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| '''Radiocarbon dating''' (or simply '''carbon dating''') is a [[radiometric dating]] technique that uses the decay of [[carbon-14]] ({{chem|14|C}}) to estimate the age of [[Organic matter|organic materials]], such as wood and leather, up to about 58,000 to 62,000 years [[Before Present]] (BP, present defined as AD 1950).<ref>{{cite journal |last=Plastino |first=W. |last2=Kaihola |first=L. |last3=Bartolomei |first3=P. |last4=Bella |first4=F. |year=2001 |title=Cosmic Background Reduction In The Radiocarbon Measurement By Scintillation Spectrometry At The Underground Laboratory Of Gran Sasso |journal=Radiocarbon |volume=43 |issue=2A |pages=157–161 |url=https://digitalcommons.library.arizona.edu/objectviewer?o=http%3A%2F%2Fradiocarbon.library.arizona.edu%2Fvolume43%2Fnumber2A%2Fazu_radiocarbon_v43_n2a_157_161_v.pdf}}</ref> Carbon dating was presented to the world by [[Willard Libby]] in 1949, for which he was awarded the [[Nobel Prize in Chemistry]].
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| Since the introduction of carbon dating, the method has been used to date many items, including samples of the [[Carbon dating the Dead Sea Scrolls|Dead Sea Scrolls]], the [[Radiocarbon 14 dating of the Shroud of Turin|Shroud of Turin]], enough [[Ancient Egypt|Egyptian]] artifacts to supply a [[Egyptian chronology|chronology]] of [[History of ancient Egypt|Dynastic Egypt]],<ref>{{cite web|url=http://www.sciencemag.org/content/328/5985/1554|title=Radiocarbon-Based Chronology for Dynastic Egypt|author=Christopher Bronk Ramsey, Michael W. Dee, Joanne M. Rowland, Thomas F. G. Higham, Stephen A. Harris, Fiona Brock, Anita Quiles, Eva M. Wild, Ezra S. Marcus, Andrew J. Shortland|work=Science|date=June 18, 2010|accessdate=January 27, 2013}}</ref> and [[Ötzi|Ötzi the Iceman]].<ref>{{cite web|url=http://www.iceman.it/en/oetzi-age|title=The Incredible Age of the Find|publisher=South Tyrol Museum of Archaeology|year=2013|accessdate=January 27, 2013}}</ref>
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| The Earth's atmosphere contains various [[isotope]]s of [[carbon]], roughly in constant proportions. These include the main stable isotope ({{chem|12|C}}) and an unstable isotope ({{chem|14|C}}). Through photosynthesis, plants absorb both forms from [[carbon dioxide]] in the atmosphere. When an organism dies, it contains the standard ratio of {{chem|14|C}} to {{chem|12|C}}, but as the {{chem|14|C}} decays with no possibility of replenishment, the proportion of carbon 14 decreases at a known constant rate. The time taken for it to reduce by half is known as the [[half-life]] of {{chem|14|C}}. The measurement of the remaining proportion of {{chem|14|C}} in organic matter thus gives an estimate of its age (a ''raw'' radiocarbon age).<ref>{{cite web|url=http://www.c14dating.com/int.html|title=The 14C Method|first=Thomas |last=Higham|accessdate=January 27, 2013}}</ref> However, over time there are small fluctuations in the ratio of {{chem|14|C}} to {{chem|12|C}} in the atmosphere, fluctuations that have been noted in natural records of the past, such as [[dendrochronology|sequences of tree rings]] and [[speleothem|cave deposits]]. These records allow fine-tuning, or "[[calibration]]", of the raw radiocarbon age, to give a more accurate estimate of the calendar date of the material. One of the most frequent uses of radiocarbon dating is to estimate the age of organic remains from archaeological sites.
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| [[Carbon]] has two stable, nonradioactive [[isotope]]s: [[carbon-12]] ({{chem|12|C}}), and [[carbon-13]] ({{chem|13|C}}), and a radioactive isotope, [[carbon-14]] ({{chem|14|C}}), also known as radiocarbon. The [[half-life]] of {{chem|14|C}} (the time it takes for half of a given amount of {{chem|14|C}} to [[radioactive decay|decay]]) is about 5,730 years, so its concentration in the atmosphere might be expected to reduce over thousands of years. However, {{chem|14|C}} is constantly being produced in the lower [[stratosphere]] and upper [[troposphere]] by [[cosmic rays]], which generate neutrons that in turn create {{chem|14|C}} when they strike [[nitrogen-14]] ({{chem|14|N}}) atoms.<ref name="Bowman_10-12">Bowman, ''Radiocarbon Dating'', pp. 10–12.</ref>
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| [[File:Carbon 14 formation and decay.svg|cenrer|thumb|400px|1: Formation of carbon-14 <br>2: Decay of carbon-14 <br>3: The equation is for living organisms, and the inequality is for dead organisms, in which the {{chem|14|C}} then decays (See 2).]]
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| The carbon dating process is described by the following [[nuclear reaction]], where n represents a neutron and p represents a [[proton]]:<ref name="CES_476">Brown, Brown & Holme, ''Chemistry for Engineering Students'', p. 476.</ref>
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| :<math>n + \mathrm{^{14}_{7}N^+} \rightarrow \mathrm{^{14}_{6}C} + p</math>
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| Once produced, the {{chem|14|C}} quickly combines with the oxygen in the atmosphere to form carbon dioxide ({{chem|CO|2}}). Carbon dioxide produced in this way diffuses in the atmosphere, is dissolved in the ocean, and is taken up by plants via photosynthesis. Animals eat the plants, and ultimately the radiocarbon is distributed throughout the [[biosphere]]. The combination of the ocean, the atmosphere and the biosphere is referred to as the carbon exchange reservoir.<ref name="Aitken_56-58">Aitken, ''Science-based Dating in Archaeology'', pp. 56–58.</ref>
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| If it is assumed that the cosmic ray flux has been constant over the last ~100,000 years, then carbon-14 has been produced at a constant rate, and since it is also lost through radioactivity at a constant rate, the proportion of radioactive to non-radioactive carbon is constant. The ratio of {{chem|14|C}} to {{chem|12|C}} in the carbon exchange reservoir is 1.5 parts of {{chem|14|C}} to 10<sup>12</sup> parts of {{chem|12|C}}.<ref name="Aitken_56-58" /> In addition, about 1% of the reservoir is made up of the stable isotope {{chem|13|C}}.<ref name="Bowman_10-12" />
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| ==Invention of the methods== | | C'est beaucoup d'argent, et la plus grande partie irait aux agriculteurs les plus riches, les entreprises et les propriétaires fonciers dans le secteur agricole .. [http://www.r2b.be/verstraete/design/disclaimer.asp?k=16-Botte-Ugg Botte Ugg] mais j'aime sa curiosité et son esprit d'aventure et son entêtement. Une expérience menée sur des personnes qui n'étaient pas allés dormir pendant près de deux jours a montré que leur rétention de la mémoire sur l'identification des visages individuels était faible et difficile pour le sujet.<br><br>En outre, les régions les plus corticales (de allocortex, tous du cortex chez les reptiles) sont un commentaire> effets épigénétiques de nutriments et de phéromones s'étendent à travers l'histoire de vie des organismes, mais de 1996 à 2012 le concept de l'épigénétique moléculaire et les effets épigénétiques sur l'hormone entraînés évolution adaptative <br><br>Il est très inquiétant, mais mon avis est que ils sont très résistants, et il est hautement improbable qu'il a fait de mal à lui-même. [http://www.verbeke-daniel.be/doeself/includes/promoties.asp?p=6-Magasin-Moncler-Bruxelles Magasin Moncler Bruxelles] Pas l'une des dispositions de ObamaCare est admissible en vertu de tout pouvoir énuméré donné au Congrès dans la Constitution et, par conséquent, ils n'ont pas été faites en vertu de la Constitution, et ils ne sont pas la loi suprême de la land.Alexander Hamilton promu cette interprétation de l'article <br><br>Cependant, la recherche a été infructueuse, de sorte que les fils a fait des maisons pour eux-mêmes. "Donc, ce sont ces premières dames qui font à la cour impériale? Ils ont été tissage tissu avec des instruments d'or», dit Makowski .. "De ce que je peux dire, il a fait un excellent travail en tant que député et aime sa communauté," Susan Davis de CAEC dit Fort McMurray Today.<br><br>Il existe une variété de styles, de couleurs, de tailles et qui peut convenir à toute personne, hommes et femmes [http://www.bistrolarmagnac.be/history/foto/contact.asp?g=83-Sneakers-Isabel-Marant-Le-Bon-Coin Sneakers Isabel Marant Le Bon Coin] confondus. Si vous avez des plantes sensibles au gel dans votre cour, je sais que je fais! les planter dans les endroits les plus favorables afin de minimiser le gel hivernal. C'est la même chose que si elles ont [http://www.lebleu.be/SpryAssets/content.asp?h=72-Bottes-Timberland-Fille Bottes Timberland Fille] tenu un rassemblement dans le parc et les gens ont commencé à faire du bruit.<br><br>Trois ans vont et viennent entre les humeurs positives et négatives. Henry Kissinger à la Maison Blanche, et en 1984 Mme Assurez-vous que la classe possède les compétences linguistiques nécessaires pour parler d'un sujet particulier, et qu'ils trouvent le sujet interesting.Here, nous avons recueilli quelques activités de conversation d'anglais langue seconde qui peuvent obtenir votre <br><br>Bien que 86 pour cent des adolescents ayant des pensées suicidaires avait vu un fournisseur de soins de santé, seulement 13 pour cent avaient consulté un spécialiste de la santé mentale. "Power à son meilleur est l'amour mettre en œuvre les exigences de la justice. Ensuite, toute tentative de changement il s'agira à partir de là où vous n'êtes pas, et qui fonctionne rarement bien (comme notre homme ivre à la recherche de ses clés sur la mauvaise rue peut attester à.).<ul> |
| In the mid-1940s, [[Willard Libby]], then at the [[University of Chicago]], realized that the decay of carbon-14 might lead to a method of dating organic matter. Libby published a paper in 1946 in which he proposed that the carbon in living matter might include carbon-14 as well as non-radioactive carbon.<ref name="Bowman_9">Bowman, ''Radiocarbon Dating'', p. 9.</ref><ref>{{vcite journal|last=Libby |first=W. F.|title=Atmospheric Helium Three and Radiocarbon from Cosmic Radiation |journal=Phys. Rev.|volume=69 |issue=671 |pages=2 |year=1946 |month=June|doi=1103/PhysRev.69.671.2 }}</ref> Libby and several collaborators proceeded to experiment with methane collected from sewage works in Baltimore, and after [[isotope enrichment|isotopically enriching]] their samples they were able to demonstrate that they contained radioactive carbon-14.
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| | <li>[http://easycooker.com.cn/forum.php?mod=viewthread&tid=1244031 http://easycooker.com.cn/forum.php?mod=viewthread&tid=1244031]</li> |
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| | <li>[http://www.pitidea.com/activity/p/41783/ http://www.pitidea.com/activity/p/41783/]</li> |
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| | <li>[http://bbs.yulebaby.com/forum.php?mod=viewthread&tid=124576&fromuid=21014 http://bbs.yulebaby.com/forum.php?mod=viewthread&tid=124576&fromuid=21014]</li> |
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| | <li>[http://www.mermaids.tw/forum/showthread.php?p=2516493#post2516493 http://www.mermaids.tw/forum/showthread.php?p=2516493#post2516493]</li> |
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| | <li>[http://www.gsg188.com/forum.php?mod=viewthread&tid=65103&fromuid=16239 http://www.gsg188.com/forum.php?mod=viewthread&tid=65103&fromuid=16239]</li> |
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| By contrast, methane created from petroleum had no radiocarbon activity. The results were summarized in a paper in ''[[Science (journal)|Science]]'' in 1947, and the authors commented that their results implied it would be possible to date materials containing carbon of organic origin.<ref name="Bowman_9" /><ref name="Anderson_1947">{{vcite journal|authors=Anderson, E. C.; Libby, W. F.; Weinhouse, S.; Reid, A. F.; Kirshenbaum, A. D.; and Grosse, A. V.|title=Radiocarbon from cosmic radiation |journal=Science |volume=105 |issue=2765 |pages=576–577 |year=1947 |month=May |doi=10.1126/science.105.2735.576 |bibcode = 1947Sci...105..576A }}</ref> Libby and [[James R. Arnold|James Arnold]] proceeded to experiment with samples of wood of known age.
