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== Chemistry == {{main|Compounds of aluminium}} Aluminium combines characteristics of pre- and post-transition metals. Since it has few available electrons for metallic bonding, like its heavier [[Group 13 element|group 13]] congeners, it has the characteristic physical properties of a post-transition metal, with longer-than-expected interatomic distances.{{sfn|Greenwood|Earnshaw|1997|pp= 222–224}} Furthermore, as Al<sup>3+</sup> is a small and highly charged cation, it is strongly polarizing and [[Chemical bond|bonding]] in aluminium compounds tends towards [[Covalent bond|covalency]];{{sfn|Greenwood|Earnshaw|1997|pp=224–227}} this behavior is similar to that of [[beryllium]] (Be<sup>2+</sup>), and the two display an example of a [[diagonal relationship]].{{sfn|Greenwood|Earnshaw|1997|pp=112–113}} The underlying core under aluminium's valence shell is that of the preceding [[noble gas]], whereas those of its heavier congeners [[gallium]], [[indium]], [[thallium]], and [[nihonium]] also include a filled d-subshell and in some cases a filled f-subshell. Hence, the inner electrons of aluminium shield the valence electrons almost completely, unlike those of aluminium's heavier congeners. As such, aluminium is the most electropositive metal in its group, and its hydroxide is in fact more basic than that of gallium.{{sfn|Greenwood|Earnshaw|1997|pp=224–227}}{{efn|In fact, aluminium's electropositive behavior, high affinity for oxygen, and highly negative [[standard electrode potential]] are all better aligned with those of [[scandium]], [[yttrium]], [[lanthanum]], and [[actinium]], which like aluminium have three valence electrons outside a noble gas core; this series shows continuous trends whereas those of group 13 is broken by the first added d-subshell in gallium and the resulting [[d-block contraction]] and the first added f-subshell in thallium and the resulting [[lanthanide contraction]].{{sfn|Greenwood|Earnshaw|1997|pp=224–227}}}} Aluminium also bears minor similarities to the metalloid boron in the same group: AlX<sub>3</sub> compounds are valence [[isoelectronic]] to BX<sub>3</sub> compounds (they have the same valence electronic structure), and both behave as [[Lewis acid]]s and readily form [[adduct]]s.{{sfn|King|1995|p=241}} Additionally, one of the main motifs of boron chemistry is [[regular icosahedron|regular icosahedral]] structures, and aluminium forms an important part of many icosahedral [[quasicrystal]] alloys, including the Al–Zn–Mg class.{{sfn|King|1995|pp=235–236}} Aluminium has a high [[chemical affinity]] to oxygen, which renders it suitable for use as a [[reducing agent]] in the [[thermite]] reaction. A fine powder of aluminium reacts explosively on contact with [[liquid oxygen]]; under normal conditions, however, aluminium forms a thin oxide layer (~5 nm at room temperature)<ref>{{Cite book |last=Hatch|first=John E.|title=Aluminum : properties and physical metallurgy|date=1984 |publisher=American Society for Metals, Aluminum Association |location=Metals Park, Ohio|pages=242 |oclc=759213422|isbn=978-1-61503-169-6}} </ref> that protects the metal from further corrosion by oxygen, water, or dilute acid, a process termed [[passivation (chemistry)|passivation]].{{sfn|Greenwood|Earnshaw|1997|pp=224–227}}<ref name="CorrAl">{{cite book |url=https://books.google.com/books?id=NAABS5KrVDYC&pg=PA81 |title=Corrosion of Aluminium|last=Vargel|first=Christian|date=2004 |publisher=Elsevier|isbn=978-0-08-044495-6|orig-year=French edition published 1999 |archive-url=https://web.archive.org/web/20160521212331/https://books.google.com/books?id=NAABS5KrVDYC&pg=PA81|archive-date=21 May 2016|url-status=live}} </ref> Aluminium is not attacked by oxidizing acids because of its passivation. This allows aluminium to be used to store reagents such as [[nitric acid]], concentrated [[sulfuric acid]], and some organic acids.