Mantle oxidation state

Mantle oxidation state can be quantified as the oxygen fugacity ($fO\_2$) of the system within the framework of thermodynamics. A higher oxygen fugacity implies a more oxygen-rich and more oxidized environment. At each given pressure-temperature conditions, for any compound or element M that bears the potential to be oxidized by oxygen{{Cite journal|last1=Zhang|first1=H.L.|last2=Hirschmann|first2=M.M.|last3=Cottrell|first3=E.|last4=Withers|first4=A.C.|date=2017|title=Effect of pressure on Fe 3+ /ΣFe ratio in a mafic magma and consequences for magma ocean redox gradients|journal=Geochimica et Cosmochimica Acta|volume=204|pages=83–103|doi=10.1016/j.gca.2017.01.023|bibcode=2017GeCoA.204...83Z|issn=0016-7037|doi-access=free}}{{Cite journal|last1=Campbell|first1=Andrew J.|last2=Danielson|first2=Lisa|last3=Righter|first3=Kevin|last4=Seagle|first4=Christopher T.|last5=Wang|first5=Yanbin|last6=Prakapenka|first6=Vitali B.|date=2009|title=High pressure effects on the iron–iron oxide and nickel–nickel oxide oxygen fugacity buffers|journal=Earth and Planetary Science Letters|volume=286|issue=3–4|pages=556–564|doi=10.1016/j.epsl.2009.07.022|bibcode=2009E&PSL.286..556C|issn=0012-821X}}

$M+\backslash frac\{x\}\{2\}O\_2\backslash rightleftharpoons\; MO\_x$

For example, if M is Fe, the redox equilibrium reaction can be Fe+1/2O₂=FeO; if M is FeO, the redox equilibrium reaction can be 2FeO+1/2O₂=Fe₂O₃.

Gibbs energy change associated with this reaction is therefore

$\backslash Delta\; G=\; G(MO\_x)-G(M)=\backslash frac\{x\}\{2\}RT\; lnfO\_2$

Along each isotherm, the partial derivation of ΔG with respect to P is ΔV,

$\backslash frac\{\backslash partial\; \backslash Delta\; G\}\{\backslash partial\; P\_\{|T\}\}=\{\backslash Delta\; V\}$.{{CN|date=May 2024}}

Combining the 2 equations above,

$\backslash frac\{\backslash partial\; (lnfO\_2))\}\{\backslash partial\; P|\_T\}=\backslash frac\{2\}\{xRT\}\backslash Delta\; V$.

Therefore,

$logfO\_2(P)=logfO\_2(1bar)+(\backslash frac\{0.8686\}\{RT\})\backslash int\_\{1bar\}^\{P\}\; \backslash Delta\; VdP$ (note that ln(e as the base) changed to log(10 as the base) in this formula.

For a closed system, there might exist more than one of these equilibrium oxidation reactions, but since all these reactions share a same $fO\_2$, examining one of them would allow extraction of oxidation state of the system.

The physics and chemistry of mantle largely depend on pressure. As mantle minerals are compressed, they are transformed into other minerals at certain depths. Seismic observations of velocity discontinuities and experimental simulations on phase boundaries both verified the structure transformations within the mantle. As such, the mantle can be further divided into three layers with distinct mineral compositions.

Since mantle mineral composition changes, the mineral hosting environment for polyvalent elements also alters. For each layer, the mineral combination governing the redox reactions is unique and will be discussed in detailed below.

Between depths of 30 and 60 km, oxygen fugacity is mainly controlled by Olivine-Orthopyroxene-Spinel oxidation reaction.

$6Fe\_2SiO\_4+O\_2\backslash rightleftharpoons3Fe\_2Si\_2O\_6+2Fe\_3O\_4$

Under deeper upper mantle conditions, Olivine-Orthopyroxene-Garnet oxygen barometer{{Cite journal|last1=McCammon|first1=C.|last2=Kopylova|first2=M. G.|date=2004-07-17|title=A redox profile of the Slave mantle and oxygen fugacity control in the cratonic mantle|journal=Contributions to Mineralogy and Petrology|volume=148|issue=1|pages=55–68|doi=10.1007/s00410-004-0583-1|issn=0010-7999|bibcode=2004CoMP..148...55M|s2cid=54778255}} is the redox reaction that is used to calibrate oxygen fugacity.
$4Fe\_2SiO\_4+2FeSiO\_3+O\_2\backslash rightleftharpoons2Fe\_3^\{2+\}Fe\_2^\{3+\}Si\_3O\_\{12\}$

In this reaction, 4 mole of ferrous ions were oxidized to ferric ions and the other 2 mole of ferrous ions remain unchanged.