| | == Chaussures Mbt Pour Femmes par exemple == |
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| For example, two wood samples taken from the tombs of two Egyptian kings, [[Zoser]] and [[Sneferu]], independently dated to 2625 BC plus or minus 75 years, were dated by radiocarbon measurement to an average of 2800 BC plus or minus 250 years.<ref name="libby49">{{cite journal |last=Arnold |first=J. R. |last2=Libby |first2=W. F. |year=1949 |title=Age Determinations by Radiocarbon Content: Checks with Samples of Known Age |journal=[[Science (journal)|Science]] |volume=110 |issue=2869 |pages=678–680 |doi=10.1126/science.110.2869.678 |jstor=1677049 |url=http://hbar.phys.msu.ru/gorm/fomenko/libby.htm |pmid=15407879|bibcode = 1949Sci...110..678A }}</ref><ref name="Aitken_60-61">Aitken, ''Science-based Dating'', pp. 60–61.</ref> These measurements, published in ''Science'' in 1949, launched the "radiocarbon revolution" in archaeology, and soon led to dramatic changes in scholarly chronologies.<ref name="Aitken_60-61" /> In 1960, Libby was awarded the [[Nobel Prize in chemistry]] for this work.<ref name="Bowman_10">Bowman, ''Radiocarbon Dating'', p. 10.</ref>
| | 3) West Palm Beach, en Floride Pour les humains, cela signifie ramasser la nourriture, la mettant dans sa bouche, gommage, de la déplacer de retour avec leur langue, et de l'avaler. La Fraternité a nié être responsable de l'attaque Mansoura. Cependant, le film est venu sous le feu après sa première représentation donnée sexuelle et violente de l'étudiant américain, et Knox ensuite poursuivi en vertu du principe que le film l'a exploitée et contenait plusieurs scènes "invraisemblables".<br><br>ESPN Outside the Lines a indiqué qu'un courtier sud de la Floride payé Manziel, une taxe de cinq chiffres plat à signer des centaines d'articles [http://www.betonsnijwerk.be/includes/boren.asp?t=32-Chaussures-Mbt-Pour-Femmes Chaussures Mbt Pour Femmes] avant et après le BCS Championship Game en Miami.Three sources anonymes dit ESPN que Manziel signé mini-casques, ballons de football, des photos et d'autres articles <br><br>La meilleure stratégie de sortie est celui qui correspond le mieux à votre petite entreprise et vos objectifs personnels. Alors que le nombre dans la société israélienne semblent favoriser une solution à deux Etats ajusté hors des frontières de [http://www.paloma-curiosa.be/includes/old/function.asp?l=119-Sacs-Longchamps-Bruxelles Sacs Longchamps Bruxelles] 1967 pré de guerre, il ya de plus en plus les appels de certains sur la droite pour trouver une solution à un seul Etat d'un Etat juif en miroir des appels de certains segments de la [http://www.stobbeldeen.be/download/spelletjes.asp?d=80-New-Balance-Pas-Cher-Belgique New Balance Pas Cher Belgique] partie arabe de une solution à un seul Etat.<br><br>"Nous avons pris toutes les précautions pour éviter un tel incident en direct en mettant les photos d'hélicoptères sur un délai de cinq secondes. La meilleure partie est que vous seriez couvrez un domaine que vous connaissez et aimez. Par ailleurs, ils devraient. Consultez la section« Que dois-je faire quand je trouve un courrier international? <br><br>Mais il [http://www.bierhandeldetroetsel.be/pics/contact.asp?g=34-Polo-Lacoste-Prix Polo Lacoste Prix] est tellement plus. Connectez-vous avec votre nom d'Apple ID et mot de passe, accédez à la section Mot de passe et de sécurité et cliquez sur Réinitialiser vos informations de sécurité .. Entrez Big Game Giveaway concours de Red Baron Pizza pour votre chance de gagner le plein prix de partie paquet valeur ultime plus de 13.000 dollars ou prix instantanés <br><br>Ne pas prendre en compte si l'on entre dans le mariage avec la dette, ce qui peut influer l'autre crédit, surtout si une urgence se produit. Le film était très lent, mais les images étaient magnifiques, et comment je m'en souviens. Lorsque Maria était de 3 et en refusant de parler l'espagnol, j'ai volontairement allumé les vidéos Dora et Dora célébré l'héritage hispanique, le bilinguisme et l'esprit aventureux.<br><br>(Quand on appelle, par exemple, un étudiant va passer la balle de laine à l'étudiant, tout en se tenant à la laine ou de ficelle.). Réagir en conséquence .. Avoir un autocollant fait avec vos nouvelles informations de boutique en ligne. Si vous allez sur ce régime, vous devez vous assurer d'obtenir «bonnes graisses» dans votre alimentation ou vous serez RAVENOUS.<ul> |
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| ==Calculating ages== | | <li>[http://www.tianwaitianrihua.com/news/html/?712561.html http://www.tianwaitianrihua.com/news/html/?712561.html]</li> |
| While a plant or animal is alive, it is exchanging carbon with its surroundings, so that the carbon it contains will have the same proportion of {{chem|14|C}} as the biosphere. Once it dies, it ceases to acquire {{chem|14|C}}, but the {{chem|14|C}} that it contains will continue to decay, and so the proportion of radiocarbon in its remains will gradually reduce. Because {{chem|14|C}} decays at a known rate, the proportion of radiocarbon can be used to determine how long it has been since a given sample stopped exchanging carbon—the older the sample, the less {{chem|14|C}} will be left.<ref name="Aitken_56-58" />
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| | | <li>[http://www.jankloco.com/activity/p/53102/ http://www.jankloco.com/activity/p/53102/]</li> |
| The equation governing the decay of a radioactive isotope is<ref name="Bowman_10-12" />
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| :<math>N = N_0e^{-\lambda t}\,</math> | | <li>[http://xelcoremunity.com/activity/p/192776/ http://xelcoremunity.com/activity/p/192776/]</li> |
| where ''N''<sub>0</sub> is the number of atoms of the isotope in the original sample (at time ''t'' = 0), and ''N'' is the number of atoms left after time ''t''.<ref name="Bowman_10-12" /> ''λ'' is a constant that depends on the particular isotope; for a given isotope it is equal to the reciprocal of the [[Radioactive decay#Time constant and mean-life|mean-life]]—i.e. the average or expected time a given atom will survive before undergoing radioactive decay.<ref name="Bowman_10-12" /> The mean-life, denoted by ''τ'', of {{chem|14|C}} is 8,267 years, so the equation above can be rewritten as:<ref>Aitken, ''Science-based Dating in Archaeology'', p. 59.</ref>
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| :<math>t = 8267 \cdot \ln(N_0/N)</math> | | <li>[http://www.49nn.com/forum.php?mod=viewthread&tid=181516 http://www.49nn.com/forum.php?mod=viewthread&tid=181516]</li> |
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| The ratio of {{chem|14|C}} atoms in the original sample, ''N''<sub>0</sub>, is taken to be the same as the ratio in the biosphere, so measuring ''N'', the number of {{chem|14|C}} atoms currently in the sample, allows the calculation of ''t'', the age of the sample.<ref name="Aitken_56-58" />
| | <li>[http://rincol.com/activity/p/10390/ http://rincol.com/activity/p/10390/]</li> |
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| The [[half-life]] of a radioactive isotope (the time it takes for half of the sample to decay, usually denoted by ''T''<sub>1/2</sub>) is a more familiar concept than the mean-life, so although the equations above are expressed in terms of the mean-life, it is more usual to quote the value of {{chem|14|C}}'s half-life than its mean-life. The currently accepted value for the half-life of radiocarbon is 5,730 years.<ref name="Bowman_10-12" /> The mean-life and half-life are related by the following equation:<ref name="Bowman_10-12" />
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| :<math>T_\frac{1}{2} = \tau \cdot \ln 2 </math>
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| The above calculations make several assumptions: for example, that the level of {{chem|14|C}} in the biosphere has remained constant over time.<ref>Bowman, ''Radiocarbon Dating'', p. 14.</ref> In fact, the level of {{chem|14|C}} in the biosphere has varied significantly and, as a result the values provided by the equation above, have to be corrected by using data from other sources, using a calibration curve, which is described in more detail below.<ref name=":0">Aitken, ''Science-based Dating in Archaeology'', pp. 61–66.</ref> For over a decade after Libby's initial work, the accepted value of the half-life for {{chem|14|C}} was 5,568 years; this was improved in the early 1960s to 5,730 years, which meant that many calculated dates in published papers were now incorrect (the error is about 3%). However, it is possible to incorporate a correction for the half-life value into the calibration curve, and so it has become standard practice to quote measured radiocarbon dates in "radiocarbon years", meaning that the dates are calculated using Libby's half-life value and have not been calibrated.<ref name=":12">Aitken, ''Science-based Dating in Archaeology'', p. 92–95.</ref> This approach has the advantage of maintaining consistency with the early papers, and also avoids the risk of a double correction for the Libby half-life value.<ref>Bowman, ''Radiocarbon Dating'', p. 42.</ref>
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| ==Carbon exchange reservoir==
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| [[File:Carbon exchange reservoir 2.svg|right|thumb|400px|Simplified version of the carbon exchange reservoir, showing proportions of carbon and relative activity of the {{chem|14|C}} in each reservoir<ref name="Bowman_13">Bowman, ''Radiocarbon Dating'', p. 13.</ref>{{#tag:ref|The data on carbon percentages in each part of the reservoir is drawn from an estimate of reservoir carbon for the mid-1990s; estimates of carbon distribution during pre-industrial times are significantly different.<ref name=GC_128-9>Goudie & Cuff, ''Environmental Change and Human Society'', pp. 128–129.</ref>|group=note}}]]The different elements of the carbon exchange reservoir vary in how much carbon they store, and in how long it takes for the {{chem|14|C}} generated by cosmic rays to fully mix with them.<ref name="Bowman_13" /> The atmosphere, which is where {{chem|14|C}} is generated, contains about 1.9% of the total carbon in the reservoirs, and the {{chem|14|C}} it contains mixes in less than 7 years.<ref name="GC_128-9" /><ref name="Warneck_690">Warneck, ''Chemistry of the Natural Atmosphere'', p. 690.</ref> The ratio of {{chem|14|C}} to {{chem|12|C}} in the atmosphere is taken as the baseline for the other reservoirs: if another reservoir has a lower ratio of {{chem|14|C}} to {{chem|12|C}}, it indicates that the carbon is older, and hence some of the {{chem|14|C}} has decayed.<ref name=":0" /> The ocean surface is an example: it contains 2.4% of the carbon in the exchange reservoir,<ref name="GC_128-9" /> but there is only about 95% as much {{chem|14|C}} as would be expected if the ratio were the same as in the atmosphere.<ref name="Bowman_13" /> The time it takes for carbon from the atmosphere to mix with the surface ocean is only a few years,<ref>Sundquist, "Geological perspectives on carbon dioxide and the carbon cycle", p. 13.</ref> but the surface waters also receive water from the deep ocean, which has over 90% of the carbon in the reservoir.<ref name=":0" /> Water in the deep ocean takes about 1,000 years to circulate back through surface waters, and so the surface waters contain a combination of older water, with depleted {{chem|14|C}}, and water recently at the surface, with {{chem|14|C}} in equilibrium with the atmosphere.<ref name=":0" />
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| Creatures living at the ocean surface have the same {{chem|14|C}} ratios as the water they live in. Using the calculation method given above to calculate the age of marine life typically gives an age of about 400 years.<ref name=":1">Bowman, ''Radiocarbon Dating'', pp. 24–27.</ref>{{#tag:ref|The age only appears to be 400 years once a correction for [[Radiocarbon dating#Fractionation|fractionation]] is made.|group = note}} Organisms on land, however, are in closer equilibrium with the atmosphere and have the same {{chem|14|C}}/{{chem|12|C}} ratio as the atmosphere.<ref name="Bowman_13" /> These organisms contain about 1.3% of the carbon in the reservoir; sea organisms have a mass of less than 1% of those on land and are not shown on the diagram.<ref name="GC_128-9" /> Accumulated dead organic matter, of both plants and animals, exceeds the mass of the biosphere by a factor of nearly 3; and since this matter is no longer exchanging carbon with its environment, it has a {{chem|14|C}}/{{chem|12|C}} ratio lower than that of the biosphere.<ref name="Bowman_13" />
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| ==Dating considerations==
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| The variation in the {{chem|14|C}}/{{chem|12|C}} ratio in different parts of the carbon exchange reservoir means that a straightforward calculation of the age of a sample based on the amount of {{chem|14|C}} it contains will often give an incorrect result. There are several other possible sources of error that need to be considered; the errors are of four general types:
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| * Variations in the {{chem|14|C}}/{{chem|12|C}} ratio in the atmosphere, both geographically and over time
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| * Isotopic fractionation
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| * Variations in the {{chem|14|C}}/{{chem|12|C}} ratio in different parts of the reservoir
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| * Contamination
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| ===Atmospheric variation===
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| In the early years of using the technique, it was understood that it depended on the atmospheric {{chem|14|C}}/{{chem|12|C}} ratio having remained the same over the preceding few thousand years. To verify the accuracy of the method, several artefacts that were datable by other techniques were tested; the results of the testing were in reasonable agreement with the true ages of the objects. However, in 1958, [[Hessel de Vries]] pointed out that this was not the case, by testing wood samples of known ages and showing there was a significant deviation from the expected {{chem|14|C}}/{{chem|12|C}} ratio. This discrepancy, often called the de Vries effect, was resolved by the study of tree-rings.<ref name="Bowman_16-20"/><ref name=Suess_1970>H.E. Suess, "Bristlecone-pine calibration of the radiocarbon time-scale 5200 B.C. to the present", in Olsson, ''Radiocarbon Variatons and Absolute Chronology'', p. 303.</ref> The comparison of overlapping series of tree-rings allowed the construction of a continuous sequence of tree-ring data that spanned 8,000 years. Carbon-dating the wood from the tree-rings themselves provided the check needed on the atmospheric {{chem|14|C}}/{{chem|12|C}} ratio: with a sample of known date, and a measurement of the value of ''N'' (the number of atoms of {{chem|14|C}} remaining in the sample), the carbon-dating equation allows the calculation of ''N''<sub>0</sub> (the number of atoms of {{chem|14|C}} in the original sample), and hence the original ratio.<ref name="Bowman_16-20">Bowman, ''Radiocarbon Dating'', pp. 16–20.</ref> Armed with the results of carbon-dating the tree rings, it became possible to construct calibration curves designed to correct the errors caused by the variation over time in the {{chem|14|C}}/{{chem|12|C}} ratio.<ref>Bowman, ''Radiocarbon Dating'', pp. 43–46.</ref> These curves are described in more detail [[Radiocarbon dating#Calibration|below]]. There are three main reasons for these variations in the historical {{chem|14|C}}/{{chem|12|C}} ratio: fluctuations in the rate at which {{chem|14|C}} is created; changes caused by glaciation; and changes caused by human activity.<ref name="Bowman_16-20" />
