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== Applications == The creation of metal alloys account for 85% of the available chromium's usage. The remainder of chromium is used in the [[chemical industry|chemical]], [[refractory]], and [[foundry]] industries.<ref>{{Cite book|url = https://books.google.com/books?id=k_-0-DWxuRgC&q=metal+alloys+account+for+85%25+of+chromium+use&pg=PA83|title = Environmental Forensics: Contaminant Specific Guide|last1 = Morrison|first1 = RD|last2 = Murphy|first2 = BL|date = 4 Aug 2010|publisher = Academic Press|isbn = 978-0-08-049478-4|language = en|access-date = 30 October 2020|archive-date = 10 June 2024|archive-url = https://web.archive.org/web/20240610050311/https://books.google.com/books?id=k_-0-DWxuRgC&q=metal+alloys+account+for+85%25+of+chromium+use&pg=PA83#v=snippet&q=metal%20alloys%20account%20for%2085%25%20of%20chromium%20use&f=false|url-status = live}}</ref> === Metallurgy === [[File:Besteck WMF Stockholm ca 1960er.jpg |thumb|right|Stainless steel cutlery made from Cromargan 18/10, containing 18% chromium]] {{Main|Chrome plating|Stainless steel}} The strengthening effect of forming stable metal carbides at grain boundaries, and the strong increase in corrosion resistance made chromium an important alloying material for steel. [[High-speed steel|High-speed tool steels]] contain 3β5% chromium. [[Stainless steel]], the primary corrosion-resistant metal alloy, is formed when chromium is introduced to [[iron]] in concentrations above 11%.<ref name="Davis 2000 p.">{{cite book |last=Davis |first=JR |title=Alloy digest sourcebook: stainless steels |publisher=ASM International |location=Materials Park, OH |year=2000 |isbn=978-0-87170-649-2 |oclc=43083287 |language=af |pages=1β5 |url=https://www.asminternational.org/documents/10192/1849770/06940G_Chapter_1.pdf/53f29213-5dd6-4499-9959-841477b385b9 |access-date=5 October 2018 |archive-date=1 July 2021 |archive-url=https://web.archive.org/web/20210701021614/https://www.asminternational.org/documents/10192/1849770/06940G_Chapter_1.pdf/53f29213-5dd6-4499-9959-841477b385b9 |url-status=dead }}</ref> For stainless steel's formation, ferrochromium is added to the molten iron. Also, nickel-based alloys have increased strength due to the formation of discrete, stable, metal, carbide particles at the grain boundaries. For example, [[Inconel]] 718 contains 18.6% chromium. Because of the excellent high-temperature properties of these nickel [[superalloy]]s, they are used in [[jet engine]]s and [[gas turbine]]s in lieu of common structural materials.<ref name="superal">{{cite web|title = Nickel-Based Superalloys|first = HK|last = Bhadeshia|url = http://www.msm.cam.ac.uk/phase-trans/2003/Superalloys/superalloys.html|access-date = 17 Feb 2009|publisher = University of Cambridge|archive-url = https://web.archive.org/web/20060825053006/http://www.msm.cam.ac.uk/phase-trans/2003/Superalloys/superalloys.html|archive-date = 25 August 2006}}</ref> [[ASTM]] B163 relies on chromium for condenser and heat-exchanger tubes, while [[castings]] with high strength at elevated temperatures that contain chromium are standardised with ASTM A567.<ref name="iarc49">{{cite journal |title=Chromium, Nickel and Welding |journal=IARC Monographs |date=1990 |volume=49 |pages=49β50 |publisher=International Agency for Research on Cancer}}</ref> [[American Iron and Steel Institute|AISI]] type 332 is used where high temperature would normally cause [[carburization]], [[oxidation]] or [[corrosion]].<ref name="azom332">{{cite news |title=Stainless Steel Grade 332 (UNS S33200) |url=https://www.azom.com/article.aspx?ArticleID=8271 |publisher=AZoNetwork |date=5 March 2013 |access-date=1 June 2021 |archive-date=3 June 2021 |archive-url=https://web.archive.org/web/20210603050412/https://www.azom.com/article.aspx?ArticleID=8271 |url-status=live }}</ref> [[Incoloy]] 800 "is capable of remaining stable and maintaining its [[austenitic]] structure even after long time exposures to high temperatures".