Velocity-addition formula: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Guy vandegrift
m →‎Derivation: included link to four-velocity. Perhaps 4-velocity should also be briefly defined in this section?
en>DVdm
Undid revision 628080186 by 140.78.186.253 (talk) In the literature it's a flying insect
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
{{Use dmy dates|date=May 2013}}
Marvella is what you can call her but it's not the most feminine title out there. Body developing is what my family members and I enjoy. North Dakota is our beginning location. In her professional lifestyle she is a payroll clerk but she's usually wanted her own business.<br><br>Also visit my blog post [http://Ref.pw/dietfooddelivery78594 healthy food delivery]
[[File:Mineraly.sk - chryzotil.jpg|right|thumb|A sample of serpentinite rock, partially made up of [[chrysotile]], from Slovakia]]
[[File:Serpentinite.JPG|right|thumb|Sample of serpentinite from the [[Golden Gate National Recreation Area]], California, USA]]
'''Serpentinite''' is a [[Rock (geology)|rock]] composed of one or more [[serpentine group]] [[mineral]]s. Minerals in this group are formed by '''serpentinization''', a hydration and [[metamorphic rock|metamorphic]] transformation of [[ultramafic]] rock from the Earth's [[Mantle (geology)|mantle]]. The alteration is particularly important at the [[sea floor]] at [[plate tectonics|tectonic plate]] boundaries.
 
== Formation and petrology ==
Serpentinization is a geological low-temperature [[metamorphic rock|metamorphic]] process involving heat and water in which low-[[silica]] [[mafic]] and [[ultramafic]] rocks are [[oxidation|oxidized]] (anaerobic oxidation of Fe<sup>2+</sup> by the protons of water leading to the formation of H<sub>2</sub>) and [[hydrolyzed]] with water into serpentinite. [[Peridotite]], including [[dunite]], at and near the seafloor and in mountain belts is converted to [[Serpentine group|serpentine]], [[brucite]], [[magnetite]], and other minerals — some rare, such as [[awaruite]] (Ni<sub>3</sub>Fe), and even native [[iron]]. In the process large amounts of water are absorbed into the rock increasing the volume and destroying the structure.<ref name=LC>[http://www.lostcity.washington.edu/science/chemistry/serpentinization.html Serpentinization: The heat engine at Lost City and sponge of the oceanic crust]</ref>
 
The density changes from 3.3 to 2.7 g/cm<sup>3</sup> with a concurrent volume increase on the order of 30-40%. The reaction is highly [[exothermic]] and rock temperatures can be raised by about {{convert|260|Celsius}},<ref name=LC/> providing an energy source for formation of non-volcanic [[hydrothermal vent]]s. The magnetite-forming chemical reactions produce [[hydrogen]] gas under anaerobic conditions prevailing deep in the [[mantle (geology)|mantle]], far from the [[Atmosphere of Earth|Earth's atmosphere]]. [[Carbonate]]s and [[sulfate]]s are subsequently reduced by hydrogen and form [[methane]] and [[hydrogen sulfide]]. The hydrogen, methane, and hydrogen sulfide provide energy sources for deep sea [[chemotroph]] [[microorganism]]s.<ref name=LC/>
 
=== Serpentinite reactions ===
Serpentinite is formed from [[olivine]] via several reactions, some of which are complementary. Olivine is a [[solid solution]] between the [[magnesium]]-endmember [[forsterite]] and the [[iron]]-endmember [[fayalite]]. Serpentinite reactions 1a and 1b, below, exchange silica between forsterite and fayalite to form serpentine group minerals and magnetite. These are highly exothermic reactions.
 