Garnet-Garnet{{Cite journal|last1=Kiseeva|first1=Ekaterina S.|last2=Vasiukov|first2=Denis M.|last3=Wood|first3=Bernard J.|last4=McCammon|first4=Catherine|last5=Stachel|first5=Thomas|last6=Bykov|first6=Maxim|last7=Bykova|first7=Elena|last8=Chumakov|first8=Aleksandr|last9=Cerantola|first9=Valerio|date=2018-01-22|title=Oxidized iron in garnets from the mantle transition zone|journal=Nature Geoscience|volume=11|issue=2|pages=144–147|doi=10.1038/s41561-017-0055-7|issn=1752-0894|url=http://bib-pubdb1.desy.de/record/418155|bibcode=2018NatGe..11..144K|s2cid=23720021}} reaction can be used to estimate the redox state of transition zone.

$2Ca\_3Al\_2Si\_3O\_\{12\}+\backslash frac\{4\}\{3\}Fe\_3Al\_2Si\_3O\_\{12\}+2.5Mg\_4Si\_4O\_\{12\}+O\_2$

\rightleftharpoons2Ca_3Fe_2Si_3O_{12}+\frac{10}{3}Mg_3Al_2Si_3O_{12}+SiO_2

File:Garnet-Group-215473.jpg

A recent study showed that the oxygen fugacity of transition referred from Garnet-Garnet reaction is -0.26 $logfO\_2$ to +3 $logfO\_2$ relative to the Fe-FeO (IW, iron- wütstite) oxygen buffer.

Disproportionation of ferrous iron at lower mantle conditions also affect the mantle oxidation state. This reaction is different from the reactions mentioned above as it does not incorporate the participation of free oxygen.

$3Fe^\{2+\}(Fp)\backslash rightleftharpoons\; Fe+2Fe^\{3+\}(Bdg)$,{{Cite journal|last1=Rubie|first1=David C.|last2=Trønnes|first2=Reidar G.|last3=Catherine A. McCammon|last4=Langenhorst|first4=Falko|last5=Liebske|first5=Christian|last6=Frost|first6=Daniel J.|date=2004|title=Experimental evidence for the existence of iron-rich metal in the Earth's lower mantle|journal=Nature|language=en|volume=428|issue=6981|pages=409–412|doi=10.1038/nature02413|pmid=15042086|issn=1476-4687|bibcode=2004Natur.428..409F|s2cid=32948214}}

FeO resides in the form of ferropericlase (Fp) and Fe₂O₃ resides in the form of bridgmanite (Bdg). There is no oxygen fugacity change associated with the reaction. However, as the reaction products differ in density significantly, the metallic iron phase could descend downwards to the Earth's core and get separated from the mantle. In this case, the mantle loses metallic iron and becomes more oxidized.

File:Diamond-diamond macle1.jpgThe equilibrium reaction involving diamond isFile:Flux of crustal material in the mantle.jpg

$Mg\_2Si\_2O\_6+2MgCO\_3\backslash rightleftharpoons2Mg\_2SiO\_4+2C(Diamond)+2O\_2$.

Examining the oxygen fugacity of the upper mantle and transition enables us to compare it with the conditions (equilibrium reaction shown above) required for diamond formation. The results show that the $logfO\_2$ is usually 2 units lower than the carbonate-carbon reaction which means favoring the formation of diamond at transition zone conditions.

It has also been reported that pH decrease would also facilitate the formation of diamond in Mantle conditions.{{Cite journal|last1=Sverjensky|first1=Dimitri A.|last2=Huang|first2=Fang|date=2015-11-03|title=Diamond formation due to a pH drop during fluid–rock interactions|journal=Nature Communications|volume=6|issue=1|pages=8702|doi=10.1038/ncomms9702|pmid=26529259|issn=2041-1723|bibcode=2015NatCo...6.8702S|pmc=4667645}}

$HCOO^\{-\}+H^++H\_\{2,aq\}\; \backslash rightleftharpoons\; C\_\{diamond\}+2H\_2O$

$CH\_3CH\_2COO^-+H^+\backslash rightleftharpoons3C\_\{diamond\}+H\_\{2,aq\}+2H\_2O$

where the subscript aq means 'aqueous', implying H₂ is dissolved in the solution.