<ref name="Ullmann">{{cite book |last1=Frank|first1=W.B.|title=Ullmann's Encyclopedia of Industrial Chemistry|title-link=Ullmann's Encyclopedia of Industrial Chemistry|date=2009 |publisher=Wiley-VCH|isbn=978-3-527-30673-2|chapter=Aluminum|doi=10.1002/14356007.a01_459.pub2}}</ref> In hot concentrated [[hydrochloric acid]], aluminium reacts with water with evolution of hydrogen, and in aqueous [[sodium hydroxide]] or [[potassium hydroxide]] at room temperature to form [[aluminates]]—protective passivation under these conditions is negligible.<ref name="Beal1999">{{cite book|url=https://books.google.com/books?id=Askwi3lXdlcC&pg=PA90|title=Engine Coolant Testing : Fourth Volume|last=Beal|first=Roy E.|year=1999|publisher=ASTM International|isbn=978-0-8031-2610-7|page=90|archive-url=https://web.archive.org/web/20160424071051/https://books.google.com/books?id=Askwi3lXdlcC&pg=PA90|archive-date=24 April 2016|url-status=live}}</ref> [[Aqua regia]] also dissolves aluminium.<ref name="Ullmann" /> Aluminium is corroded by dissolved [[chlorides]],<ref>{{Cite journal |last1=Xhanari |first1=Klodian |last2=Finšgar |first2=Matjaž |date=December 2019 |title=Organic corrosion inhibitors for aluminum and its alloys in chloride and alkaline solutions: A review |journal=Arabian Journal of Chemistry |language=en |volume=12 |issue=8 |pages=4648 |doi=10.1016/j.arabjc.2016.08.009|doi-access=free }}</ref> such as common [[sodium chloride]]. The oxide layer on aluminium is also destroyed by contact with [[mercury (element)|mercury]] due to [[Amalgam (chemistry)|amalgamation]] or with salts of some electropositive metals.{{sfn|Greenwood|Earnshaw|1997|pp=224–227}} As such, the strongest aluminium alloys are less corrosion-resistant due to [[galvanic cell|galvanic]] reactions with alloyed [[copper]],<ref name="Polmear1995" /> and aluminium's corrosion resistance is greatly reduced by aqueous salts, particularly in the presence of dissimilar metals.{{sfn|Greenwood|Earnshaw|1997|pp= 222–224}} Aluminium reacts with most nonmetals upon heating, forming compounds such as [[aluminium nitride]] (AlN), [[aluminium sulfide]] (Al<sub>2</sub>S<sub>3</sub>), and the aluminium halides (AlX<sub>3</sub>). It also forms a wide range of [[intermetallic compound]]s involving metals from every group on the periodic table.{{sfn|Greenwood|Earnshaw|1997|pp=224–227}} === Inorganic compounds === The vast majority of compounds, including all aluminium-containing minerals and all commercially significant aluminium compounds, feature aluminium in the oxidation state 3+. The [[coordination number]] of such compounds varies, but generally Al<sup>3+</sup> is either six- or four-coordinate. Almost all compounds of aluminium(III) are colorless.{{sfn|Greenwood|Earnshaw|1997|pp=224–227}} [[File:AlHydrolysis.png|thumb|upright=1.0|right|Aluminium hydrolysis as a function of pH. Coordinated water molecules are omitted.<ref>*{{cite book |last1=Baes|first1=C. F. |last2=Mesmer|first2=R. E. |title=The Hydrolysis of Cations|year=1986|orig-year=1976 |publisher=Robert E. Krieger|isbn=978-0-89874-892-5}}</ref>]] In aqueous solution, Al<sup>3+</sup> exists as the hexaaqua cation [Al(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup>, which has an approximate [[acid dissociation constant|K<sub>a</sub>]] of 10<sup>−5</sup>.{{sfn|Greenwood|Earnshaw|1997|pp=242–252}} Such solutions are acidic as this cation can act as a proton donor and progressively [[hydrolysis|hydrolyze]] until a [[Precipitation (chemistry)|precipitate]] of [[aluminium hydroxide]], Al(OH)<sub>3</sub>, forms. This is useful for [[Sedimentation (water treatment)|clarification]] of water, as the precipitate nucleates on [[Suspension (chemistry)|suspended]] particles in the water, hence removing them. Increasing the pH even further leads to the hydroxide dissolving again as [[aluminate]], [Al(H<sub>2</sub>O)<sub>2</sub>(OH)<sub>4</sub>]<sup>−</sup>, is formed. Aluminium hydroxide forms both salts and aluminates and dissolves in acid and alkali, as well as on fusion with acidic and basic oxides.