'''Reaction 1a''':<br>
''Fayalite + water → magnetite + aqueous silica + hydrogen''
:3Fe<sub>2</sub>SiO<sub>4</sub> + 2H<sub>2</sub>O → 2Fe<sub>3</sub>O<sub>4</sub> + 3SiO<sub>2</sub> + 2H<sub>2</sub>
<br>
'''Reaction 1b''':<br>
''Forsterite + aqueous silica → serpentine''
:3Mg<sub>2</sub>SiO<sub>4</sub> + SiO<sub>2</sub> + 4H<sub>2</sub>O → 2Mg<sub>3</sub>Si<sub>2</sub>O<sub>5</sub>(OH)<sub>4</sub>
<br>
'''Reaction 1c''':<br>
''Forsterite + water → serpentine + brucite''
:2Mg<sub>2</sub>SiO<sub>4</sub> + 3H<sub>2</sub>O → Mg<sub>3</sub>Si<sub>2</sub>O<sub>5</sub>(OH)<sub>4</sub> + Mg(OH)<sub>2</sub>
 
Reaction 1c describes the hydration of olivine with water only to yield serpentine and Mg(OH)<sub>2</sub> ([[brucite]]). Serpentine is stable at high pH in the presence of brucite like calcium silicate hydrate, ([[calcium silicate hydrate|C-S-H]]) phases formed along with [[portlandite]] (Ca(OH)<sub>2</sub>) in hardened Portland [[cement]] paste after the hydration of [[belite]] (Ca<sub>2</sub>SiO<sub>4</sub>), the artificial calcium equivalent of forsterite.
 
'''Analogy of reaction 1c with belite hydration in ordinary Portland cement''':<br>
''Belite + water → C-S-H phase + portlandite''
:2 Ca<sub>2</sub>SiO<sub>4</sub> + 4 H<sub>2</sub>O → 3 CaO · 2 SiO<sub>2</sub> · 3 H<sub>2</sub>O + Ca(OH)<sub>2</sub>
 
After reaction, the poorly soluble reaction products ([[silicic acid|aqueous silica]] or dissolved [[magnesium]] [[ion]]s) can be transported in solution out of the serpentinized zone by [[diffusion]] or [[advection]].
 
A similar suite of reactions involves [[pyroxene]]-group minerals, though less readily and with complication of the additional end-products due to the wider compositions of pyroxene and pyroxene-olivine mixes. [[Talc]] and magnesian [[Chlorite group|chlorite]] are possible products, together with the serpentine minerals [[antigorite]], [[lizardite]], and [[chrysotile]]. The final mineralogy depends both on rock and fluid compositions, temperature, and pressure. Antigorite forms in reactions at temperatures that can exceed 600°C during metamorphism, and it is the [[serpentine group]] mineral stable at the highest temperatures. Lizardite and chrysotile can form at low temperatures very near the Earth's surface. Fluids involved in serpentinite formation commonly are highly reactive and may transport [[calcium]] and other elements into surrounding rocks; fluid reaction with these rocks may create [[metasomatism|metasomatic]] reaction zones enriched in calcium and called rodingites.
 
In the presence of carbon dioxide, however, serpentinitization may form either magnesite (MgCO<sub>3</sub>) or generate methane (CH<sub>4</sub>). It is thought that some hydrocarbon gases may be produced by serpentinite reactions within the oceanic crust.
 
'''Reaction 2a''':
:''Olivine  + water + carbonic acid → serpentine + magnetite + methane''
 
:<math>\mathrm{(Fe,Mg)_2SiO_4 + n H_2O + CO_2}</math> → <math>\mathrm{Mg_3Si_2O_5(OH)_4 + Fe_3O_4 + CH_4}</math>
<br>
or, in balanced form:
:<math>\mathrm{18 Mg_2SiO_4 + 6 Fe_2SiO_4 + 26 H_2O + CO_2}</math> → <math>\mathrm{12 Mg_3Si_2O_5(OH)_4 + 4 Fe_3O_4 + CH_4}</math>
<br>
'''Reaction 2b''':
:''Olivine  + water + carbonic acid → serpentine + magnetite + magnesite + silica''
 
:<math>\mathrm{(Fe,Mg)_2SiO_4 + n H_2O + CO_2}</math> → <math>\mathrm{Mg_3Si_2O_5(OH)_4 + Fe_3O_4 + MgCO_3 + SiO_2}</math>
<br>
Reaction 2a is favored if the serpentinite is Mg-poor or if there isn't enough carbon dioxide to promote [[talc]] formation. Reaction 2b is favored in highly magnesian compositions and low partial pressure of carbon dioxide. 
 