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| ====Variations in {{chem|14|C}} production====
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| Two different trends can be seen in the tree ring series. First, there is a long term oscillation with a period of about 9,000 years, which causes radiocarbon dates to be older than true dates for the last 2,000 years, and too young before that. The known fluctuations in the earth's magnetic field strength match up quite well with this oscillation: cosmic rays are deflected by magnetic fields, so when there is a lower magnetic field, more {{chem|14|C}} is produced, leading to a younger apparent age for samples from those periods. Conversely, a higher magnetic field leads to lower {{chem|14|C}} production and an older apparent age. A secondary oscillation is thought to be caused by variations in sunspot activity, which has two separate periods: a longer-term, 200-year oscillation, combined with a shorter 11-year cycle. Sunspots cause changes in the solar system's magnetic field and corresponding changes to the cosmic ray flux, and hence to the production of {{chem|14|C}}.<ref name="Bowman_16-20" />
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| Over geological timescales, the earth's magnetic field can reverse, both locally and globally. These global [[geomagnetic reversal]]s, and shorter, often localized [[Geomagnetic excursion|polar excursion]]s, would have had a significant impact on global {{chem|14|C}} production, since the geomagnetic field falls to a low value for thousands of years. However, there are no well-established occurrences of either of these events in the recent enough past for there to have been an appreciable effect on present-day {{chem|14|C}} measurements. There is some evidence for polarity excursions, but they may not have been global; if they were local they would not have had any noticeable impact on {{chem|14|C}} production.<ref>Aitken, ''Science-based Dating in Archaeology'', pp. 68–69.</ref>
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| Since the earth's magnetic field varies with latitude, the rate of {{chem|14|C}} production changes with latitude too, but atmospheric mixing is rapid enough that these variations amount to less than 0.5% of the global {{Chem|14 = |C = }} concentration.<ref name="Bowman_16-20" /> This is close to the limit of detectability in most years,<ref>Rasskazov, Brandt & Brandt, ''Radiogenic Isotopes in Geologic Processes'', p. 40.</ref> but the effect can be seen clearly in tree rings from years such as 1963, when {{chem|14|C}} from nuclear testing rose sharply through the year.<ref name="Grootes">Grootes, "Subtle 14C Signals", p. 219–221.</ref> The latitudinal variation in {{chem|14|C}} was much larger than normal that year, and tree rings from different latitudes show corresponding variations in their {{chem|14|C}} content.<ref name="Grootes" />
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| {{chem|14|C}} can also be produced at ground level, primarily by cosmic rays that penetrate the atmosphere as far as the earth's surface, and by spontaneous fission of naturally occurring uranium. These sources of neutrons only produce {{chem|14|C}} at a rate of 1 x 10<sup>−4</sup> atoms per gram per second, which is not enough to have a significant impact on dating.<ref name="Grootes">Grootes, "Subtle 14C Signals", p. 222–223.</ref><ref name="Ramsay">{{cite doi|10.1111/j.1475-4754.2008.00394.x}}</ref> At higher altitudes, the neutron flux can be substantially higher,<ref name="Bowman_20-23">Bowman, ''Radiocarbon Dating'', pp. 20–23.</ref>{{#tag:ref|Even at an altitude of 3 km, the neutron flux is only 3% of the value in the stratosphere where most {{chem|14|C}} is created; at sea level the value is less than 0.5% of the value in the stratosphere.<ref name=Bowman_20-23/>|group=note}} and in addition, trees at higher altitude are more likely to be struck by lightning, which produces neutrons. However, experiments in which wood samples have been irradiated with neutrons indicate that the effect on {{chem|14|C}} content is minor; though for very old trees (such as some bristlecone pines) that grow at altitude, some effect can be seen.<ref name="Bowman_20-23" />
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| ====Impact of climatic cycles====
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| Because the solubility of {{chem|CO|2}} in water increases with lower temperatures, glacial periods would have led to the faster absorption of atmospheric {{chem|CO|2}} by the oceans. In addition, any carbon stored in the glaciers would be depleted in {{chem|14|C}} over the life of the glacier; when the glacier melted, as the climate warmed, the depleted carbon would be released, reducing the global {{chem|14|C}}/{{chem|12|C}} ratio. The changes in climate would also cause changes in the biosphere, with warmer periods leading to more plant and animal life. The effect of these factors on radiocarbon dating is not known.<ref name="Bowman_16-20" />
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| ====The effects of human activity====
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| [[Image:Radiocarbon bomb spike.svg|thumb|300px|right|Atmospheric {{chem|14|C}}, New Zealand<ref>{{cite web |url=http://cdiac.esd.ornl.gov/trends/co2/welling.html |title=Atmospheric δ{{chem|14|C}} record from Wellington |work=[[Carbon Dioxide Information Analysis Center]] |accessdate=1 May 2008}}</ref> and Austria.<ref>{{cite web |url=http://cdiac.esd.ornl.gov/trends/co2/cent-verm.html |title= δ{{chem|14|CO|2}} record from Vermunt |work=Carbon Dioxide Information Analysis Center |accessdate=1 May 2008}}</ref> The New Zealand curve is representative of the Southern Hemisphere; the Austrian curve is representative of the Northern Hemisphere. Atmospheric nuclear weapon tests almost doubled the concentration of {{chem|14|C}} in the Northern Hemisphere.<ref>{{cite web |url=http://www1.phys.uu.nl/ams/Radiocarbon.htm |title= Radiocarbon dating |publisher=[[Utrecht University]] |accessdate=1 May 2008}}</ref> The date that the [[Partial Test Ban Treaty]] (PTBT) went into effect is marked on the graph.]]Coal and oil began to be burned in large quantities during the 1800s. Both coal and oil are sufficiently old that they contain little detectable {{chem|14|C}} and, as a result, the {{chem|CO|2}} released substantially diluted the atmospheric {{chem|14|C}}/{{chem|12|C}} ratio. Dating an object from the early 20th century hence gives an apparent date older than the true date; and for the same reason, {{chem|14|C}} concentrations in the neighbourhood of large cities are lower than the atmospheric average. This fossil fuel effect (also known as the Suess effect, after [[Hans Suess]], who first reported it in 1955) would only amount to a reduction of 0.2% in {{chem|14|C}} activity if the additional carbon from fossil fuels were distributed throughout the carbon exchange reservoir, but because of the long delay in mixing with the deep ocean, the actual effect is a 3% reduction.<ref name="Bowman_16-20" /><ref name="Aitken_71-72" />
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| A much larger effect comes from above-ground nuclear testing, which released large numbers of neutrons and created {{chem|14|C}}. From about 1950 until 1963, when atmospheric nuclear testing was banned, it is estimated that several tonnes of {{chem|14|C}} were created. If all this extra {{chem|14|C}} had immediately been spread across the entire carbon exchange reservoir, it would have led to an increase in the {{chem|14|C}}/{{chem|12|C}} ratio of only a few per cent, but the immediate effect was to almost double the amount of {{chem|14|C}} in the atmosphere, with the peak level occurring in about 1965. The level has since dropped<!--'again' only valid if it had dropped before-->, as the "bomb carbon" (as it is sometimes called) percolates into the rest of the reservoir.<ref name="Bowman_16-20" /><ref name="Aitken_71-72">Aitken, ''Science-based Dating in Archaeology'', pp. 71–72.</ref><ref name="PTBT">{{cite web|url=http://www.state.gov/t/isn/4797.htm|title=Limited Test Ban Treaty|work=Science Magazine|accessdate=July 26, 2013}}</ref>
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| ===Fractionation===
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| Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. Two different photosynthetic processes exist: the [[C3 carbon fixation|C3]] pathway, and the [[C4 carbon fixation|C4]] pathway. About 90% of all plant life uses the C3 process; the remaining plants either use C4 or are [[Crassulacean acid metabolism|CAM]] plants, which can use either C3 or C4 depending on the environmental conditions. Both the C3 and C4 photosynthesis pathways show a preference for lighter carbon, with {{chem|12|C}} being absorbed slightly more easily than {{chem|13|C}}, which in turn is more easily absorbed than {{chem|14|C}}. The differential uptake of the three carbon isotopes leads to {{chem|13|C}}/{{chem|12|C}} and {{chem|14|C}}/{{chem|12|C}} ratios in plants that differ from the ratios in the atmosphere. This effect is known as isotopic fractionation.<ref name="Bowman_20-23" /><ref name="Leng_246">Maslin, Mark A. & Swann, George E. A., "Isotopes in Marine Sediments", in Leng (ed.), ''Isotopes in Palaeoenvironmental Research'', p. 246.</ref>
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| To determine the degree of fractionation that takes place in a given plant, the amounts of both {{chem|12|C}} and {{chem|13|C}} are measured, and the resulting {{chem|13|C}}/{{chem|12|C}} ratio is then compared to a standard ratio known as PDB. The resulting value, known as {{delta|13|C|link}}, is calculated as follows:<ref name="Bowman_20-23" />
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| :<math>\mathrm{\delta ^{13}C} = \Biggl( \mathrm{\frac{\bigl( \frac{^{13}C}{^{12}C} \bigr)_{sample}}{\bigl( \frac{^{13}C}{^{12}C} \bigr)_{PDB}}} -1 \Biggr) \times 1000\ ^{o}\!/\!_{oo}</math>
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| where the ‰ ([[permil]]) sign indicates parts per thousand.<ref name="Bowman_20-23" /> This can be rewritten as:<ref name="BO_186">Miller & Wheeler, ''Biological Oceanography'', p. 186.</ref>
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| :<math>\mathrm{\delta ^{13}C} = \frac{\mathrm{\Bigl( \frac{^{13}C}{^{12}C} \Bigr)_{sample}} - {\Bigl( \frac{^{13}C}{^{12}C} \Bigr)_{PDB}} }{\bigl( \frac{^{13}C}{^{12}C} \bigr)_{PDB}} \times 1000\ ^{o}\!/\!_{oo}</math>
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| which makes it apparent that {{delta|13|C}} is proportional to the difference between the {{chem|13|C}}/{{chem|12|C}} ratios in the PDB standard and in the sample.<ref name="BO_186" /> Because the PDB standard contains an unusually high proportion of {{chem|13|C}},{{#tag:ref|The PDB value is 11.1‰.<ref name=BO_186/>|group=note}} most measured {{delta|13|C}} values are negative. Values for C3 plants typically range from −30‰ to −22‰, with an average of −27‰; for C4 plants the range is −15‰ to −9‰, and the average is −13‰.<ref name="Leng_246" /> Atmospheric {{chem|CO|2}} has a {{delta|13|C}} of −8‰.<ref name="Bowman_20-23" />
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| [[File:NR sheep.jpg|thumb|300px|left|Sheep on the beach in [[North Ronaldsay]]. In the winter, these sheep eat seaweed, which has a higher {{delta|13|C}} content than grass; samples from these sheep have a {{delta|13|C}} value of about −13‰, which is much higher than for sheep that feed on grasses.<ref name="Bowman_20-23" />]]For marine organisms, the details of the photosynthesis reactions are less well understood. Measured {{delta|13|C}} values for marine plankton range from −31‰ to −10‰; most lie between −22‰ and −17‰. The {{delta|13|C}} values for marine photosynthetic organisms also depend on temperature. At higher temperatures, {{chem|CO|2}} has poor solubility in water, which means there is less {{chem|CO|2}} available for the photosynthetic reactions. Under these conditions, fractionation is reduced, and at temperatures above 14°C the {{delta|13|C}} values are correspondingly higher, reaching −13‰. At lower temperatures, {{chem|CO|2}} becomes more soluble and hence more available to the marine organisms; fractionation increases and {{delta|13|C}} values can be as low as −32‰.<ref name="Leng_246" />
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| The {{delta|13|C}} value for animals depends on their diet. An animal that eats food with high {{delta|13|C}} values will have a higher {{delta|13|C}} than one that eats food with lower {{delta|13|C}} values.<ref name="Bowman_20-23" /> The animal's own biochemical processes can also impact the results: for example, both bone minerals and bone collagen typically have a higher concentration of {{chem|13|C}} than is found in the animal's diet, though for different biochemical reasons. The enrichment of bone {{chem|13|C}} also implies that excreted material is depleted in {{Chem|13|C}} relative to the diet.<ref>Margaret J. Schoeninger, "Diet Reconstruction and Ecology Using Stable Isotope Ratios", in Larsen, ''A Companion to Biological Anthropology'', p. 446.</ref>
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| Since {{chem|13|C}} makes up about 1% of the carbon in a sample, the {{chem|13|C}}/{{chem|12|C}} ratio can be accurately measured by [[mass spectrometry]].<ref name=":0" /> Typical values of {{delta|13|C}} have been found by experiment for many plants, as well as for different parts of animals such as bone [[collagen]], but when dating a given sample it is better to determine the {{delta|13|C}} value for that sample directly than to rely on the published values.<ref name="Bowman_20-23" /> The depletion of {{chem|13|C}} relative to {{chem|12|C}} is proportional to the difference in the atomic masses of the two isotopes, so once the {{delta|13|C}} value is known, the depletion for {{chem|14|C}} can be calculated: it will be twice the depletion of {{chem|13|C}}.<ref name=":0" />
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| The carbon exchange between atmospheric {{chem|CO|2}} and carbonate at the ocean surface is also subject to fractionation, with {{chem|14|C}} in the atmosphere more likely than {{chem|12|C}} to dissolve in the ocean. The result is an overall increase in the {{chem|14|C}}/{{chem|12|C}} ratio in the ocean of 1.5%, relative to the {{chem|14|C}}/{{chem|12|C}} ratio in the atmosphere. This increase in {{chem|14|C}} concentration almost exactly cancels out the decrease caused by the upwelling of water (containing old, and hence {{chem|14|C}} depleted, carbon) from the deep ocean, so that direct measurements of {{chem|14|C}} radiation are similar to measurements for the rest of the biosphere. Correcting for isotopic fractionation, as is done for all radiocarbon dates to allow comparison between results from different parts of the biosphere, gives an apparent age of about 400 years for ocean surface water.<ref name=":0" />
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| ===Reservoir effects===
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| Libby's original exchange reservoir hypothesis assumed that the exchange reservoir is constant all over the world,<ref name=":2" /> but it has since been discovered that there are several causes of variation in the {{chem|14|C}}/{{chem|12|C}} ratio across the reservoir.<ref name=":1" />