{{sfn|Greenwood|Earnshaw|1997|pp=224–227}} This behavior of Al(OH)<sub>3</sub> is termed [[amphoterism]] and is characteristic of weakly basic cations that form insoluble hydroxides and whose hydrated species can also donate their protons. One effect of this is that [[aluminium salt]]s with weak acids are hydrolyzed in water to the aquated hydroxide and the corresponding nonmetal hydride: for example, [[aluminium sulfide]] yields [[hydrogen sulfide]]. However, some salts like [[aluminium carbonate]] exist in aqueous solution but are unstable as such; and only incomplete hydrolysis takes place for salts with strong acids, such as the halides, [[aluminium nitrate|nitrate]], and [[aluminium sulfate|sulfate]]. For similar reasons, anhydrous aluminium salts cannot be made by heating their "hydrates": hydrated aluminium chloride is in fact not AlCl<sub>3</sub>·6H<sub>2</sub>O but [Al(H<sub>2</sub>O)<sub>6</sub>]Cl<sub>3</sub>, and the Al–O bonds are so strong that heating is not sufficient to break them and form Al–Cl bonds. This reaction is observed instead:{{sfn|Greenwood|Earnshaw|1997|pp=224–227}} :2[Al(H<sub>2</sub>O)<sub>6</sub>]Cl<sub>3</sub> {{overunderset|→|heat| }} Al<sub>2</sub>O<sub>3</sub> + 6 HCl + 9 H<sub>2</sub>O All four [[Halide|trihalides]] are well known. Unlike the structures of the three heavier trihalides, [[aluminium fluoride]] (AlF<sub>3</sub>) features six-coordinate aluminium, which explains its involatility and insolubility as well as high [[heat of formation]]. Each aluminium atom is surrounded by six fluorine atoms in a distorted [[octahedron|octahedral]] arrangement, with each fluorine atom being shared between the corners of two octahedra. Such {AlF<sub>6</sub>} units also exist in complex fluorides such as [[cryolite]], Na<sub>3</sub>AlF<sub>6</sub>.{{efn|These should not be considered as [AlF<sub>6</sub>]<sup>3−</sup> complex anions as the Al–F bonds are not significantly different in type from the other M–F bonds.{{sfn|Greenwood|Earnshaw|1997|pp=233–237}}}} AlF<sub>3</sub> melts at {{convert|1290|°C|0|abbr=on}} and is made by reaction of [[aluminium oxide]] with [[hydrogen fluoride]] gas at {{convert|700|°C|-2|abbr=on}}.{{sfn|Greenwood|Earnshaw|1997|pp=233–237}} With heavier halides, the coordination numbers are lower. The other trihalides are [[Dimer (chemistry)|dimeric]] or [[polymer]]ic with tetrahedral four-coordinate aluminium centers.{{efn|Such differences in coordination between the fluorides and heavier halides are not unusual, occurring in Sn<sup>IV</sup> and Bi<sup>III</sup>, for example; even bigger differences occur between [[carbon dioxide|CO<sub>2</sub>]] and [[silicon dioxide|SiO<sub>2</sub>]].{{sfn|Greenwood|Earnshaw|1997|pp=233–237}}}} [[Aluminium trichloride]] (AlCl<sub>3</sub>) has a layered polymeric structure below its melting point of {{convert|192.4|°C|0|abbr=on}} but transforms on melting to Al<sub>2</sub>Cl<sub>6</sub> dimers. At higher temperatures those increasingly dissociate into trigonal planar AlCl<sub>3</sub> monomers similar to the structure of [[boron trichloride|BCl<sub>3</sub>]]. [[Aluminium tribromide]] and [[aluminium triiodide]] form Al<sub>2</sub>X<sub>6</sub> dimers in all three phases and hence do not show such significant changes of properties upon phase change.