<ref name="azom800">{{cite news |publisher=AZoNetwork |title=Super Alloy INCOLOY Alloy 800 (UNS N08800) |url=https://www.azom.com/article.aspx?ArticleID=9517 |date=3 July 2013 |access-date=1 June 2021 |archive-date=3 June 2021 |archive-url=https://web.archive.org/web/20210603104203/https://www.azom.com/article.aspx?ArticleID=9517 |url-status=live }}</ref> [[Nichrome]] is used as resistance wire for heating elements in things like [[toasters]] and space heaters. These uses make chromium a [[strategic material]]. Consequently, during World War II, U.S. road engineers were instructed to avoid chromium in yellow road paint, as it "may become a critical material during the emergency".<ref>{{Cite web |url=https://ceprofs.civil.tamu.edu/ghawkins/MUTCD-History_files/1942MUTCD.pdf |title=Manual On Uniform Traffic Control Devices (War Emergency Edition) |page=52 |publisher=American Associan of State Highway Officials |date=November 1942 |location=Washington, DC |access-date=July 8, 2021 |archive-date=29 April 2021 |archive-url=https://web.archive.org/web/20210429061859/https://ceprofs.civil.tamu.edu/ghawkins/MUTCD-History_files/1942MUTCD.pdf |url-status=live }}</ref> The United States likewise considered chromium "essential for the German war industry" and made intense diplomatic efforts to keep it out of the hands of [[Nazi Germany]].<ref>{{Cite web|last=State Department|first=United States|title=Allied Relations and Negotiations with Turkey|url=https://1997-2001.state.gov/regions/eur/rpt_9806_ng_turkey.pdf|url-status=live|archive-url=https://web.archive.org/web/20201109142429/https://1997-2001.state.gov/regions/eur/rpt_9806_ng_turkey.pdf |archive-date=9 November 2020 }}</ref> [[File:Motorcycle Reflections bw edit.jpg|thumb|left|Decorative chrome plating on a motorcycle]] The high hardness and corrosion resistance of unalloyed chromium makes it a reliable metal for surface coating; it is still the most popular metal for sheet coating, with its above-average durability, compared to other coating metals.<ref>{{cite web |last1=Breitsameter |first1=M |title=Thermal Spraying versus Hard Chrome Plating |url=https://www.azom.com/article.aspx?ArticleID=1576 |website=Azo Materials |publisher=AZoNetwork |access-date=1 October 2018 |date=2002-08-15 |archive-date=23 April 2021 |archive-url=https://web.archive.org/web/20210423034449/https://www.azom.com/article.aspx?ArticleID=1576 |url-status=live }}</ref> A layer of chromium is deposited on pretreated metallic surfaces by [[electroplating]] techniques. There are two deposition methods: thin, and thick. Thin deposition involves a layer of chromium below 1 ΞΌm thickness deposited by [[chrome plating]], and is used for decorative surfaces. Thicker chromium layers are deposited if wear-resistant surfaces are needed. Both methods use acidic chromate or [[dichromate]] solutions. To prevent the energy-consuming change in oxidation state, the use of chromium(III) sulfate is under development; for most applications of chromium, the previously established process is used.<ref name="Crplating" /> In the [[chromate conversion coating]] process, the strong oxidative properties of chromates are used to deposit a protective oxide layer on metals like aluminium, zinc, and cadmium. This [[Passivation (chemistry)|passivation]] and the self-healing properties of the chromate stored in the chromate conversion coating, which is able to migrate to local defects, are the benefits of this coating method.<ref name="Edwards">{{cite book |last = Edwards |first = J |title = Coating and Surface Treatment Systems for Metals |publisher = Finishing Publications Ltd. and ASMy International |date = 1997|pages = 66β71 |isbn = 978-0-904477-16-0}}</ref> Because of environmental and health regulations on chromates, alternative coating methods are under development.