The degree to which a mass of ultramafic rock undergoes serpentinisation depends on the starting rock composition and on whether or not fluids transport [[calcium]], [[magnesium]] and other elements away during the process. If an olivine composition contains sufficient fayalite, then olivine plus water can completely metamorphose to serpentine and magnetite in a closed system. In most ultramafic rocks formed in the [[Earth's mantle]], however, the olivine is about 90% forsterite endmember, and for that olivine to react completely to serpentine, magnesium must be transported out of the reacting volume. 
 
Serpentinitization of a mass of peridotite usually destroys all previous textural evidence because the serpentine minerals are weak and behave in a very ductile fashion. However, some masses of serpentinite are less severely deformed, as evidenced by the apparent preservation of [[rock microstructure|textures]] inherited from the peridotite, and the serpentinites may have behaved in a rigid fashion.
 
===Hydrogen production by anaerobic oxidation of fayalite ferrous ions===
In the absence of atmospheric oxygen (O<sub>2</sub>), in deep geological conditions prevailing far away from Earth atmosphere, hydrogen (H<sub>2</sub>) is produced by the anaerobic oxidation of ferrous ions (Fe<sup>2+</sup>) present in the crystal lattice of the iron-endmember [[fayalite]] by the protons (H<sup>+</sup>) of water.<ref>{{cite web
| title = Methane and hydrogen formation from rocks – Energy sources for life
| url = http://www.lostcity.washington.edu/science/chemistry/methane.html
| accessdate = 2011-11-06
}}</ref><ref>{{Cite journal
| last = Sleep
| first = N.H.
| coauthors = A. Meibom, Th. Fridriksson, R.G. Coleman, D.K. Bird
| year = 2004
| title = H<sub>2</sub>-rich fluids from serpentinization: Geochemical and biotic implications
| journal = Proceedings of the National Academy of Sciences of the United States of America
| volume = 101
| issue = 35
| pages = 12818–12823
| doi = 10.1073/pnas.0405289101
| url = http://www.pnas.org/content/101/35/12818.abstract
| accessdate = 2011-11-06
|bibcode = 2004PNAS..10112818S }}</ref>
 
Considering three formula units of fayalite (Fe<sub>2</sub>(SiO<sub>4</sub>)) for the purpose of stoechiometry and reaction mass balance, four ferrous ions will undergo oxidation by water protons while the two remaining will stay unoxidised. Neglecting the orthosilicate anions not involved in the redox process, it is then possible to schematically write the two half-redox reactions as follows:
 
:4 (Fe<sup>2+</sup> → Fe<sup>3+</sup> + e<sup>–</sup>) (oxidation of ferrous ions)
:2 (H<sub>2</sub>O + 2 e<sup>–</sup> → O<sup>2–</sup> + H<sub>2</sub>) (reduction of protons into hydrogen)
This leads to the global redox reaction involving ferrous ions oxidation by water:
:4 Fe<sup>2+</sup> + 2 H<sub>2</sub>O → 4 Fe<sup>3+</sup> + 2 O<sup>2–</sup> + 2 H<sub>2</sub>
 
The two unoxidised ferrous (Fe<sup>2+</sup>) ions still available in the three formula units of fayalite finally combine with the four ferric (Fe<sup>3+</sup>) cations and oxide anions (O<sup>2–</sup>) to form two formula units of magnetite (Fe<sub>3</sub>O<sub>4</sub>).
 