{{sfn|Greenwood|Earnshaw|1997|pp=233–237}} These materials are prepared by treating aluminium with the halogen. The aluminium trihalides form many [[addition compound]]s or complexes; their [[Lewis acid]]ic nature makes them useful as [[catalysis|catalysts]] for the [[Friedel–Crafts reaction]]s. Aluminium trichloride has major industrial uses involving this reaction, such as in the manufacture of [[anthraquinone]]s and [[styrene]]; it is also often used as the precursor for many other aluminium compounds and as a reagent for converting nonmetal fluorides into the corresponding chlorides (a [[Transhalogenation|transhalogenation reaction]]).{{sfn|Greenwood|Earnshaw|1997|pp=233–237}} Aluminium forms one stable oxide with the [[chemical formula]] Al<sub>2</sub>O<sub>3</sub>, commonly called [[alumina]].<ref>{{Cite book |url=https://books.google.com/books?id=MYAABAAAQBAJ&q=Aluminium+forms+one+stable+oxide,+known+by+its+mineral+name+corundum&pg=PA14|title=Pigment Compendium |last1=Eastaugh|first1=Nicholas|last2=Walsh|first2=Valentine|last3=Chaplin|first3=Tracey|last4=Siddall|first4=Ruth|date=2008 |publisher=Routledge|isbn=978-1-136-37393-0|language=en|access-date=1 October 2020 |archive-date=15 April 2021|archive-url=https://web.archive.org/web/20210415083327/https://books.google.com/books?id=MYAABAAAQBAJ&q=Aluminium+forms+one+stable+oxide,+known+by+its+mineral+name+corundum&pg=PA14|url-status=live}} </ref> It can be found in nature in the mineral [[corundum]], α-alumina;<ref>{{Cite book |url=https://books.google.com/books?id=X2NZAAAAYAAJ&q=Aluminium+forms+one+stable+oxide,+known+by+its+mineral+name+corundum&pg=PA718 |title=A treatise on chemistry|last1=Roscoe|first1=Henry Enfield|last2=Schorlemmer|first2=Carl|date=1913 |publisher=Macmillan|language=en|access-date=1 October 2020 |archive-date=15 April 2021|archive-url=https://web.archive.org/web/20210415111928/https://books.google.com/books?id=X2NZAAAAYAAJ&q=Aluminium+forms+one+stable+oxide,+known+by+its+mineral+name+corundum&pg=PA718|url-status=live}} </ref> there is also a γ-alumina phase.{{sfn|Greenwood|Earnshaw|1997|pp=242–252}} Its crystalline form, corundum, is very hard ([[Mohs hardness]] 9), has a high melting point of {{convert|2045|°C|0|abbr=on}}, has very low volatility, is chemically inert, and a good electrical insulator, it is often used in abrasives (such as toothpaste), as a refractory material, and in [[ceramics]], as well as being the starting material for the electrolytic production of aluminium. [[Sapphire]] and [[ruby]] are impure corundum contaminated with trace amounts of other metals.{{sfn|Greenwood|Earnshaw|1997|pp=242–252}} The two main oxide-hydroxides, AlO(OH), are [[boehmite]] and [[diaspore]]. There are three main trihydroxides: [[bayerite]], [[gibbsite]], and [[nordstrandite]], which differ in their crystalline structure ([[polymorphism (materials science)|polymorphs]]). Many other intermediate and related structures are also known.{{sfn|Greenwood|Earnshaw|1997|pp=242–252}} Most are produced from ores by a variety of wet processes using acid and base.{{Ambiguous|reason=What does "most" refers to? Trihydroxides? Oxides?|date=April 2025}} Heating the hydroxides leads to formation of corundum. These materials are of central importance to the production of aluminium and are themselves extremely useful. Some mixed oxide phases are also very useful, such as [[spinel]] (MgAl<sub>2</sub>O<sub>4</sub>), Na-β-alumina (NaAl<sub>11</sub>O<sub>17</sub>), and [[tricalcium aluminate]] (Ca<sub>3</sub>Al<sub>2</sub>O<sub>6</sub>, an important mineral phase in [[Portland cement]]).