<ref>{{Cite journal |journal=Surface and Coatings Technology |volume=140 |issue=1 |date=2001 |doi=10.1016/S0257-8972(01)01003-9 |title=Effects of chromate and chromate conversion coatings on corrosion of aluminum alloy 2024-T3 |vauthors= Zhao J, Xia L, Sehgal A, Lu D, McCreery RL, Frankel GS |pages=51β57 |hdl=1811/36519 |hdl-access=free }}</ref> Chromic acid [[anodizing]] (or Type I anodizing) of aluminium is another electrochemical process that does not lead to the deposition of chromium, but uses [[chromic acid]] as an electrolyte in the solution. During anodization, an oxide layer is formed on the aluminium. The use of chromic acid, instead of the normally used sulfuric acid, leads to a slight difference of these oxide layers.<ref name="surface">{{Cite book| title = ASM Handbook: Surface Engineering|last1 = Cotell|first1 = CM|last2=Sprague|first2 = JA|last3 = Smidt|first3 = FA|url = https://books.google.com/books?id=RGtsPjqUwy0C&pg=PA484|access-date = 17 Feb 2009|publisher = ASM International|isbn = 978-0-87170-384-2|date = 1994}}</ref> The high toxicity of Cr(VI) compounds, used in the established chromium electroplating process, and the strengthening of safety and environmental regulations demand a search for substitutes for chromium, or at least a change to less toxic chromium(III) compounds.<ref name="Crplating" /> === Pigment === The mineral [[crocoite]] (which is also [[lead chromate]] PbCrO<sub>4</sub>) was used as a yellow pigment shortly after its discovery. After a synthesis method became available starting from the more abundant chromite, [[chrome yellow]] was, together with [[cadmium yellow]], one of the most used yellow pigments. The pigment does not photodegrade, but it tends to darken due to the formation of chromium(III) oxide. It has a strong color, and was used for school buses in the United States and for the postal services (for example, the [[Deutsche Post]]) in Europe. The use of chrome yellow has since declined due to environmental and safety concerns and was replaced by organic pigments or other alternatives that are free from lead and chromium. Other pigments that are based around chromium are, for example, the deep shade of red pigment [[chrome red]], which is simply lead chromate with [[lead(II) hydroxide]] (PbCrO<sub>4</sub>Β·Pb(OH)<sub>2</sub>). A very important chromate pigment, which was used widely in metal primer formulations, was zinc chromate, now replaced by zinc phosphate. A wash primer was formulated to replace the dangerous practice of pre-treating aluminium aircraft bodies with a phosphoric acid solution. This used zinc tetroxychromate dispersed in a solution of [[polyvinyl butyral]]. An 8% solution of phosphoric acid in solvent was added just before application. It was found that an easily oxidized alcohol was an essential ingredient. A thin layer of about 10β15 ΞΌm was applied, which turned from yellow to dark green when it was cured. There is still a question as to the correct mechanism. Chrome green is a mixture of [[Prussian blue]] and [[chrome yellow]], while the chrome oxide green is [[chromium(III) oxide]].<ref name="Cryel">{{Cite book|chapter-url = https://books.google.com/books?id=bdQVgKWl3f4C&pg=PA106|title = Painting Materials: A Short Encyclopaedia|first = Rutherford John|last = Gettens|publisher = Courier Dover Publications|date = 1966|isbn = 978-0-486-21597-6|pages = 105β106|chapter =Chrome yellow}}</ref> Chromium oxides are also used as a green pigment in the field of glassmaking and also as a glaze for ceramics.<ref>Gerd Anger et al. "Chromium Compounds" Ullmann's Encyclopedia of Industrial Chemistry 2005, Wiley-VCH, Weinheim. {{doi|10.1002/14356007.a07_067}}</ref> Green chromium oxide is extremely [[lightfastness|lightfast]] and as such is used in cladding coatings. It is also the main ingredient in [[infrared]] reflecting paints, used by the armed forces to paint vehicles and to give them the same infrared reflectance as green leaves.