF6]- + [NO]+[BrF6]- + F2

The anions are less reactive compared to the cations, and are generally weaker oxidants than their parent interhalogens. They are less reactive towards organic compounds, and some salts are of quite high thermal stability. Salts containing polyhalogen anions of the type M+[XmYnZp]- (where m+n+p = 3, 5, 7, 9...) tend to dissociate into simple monohalide salts between M+ and the most [[electronegative]] halogen, so that the monohalide has the highest lattice energy. An interhalogen is usually formed as the other product. The salt [Me4N]+[ClF4]- decomposes at about 100°C, and salts of [ClF6]- are thermally unstable and can explode even at -31°C.<ref name="AdvInorgChem" />

==References==
{{reflist}}

*
*
*
*



[[Category:Halogens]]

Image moment

2014-01-11T00:40:09Z

87.219.204.227: /* External links */

{{No footnotes|date=May 2012}}
[[Image:TyTunnelling.png|thumb|right|Schematic representation (similar to [[band diagram]]) of an electron tunnelling through a barrier]]In physics, a '''Coulomb blockade''' (abbreviated CB), named after [[Charles-Augustin de Coulomb]]'s electrical force, is the increased [[electrical resistance|resistance]] at small [[voltage bias|bias voltage]]s of an electronic device comprising at least one low-[[capacitance]] [[tunnel junction]]. Because of the CB, the resistances of devices are not constant at low bias voltages, but increase to infinity for biases under a certain threshold (i.e. no current flows). When few electrons are involved and an external static magnetic field is applied, Coulomb blockade provides the ground for [[spin blockade]] (also called Pauli blockade) which includes quantum mechanical effects due to spin interactions between the electrons.

==Coulomb blockade in a tunnel junction==
A tunnel junction is, in its simplest form, a thin insulating barrier between two conducting [[electrode]]s. If the electrodes are [[Superconductivity|superconducting]], [[Cooper pair]]s (with a [[charge (physics)|charge]] of two [[elementary charge]]s) carry the current. In the case that the electrodes are ''normalconducting'', i.e. neither [[Superconductivity|superconducting]] nor [[Semiconductor|semiconducting]], [[electron]]s (with a charge of one [[elementary charge]]) carry the current. The following reasoning is for the case of tunnel junctions with an insulating barrier between two
normal conducting electrodes (NIN junctions).

According to the laws of [[classical electrodynamics]], no current can flow through an insulating barrier. According to the laws of [[quantum mechanics]], however, there is a nonvanishing (larger than zero)
[[probability]] for an electron on one side of the barrier to reach the other side (see [[quantum tunnelling]]). When a [[bias voltage]] is applied, this means that there will be a current, and, neglecting additional effects, the tunnelling current will be proportional to the bias voltage. In electrical terms, the tunnel junction behaves as a [[resistor]] with a constant resistance, also known as an [[Ohm's law|ohmic resistor]]. The resistance depends [[exponential function|exponentially]] on the barrier thickness. Typical barrier thicknesses are on the order of one to several [[nanometer]]s.

An arrangement of two conductors with an insulating layer in between not only has a resistance, but also a finite [[capacitance]]. The insulator is also called [[dielectric]] in this context, the tunnel junction behaves as a [[capacitor]].

Due to the discreteness of electrical charge, current through a tunnel junction is a series of events in which exactly one electron passes (''tunnels'') through the tunnel barrier (we neglect cotunneling, in which two electrons tunnel simultaneously). The tunnel junction capacitor is charged with one elementary charge by the tunnelling electron, causing a [[voltage]] buildup <math>U=e/C</math>, where <math>e</math> is the [[elementary charge]] of 1.6×10−19 [[coulomb]] and <math>C</math> the capacitance of the junction. If the capacitance is very small, the voltage buildup can be large enough to prevent another electron from tunnelling. The electrical current is then suppressed at low bias voltages and the resistance of the device is no longer constant. The increase of the [[Electrical resistance#Differential resistance|differential resistance]] around zero bias is called the Coulomb blockade.

==Observing the Coulomb blockade ==

In order for the Coulomb blockade to be observable, the temperature has to be low enough so that the characteristic charging energy (the energy that is required to charge the junction with one elementary charge) is larger than the thermal energy of the charge carriers. In the past, for capacitances above 1 [[femtofarad]] (10−15 [[farad]]), this implied that the temperature has to be below about 1 [[kelvin]]. This temperature range is routinely reached for example by 3He refrigerators. Thanks to small sized quantum dots of only few nanometers, Coulomb blockade has been observed next above liquid helium temperature, up to room temperature. <ref>{{cite doi|10.1021/nl1044692}}</ref>