{{sfn|Greenwood|Earnshaw|1997|pp=242–252}} The only stable [[chalcogenide]]s under normal conditions are [[aluminium sulfide]] (Al<sub>2</sub>S<sub>3</sub>), [[aluminium selenide|selenide]] (Al<sub>2</sub>Se<sub>3</sub>), and [[aluminium telluride|telluride]] (Al<sub>2</sub>Te<sub>3</sub>). All three are prepared by direct reaction of their elements at about {{convert|1000|°C|-2|abbr=on}} and quickly hydrolyze completely in water to yield aluminium hydroxide and the respective [[hydrogen chalcogenide]]. As aluminium is a small atom relative to these chalcogens, these have four-coordinate tetrahedral aluminium with various polymorphs having structures related to [[wurtzite]], with two-thirds of the possible metal sites occupied either in an orderly (α) or random (β) fashion; the sulfide also has a γ form related to γ-alumina, and an unusual high-temperature hexagonal form where half the aluminium atoms have tetrahedral four-coordination and the other half have trigonal bipyramidal five-coordination.{{sfn|Greenwood|Earnshaw|1997|pp=252–257}} Four [[pnictide]]s – [[aluminium nitride]] (AlN), [[aluminium phosphide]] (AlP), [[aluminium arsenide]] (AlAs), and [[aluminium antimonide]] (AlSb) – are known. They are all [[III-V semiconductor]]s isoelectronic to [[silicon]] and [[germanium]], all of which but AlN have the [[zinc blende]] structure. All four can be made by high-temperature (and possibly high-pressure) direct reaction of their component elements.{{sfn|Greenwood|Earnshaw|1997|pp=252–257}} <!-- [[Aluminium carbide]] (Al<sub>4</sub>C<sub>3</sub>) is made by heating a mixture of the elements above {{convert|1000|°C|-2|abbr=on}}. The pale yellow crystals consist of tetrahedral aluminium centers. It reacts with water or dilute acids to give [[methane]]. The [[metal acetylide|acetylide]], Al<sub>2</sub>(C<sub>2</sub>)<sub>3</sub>, is made by passing [[acetylene]] over heated aluminium. [[Aluminium nitride]] (AlN) is the only nitride known for aluminium. Unlike the oxides, it features tetrahedral Al centers. It can be made from the elements at {{convert|800|°C|-2|abbr=on}}. It is air-stable material with a usefully high [[thermal conductivity]]. [[Aluminium phosphide]] (AlP) is made similarly; it hydrolyses to give [[phosphine]]: : AlP + 3 H<sub>2</sub>O → Al(OH)<sub>3</sub> + PH<sub>3</sub>--> [[Aluminium alloy]]s well with most other metals (with the exception of most [[alkali metals]] and group 13 metals) and over 150 [[intermetallics]] with other metals are known. Preparation involves heating fixed metals together in certain proportion, followed by gradual cooling and [[Annealing (metallurgy)|annealing]]. Bonding in them is predominantly [[Metallic bonding|metallic]] and the crystal structure primarily depends on efficiency of packing.<ref>{{Cite book |last=Downs|first=A. J. |url=https://books.google.com/books?id=v-04Kn758yIC&q=intermetallic+aluminium&pg=PA218 |title=Chemistry of Aluminium, Gallium, Indium and Thallium|date=1993 |publisher=Springer Science & Business Media|isbn=978-0-7514-0103-5|pages=218|language=en|access-date=1 October 2020 |archive-date=15 April 2021|archive-url=https://web.archive.org/web/20210415115039/https://books.google.com/books?id=v-04Kn758yIC&q=intermetallic+aluminium&pg=PA218|url-status=live}}</ref> There are few compounds with lower oxidation states. A few [[aluminium(I)]] compounds exist: AlF, AlCl, AlBr, and AlI exist in the gaseous phase when the respective trihalide is heated with aluminium, and at cryogenic temperatures.{{sfn|Greenwood|Earnshaw|1997|pp=233–237}} A stable derivative of aluminium monoiodide is the cyclic [[adduct]] formed with [[triethylamine]], Al<sub>4</sub>I<sub>4</sub>(NEt<sub>3</sub>)<sub>4</sub>. Al<sub>2</sub>O and Al<sub>2</sub>S also exist but are very unstable.