Finally, considering the required rearrangement of the orthosilicate anions into free silica (SiO<sub>2</sub>) and free oxide anions (O<sup>2–</sup>), it is possible to write the complete reaction of anaerobic oxidation and hydrolysis of fayalite according to the following mass balance:
 
:3 Fe<sub>2</sub>SiO<sub>4</sub> + 2 H<sub>2</sub>O → 2 Fe<sub>3</sub>O<sub>4</sub> + 3 SiO<sub>2</sub> + 3 H<sub>2</sub>
:''fayalite + water → magnetite + quartz + hydrogen''
 
This reaction closely resembles the [[Schikorr reaction]] observed in the anaerobic oxidation of the [[ferrous hydroxide]] in contact with water:
 
:3 Fe(OH)<sub>2</sub> → Fe<sub>3</sub>O<sub>4</sub> + 2 H<sub>2</sub>O  + H<sub>2</sub>
:''ferrous hydroxide → magnetite + water + hydrogen''
 
===Abiotic methane production on Mars by serpentinization===
The presence of traces of [[atmosphere of Mars#Methane|methane in the atmosphere of Mars]] has been hypothesized to be a possible evidence for [[life on Mars (planet)|life on Mars]] if methane was produced by [[bacteria]]l activity. Serpentinization has been proposed as an alternative non-biological source for the observed methane traces.<ref>{{cite journal|url=http://www.americanscientist.org/issues/pub/life-on-mars|title=Life on Mars?|date=March–April 2006|journal=American Scientist|accessdate=1 June 2009}}</ref><ref>{{cite web|url=http://www.redorbit.com/news/space/1623762/methane_evidence_of_life_on_mars_update/index.html|title=Methane: Evidence of life on Mars?|date=15 January 2009|publisher=redorbit.com|accessdate=1 June 2009}}</ref>
 
==Impact on agriculture==
Soil cover over serpentinite bedrock tends to be thin or absent. Soil with serpentine is poor in calcium and other major plant nutrients, but rich in elements toxic to plants such as chromium and nickel.<ref>[http://vulcan.wr.usgs.gov/LivingWith/VolcanicPast/Notes/serpentine.html "CVO Website - Serpentine and serpentinite"], ''USGS/NPS Geology in the Parks Website'', September 2001, accessed 27 February 2011.</ref>
 
==Uses for serpentinite==
===Decorative stone in architecture===
Grades of serpentinite higher in calcite, along with the [[verd antique|breccia form of serpentinite]], have historically been used as decorative stones for their marble-like qualities. Popular sources in Europe before contact with the Americas were the mountainous [[Piedmont]] region of Italy and [[Larissa, Greece]].<ref>Ashurst, John. Dimes, Francis G. ''Conservation of building and decorative stone''. Elsevier Butterworth-Heinemann, 1990, p. 51.</ref>
 
===Carvingstone Tools, Oil lamp-known as the Qulliq and Inuit Sculpture===
{{Anchors|Inuit|Qulliq}}Inuit and Aboriginal Peoples of the Arctic Areas and less so of southern areas used the carved bowl shaped serpentinite Qulliq or [[Kudlik]] lamp with wick, to burn oil or fat to heat, make light and cook with. Inuit made tools and more recently carvings of animals for commerce.
 
<gallery widths="220px" heights="220px" >
File:Serpentinite_Walrus_2012.jpg|Magnetic Serpentine Walrus
File:Qulliq_1999-04-01.jpg|[[Inuit]] Elder tending the Qulliq, a ceremonial oil lamp made of serpentinite.
</gallery>
 
===Swiss ovenstone===
A variety of [[Chlorite group|chlorite]] [[talc]] [[schist]] associated with Alpine serpentinite is found in [[Val d’Anniviers]], [[Switzerland]] and was used as ''ovenstone'' in stove construction.<ref>[http://www.rsc.org/delivery/_ArticleLinking/DisplayArticleForFree.cfm?doi=CA8987405232&JournalCode=CA Talcose-schist from Canton Valais. By Thomags Bonney, (Geol. Mag., 1897, N.S., &#91;iv&#93;, 4, 110--116) abstract]</ref>
 