To make a tunnel junction in [[plate condenser]] geometry with a capacitance of 1 femtofarad, using an oxide layer of electric [[permittivity]] 10 and thickness one [[nanometer]], one has to create electrodes with dimensions of approximately 100 by 100 nanometers. This range of dimensions is routinely reached for example by [[electron beam lithography]] and appropriate [[pattern transfer]] technologies, like the [[Niemeyer-Dolan technique]], also known as [[Niemeyer-Dolan technique|shadow evaporation technique]]. The integration of quantum dot fabrication with standard industrial technology has been achieved for silicon. CMOS process for obtaining massive production of single electron quantum dot transistors with channel size down to 20 nm x 20 nm has been implemented. <ref>{{cite doi|10.1088/0957-4484/23/21/215204|url=http://arxiv.org/pdf/1203.4811.pdf|format=pdf}}</ref>

==Single electron transistor==
[[Image:Set schematic.svg|thumb|right|Schematic of a single electron transistor]]
[[Image:Single electron transistor.svg|thumb|right|Energylevels of source, island and drain (from left to right) in a single electron transistor for both the blocking state (upper part) and the transmitting state (lower part).]]
[[Image:TySETimage.png|thumb|right|Single electron transistor with [[niobium]] leads and [[aluminium]] island]]
The simplest device in which the effect of Coulomb blockade can be observed is the so-called '''single electron transistor'''. It consists of two electrodes known as the ''drain'' and the ''source'', connected through tunnel junctions to one common electrode with a low [[Capacitance#Self-capacitance|self-capacitance]], known as the ''island''. The electrical potential of the island can be tuned by a third electrode, known as the ''gate'', capacitively coupled to the island. 

In the blocking state no accessible energy levels are within tunneling range of the electron (red) on the source contact. All energy levels on the island electrode with lower energies are occupied.

When a positive voltage is applied to the gate electrode the energy levels of the island electrode are lowered. The electron (green 1.) can tunnel onto the island (2.), occupying a previously vacant energy level. From there it can tunnel onto the drain electrode (3.) where it inelastically scatters and reaches the drain electrode Fermi level (4.).

The energy levels of the island electrode are evenly spaced with a separation of <math>\Delta E.</math> This gives rise to a self-capacitance <math>C</math> of the island, defined as
:<math>C=\frac{e^2}{\Delta E}.</math>
To achieve the Coulomb blockade, three criteria have to be met:
# The bias voltage must be lower than the [[elementary charge]] divided by the self-capacitance of the island: <math>V_\text{bias} < \frac{e}{C}</math> ;
# The thermal energy in the source contact plus the thermal energy in the island, i.e. <math>k_BT,</math> must be below the charging energy: <math>k_BT < \frac{e^2}{C},</math> or else the electron will be able to pass the QD via thermal excitation; and
# The tunneling resistance, <math>R_t,</math> should be greater than <math>\frac{h}{e^2},</math> which is derived from Heisenberg's [[uncertainty principle]]. <ref>{{Cite thesis |type=Ph.D. |chapter=2.5 Minimum Tunnel Resistance for Single Electron Charging |title=About Single-Electron Devices and Circuits |url=http://www.iue.tuwien.ac.at/phd/wasshuber/node20.html |last=Wasshuber |first= Christoph|year= 1997|publisher= Vienna University of Technology |accessdate= 12/5/2012}}</ref>

==Coulomb blockade thermometer==

A typical Coulomb blockade thermometer (CBT) is made from an array of metallic islands, connected to each other through a thin insulating layer. A tunnel junction forms between the islands, and as voltage is applied, electrons may tunnel across this junction. The tunneling rates and hence the conductance vary according to the charging energy of the islands as well as the thermal energy of the system.

Coulomb blockade thermometer is a primary [[thermometer]] based on electric conductance characteristics of tunnel junction arrays. The parameter V½=5.439NkBT/e, the full width at half
minimum of the measured differential conductance dip over an array of N junctions together with the [[physical constants]] provide the absolute temperature.

==References==
{{reflist}}

* ''Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures'', eds. H. Grabert and M. H. Devoret (Plenum Press, New York, 1992)

* D.V. Averin and K.K Likharev, in ''Mesoscopic Phenomena in Solids'', eds. B.L. Altshuler, P.A. Lee, and R.A. Webb (Elsevier, Amsterdam, 1991)

* Fulton, T.A. & Dolan, G.J. "Observation of single-electron charging effects in small tunnel junctions" ''Phys. Rev. Lett.'' '''59''', 109-112 (1987), {{doi|10.1103/PhysRevLett.59.109}}

==External links==
* [http://books.google.com/books?id=TNZyxqXGFY8C Computational Single-Electronics book]
* [http://nanohub.org/resources/756 Online lecture on Coulomb Blockade] by S. Datta (2004)

{{DEFAULTSORT:Coulomb Blockade}}
[[Category:Nanoelectronics]]
[[Category:Quantum electronics]]
[[Category:Mesoscopic physics]]