<ref>{{cite book|last1 = Marrion|first1 = Alastair|title = The chemistry and physics of coatings|url = https://books.google.com/books?id=Iz0RQK0oMWUC&pg=PA287|date = 2004|publisher = Royal Society of Chemistry|isbn = 978-0-85404-604-1|pages = 287β}}</ref> === Other uses === [[File:5 Maiman Laser Components.jpg|thumb|alt=Components of original ruby laser.|Red crystal of a ruby laser]] Chromium(III) ions present in [[corundum]] crystals (aluminium oxide) cause them to be colored red; when corundum appears as such, it is known as a [[ruby]]. If the corundum is lacking in chromium(III) ions, it is known as a [[sapphire]].<ref group=note>Any color of corundum (disregarding red) is known as a sapphire. If the corundum is red, then it is a ruby. Sapphires are not required to be blue corundum crystals, as sapphires can be other colors such as yellow and purple</ref> A red-colored artificial ruby may also be achieved by doping chromium(III) into artificial corundum crystals, thus making chromium a requirement for making synthetic rubies.<ref group=note>When {{chem|Cr|3+}} replaces {{chem|Al|3+}} in [[corundum]] (aluminium oxide, Al<sub>2</sub>O<sub>3</sub>), [[pink sapphire]] or [[ruby]] is formed, depending on the amount of chromium.</ref><ref>{{Cite journal|doi = 10.1524/zkri.1964.120.4-5.359|journal = Zeitschrift fΓΌr Kristallographie|volume = 120|pages = 359β363|date = 1964|title = The chromium position in ruby|first2 = RE|last2 = Newnham|first1 = SC|last1 = Moss|url = http://rruff.geo.arizona.edu/doclib/zk/vol120/ZK120_359.pdf|issue = 4β5|bibcode = 1964ZK....120..359M|access-date = 27 April 2009|archive-date = 8 March 2012|archive-url = https://web.archive.org/web/20120308105622/http://rruff.geo.arizona.edu/doclib/zk/vol120/ZK120_359.pdf|url-status = live}}</ref> Such a synthetic ruby crystal was the basis for the first [[laser]], produced in 1960, which relied on [[stimulated emission]] of light from the chromium atoms in such a crystal. Ruby has a laser transition at 694.3 nanometers, in a deep red color.<ref name="WebbJones2004">{{cite book|last1 = Webb|first1 = Colin E|last2 = Jones|first2 = Julian DC|title = Handbook of Laser Technology and Applications: Laser design and laser systems|url = https://books.google.com/books?id=DEgn44m6OREC&pg=PA323|year = 2004|publisher = CRC Press|isbn = 978-0-7503-0963-9|pages = 323β}}</ref> Chromium(VI) salts are used for the preservation of wood. For example, [[chromated copper arsenate]] (CCA) is used in [[timber treatment]] to protect wood from decay fungi, wood-attacking insects, including [[termites]], and marine borers.<ref name="Hings">{{cite journal |title = Leaching of chromated copper arsenate wood preservatives: a review|journal = Environmental Pollution|last1 = Hingston|first1 = J|last2 = Collins|first2 = CD|last3 = Murphy|first3 = RJ|last4 = Lester|first4 = JN|volume = 111|issue = 1|pages = 53β66|date = 2001|doi = 10.1016/S0269-7491(00)00030-0 |pmid = 11202715 }}</ref> The formulations contain chromium based on the oxide CrO<sub>3</sub> between 35.3% and 65.5%. In the United States, 65,300 metric tons of CCA solution were used in 1996.<ref name="Hings" /> Chromium(III) salts, especially [[chrome alum]] and [[chromium(III) sulfate]], are used in the tanning of [[leather]]. The chromium(III) stabilizes the leather by cross linking the [[collagen]] fibers.<!-- https://books.google.com/books?id=b1ICltm2IdAC --><ref>{{Cite journal|title = A Conformational Study of Collagen as Affected by Tanning Procedures|last1 = Brown|first1 = EM|journal = Journal of the American Leather Chemists Association |date = 1997|pages = 225β233|volume = 92}}</ref> Chromium tanned leather can contain 4β5% of chromium, which is tightly bound to the proteins.<ref name="NRC" /> Although the form of chromium used for tanning is not the toxic hexavalent variety, there remains interest in management of chromium in the tanning industry. Recovery and reuse, direct/indirect recycling,<ref>{{Cite journal|last1=Sreeram|first1=K.|title=Sustaining tanning process through conservation, recovery and better utilization of chromium|journal=Resources, Conservation and Recycling|volume=38|pages=185β212|date=2003|doi=10.1016/S0921-3449(02)00151-9|issue=3|last2=Ramasami|first2=T.