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| ====Marine effect====
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| The {{chem|CO|2}} in the atmosphere transfers to the ocean by dissolving in the surface water as carbonate and bicarbonate ions; at the same time the carbonate ions in the water are returning to the air as {{chem|CO|2}}.<ref name=":2">Libby, ''Radiocarbon dating'', p. 6.</ref> This exchange process brings{{chem|14|C}} from the atmosphere into the surface waters of the ocean, but the {{chem|14|C}} thus introduced takes a long time to percolate through the entire volume of the ocean. The deepest parts of the ocean mix very slowly with the surface waters, and the mixing is known to be uneven. The main mechanism that brings deep water to the surface is upwelling. Upwelling is more common in regions closer to the equator; it is also influenced by other factors such as the topography of the local ocean bottom and coastlines, the climate, and wind patterns. Overall, the mixing of deep and surface waters takes far longer than the mixing of atmospheric {{chem|CO|2}} with the surface waters, and as a result water from some deep ocean areas has an apparent radiocarbon age of several thousand years. Upwelling mixes this "old" water with the surface water, giving the surface water an apparent age of about several hundred years (after correcting for fractionation).<ref name=":1" /> This effect is not uniform—the average effect is about 440 years, but there are local deviations of several hundred years for areas that are geographically close to each other.<ref name=":1" /><ref name=":3" /> The effect also applies to marine organisms such as shells, and marine mammals such as whales and seals, which have radiocarbon ages that appear to be hundreds of years old.<ref name=":1" /> These marine reservoir effects vary over time as well as geographically; for example, there is evidence that during the [[Younger Dryas]], a period of cold climatic conditions about 12,000 years ago, the apparent difference between the age of surface water and the contemporary atmosphere increased from between 400 and 600 years to about 900 years until the climate warmed again.<ref name=":3">Cronin, ''Paleoclimate, p. 35.''</ref>
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| ====Hard water effect====
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| If the carbon in freshwater is partly acquired from aged carbon, such as rocks, then the result will be a reduction in the {{chem|14|C}}/{{chem|12|C}} ratio in the water. For example, rivers that pass over [[limestone]], which is mostly composed of [[calcium carbonate]], will acquire carbonate ions. Similarly, groundwater can contain carbon derived from the rocks through which it has passed. These rocks are usually so old that they no longer contain any measurable {{chem|14|C}}, so this carbon lowers the {{chem|14|C}}/{{chem|12|C}} ratio of the water it enters, which can lead to apparent ages of thousands of years for both the affected water and the plants and freshwater organisms that live in it.<ref name=":0" /> This is known as the [[hard water]] effect, because it is often associated with calcium ions, which are characteristic of hard water; however, there can be other sources of carbon that have the same effect, such as [[humus]]. The effect is not necessarily confined to freshwater species—at a river mouth, the outflow may affect marine organisms. It can also affect terrestrial snails that feed in areas where there is a high chalk content, though no measurable effect has been found for land plants in soil with a high carbonate content—it appears that almost all the carbon for these plants is derived from photosynthesis and not from the soil.<ref name=":1" />
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| It is not possible to deduce the impact of the effect by determining the hardness of the water: the aged carbon is not necessarily immediately incorporated into the plants and animals that are affected, and the delay has an impact on their apparent age. The effect is very variable and there is no general offset that can be applied; the usual way to determine the size of the effect is to measure the apparent age offset of a modern sample.<ref name=":1" />
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| ====Volcanoes====
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| [[Volcanic eruptions]] eject large amounts of carbon into the air. The carbon is of geological origin and has no detectable {{chem|14|C}}, so the {{chem|14|C}}/{{chem|12|C}} ratio in the vicinity of the volcano is depressed relative to surrounding areas. Dormant volcanoes can also emit aged carbon. Plants that photosynthesize this carbon also have lower {{chem|14|C}}/{{chem|12|C}} ratios: for example, plants on the Greek island of [[Santorini]], near the volcano, have apparent ages of up to a thousand years. These effects are hard to predict—the town of [[Akrotiri (Santorini)|Akrotiri]], on Santorini, was destroyed in a volcanic eruption thousands of years ago, but radiocarbon dates for objects recovered from the ruins of the town show surprisingly close agreement with dates derived from other means. If the dates for Akrotiri are confirmed, it would indicate that the volcanic effect in this case was minimal.<ref name=":1" />
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| ====Hemisphere effect====
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| The northern and southern hemispheres have atmospheric circulation systems that are sufficiently independent of each other that there is a noticeable time lag in mixing between the two. The atmospheric {{chem|14|C}}/{{chem|12|C}} ratio is lower in the southern hemisphere, with an apparent additional age of 30 years for radiocarbon results from the south as compared to the north. This is probably because the greater surface area of ocean in the southern hemisphere means that there is more carbon exchanged between the ocean and the atmosphere than in the north. Since the surface ocean is depleted in {{chem|14|C}} because of the marine effect, {{chem|14|C}} is removed from the southern atmosphere more quickly than in the north.<ref name=":1" />
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| ====Island effect====
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| It has been suggested that an "island effect" might exist, by analogy with the mechanism thought to explain the hemisphere effect—since islands are surrounded by water, the carbon exchange between the water and atmosphere might reduce the {{chem|14|C}}/{{chem|12|C}} ratio on an island. Within a hemisphere, however, atmospheric mixing is apparently rapid enough that no such effect exists: two calibration curves assembled in Seattle and Belfast laboratories, with results from North American trees and Irish trees, respectively, are in close agreement, instead of the Irish samples appearing to be older, as would be the case if there were an island effect.<ref name=":1" />
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| ===Contamination===
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| Any addition of carbon to a sample of a different age will cause the measured date to be inaccurate. Contamination with modern carbon causes a sample to appear to be younger than it really is: the effect is greater for older samples. If a sample that is in fact 17,000 years old is contaminated so that 1% of the sample is actually modern carbon, it will appear to be 600 years younger; for a sample that is 34,000 years old the same amount of contamination would cause an error of 4,000 years. Contamination with old carbon, with no remaining {{chem|14|C}}, causes an error in the other direction, which does not depend on age—a sample that has been contaminated with 1% old carbon will appear to be about 80 years older than it really is, regardless of the date of the sample.<ref>Aitken, ''Science-based Dating in Archaeology'', pp. 85–86.</ref> The equation for the radioactivity of a sample that has been contaminated with other carbon is
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| :<math>A_m = fA_x + (1-f)A_s</math>
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| where A<sub>m</sub> is the measured radioactivity of the sample, A<sub>x</sub> is the radioactivity of the contaminating material, A<sub>s</sub> is the radioactivity of the original sample prior to contamination, and f is the fraction of the carbon in the sample that is from the contaminant.<ref name="Bowman_27-28">Bowman, ''Radiocarbon Dating'', pp. 27–28.</ref>
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| Contamination can occur if the sample is brought into contact with or packed in materials that contain carbon. Cotton wool, cigarette ash, paper labels, cloth bags, and some conservation chemicals such as polyvinyl acetate can all be sources of modern carbon.<ref name="Bowman_27-28" /> Labels should be added to the outside of the container, not placed inside the bag or vial with the sample. Glass wool is acceptable as packing material instead of cotton wool.<ref name=Aitken_89>Aitken, ''Science-based Dating in Archaeology'', p. 89.</ref> Samples should be packed in glass vials or aluminium foil if possible;<ref name="Bowman_27-28" /><ref name=":4">Burke, Smith and Zimmerman, ''The Archaeologist's Field Handbook'', p. 175.</ref> polyethylene bags are also acceptable but some plastics, such as PVC, can contaminate the sample.<ref name=Aitken_89/> Contamination can also occur before the sample is collected: [[humic acid]]s or carbonate from the soil can leach into a sample, and for some sample types, such as shells, there is the possibility of carbon exchange between the sample and the environment, depleting the sample's {{chem|14|C}} content.<ref name="Bowman_27-28" />
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| ==Samples ==
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| Samples for dating need to be converted into a form suitable for measuring the {{chem|14|C}} content; this can mean conversion to gaseous, liquid, or solid form, depending on the measurement technique to be used. Before this can be done, however, the sample must be treated to remove any contamination and any unwanted constituents.<ref name="Bowman_27-28" /> This includes removing visible contaminants, such as rootlets that may have penetrated the sample since its burial.<ref name=Bowman_28-30>Bowman, ''Radiocarbon Dating'', pp. 28-30.</ref>
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| ===Pretreatment===
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| Two common contaminants are humic acid, which can be removed with an alkali wash, and carbonates, which can be removed with acid. These treatments can damage the structural integrity of the sample and remove significant volumes of material, so the exact treatment decided on will depend on the sample size and the amount of carbon needed for the chosen measurement technique.<ref name=":8">Aitken, ''Science-based Dating in Archaeology'', pp. 86-89.</ref>
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| ====Wood and charcoal====
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| Wood contains cellulose, lignin, and other compounds; of these, cellulose is the least likely to have exchanged carbon with the sample's environment, so it is common to reduce a wood sample to just the cellulose component before testing. However, this can reduce the volume of the sample down to 20% of the original size, so testing of the whole wood is often performed as well. Charcoal is less likely than wood to have exchanged carbon with its environment, but a charcoal sample is likely to have absorbed humic acid and/or carbonates, which must be removed with alkali and acid washes.<ref name=Bowman_28-30/><ref name=":8" />
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| ====Bone====
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| Unburnt bone was once thought to be a poor candidate for radiocarbon dating,<ref>Libby, ''Radiocarbon Dating'', p. 45.</ref> but is now possible to test it accurately. The constituents of bone include [[protein]]s, which contain carbon; bone's structural strength comes from [[calcium hydroxyapatite]], which is easily contaminated with carbonates from ground water. Removing the carbonates also destroys the calcium hydroxyapatite, and so it is usual to date bone using the remaining protein fraction after washing away the calcium hydroxyapatite and contaminating carbonates. This protein component is called [[collagen]]. Collagen is sometimes degraded, in which case it may be necessary to separate the proteins into individual amino acids and measure their respective ratios and {{chem|14|C}} activity. It is possible to detect if there has been any degradation of the sample by comparing the relative volume of each amino acid with the known profile for bone. If so, separating the amino acids may be necessary to allow independent testing of each one—agreement between the results of several different amino acids indicates that the dating is reliable. [[Hydroxyproline]], one of the constituent amino acids in bone, was once thought to be a reliable indicator as it was not known to occur except in bone, but it has since been detected in groundwater.<ref name=Bowman_28-30/>
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| For burnt bone, testability depends on the conditions under which the bone was burnt. The proteins in burnt bone are usually destroyed, which means that after acid treatment, nothing testable will be left of the bone. Degradation of the protein fraction can also occur in hot, arid conditions, without actual burning; then the degraded components can be washed away by groundwater. However, if the bone was heated under reducing conditions, it (and associated organic matter) may have been carbonized. In this case the sample is often usable.<ref name=Bowman_28-30/>
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| ====Shell====
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| Shells from both marine and land organisms consist almost entirely of calcium carbonate, either as [[aragonite]] or as [[calcite]], or some mixture of the two. Calcium carbonate is very susceptible to dissolving and recrystallizing; the recrystallized material will contain carbon from the sample's environment, which may be of geological origin. The recrystallized calcium carbonate is generally in the form of calcite, and often has a powdery appearance; samples of a shiny appearance are preferable, and if in doubt, examination by light or electron microscope, or by X-ray diffraction and infrared spectroscopy, can determine whether recrystallization has occurred.<ref> Jan Šilar, "Application of Environmental Radionuclides in Radiochronology", in Tykvar and Berg, eds., ''Man-Made and Natural Radioactivity in Environmental Pollution and Radiochronology'', p. 166.</ref>
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| In cases where it is not possible to find samples that are free of recrystallization, acid washes of increasing strength, followed by dating part of the sample after each wash, can be used: the dates obtained from each sample will vary with the degree of contamination, but when the contaminated layers are removed, consecutive measurements will be consistent with each other. It is also possible to test [[conchiolin]], which is an organic protein found in shell, but this only constitutes 1-2% of shell material.<ref name=":8" />