<ref name="al1">{{cite journal |last1=Dohmeier |first1=C. |last2=Loos |first2=D. |last3=Schnöckel |first3=H. |date=1996 |title=Aluminum(I) and Gallium(I) Compounds: Syntheses, Structures, and Reactions |journal=[[Angewandte Chemie International Edition]] |volume=35 |issue=2 |pages=129–149 |doi=10.1002/anie.199601291 }}</ref> Very simple aluminium(II) compounds are invoked or observed in the reactions of Al metal with oxidants. For example, [[aluminium monoxide]], AlO, has been detected in the gas phase after explosion<ref>{{cite journal |last1=Tyte |first1=D.C. |date=1964 |title=Red (B2Π–A2σ) Band System of Aluminium Monoxide |journal=[[Nature (journal)|Nature]] |volume=202 |issue=4930 |pages=383–384 |bibcode=1964Natur.202..383T |doi=10.1038/202383a0 |s2cid=4163250 }}</ref> and in stellar absorption spectra.<ref>{{cite journal |last1=Merrill |first1=P.W. |last2=Deutsch |first2=A.J. |last3=Keenan |first3=P.C. |date=1962 |title=Absorption Spectra of M-Type Mira Variables |journal=[[The Astrophysical Journal]] |volume=136 |page=21 |bibcode=1962ApJ...136...21M |doi=10.1086/147348 }}</ref> More thoroughly investigated are compounds of the formula R<sub>4</sub>Al<sub>2</sub> which contain an Al–Al bond and where R is a large organic [[ligand]].<ref>{{Cite book |last=Uhl |first=W. |title=Advances in Organometallic Chemistry Volume 51 |chapter=Organoelement Compounds Possessing Al–Al, Ga–Ga, In–In, and Tl–Tl Single Bonds |date=2004 |volume=51 |pages=53–108 |doi=10.1016/S0065-3055(03)51002-4 |isbn=978-0-12-031151-4 }}</ref> === Organoaluminium compounds and related hydrides === {{main|Organoaluminium chemistry}} [[File:Trimethylaluminium-from-xtal-3D-bs-17-25.png|thumb|upright=1.0|Structure of [[trimethylaluminium]], a compound that features five-coordinate carbon.]] A variety of compounds of empirical formula AlR<sub>3</sub> and AlR<sub>1.5</sub>Cl<sub>1.5</sub> exist.<ref>{{cite book |last1=Elschenbroich |first1=C. |date=2006 |title=Organometallics |publisher=Wiley-VCH |isbn=978-3-527-29390-2 }}</ref> The aluminium trialkyls and triaryls are reactive, volatile, and colorless liquids or low-melting solids. They catch fire spontaneously in air and react with water, thus necessitating precautions when handling them. They often form dimers, unlike their boron analogues, but this tendency diminishes for branched-chain alkyls (e.g. [[isopropyl|Pr<sup>''i''</sup>]], [[isobutyl|Bu<sup>''i''</sup>]], Me<sub>3</sub>CCH<sub>2</sub>); for example, [[triisobutylaluminium]] exists as an equilibrium mixture of the monomer and dimer.{{sfn|Greenwood|Earnshaw|1997|pp=257–67}}<ref>{{cite journal |title=The monomer-dimer equilibria of liquid aluminum alkyls|year=1970|last1=Smith|first1=Martin B. |journal=Journal of Organometallic Chemistry|pages=273–281|issue=2|doi=10.1016/S0022-328X(00)86043-X|volume=22}} </ref> These dimers, such as [[trimethylaluminium]] (Al<sub>2</sub>Me<sub>6</sub>), usually feature tetrahedral Al centers formed by dimerization with some alkyl group bridging between both aluminium atoms. They are [[HSAB theory|hard acid]]s and react readily with ligands, forming adducts. In industry, they are mostly used in alkene insertion reactions, as discovered by [[Karl Ziegler]], most importantly in "growth reactions" that form long-chain unbranched primary alkenes and alcohols, and in the low-pressure polymerization of [[ethene]] and [[propene]]. There are also some [[heterocycle|heterocyclic]] and cluster organoaluminium compounds involving Al–N bonds.{{sfn|Greenwood|Earnshaw|1997|pp=257–67}} The industrially most important aluminium hydride is [[lithium aluminium hydride]] (LiAlH<sub>4</sub>), which is used as a reducing agent in [[organic chemistry]]. It can be produced from [[lithium hydride]] and [[Aluminium chloride|aluminium trichloride]].{{sfn|Greenwood|Earnshaw|1997|pp=227–232}} The simplest hydride, [[aluminium hydride]] or alane, is not as important. It is a polymer with the formula (AlH<sub>3</sub>)<sub>''n''</sub>, in contrast to the corresponding [[boron hydride]] that is a dimer with the formula (BH<sub>3</sub>)<sub>2</sub>.{{sfn|Greenwood|Earnshaw|1997|pp=227–232}}
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