|bibcode=2003RCR....38..185S }}</ref> and "chrome-less" or "chrome-free" tanning are practiced to better manage chromium usage.<ref>{{cite journal |last1=Qiang |first1=Taotao |last2=Gao |first2=Xin |last3=Ren |first3=Jing |last4=Chen |first4=Xiaoke |last5=Wang |first5=Xuechuan |title=A Chrome-Free and Chrome-Less Tanning System Based on the Hyperbranched Polymer |journal= ACS Sustainable Chemistry & Engineering|date=9 December 2015 |volume=4 |issue=3 |pages=701β707 |doi=10.1021/acssuschemeng.5b00917 }}</ref> The high heat resistivity and high melting point makes [[chromite]] and chromium(III) oxide a material for high temperature refractory applications, like [[blast furnace]]s, cement [[kiln]]s, molds for the firing of [[brick]]s and as foundry sands for the [[Casting (metalworking)|casting]] of metals. In these applications, the refractory materials are made from mixtures of chromite and magnesite. The use is declining because of the environmental regulations due to the possibility of the formation of chromium(VI).<ref name="IndMin" /> <!--10.1006/rtph.1997.1132 10.1007/BF01285116--><ref name="Barnhart1997">{{cite journal|last1=Barnhart|first1=Joel|title=Occurrences, Uses, and Properties of Chromium|journal=Regulatory Toxicology and Pharmacology|volume=26|issue=1|year=1997|pages=S3βS7|issn=0273-2300|doi=10.1006/rtph.1997.1132|pmid=9380835}}</ref> Several chromium compounds are used as [[catalyst]]s for processing hydrocarbons. For example, the [[Phillips catalyst]], prepared from chromium oxides, is used for the production of about half the world's [[polyethylene]].<ref>{{Cite journal|journal = Catalysis Today|volume = 51|issue = 2|date = 1999|pages = 215β221|doi = 10.1016/S0920-5861(99)00046-2|title = Olefin polymerization over supported chromium oxide catalysts|first1 = Bert M|last1 = Weckhuysen|last2 = Schoonheydt|first2 = Robert A|url = https://dspace.library.uu.nl/bitstream/handle/1874/21357/weckh_99_olefinpolymerization.pdf|hdl = 1874/21357|s2cid = 98324455|access-date = 5 October 2018|archive-date = 14 April 2021|archive-url = https://web.archive.org/web/20210414090528/https://dspace.library.uu.nl/bitstream/handle/1874/21357/weckh_99_olefinpolymerization.pdf|url-status = live}}</ref> Fe-Cr mixed oxides are employed as high-temperature catalysts for the [[water gas shift reaction]].<ref>{{cite book | chapter-url = https://books.google.com/books?id=YlJRAAAAMAAJ|first1 = MVE|last1 = Twigg|title = Catalyst Handbook|chapter = The Water-Gas Shift Reaction |isbn = 978-0-7234-0857-4 |date = 1989| publisher=Taylor & Francis }}</ref><ref>{{cite journal |doi = 10.1016/0920-5861(94)00135-O | title = Water-gas shift reaction: Finding the mechanistic boundary |date=1995 |last1 = Rhodes|first1 = C|journal = Catalysis Today|volume = 23|pages = 43β58|last2 = Hutchings | first2 = GJ|last3 = Ward|first3 = AM}}</ref> [[Copper chromite]] is a useful [[hydrogenation]] catalyst.<ref>{{OrgSynth |last1 = Lazier|first1 = WA|last2 = Arnold |first2 = HR|name-list-style = amp|year = 1939|title = Copper Chromite Catalyst|volume = 19|pages = 31|collvol = 2|collvolpages = 142|prep = CV2P0142}}</ref> === Uses of compounds === * [[Chromium(IV) oxide]] (CrO<sub>2</sub>) is a [[magnetism|magnetic]] compound. Its ideal shape [[anisotropy]], which imparts high [[coercivity]] and remnant magnetization, made it a compound superior to Ξ³-Fe<sub>2</sub>O<sub>3</sub>. Chromium(IV) oxide is used to manufacture [[magnetic tape]] used in high-performance audio tape and standard [[compact audio cassette|audio cassettes]].<ref>{{Cite book|chapter-url = https://books.google.com/books?id=rNifWsBxnWkC&pg=PA32| title =The foundations of magnetic recording|first = John C.|last = Mallinson|publisher = Academic Press|date = 1993|isbn = 978-0-12-466626-9|chapter = Chromium Dioxide | page = 32}}</ref> * [[Chromium(III) oxide]] (Cr<sub>2</sub>O<sub>3</sub>) is a metal polish known as green rouge.