===Neutron shield in nuclear reactors===
Serpentinite has a significant amount of [[bound water]], hence it contains abundant [[hydrogen]] atoms able to slow down [[neutron]]s by [[elastic collision]] (neutron [[thermalization]] process). Because of this serpentinite can be used as dry filler inside [[steel]] jackets in some designs of [[nuclear reactor]]s. For example in [[RBMK]] series it was used for top [[radiation shielding]] to protect operators from escaping neutrons.<ref>{{Cite web
| last = Lithuanian Energy Institute
| title = Design of structures, components, equipments and systems
| work = Ignalina Source Book
| accessdate = 2011-05-28
| date = 2011-05-28
| url = http://www.lei.lt/insc/sourcebook/sob3/sob33.html
}}</ref> Serpentine can also be added as [[Construction aggregate|aggregate]] to special [[concrete]] used in nuclear reactor shielding to increase the concrete density (2.6&nbsp;g/cm<sup>3</sup>) and its [[neutron capture]] [[Cross section (physics)|cross section]].<ref>{{Cite conference
| last = Aminian
| first = A.
| last2 = Nematollahi
| first2 = M.R.
| last3 = Haddad
| first3 = K.
| last4 = Mehdizadeh
| first4 = S.
| date = 3-8 June 2007
| title = Determination of shielding parameters for different types of concretes by Monte Carlo methods
| location = Istanbul, Turkey
| conference = ICENES 2007: International Conference on Emerging Nuclear Energy Systems. Session 12B: Radiation effects
| pages = 7
| url = http://www.icenes2007.org/icenes_proceedings/manuscripts.pdf/Session%2012B/DETERMINATION%20OF.pdf
}}</ref><ref>{{Cite journal
| last = Abulfaraj
| first = Waleed H.
| coauthors = Salah M. Kamal
| title = Evaluation of ilmenite serpentine concrete and ordinary concrete as nuclear reactor shielding
| journal = Radiation Physics and Chemistry
| volume = 44
| issue = 1-2
| pages = 139–148
| doi = 10.1016/0969-806X(94)90120-1
| issn = 0969-806X
| accessdate = 2011-05-28
|bibcode = 1994RaPC...44..139A }}</ref>
 
==Cultural references==
It is the state rock of [[California]], USA and the California Legislature specified that serpentine was "the official State Rock and lithologic emblem."<ref>California Government Code § 425.2; ''see'' http://www.leginfo.ca.gov/cgi-bin/displaycode?section=gov&group=00001-01000&file=420-429.8</ref>
 
==See also==
* [[Serpentine group]]
* [[Serpentine soil]], a soil derived from the serpentine mineral
* [[Schikorr reaction]], involving also the formation of magnetite and hydrogen by a very similar mechanism
* [[Belite#Hydration|Hydration of belite in cement]] (analogous to forsterite hydration)
* [[Cement chemist notation]], also useful for silicate and oxide reactions in mineralogy
* [[Chrysotile#Chemical properties|Chrysotile dehydration]]
* [[Lost City (hydrothermal field)]]
* [[Mineral redox buffer#Common redox buffers and mineralogy|Common redox mineral buffer]] – FMQ: fayalite-magnetite-quartz
* [[Nephrite]]
* [[Carbon sequestration]]
* [[Talc carbonate]]
* [[Soapstone]]
 
== References ==
{{reflist}}
 
== External links ==
* [http://www.lostcity.washington.edu/story/Serpentinization]  The Lost City hydrothermal field,  [[Mid-Atlantic ridge]]: serpentinization, the driving force of the system.
* [http://www.pnas.org/cgi/content/full/101/35/12818 H<sub>2</sub>-rich fluids from serpentinization: Geochemical and biotic implications]:  [[Proceedings of the National Academy of Science]].
 
{{commons category|Serpentinite}}
 
[[Category:Metamorphic petrology]]
[[Category:Metamorphic rocks]]

Latest revision as of 17:42, 3 October 2014

Marvella is what you can call her but it's not the most feminine title out there. Body developing is what my family members and I enjoy. North Dakota is our beginning location. In her professional lifestyle she is a payroll clerk but she's usually wanted her own business.

Also visit my blog post healthy food delivery