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| ====Other materials====
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| * '''Peat'''. The three major components of peat are humic acid, [[humins]], and fulvic acid. Of these, humins give the most reliable date as they are insoluble in alkali and less likely to contain contaminants from the sample's environment.<ref name=":8" /> A particular difficulty with dried peat is the removal of rootlets, which are likely to be hard to distinguish from the sample material.<ref name=Bowman_28-30/>
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| * '''Soil and sediments'''. Soil contains organic material, but because of contamination by humic acid of more recent origin, it is very difficult to get satisfactory radiocarbon dates. It is preferable to sieve the soil for fragments of organic origin, and date the fragments with methods that are tolerant of small sample sizes.<ref name=":8" />
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| * Other types of sample that have been successfully dated include ivory, paper, textiles, individual seeds and grains, straw from within mud bricks, and charred food remains found in pottery.<ref name=":8" />
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| ===Isotopic enrichment===
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| Particularly for older samples, it may be useful to enrich the amount of {{chem|14|C}} in the sample before testing. This can be done with a thermal diffusion column. The process takes about a month, and requires a sample about ten times as large as would be needed otherwise, but it allows more precise measurement of the {{chem|14|C}}/{{chem|12|C}} ratio in old material, and extends the maximum age that can be reliably reported.<ref>Bowman, ''Radiocarbon Dating'', pp. 37-42.</ref>
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| ===Preparation===
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| Once contamination has been removed, samples must be converted to a form suitable for the measuring technology to be used.<ref name=":6" /> A common approach is to produce a gas, for gas counting devices: {{Chem|CO|2}} is widely used, but it is also possible to use other gases, including [[methane]], [[ethane]], [[ethylene]] and [[acetylene]].<ref name=":6" /><ref name="Aitken_76-78" /> For samples in liquid form, for [[Liquid scintillation counting|liquid scintillation counters]], [[benzene]] is used, though other liquids were tried during the early decades of the technique. Libby's first measurements were made with lamp black,<ref name=":6" /> but this technique is no longer in use; these methods were susceptible to problems caused by the {{chem|14|C}} created by nuclear testing in the 1950s and 1960s.<ref name=":6">Bowman, ''Radiocarbon Dating'', pp. 31-33.</ref> Solid targets can be used for accelerator mass spectrometry, however; usually these are graphite, though {{Chem|CO|2}} and iron carbide can also be used.<ref name=":5">Bowman, ''Radiocarbon Dating'', pp. 34-37.</ref><ref name=":7" />
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| The steps to convert the sample to the appropriate form for testing can be long and complex. To create lamp black, Libby began with acid washes if necessary to remove carbonate, and then converted the carbon in the sample to {{Chem|CO|2}} by either combustion (for organic samples) or the addition of hydrochloric acid (for shell material). The resulting gas was passed through hot copper oxide to convert any carbon monoxide to {{Chem|CO|2}}, and then dried to remove any water vapour. The gas was then condensed, and converted to calcium carbonate in order to allow the removal of any radon gas and any other combustion products such as oxides of nitrogen and sulphur. The calcium carbonate was then converted back to {{Chem|CO|2}} again, dried, and converted to carbon by passing it over heated magnesium. Hydrochloric acid was added to the resulting mixture of magnesium, magnesium oxide and carbon, and after repeated boiling, filtering, and washing with distilled water, the carbon was ground with a mortar and pestle and a half gram sample taken, weighed, and combusted. This allowed Libby to determine how much of the sample was ash, and hence to determine the purity of the carbon sample to be tested.<ref>Libby, ''Radiocarbon Dating'', pp. 45-51.</ref>
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| To create benzene for liquid scintillation counters, the sequence begins with combustion to convert the carbon in the sample to {{Chem|CO|2}}. This is then converted to lithium carbide, and then to acetylene, and finally to benzene.<ref name=":6" /> Targets for accelerator mass spectrometry are created from {{Chem|CO|2}} by catalysing the reduction of the gas in the presence of hydrogen. This results in a coating of [[filamentous carbon]] (usually referred to as graphite) on the powdered catalyst—typically cobalt or iron.<ref name=":7">Susan E. Trumbore, "Applications of Accelerator Mass Spectrometry to Soil Science", in Boutton & Yamasaki, ''Mass Spectrometry of Soils'', p. 318.</ref>
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| ===Sample sizes===
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| How much sample material is needed to perform testing depends on what is being tested, and also which of the two testing technologies is being used: detectors that record radioactivity, known as beta counters, or atomic mass spectrometers (AMS). A rough guide follows; the weights given, in grams, are for dry samples, and assume that a visual inspection has been done to remove foreign objects.<ref name=":6" />
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| | |
| {| class="wikitable"
| |
| |-
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| | rowspan="2" | '''Sample material'''
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| | colspan="2" style="text-align: center;" | '''Mass (g)'''
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| |-
| |
| | '''For beta<br />counters''' || '''For AMS'''
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| |-
| |
| | Whole wood || 10–25 || 0.05–0.1
| |
| |-
| |
| | Wood (for cellulose testing) || 50–100 || 0.2–0.5
| |
| |-
| |
| | Charcoal || 10–20 || 0.01–0.1
| |
| |-
| |
| | Peat || 50–100 || 0.1–0.2
| |
| |-
| |
| | Textiles || 20–50 || 0.02–0.05
| |
| |-
| |
| | Bone || 100–400 || 0.5–1.0
| |
| |-
| |
| | Shell || 50–100 || 0.05–0.1
| |
| |-
| |
| | Sediment/soils || 100–500 || 5.0–25.0
| |
| |}
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| | |
| ==Measurement==
| |
| For decades after Libby performed the first radiocarbon dating experiments, the only way to measure the {{chem|14|C}} in a sample was to detect the [[radioactive decay]] of individual carbon [[atom]]s.<ref name=":5" /> In this approach, what is measured is the activity, in number of decay events per unit mass per time period, of the sample.<ref name=Aitken_76-78>Aitken, ''Science-based Dating in Archaeology'', pp. 76-78.</ref> This method is also known as "beta counting", because it is the beta particles emitted by the decaying {{chem|14|C}} atoms that are detected.<ref>Walker, ''Quaternary Dating Methods'', p. 20.</ref> In the late 1970s an alternative approach became available: directly counting the number of {{Chem|14|C}} and {{Chem|12|C}} atoms in a given sample, via accelerator mass spectrometry, usually referred to as AMS.<ref name=":5" /> AMS counts the {{chem|14|C}}/{{chem|12|C}} ratio directly, instead of the activity of the sample, but measurements of activity and {{chem|14|C}}/{{chem|12|C}} ratio can be converted into each other exactly.<ref name=Aitken_76-78/> For some time, beta counting methods were more accurate than AMS, but there is now little to choose between them, though AMS still cannot compete with the very highest-precision beta counting laboratories, which can provide results with a standard error of ± 20 years.<ref name=":14">Walker, ''Quaternary Dating Methods'', p. 23.</ref>
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| ===Beta counting===
| |
| Libby's first detector was a Geiger counter of his own design. He coated the inner surface of a cylinder with carbon in the form of lamp black (soot), and inserted it into the counter in such a way that the counting wire was inside the sample cylinder, in order that there should be no material between the sample and the wire.<ref name=":6" /> Any interposing material would have interfered with the detection of radioactivity; the beta particles emitted by decaying {{Chem|14|C}} are so weak that half are stopped by a 0.01 mm thickness of aluminium.<ref name="Aitken_76-78" />
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| Libby's method was soon superseded by gas [[proportional counter]]s, which were less affected by bomb carbon. These counters record bursts of ionization caused by the beta particles emitted by the decaying {{Chem|14|C}} atoms; the bursts are proportional to the energy of the particle, so other sources of ionization, such as background radiation, can be identified and ignored. The counters are surrounded by lead or steel shielding, to eliminate background radiation and to reduce the incidence of cosmic rays. In addition, [[Electronic anticoincidence|anticoincidence]] detectors are used; these record events outside the counter, and any event recorded simultaneously both inside and outside the counter is regarded as an extraneous event and ignored.<ref name="Aitken_76-78" />
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| The other common technology used for measuring {{Chem|14|C}} activity is [[liquid scintillation counting]], which was invented in 1950, but which had to wait until the early 1960s, when efficient methods of benzene synthesis were developed, to become competitive with gas counting; after 1970 liquid counters became the more common technology choice for newly constructed dating laboratories. The counters work by detecting flashes of light caused by the beta particles emitted by {{chem|14|C}} as they interact with a fluorescing agent added to the benzene. Like gas counters, liquid scintillation counters require shielding and anticoincidence counters.<ref>Theodórsson, ''Measurement of Weak Radioactivity, p. 24.''</ref><ref>Michael F. L'Annunziata & Michael J. Kessler, "Liquid Scintillation Analysis: Principles and Practice", in L'Annunziata, ''Handbook of Radioactivity Analysis'', p. 424.</ref>
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| For both types of counter, what is measured is a number of beta particles detected in a given time period. Since the mass of the sample is known, this can be converted to a standard measure of activity in units of either counts per minute per gram of carbon (cpm/g C), or [[becquerel]]s per kg (Bq/kg C, in [[SI units]]). Each measuring device will also be used to measure the activity of a blank sample—a sample prepared from carbon old enough to have no activity. This provides a value for the background radiation, which must be subtracted from the original sample's measured activity to get the activity due to the sample's {{Chem|14|C}}. In addition, a sample with a standard activity will be measured, in order to provide a baseline for comparison.<ref name=":10" />
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| ===[[Accelerator mass spectrometry]]===
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| [[File:Accelerator mass spectrometer schematic for radiocarbon.svg|thumb|400px|Simplified schematic layout of an accelerator mass spectrometer used for counting carbon isotopes for carbon dating]]AMS counts the atoms of {{Chem|14|C}} and {{Chem|12|C}} atoms in a given sample, determining the {{chem|14|C}}/{{chem|12|C}} ratio directly. The sample, often in the form of graphite, is made to emit negatively charged C<sup>-</sup> ions, which are injected into an [[Particle accelerator|accelerator]]. The ions are accelerated, and passed through a stripper, which removes several electrons, so that the ions emerge with a positive charge. The C<sup>3+</sup> ions are then passed through a magnet that curves their path; the heavier ions are curved less than the lighter ones, so the different isotopes emerge as separate streams of ions. A particle detector then records the number of ions detected in the {{Chem|14|C}} stream, but {{Chem|12|C}} counts (and {{Chem|13|C}} counts, needed for calibration) are determined by measuring the electric current created in a [[Faraday cup]], since the volume of these is too great for individual ion detection. This method allows dating samples containing only a few milligrams of carbon, such as individual seeds.<ref name=":9">Aitken, ''Science-based Dating in Archaeology'', pp. 82-85.</ref>
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| The use of AMS, as opposed to simpler forms of mass spectrometer, is necessary because of the need to distinguish the carbon isotopes from other atoms or molecules that are very close in mass to them, such as {{chem|14|N}} and {{chem|13|CH}}.<ref name=":5" /> As with beta counting, both a blank sample and a standard sample are also measured, in order to determine the level of background radiation, and to check the accuracy of the setup.<ref name=":9" /> Two different kinds of blank may be measured: a sample of dead carbon that has undergone no chemical processing, in order to detect any machine background, and a sample known as a process blank made from dead carbon that is processed into target material in exactly the same way as the sample itself. Any {{Chem|14|C}} signal from the machine background blank is likely to be caused either by beams of ions that have not followed the expected path inside the detector, or by carbon hydrides such as {{chem|12|CH|2}} or {{chem|13|CH}}. A {{chem|14|C}} signal from the process blank measures the amount of contamination introduced during the preparation of the sample. These measurements are used in the subsequent calculation of the age of the sample.<ref name=":11" />
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| ===Calculations===
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| The calculations to be performed on the measurements taken depend on the technology used, since beta counters measure the sample's radioactivity, whereas AMS determines the ratio of the three different carbon isotopes in the sample.<ref>McNichol, Jull & Burr, "Converting AMS Data to Radiocarbon Values: Considerations and Conventions", pp. 313.</ref>
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| ====Standards====
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| The calculations to convert measured data to an estimate of the age of the sample require the use of several standards. One of these, the standard for normalizing {{delta|13|C}} values, has been discussed above: Pee Dee Belemnite, which had a {{chem|13|C}}/{{chem|12|C}} ratio of 1.12372%. A related standard is the use of wood, which has a {{delta|13|C}} of -25‰, as the material for which radiocarbon ages are calibrated. Since different materials have different {{delta|13|C}} values, it is possible for two samples of different materials, of the same age, to have different levels of radioactivity and different {{chem|14|C}}/{{chem|12|C}} ratios. To compensate for this, the measurements are converted to the activity, or isotope ratio, that would have been measured if the sample had been made of wood. This is possible because the {{delta|13|C}} of wood is known, and the {{delta|13|C}} of the sample material can be measured, or taken from a table of typical values. The details of the calculations for beta counting and AMS are given below.<ref name=":12" />