Deep diamonds have become important windows to look into the mineralogy of the Earth's interior. Minerals not stable at the surface could possibly be found within inclusions of superdeep diamonds{{Cite journal|last1=Zhu|first1=Feng|last2=Li|first2=Jie|last3=Liu|first3=Jiachao|last4=Lai|first4=Xiaojing|last5=Chen|first5=Bin|last6=Meng|first6=Yue|date=2019-02-18|title=Kinetic Control on the Depth Distribution of Superdeep Diamonds|journal=Geophysical Research Letters|volume=46|issue=4|pages=1984–1992|language=en|doi=10.1029/2018GL080740|bibcode=2019GeoRL..46.1984Z|doi-access=free|hdl=2027.42/148362|hdl-access=free}}—implying they were stable where these diamond crystallized. Because of the hardness of diamonds, the high pressure environment is retained even after transporting to the surface. So far, these superdeep minerals brought by diamonds include ringwoodite,{{Cite journal|last1=Pearson|first1=D. G.|last2=Brenker|first2=F. E.|last3=Nestola|first3=F.|last4=McNeill|first4=J.|last5=Nasdala|first5=L.|last6=Hutchison|first6=M. T.|last7=Matveev|first7=S.|last8=Mather|first8=K.|last9=Silversmit|first9=G.|date=2014-03-12|title=Hydrous mantle transition zone indicated by ringwoodite included within diamond|journal=Nature|volume=507|issue=7491|pages=221–224|doi=10.1038/nature13080|issn=0028-0836|url=http://bib-pubdb1.desy.de/record/168146/files/10.1038_nature13080.pdf|bibcode=2014Natur.507..221P|pmid=24622201|s2cid=205237822}} ice-VII,{{Cite journal|last1=Tschauner|first1=O.|last2=Huang|first2=S.|last3=Greenberg|first3=E.|last4=Prakapenka|first4=V. B.|last5=Ma|first5=C.|last6=Rossman|first6=G. R.|last7=Shen|first7=A. H.|last8=Zhang|first8=D.|last9=Newville|first9=M.|date=2018-03-09|title=Ice-VII inclusions in diamonds: Evidence for aqueous fluid in Earth's deep mantle|journal=Science|language=en|volume=359|issue=6380|pages=1136–1139|doi=10.1126/science.aao3030|issn=0036-8075|bibcode=2018Sci...359.1136T|pmid=29590042|doi-access=free}} cubic δ-N₂{{Cite journal|last1=Navon|first1=Oded|last2=Wirth|first2=Richard|last3=Schmidt|first3=Christian|last4=Jablon|first4=Brooke Matat|last5=Schreiber|first5=Anja|last6=Emmanuel|first6=Simon|date=2017|title=Solid molecular nitrogen ( δ -N 2 ) inclusions in Juina diamonds: Exsolution at the base of the transition zone|journal=Earth and Planetary Science Letters|language=en|volume=464|pages=237–247|doi=10.1016/j.epsl.2017.01.035|bibcode=2017E&PSL.464..237N}} and Ca-perovskite.{{Cite journal|last1=Nestola|first1=F.|last2=Korolev|first2=N.|last3=Kopylova|first3=M.|last4=Rotiroti|first4=N.|last5=Pearson|first5=D. G.|last6=Pamato|first6=M. G.|last7=Alvaro|first7=M.|last8=Peruzzo|first8=L.|last9=Gurney|first9=J. J.|date=2018-03-07|title=CaSiO3 perovskite in diamond indicates the recycling of oceanic crust into the lower mantle|journal=Nature|volume=555|issue=7695|pages=237–241|doi=10.1038/nature25972|pmid=29516998|bibcode=2018Natur.555..237N|s2cid=3763653|issn=0028-0836|url=http://discovery.ucl.ac.uk/10049984/}}

• Ultra-high-pressure metamorphism
• Polymorphism (materials science)
• Table of thermodynamic equations
• List of oxidation states of the elements

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{{Chemical equilibria}}

{{Earthsinterior}}

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