<ref name="DoiMarinescu2011">{{cite book|author1=Toshiro Doi|author2=Ioan D. Marinescu|author3=Syuhei Kurokawa|title=Advances in CMP Polishing Technologies|url=https://books.google.com/books?id=LJH9rYdKTZwC&pg=PA60|date=30 November 2011|publisher=William Andrew|isbn=978-1-4377-7860-1|pages=60β}}</ref><ref>{{cite journal|title = Chromium-based regulations and greening in metal finishing industries in the USA|volume = 5|issue = 2|year = 2002|pages = 121β133|doi = 10.1016/S1462-9011(02)00028-X|first1 = Anil|last1 = Baral|journal = Environmental Science & Policy|last2 = Engelken|first2 = Robert D.|bibcode = 2002ESPol...5..121B}}</ref> <!--{{doi|10.1016/0026-0576(95)99364-G}} {{doi|10.1016/S0026-0576(02)82003-7}} https://books.google.de/books?id=LJH9rYdKTZwC&pg=PA60 --> * [[Chromic acid]] is a powerful oxidizing agent and is a useful compound for cleaning laboratory glassware of any trace of organic compounds.<ref>{{cite web |last1=Soderberg |first1=Tim |title=Oxidizing Agents |url=https://chem.libretexts.org/Bookshelves/Organic_Chemistry/Map%3A_Organic_Chemistry_(Smith)/Chapter_12%3A_Oxidation_and_Reduction/12.07_Oxidizing_Agents |website=LibreTexts |publisher=MindTouch |access-date=8 September 2019 |date=3 June 2019 |archive-date=22 April 2021 |archive-url=https://web.archive.org/web/20210422223905/https://chem.libretexts.org/Bookshelves/Organic_Chemistry/Map:_Organic_Chemistry_(Smith)/Chapter_12:_Oxidation_and_Reduction/12.07_Oxidizing_Agents |url-status=live }}</ref> It is prepared by dissolving [[potassium dichromate]] in concentrated sulfuric acid, which is then used to wash the apparatus. [[Sodium dichromate]] is sometimes used because of its higher solubility (50 g/L versus 200 g/L respectively). The use of dichromate cleaning solutions is now phased out due to the high toxicity and environmental concerns. Modern cleaning solutions are highly effective and chromium free.<ref name="Roth1994">{{cite book|last1 = Roth|first1 = Alexander|title = Vacuum Sealing Techniques|url = https://books.google.com/books?id=sdKAPJh5RgQC&pg=PA118|year = 1994|publisher = Springer Science & Business Media|isbn = 978-1-56396-259-2|pages=118β}}</ref> * [[Potassium dichromate]] is a chemical [[reagent]], used as a titrating agent.<ref>{{cite web |last1=Lancashire |first1=Robert J |title=Determination of iron using potassium dichromate: Redox indicators |url=http://wwwchem.uwimona.edu.jm/lab_manuals/c10expt31.html |publisher=The Department of Chemistry UWI, Jamaica |access-date=8 September 2019 |date=27 October 2008 |archive-date=18 April 2021 |archive-url=https://web.archive.org/web/20210418125750/http://wwwchem.uwimona.edu.jm/lab_manuals/c10expt31.html |url-status=live }}</ref> * [[Chromate and dichromate|Chromate]]s are added to drilling muds to prevent corrosion of steel under wet conditions.<ref>{{cite book|title = Corrosion in the Petrochemical Industry|first = Linda|last = Garverick|publisher = ASM International|date = 1994|isbn = 978-0-87170-505-1|url = https://books.google.com/books?id=qTfNZZRO758C&pg=PA278|access-date = 5 June 2020|archive-date = 10 June 2024|archive-url = https://web.archive.org/web/20240610045936/https://books.google.com/books?id=qTfNZZRO758C&pg=PA278#v=onepage&q&f=false|url-status = live}}</ref> * [[Chrome alum]] is [[Chromium(III) potassium sulfate]] and is used as a [[mordant]] (i.e., a fixing agent) for dyes in fabric and in [[tanning (leather)|tanning]].<ref name="Ul-Islam2017">{{cite book|author=Shahid Ul-Islam|title=Plant-Based Natural Products: Derivatives and Applications|url=https://books.google.com/books?id=jYMtDwAAQBAJ&pg=PA74|date=18 July 2017|publisher=Wiley|isbn=978-1-119-42388-1|pages=74β|access-date=17 October 2018|archive-date=10 June 2024|archive-url=https://web.archive.org/web/20240610050514/https://books.google.com/books?id=jYMtDwAAQBAJ&pg=PA74#v=onepage&q&f=false|url-status=live}}</ref>
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