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| Another standard is the use of 1950 as "present", in the sense that a calculation that shows that a sample's likely age is 500 years "before present" means that it is likely to have come from about the year 1450. This convention is necessary in order to keep published radiocarbon results comparable to each other; without this convention, a given radiocarbon result would be of no use unless the year it was measured was also known—an age of 500 years published in 2010 would indicate a likely sample date of 1510, for example. In order to allow measurements to be converted to the 1950 baseline, a standard activity level is defined for the radioactivity of wood in 1950. Because of the fossil fuel effect, this is not actually the activity level of wood from 1950; the activity would have been somewhat lower.<ref name=":18" /> The fossil fuel effect was eliminated from the standard value by measuring wood from 1890, and using the radioactive decay equations to determine what the activity would have been at the year of growth. The resulting standard value, A<sub>abs</sub>, is 226 becquerels per kilogram of carbon.<ref name=":13">L'Annunziata, ''Radioactivity'', p. 528.</ref>
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| Both beta counting and AMS measure standard samples as part of their methodology. These samples contain carbon of a known activity.<ref name=":9" /> The first standard, Oxalic Acid SRM 4990C, also referred to as HOxI, was a 1,000 lb batch of oxalic acid created in 1955 by the National Institute of Standards and Technology (NIST). Since it was created after the start of atomic testing, it incorporates bomb carbon, so measured activity is higher than the desired standard. This is addressed by defining the standard to be 0.95 times the activity of HOxI.<ref name=":13" />
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| All of this first standard has long since been consumed, and later standards have been created, each of which has a given ratio to the desired standard activity. A secondary oxalic acid standard, HOxII, 1,000 lb of which was prepared by NIST in 1977 from French beet harvests, is now in wide use.<ref>J. Terasmae, "Radiocarbon Dating: Some Problems and Potential Developments", in Mahaney, ''Quaternay Dating Methods'', p. 5.</ref>
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| ====Calculations for beta counting devices====
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| To determine the age of a sample whose activity has been measured by beta counting, the ratio of its activity to the activity of the standard must be found. The equation:<ref name=":10">Eriksson Stenström et al., "A guide to radiocarbon units and calculations", p. 3.</ref>
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| :<math>A_s = A_{std} \left ( \frac{M_s - M_b}{M_{std} - M_b} \right ) </math>
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| gives the required ratio, where A<sub>s</sub> is the true activity of the sample, A<sub>std</sub> is the true activity of the standard, M<sub>s</sub> is the measured activity of the sample, M<sub>std</sub> is the measured activity of the standard, and M<sub>b</sub> is the measured activity of the blank.<ref name=":10" />
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| A correction must also be made for fractionation. The fractionation correction converts the {{chem|14|C}}/{{chem|12|C}} ratio for the sample to the ratio it would have had if the material was wood, which has a {{delta|13|C}} value of -25‰. This is necessary because determining the age of the sample requires a comparison of the amount of {{chem|14|C}} in the sample with what it would have had if it newly formed from the biosphere. The standard used for modern carbon is wood, with a baseline date of 1950.<ref name=":12" />
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| Correcting for fractionation changes the activity measured in the sample to the activity it would have if it were wood of the same age as the sample. The calculation requires the definition of a {{chem|13|C}} fractionation factor, which is defined for any sample material as<ref name=":18">Eriksson Stenstrom et al. ''A Guide to Radiocarbon Units and Calculations'', p. 6.</ref>
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| :<math>Frac_{13/12 (sample)} = \frac {(^{13}C/^{12}C)_{wood}}{{(^{13}C/^{12}C)_{sample}}}</math>
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| The {{chem|14|C}} fractionation factor, Frac<sub>14/12</sub>, is approximately the square of this, to an accuracy of 1‰:<ref name=":18"/>
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| :<math>Frac_{14/12 (sample)} = (Frac_{13/12 (sample)})^2</math>
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| Multiplying the measured activity for the sample by the {{chem|14|C}} fractionation factor converts it to the activity that it would have had had the sample been wood:<ref name=":18"/>
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| :<math>A_{sn} = A_sFrac_{14/12(s)}</math>
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| where A<sub>sn</sub> is the normalized activity for the sample, and Frac<sub>14/12 (s)</sub> is the {{chem|14|C}} fractionation factor for the sample.<ref name=":18"/>
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| The equation for δ13C given earlier can be rearranged to<ref name=":18"/>
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| :<math>\left ( \frac {^{13}C}{^{12}C} \right )_{sample} = \left ( 1 + \frac {\delta^{13}C}{1000} \right ) \left ( \frac {^{13}C}{^{12}C} \right )_{PDB}</math>
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| Substituting this in the {{chem|14|C}} fractionation factor, and also substituting the value for δ13C for wood of -25‰, gives the following expression:<ref name=":18"/>
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| :<math>A_{sn} = A_s \left ( \frac {\left (1 - \frac {25}{1000} \right )\left ( \frac {^{13}C}{^{12}C} \right )_{PDB}}{\left (1 + \frac {\delta^{13}C}{1000} \right )\left ( \frac {^{13}C}{^{12}C} \right )_{PDB}} \right )^2</math>
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| where the δ13C value remaining in the equation is the value for the sample itself. This can be measured directly, or simply looked up in a table of characteristic values for the type of sample material—this latter approach leads to increased uncertainty in the result, as there is a range of possible δ13C values for each possible sample material. Cancelling the PDB {{chem|13|C}}/{{chem|12|C}} ratio reduces this to:<ref name=":18"/>
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| :<math>A_{sn} = A_s \left ( \frac {\left (1 - \frac {25}{1000} \right )}{\left (1 + \frac {\delta^{13}C}{1000} \right )} \right )^2</math>
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| ====AMS calculations====
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| The results from AMS testing are in the form of ratios of {{chem|12|C}}, {{chem|13|C}}, and {{chem|14|C}}. These ratios are used to calculate F<sub>m</sub>, the "fraction modern", defined as
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| :<math>F_m = \frac{R_{norm}}{R_{modern}}</math>
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| where R<sub>norm</sub> is the {{chem|14|C}}/{{chem|12|C}} ratio for the sample, after correcting for fractionation, and R<sub>modern</sub> is the standard {{chem|14|C}}/{{chem|12|C}} ratio for modern carbon.<ref name=":11">McNichol, Jull & Burr, "Converting AMS Data to Radiocarbon Values: Considerations and Conventions", pp. 315-318.</ref>
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| The calculation begins by subtracting the ratio measured for the machine blank from the other sample measurements. That is:
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| :<math>R'_s = R_s - R_{mb}</math>
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| :<math>R'_{std} = R_{std} - R_{mb}</math>
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| :<math>R'_{pb} = R_{pb} - R_{mb}</math>
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| where R<sub>s</sub> is the measured sample {{chem|14|C}}/{{chem|12|C}} ratio; R<sub>std</sub> is the measured ratio for the standard; R<sub>pb</sub> is the measured ratio for the process blank, and R<sub>mb</sub> is the measured ratio for the machine blank. The next step, to correct for fractionation, can be done using either the {{chem|14|C}}/{{chem|12|C}} ratio or the {{chem|14|C}}/{{chem|13|C}} ratio, and also depends on which of the two possible standards was measured: HOxI or HoxII. R'<sub>std</sub> is then R'<sub>HOxI</sub> or R'<sub>HOxII</sub>, depending on which standard was used. The four possible equations are as follows. First, if the {{chem|14|C}}/{{chem|12|C}} ratio is used to perform the fractionation correction, the following two equations apply, one for each standard.<ref name=":11"/>
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| :<math>R_{HOxI,-19} = R'_{HoxI}\left ( \frac {1 + \frac {-19} {1000}} {1 + \frac {\delta^{13}C_{HoXI}} {1000}}\right )^2</math>
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| :<math>R_{HOxII,-25} = R'_{HoxII}\left ( \frac {1 + \frac {-25} {1000}} {1 + \frac {\delta^{13}C_{HoXII}} {1000}} \right )^2</math>
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| If the {{chem|14|C}}/{{chem|13|C}} ratio is used instead, then the equations for each standard are:<ref name=":11"/>
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| :<math>R_{HOxI,-19} = R'_{HoxI}\left ( \frac {1 + \frac {-19} {1000}} {1 + \frac {\delta^{13}C_{HoXI}} {1000}} \right )</math>
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| :<math>R_{HOxII,-25} = R'_{HoxII}\left ( \frac {1 + \frac {-25} {1000}} {1 + \frac {\delta^{13}C_{HoXII}} {1000}} \right )</math>
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| The δ13C values in the equations measure the fractionation in the standards as {{chem|CO|2}}, prior to their conversion to graphite to use as a target in the spectrometer. This assumes that the conversion to graphite does not introduce significant additional fractionation.<ref name=":11"/>
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| Once the appropriate value above has been calculated, R<sub>modern</sub> can be determined; it is<ref name=":11"/>
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| :<math>R_{modern} = 0.95R_{HOxI,-19} = .7459R_{HOx2,-25}</math>
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| The values 0.95 and 0.7459 are part of the definition of the two standards; they convert the {{chem|14|C}}/{{chem|12|C}} ratio in the standards to the ratio that modern carbon would have had in 1950 if there had been no fossil fuel effect.<ref name=":11"/>
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| Since it is common practice to measure the standards repeatedly during an AMS run, alternating the standard target with the sample being measured, there are multiple measurements available for the standard, and these measurements provide a couple of options in the calculation of R<sub>modern</sub>. Different labs use this data in different ways; some simply average the values, while others consider the measurements made on the standard target as a series, and interpolate the readings that would have been measured during the sample run, if the standard had been measured at that time instead.<ref name=":11"/>
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| Next, the uncorrected fraction modern is calculated; "uncorrected" means that this intermediate value does not include the fractionation correction.<ref name=":11"/>
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| :<math>Fm_{uc} = \frac {R'_s} {R_{modern}}</math>
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| Now the measured fraction modern can be determined, by correcting for fractionation. As above there are two equations, depending on whether the {{chem|14|C}}/{{chem|12|C}} or {{chem|14|C}}/{{chem|13|C}} ratio is being used. If the {{chem|14|C}}/{{chem|12|C}} ratio is being used:<ref name=":11"/>
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| :<math>Fm_{ms} = Fm_{uc}\left ( \frac {1 + \frac {-25} {1000}} {1 + \frac {\delta 13C_s} {1000}} \right )^2</math>
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| If the {{chem|14|C}}/{{chem|13|C}} ratio is being used:<ref name=":11"/>
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| :<math>Fm_{ms} = Fm_{uc}\left ( \frac {1 + \frac {-25} {1000}} {1 + \frac {\delta13C_s} {1000}} \right )</math>
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| The δ13C<sub>s</sub> value is from the sample itself, measured on {{chem|CO|2}} prepared while converting the sample to graphite.<ref name=":11"/>
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| The final step is to adjust Fm<sub>ms</sub> for the measured fraction modern of the process blank, Fm<sub>pb</sub>, which is calculated as above for the sample. One approach{{#tag:ref|McNichol & Burr give two other calculations, one of which can be shown to be equivalent to the one given here. The other depends on the process blank being the same mass as the sample.<ref name=":11"/>|group=note}} is to determine the mass of the measured carbon, C<sub>ms</sub>, along with C<sub>pb</sub>, the mass of the process blank, and C<sub>s</sub>, the mass of the sample. The final fraction modern,Fm<sub>s</sub> is then<ref name=":11"/>
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| :<math>Fm_s = \frac {Fm_{ms}C_{ms} - Fm_{pb}C_{pb}} {C_s}</math>
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| The fraction modern is then converted to an age in "radiocarbon years", meaning that the calculation uses Libby's half-life of 5,568 years, not the more accurate modern value of 5,730 years, and that no calibration has been done:<ref>{{cite web |url=http://www.whoi.edu/nosams/page.do?pid=40146 |title=Radiocarbon Data Calculations: NOSAMS|publisher=Woods Hole Oceanographic Institution|year=2007|accessdate=August 27, 2013}}</ref>
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| :<math>Age = -8033 ln (Fm)</math>
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| ===Errors and reliability===
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| There are several possible sources of error in both the beta counting and AMS methods, although laboratories vary in how they report errors. All laboratories report counting statistics—that is, statistics showing possible errors in counting the decay events or number of atoms—with an error term of 1σ (i.e. 68% confidence that the true value is within the given range).<ref name=Taylor_102-104 /> These errors can be reduced by extending the counting duration: for example, testing a modern benzene sample will find about eight decay events per minute per gram of benzene, and 250 minutes of counting will suffice to give an error of ± 80 years, with 68% confidence. If the benzene sample contains carbon that is about 5,730 years old (the half-life of {{chem|14|C}}), then there will only be half as many decay events per minute, but the same error term of 80 years could be obtained by doubling the counting time to 500 minutes.<ref name="Bowman_38-39">Bowman, ''Radiocarbon Dating'', pp. 38–39.</ref><ref name=Taylor_124>Taylor, ''Radiocarbon Dating'', p. 124.</ref> Note that the error term is not symmetric, though the effect is negligible for recent samples; for a sample with an estimated age of 30,600 years, the error term might be +1600 to -1300.<ref name=Taylor_102-104>Taylor, ''Radiocarbon Dating'', p. 102−104.</ref>
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| To be completely accurate, the error term quoted for the reported radiocarbon age should incorporate counting errors not only from the sample, but also from counting decay events for the reference sample, and for blanks. It should also incorporate errors on every measurement taken as part of the dating method, including, for example, the δ13C term for the sample, or any laboratory conditions being corrected for such as temperature or voltage. These errors should then be [[Propagation of uncertainty|mathematically combined]] to give an overall term for the error in the reported age, but in practice laboratories differ, not only in the terms they choose to include in their error calculations, but also in the way they combine errors. The resulting 1σ estimates have been shown to typically underestimate the true error, and it has even been suggested that doubling the given 1σ error term results in a more accurate value.<ref name="Bowman_38-39" /><ref name=Taylor_102-104 />
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| The usual presentation of a radiocarbon date, as a specific date plus or minus an error term, obscures the fact that the true age of the object being measured may lie outside the range of dates quoted. In 1970, the British Museum radiocarbon laboratory ran weekly measurements on the same sample for six months. The results varied widely (though consistently with a normal distribution of errors in the measurements), and included multiple date ranges (of 1σ confidence) that did not overlap with each other. The extreme measurements included one with a maximum age of under 4,400 years, and another with a minimum age of over 4,500 years.<ref>Taylor, ''Radiocarbon Dating'', pp. 125−126.</ref>
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| It is also possible for laboratories to have systematic errors, caused by weaknesses in their methodologies. For example, if 1% of the benzene in a modern reference sample is allowed to evaporate, the resulting radiocarbon age will be too young by about 80 years. Laboratories work to detect these errors both by testing their own procedures, and by periodic inter-laboratory comparisons of a variety of different samples; any laboratories whose results differ from the consensus radiocarbon age by too great an amount may be suffering from systematic errors. Even if the systematic errors are not corrected, the laboratory can estimate the magnitude of the effect and include this in the published error estimates for their results.<ref>Bowman, ''Radiocarbon Dating'', pp. 40−41.</ref>
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| The limit of measurability is approximately eight half-lives, or about 45,000 years. Samples older than this will typically be reported as having an infinite age. Some techniques have been developed to extend the range of dating further into the past, including isotopic enrichment, or large samples and very high precision counters. These methods have in some cases increased the maximum age that can be reported for a sample to 60,000 and even 75,000 years.<ref name=":14" />
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| ==Calibration==
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| The calculations given above produce dates in radiocarbon years: that is, dates which represent the age the sample would be if the {{chem|14|C}}/{{chem|12|C}} ratio had been constant historically.<ref name=Taylor_133>Taylor, ''Radiocarbon Dating'', p. 133.</ref> Although Libby had pointed out as early as 1955 the possibility that this assumption was incorrect, it was not until discrepancies began to accumulate between measured ages and known historical dates for artefacts that it became clear that a correction would need to be applied to radiocarbon ages to obtain calendar dates.<ref name=Aitken_66-67 />
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| To produce a curve that can be used to relate calendar years to radiocarbon years, a sequence of securely dated samples is needed which can be tested to determine their radiocarbon age. The study of tree-rings ([[dendrochronology]]) led to the first such sequence: tree-rings from individual pieces of wood show characteristic sequences of rings that vary in thickness because of environmental factors such as the amount of rainfall in a given year. These factors affect all trees in an area, so examining tree-ring sequences from old wood allows the identification of overlapping sequences. In this way, an uninterrupted sequence of tree-rings can be extended far into the past. The first such published sequence, based on bristlecone pine tree-rings, was created in the 1960s by [[Wesley Ferguson]].<ref name=Taylor_19-21>Taylor, ''Radiocarbon Dating'', pp. 19–21.</ref> [[Hans Suess]] used this data to publish the first calibration curve for radiocarbon dating in 1967.<ref name=Bowman_16-20 /><ref name=Aitken_66-67>Aitken, ''Science-based Dating in Archaeology, p. 66–67.</ref><ref name=Suess_1970/> The curve showed two types of variation from the straight line: a long term fluctuation with a period of about 9,000 years, and a shorter term variation, often referred to as "wiggles", with a period of decades. Suess said he drew the line showing the wiggles by "cosmic ''schwung''" — freehand, in other words. It was unclear for some time whether the wiggles were real or not, but they are now well-established.<ref name=Bowman_16-20 /><ref name=Suess_1970/>
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| The calibration method also assumes that the temporal variation in {{chem|14|C}} level is global, such that a small number of samples from a specific year are sufficient for calibration. This was experimentally verified in the 1980s.<ref name=Aitken_66-67/>
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| Over the next thirty years many calibration curves were published,using a variety of methods and statistical approaches.<ref name=Bowman_45>Bowman, ''Radiocarbon Dating'', p. 45.</ref> These were superseded by the INTCAL series of curves, beginning with INTCAL98, published in 1998, and updated in 2004, 2009, and, most recently, 2013. The improvements to these curves are based on new data gathered from tree rings, [[Varve|varves]], coral, and other studies. Significant additions to the datasets used for INTCAL13 include non-varved marine foraminifera data, and U-Th dated speleothems.<ref name=INTCAL13>{{Cite journal | last1 = Reimer | first1 = P. | title = IntCal13 and Marine13 Radiocarbon Age Calibration Curves 0–50,000 Years cal BP | doi = 10.2458/azu_js_rc.55.16947 | journal = Radiocarbon | volume = 55 | issue = 4 | pages = 1869–1887 | year = 2013 | accessdate=1 January 2014}}</ref>
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| Marine reservoir variations are partly handled by a special marine calibration curve.<ref>{{cite journal |last=Stuiver |first=M. |last2=Braziunas |first2=T. F. |title=Modelling atmospheric {{chem|14|C}} influences and {{chem|14|C}} ages of marine samples to 10,000 BC |journal=Radiocarbon |volume=35 |year=1993 |issue=1 |pages=137}}</ref>
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| [[File:Radiocarbon Date Calibration Curve.svg|thumb|300px|right|Calibration curve for the radiocarbon dating scale. Data sources: Reimer, P. J., ''et al.'' (1998).<ref>{{cite journal |author= Reimer, P. J.; Baillie, M. G. L.; Bard, E.; Bayliss, A.; Beck, J. W.; Bertrand, C. J. H.; Blackwell, P. G.; Buck, C. E.; Burr, G. S.; Cutler, K. B.; Damon, P. E.; Edwards, R. L.; Fairbanks, R. G.; Friedrich, M.; Guilderson, T. P.; Hogg, A. G.; Hughen, K. A.; Kromer, B.; McCormac, G.; Manning, S.; Bronk Ramsey, C.; Reimer, R. W.; Remmele, S.; Southon, J. R.; Stuiver, M.; Talamo, S.; Taylor, F. W.; van der Plicht, J.; Weyhenmeyer, C. E. |year=2004 |title=IntCal04 Terrestrial radiocarbon age calibration|journal=Radiocarbon |volume=46 |pages=1029–58 |url=http://serc.carleton.edu/vignettes/collection/35379.html}}</ref> Samples with a real date more recent than AD 1950 are dated and/or tracked using the N- & S-Hemisphere graphs.]]As the graph to the right shows, the uncalibrated, raw BP date underestimates the actual age by 3,000 years at 15000 BP. The underestimation generally runs about 10% to 20%, with 3% of that underestimation attributable to the use of 5,568 years as the half-life of {{chem|14|C}} instead of the more accurate 5,730 years.<ref>[http://c14.arch.ox.ac.uk/embed.php?File=calibration.html Radiocarbon Calibration] University of Oxford, Radiocarbon Web Info, Version 130 Issued 19/Mar/2012, retrieved 6/July/2012</ref>
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| The calibration curves can vary significantly from a straight line, so comparison of uncalibrated radiocarbon dates (e.g., plotting them on a graph or subtracting dates to give elapsed time) is likely to give misleading results. There are also significant plateaus in the curves, such as the one from 11,000 to 10,000 radiocarbon years BP, which is believed to be associated with changing ocean circulation during the [[Younger Dryas]] period. Over the historical period (from 0 to 10,000 years BP), the average width of the uncertainty of calibrated dates was found to be 335 years - in well-behaved regions of the calibration curve the width decreased to about 113 years, while in ill-behaved regions it increased to a maximum of 801 years. Significantly, in the ill-behaved regions of the calibration curve, increasing the precision of the measurements does not have a significant effect on increasing the accuracy of the dates.<ref>These results were obtained from a [[Monte Carlo method|Monte Carlo]] analysis calibrating simulated measurements of varying precision using the 1993 version of the calibration curve. The width of the uncertainty represents a 2σ uncertainty (that is, a likelihood of 95% that the date appears between these limits). {{cite journal |last=Niklaus |first=T. R. |last2=Bonani |first2=G. |last3=Suter |first3=M. |last4=Wölfli |first4=W. |title=Systematic investigation of uncertainties in radiocarbon dating due to fluctuations in the calibration curve |journal=Nuclear Instruments and Methods in Physics Research |volume=92 |year=1994 |pages=194–200 |doi= 10.1016/0168-583X(94)96004-6 |edition=B|bibcode = 1994NIMPB..92..194N }}</ref>
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| The 2004 version of the calibration curve extends back quite accurately to 26,000 years BP. Any errors in the calibration curve do not contribute more than ±16 years to the measurement error during the historic and late prehistoric periods (0–6,000 yrs BP) and no more than ±163 years over the entire 26,000 years of the curve, although its shape can reduce the accuracy as mentioned above.<ref>{{cite journal |last=Reimer |first=Paula J |author2=''et al.'' |year=2004 |title=INTCAL04 Terrestrial Radiocarbon Age Calibration, 0–26 Cal Kyr BP |journal=Radiocarbon |volume=46 |issue=3 |pages=1029–1058 |url=http://digitalcommons.library.arizona.edu/objectviewer?o=http://radiocarbon.library.arizona.edu/Volume46/Number3/azu_radiocarbon_v46_n3_1029_1058_v.pdf
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| }} A web interface is [http://calib.qub.ac.uk/calib/calib.html here].</ref>
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| ===Speleothem studies extend {{chem|14|C}} calibration===
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| [[Speleothem]]s (such as [[stalagmite]]s) are [[calcium carbonate]] deposits that form from drips in [[limestone]] caves. Individual speleothems can be tens of thousands of years old.<ref>{{cite journal |last=Wang |first=Y. J. |title=A High-Resolution Absolute-Dated Late Pleistocene Monsoon Record from Hulu Cave, China |journal=[[Science (journal)|Science]] |year=2001 |volume=294 |issue=5550 |pages=2345–2348 |doi=10.1126/science.1064618 |pmid=11743199 |last2=Cheng |first2=H. |last3=Edwards |first3=R. L. |last4=An |first4=Z. S. |last5=Wu |first5=J. Y. |last6=Shen |first6=C. C. |last7=Dorale |first7=J. A. |bibcode = 2001Sci...294.2345W }}</ref> Scientists are attempting to extend the record of atmospheric carbon-14 by measuring radiocarbon in speleothems that have been independently dated using [[uranium-thorium dating]].<ref>{{cite journal |last=Beck |first=J. W. |title=Extremely large variations of atmospheric C-14 concentration during the last glacial period |journal=[[Science (journal)|Science]] |year=2001 |volume=292 |pages=2453–2458 |doi=10.1126/science.1056649 |pmid=11349137 |last2=Richards |first2=D. A. |last3=Edwards |first3=R. L. |last4=Silverman |first4=B. W. |last5=Smart |first5=P. L. |last6=Donahue |first6=D. J. |last7=Hererra-Osterheld |first7=S. |last8=Burr |first8=G. S. |last9=Calsoyas |first9=L.|displayauthors=9 |issue=5526 |bibcode = 2001Sci...292.2453B }}</ref><ref name="Hoffmann DL 2010 1–10">{{cite journal |last=Hoffmann |first=D. L. |title=Towards radiocarbon calibration beyond 28 ka using speleothems from the Bahamas |journal=[[Earth and Planetary Science Letters]] |year=2010 |volume=289 |pages=1–10 |doi=10.1016/j.epsl.2009.10.004 |last2=Beck |first2=J. Warren |last3=Richards |first3=David A. |last4=Smart |first4=Peter L. |last5=Singarayer |first5=Joy S. |last6=Ketchmark |first6=Tricia |last7=Hawkesworth |first7=Chris J. |bibcode=2010E&PSL.289....1H}}</ref> These results are improving the calibration for the radiocarbon technique and extending its usefulness to 45,000 years into the past.<ref>{{cite web|last=Jensen |first=M. N. |url=http://www.physics.arizona.edu/physics/public/beck-citizen.html |title=Peering deep into the past|publisher=[[University of Arizona]], Department of Physics |year=2001|deadurl=yes}}</ref> Initial results from a cave in the [[Bahamas]] suggested a peak in the amount of carbon-14 that was twice as high as modern levels.<ref>{{cite web|last=Pennicott |first=K |url=http://physicsworld.com/cws/article/news/2676 |title=Carbon clock could show the wrong time|work=PhysicsWeb|date=10 May 2001}}</ref> A recent study does not reproduce this extreme shift and suggests that analytical problems may have produced the anomalous result.<ref name="Hoffmann DL 2010 1–10"/>
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| ==Reporting dates==
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| Several different formats for citing radiocarbon results have been used since the first samples were dated. As of 2014, the standard format required by the journal ''Radiocarbon'' is as follows.<ref name=Radiocarbon_Authors>*{{cite web |url= http://www.radiocarbon.org/Authors/author-info.pdf |title= Radiocarbon: Information for Authors |author=<!--Staff writer(s); no by-line.--> |date= May 25, 2011 | website= Radiocarbon |publisher= University of Arizona | pages=5–7 | accessdate=January 1, 2014}}</ref>
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| Uncalibrated dates should be reported as "<laboratory>: <{{chem|14|C}} year> ± <range> BP", where:
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| * <laboratory> identifies the laboratory that tested the sample, and the sample ID
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| * <{{chem|14|C}} year> is the laboratory's determination of the age of the sample, in radiocarbon years
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| * <range> is the laboratory's estimate of the error in the age, at 1 σ confidence.
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| * BP stands for "before present", referring to the reference date of 1950, so that 500 BP means the year 1450 AD.
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| For example, the uncalibrated date "UtC-2020: 3510 ± 60 BP" indicates that the sample was tested by the Utrecht van der Graaf Laboratorium, where it has a sample number of 2020, and that the uncalibrated age is 3510 years before present, ± 60 years. Related forms are sometimes used: for example, "10 ka BP" means 10,000 radiocarbon years before present, and {{chem|14|C}} yr BP might be used to distinguish the uncalibrated date from a date derived from another dating method such as thermoluminescence.<ref name=Radiocarbon_Authors/>
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| ''Radiocarbon'' gives two options for reporting calibrated dates. A common format is "cal <date-range> <confidence>", where:
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| * <date-range> is the range of dates corresponding to the given confidence level
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| * <confidence> indicates the confidence level for the given date range.
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| For example, "cal 1220–1281 AD (1σ)" means a calibrated date for which the true date lies between 1220 AD and 1281 AD, with the confidence level given as 1σ, or one standard deviation. Calibrated dates can also be expressed as BP instead of using BC and AD. The curve used to calibrate the results should be the latest available INTCAL curve. Calibrated dates should also identify any programs, such as OxCal, used to perform the calibration.<ref name=Radiocarbon_Authors/>
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| ==Examples==
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| *[[Ancient footprints of Acahualinca]]
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| *[[Chauvet Cave]]
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| *[[Carbon dating the Dead Sea Scrolls|The Dead Sea Scrolls]]
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| *[[Dolaucothi]]
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| *[[Eve of Naharon]]
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| *[[Haraldskær Woman]]
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| *[[Kennewick Man]]
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| *[[Shroud of Turin]]
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| *[[Roopkund|Skeleton Lake]]
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| *[[Minoan eruption]]
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| *[[Vinland map]]
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| ==See also==
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| * [[Cosmogenic isotope]]s
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| * [[Old wood]]
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| ==Notes==
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| {{reflist|group=note}}
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| ==Footnotes==
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| {{reflist|2}}
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| ==References==
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| {{refbegin}}
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| *{{cite book |first=M. J. |last=Aitken |title=Science-based Dating in Archaeology |year=1990 |location=London |publisher=Longman |isbn=0-582-49309-9}}
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| *Boutton, Thomas W. & Yamasaki, Shin-ichi (eds.) (1996). ''Mass Spectrometry of Soils''. New York: Marcel Dekker, Inc. ISBN 0-8247-9699-3
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| *{{cite book |first=Sheridan |last=Bowman |title=Radiocarbon Dating |year=1995 |origyear=1990 |location=London|publisher=British Museum Press |isbn=0-7141-2047-2 }}
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| *{{cite book |first=Larry |last=Brown |last2=Brown |first2=Lawrence Steven |last3=Holme |first3=Tom |title= Chemistry for Engineering Students |year=2010 |origyear= 2006 |edition = 2nd |location=Belmont, CA|publisher=Brooks/Cole |isbn=978-1-4390-4791-0 }}
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| *{{cite book |first=Heather |last=Burke |last2=Smith |first2=Claire |last3=Zimmerman |first3=Larry J. |title= The Archaeologist's Field Handbook |year=2009 |edition = North American |location=Lanham, MD |publisher=AltaMira Press |isbn=978-0-7591-0882-0 }}
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| *{{cite book |first=Thomas M. |last=Cronin |title= Paleoclimates: Understanding Climate Change Past and Present |year=2010 |location=New York |publisher=Columbia University Press |isbn=978-0-231-14494-0 }}
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| *{{cite journal |last=Currie |first=L. |year=2004 |title=The Remarkable Metrological History of Radiocarbon Dating II |journal=J. Res. Natl. Inst. Stand. Technol. |volume=109 |pages=185–217 |url=http://nvl.nist.gov/pub/nistpubs/jres/109/2/j92cur.pdf}}
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| *Eriksson Stenström, Kristina; Skog, Göran; Georgiadou, Elisavet; Genberg, Johan; & Johansson, Anette. "[http://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=2173656&fileOId=2173661 A guide to radiocarbon units and calculations]". 2011. Lund:Lund University.
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| *{{cite book |first=Ian J. | last=Fairchild | last2=Baker |first2=Andy | title=Speleothem Science: From Process to Past Environments |year=2012 | location= Oxford | publisher=John Wiley & Sons | isbn=978-1-4051-9620-8 }}
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| *{{cite journal |last=Friedrich |first=M. |coauthors=''et al.'' |year=2004 |title=The 12,460-Year Hohenheim Oak and Pine Tree-Ring Chronology from Central Europe—a Unique Annual Record for Radiocarbon Calibration and Paleoenvironment Reconstructions |journal=Radiocarbon |volume=46 |pages=1111–1122}}
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| *Goudie, Andrew & Cuff, David J. (eds.) (2001). ''Encyclopedia of Global Change: Environmental Change and Human Society, Volume 1''. Oxford: Oxford University Press. ISBN 0-19-514518-6
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| * Gove, H. E. (1999) ''From Hiroshima to the Iceman.'' The Development and Applications of Accelerator Mass Spectrometry. Bristol: Institute of Physics Publishing.
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| *Grootes (1992). "Subtle {{chem|14|C}} Signals: The Influence of Atmospheric Mixing, Growing Season and In-Situ Production". ''Radiocarbon'' '''34''' (2): 219–225.
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| *{{cite journal |last=Kovar |first=Anton J. |year=1966 |title=Problems in Radiocarbon Dating at Teotihuacan |journal=American Antiquity |volume=31 |pages=427–430 |doi=10.2307/2694748 |jstor=2694748 |issue=3 |publisher=Society for American Archaeology}}
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| *L'Annunziata, Michael F. (ed.) (2012). ''Handbook of Radioactivity Analysis''. Oxford: Academic Press. ISBN 978-0-12-384873-4
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| *L'Annunziata, Michael F. (2007). ''Radioactivity: Introduction and History''. Oxford: Elsevier. ISBN 978-0-444-52715-8
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| *Larsen, Clark Spencer (ed.) (2010). ''A Companion to Biological Anthropology''. Oxford: Blackwell. ISBN 978-1-4051-8900-2
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| *Leng, Melanie J. (ed.) (2006). ''Isotopes in Palaeoenvironmental Research''. Dordrecht: Springer. ISBN 978-1-4020-2503-7
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| *Mahaney, W.C. (ed.) (1984). ''Quaternary Dating Methods''. Amsterdam: Elsevier. ISBN 0-444-42392-3
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| *{{cite journal |last=McNichol |first=A. P. |last2=Jull |first2=A. T. S. |last3=Burr |first3=G. S. |year=2001 |title= Converting AMS Data To Radiocarbon Values: Considerations And Conventions|journal=Radiocarbon |volume=43 |pages=313–320 |url=https://journals.uair.arizona.edu/index.php/radiocarbon/article/view/3969/3394}}
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| *{{cite book |first=Charles B.|last=Miller |title=Biological Oceanography |first2= Patricia A. |last2=Miller |year=2012 |origyear=2003 |edition=2nd |location=Oxford |publisher=John Wiley & Sons |isbn=978-1-4443-3301-5 }}
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| *{{cite journal |last=Lorenz |first=R. D. |last2=Jull |first2=A. J. T. |last3=Lunine |first3=J. I. |last4=Swindle |first4=T. |year=2002 |title=Radiocarbon on Titan |journal=Meteoritics and Planetary Science |volume=37 |issue=6 |pages=867–874 |doi=10.1111/j.1945-5100.2002.tb00861.x|bibcode = 2002M&PS...37..867L }}
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| *{{cite journal |last=Mook |first=W. G. |last2=van der Plicht |first2=J. |year=1999 |title=Reporting {{chem|14|C}} activities and concentrations |journal=Radiocarbon |volume=41 |pages=227–239 |url=http://digitalcommons.library.arizona.edu/index.php/objectviewer?o=http://radiocarbon.library.arizona.edu/Volume41/Number3/azu_radiocarbon_v41_n3_227_239_v.pdf}}
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| *Noller, Jay Stratton; Sowers, Janet M.; & Lettis, William R. (eds.) (2000). ''Quaternary Geochronology: Methods and Applications''. Washington: American Geophysical Union. ISBN 0-87590-950-7
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| *Olsson, Ingrid U. (ed.) (1970). ''Radiocarbon Variations and Absolute Chronology''. New York: John Wiley & Sons, Inc.
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| *{{cite web |url= http://www.radiocarbon.org/Authors/author-info.pdf |title= Radiocarbon: Information for Authors |author=<!--Staff writer(s); no by-line.--> |date= May 25, 2011 | website= Radiocarbon |publisher= University of Arizona |accessdate=January 1, 2014}}
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| *{{cite book |first=Sergei V. |last=Rasskazov |last2=Brandt |first2=Sergei Borisovich |last3=Brandt |first3=Ivan S. |title=Radiogenic Isotopes in Geologic Processes |year=2009 |location=Dordrecht |publisher=Springer |isbn=978-90-481-2998-0 }}
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| *{{cite book |first=R.E. |last=Taylor |title=Radiocarbon Dating |year=1987 |location=London |publisher=Academic Press |isbn=0-12-433663-9 }}
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| *{{cite book |first=Páll |last=Theodórsson |title=Measurement of Weak Radioactivity |year=1996 |location=Singapore |publisher=World Scientific Publishing |isbn=9810223153 }}
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| *Tykva, Richard and Berg, Dieter (eds.) (2004). ''Man-made and Natural Radioactivity in Environmental Pollution and Radiochronology''. Dordrecht: Kluwer Academic Publishers. ISBN 1-4020-1860-6
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| *{{cite book |first=Mike |last=Walker |title=Quaternary Dating Methods |year=2005 |location=Chichester |publisher=John Wiley & Sons |isbn=978-0-470-86927-7 }}
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| *{{cite book |first=Peter |last=Warneck |title=Chemistry of the Natural Atmosphere |year=2000 |location=London|publisher=Academic Press |isbn=0-12-735632-0 }}
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| * Weart, S. (2004) ''[http://www.aip.org/history/climate/Radioc.htm The Discovery of Global Warming - Uses of Radiocarbon Dating]''.
| |
| * Willis, E.H. (1996) ''[http://www.quaternary.group.cam.ac.uk/history/radiocarbon/ Radiocarbon dating in Cambridge: some personal recollections. A Worm's Eye View of the Early Days]''.
| |
| {{refend}}
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| | |
| ==External links==
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| *[http://www.radiocarbon.org/ ''Radiocarbon'' - The main international journal of record for research articles and date lists relevant to {{chem|14|C}}]
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| *[http://www.c14dating.com/ C14dating.com - General information on Radiocarbon dating]
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| *[http://calib.org/ calib.org - Calibration program, Marine Reservoir database, and bomb calibration]
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| *[http://www.whoi.edu/nosams/page.do?pid=40138.html NOSAMS: National Ocean Sciences Accelerator Mass Spectrometry Facility at the Woods Hole Oceanographic Institution]
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| *[http://c14.arch.ox.ac.uk/calibration.html Discussion of calibration] (from University of Oxford)
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| *[http://www.radiocarbon.org/Info/index.html Several calibration programs can be found at www.radiocarbon.org]
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| *[http://www.calpal-online.de CalPal Online (Cologne Radiocarbon Calibration & Paleoclimate Research Package)]
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| *[http://c14.arch.ox.ac.uk/oxcal.html OxCal program (Oxford Calibration)]
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| *[http://radiocarbon.ldeo.columbia.edu/research/radiocarbon.htm Fairbanks' Radiocarbon Calibration program (for prior to 12400 BP)]
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| *[http://id-archserve.ucsb.edu/anth3/courseware/Chronology/08_Radiocarbon_Dating.html Notes on radiocarbon dating, including movies illustrating the atomic physics] (from UC Santa Barbara)
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| *[http://science.howstuffworks.com/environmental/earth/geology/carbon-14.htm, Carbon Dating-How it works?]
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| *[http://www.physics.org/article-questions.asp?id=117, How is physics used in archaeology?] (from physics.org)
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| {{Chronology}}
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| {{DEFAULTSORT:Radiocarbon Dating}}
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| [[Category:Radiometric dating]]
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| [[Category:Radioactivity]]
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| [[Category:Carbon]]
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| [[Category:Isotopes of carbon]]
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| [[Category:American inventions]]
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| [[Category:Conservation and restoration]]
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| [[Category:Radiocarbon dating|*]]
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| {{Link GA|de}}
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| [[lt:Radiometrinis datavimas]]
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| [[ml:കാര്ബണ് പഴക്കനിര്ണ്ണയം]]
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