Editing Radiocarbon dating (section)

==Dating considerations==
{{Main|Radiocarbon dating considerations}}
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:
* variations in the {{chem|14|C}}/{{chem|12|C}} ratio in the atmosphere, both geographically and over time;
* isotopic fractionation;
* variations in the {{chem|14|C}}/{{chem|12|C}} ratio in different parts of the reservoir;
* contamination.

===Atmospheric variation===
[[Image:Hemispheric 14C graphs 1950s to 2010.png|thumb|Atmospheric {{chem|14|C}} for the northern and southern hemispheres, showing percentage excess above pre-bomb levels. The [[Partial Test Ban Treaty]] went into effect on 10 October 1963.<ref name=Hua_etal/>]]

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<!-- This article uses British English, so please do not change this to "artifact". --> that were datable by other techniques were tested; the results of the testing were in reasonable agreement with the true ages of the objects. Over time, however, discrepancies began to appear between the known chronology for the oldest Egyptian dynasties and the radiocarbon dates of Egyptian artefacts. Neither the pre-existing Egyptian chronology nor the new radiocarbon dating method could be assumed to be accurate, but a third possibility was that the {{chem|14|C}}/{{chem|12|C}} ratio had changed over time. The question was resolved by the [[Dendrochronology|study of tree rings]]:<ref name=Bowman_16>Bowman (1995), pp. 16–20.</ref><ref name=Suess_1970>Suess (1970), p.&nbsp;303.</ref><ref name=Taylor2014>Taylor & Bar-Yosef (2014), pp. 50–52.</ref> comparison of overlapping series of tree rings allowed the construction of a continuous sequence of tree-ring data that spanned 8,000 years.<ref name=Bowman_16/> (Since that time the tree-ring data series has been extended to 13,900 years.)<ref name=INTCAL13>{{Cite journal|last1=Reimer|first1=Paula J.|last2=Bard|first2=Edouard|last3=Bayliss|first3=Alex|last4=Beck|first4=J. Warren|last5=Blackwell|first5=Paul G.|last6=Ramsey|first6=Christopher Bronk|last7=Buck|first7=Caitlin E.|last8=Cheng|first8=Hai|last9=Edwards|first9=R. Lawrence|date=2013|title=IntCal13 and Marine13 Radiocarbon Age Calibration Curves 0–50,000 Years cal BP|journal=Radiocarbon|volume=55|issue=4|pages=1869–1887|doi=10.2458/azu_js_rc.55.16947|issn=0033-8222|doi-access=free|bibcode=2013Radcb..55.1869R |hdl=10289/8955|hdl-access=free}}</ref> In the 1960s, [[Hans Suess]] was able to use the tree-ring sequence to show that the dates derived from radiocarbon were consistent with the dates assigned by Egyptologists. This was possible because although annual plants, such as corn, have a {{chem|14|C}}/{{chem|12|C}} ratio that reflects the atmospheric ratio at the time they were growing, trees only add material to their outermost tree ring in any given year, while the inner tree rings don't get their {{chem|14|C}} replenished and instead start losing {{chem|14|C}} through decay. Hence each ring preserves a record of the atmospheric {{chem|14|C}}/{{chem|12|C}} ratio of the year it grew in. Carbon-dating the wood from the tree rings themselves provides 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 sample at the time the tree ring was formed – and hence the {{chem|14|C}}/{{chem|12|C}} ratio in the atmosphere at that time.<ref name=Bowman_16/><ref name=Taylor2014/> Equipped 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 name=renamed_from_18_on_20200701175743>Bowman (1995), pp. 43–49.</ref> These curves are described in more detail [[Radiocarbon dating#Calibration|below]].

Coal and oil began to be burned in large quantities during the 19th century. Both are sufficiently old that they contain little or no 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. 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/><ref name=Aitken_71>Aitken (1990), pp.&nbsp;71–72.</ref>

A much larger effect comes from above-ground nuclear testing, which released large numbers of neutrons into the atmosphere, resulting in the creation of {{chem|14|C}}. From about 1950 until 1963, when atmospheric nuclear testing was [[Partial Nuclear Test Ban Treaty|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 1964 for the northern hemisphere, and in 1966 for the southern hemisphere. The level has since dropped, as this [[bomb pulse]] or "bomb carbon" (as it is sometimes called) percolates into the rest of the reservoir.<ref name=Bowman_16/><ref name=Aitken_71/><ref name=PTBT>{{cite web|url=https://2009-2017.state.gov/t/isn/4797.htm|title=Treaty Banning Nuclear Weapon Tests in the Atmosphere, in Outer Space and Under Water|publisher=US Department of State|access-date=2 February 2015}}</ref><ref name=Hua_etal>{{Cite journal|last1=Hua|first1=Quan|last2=Barbetti|first2=Mike|last3=Rakowski|first3=Andrzej Z.|date=2013|title=Atmospheric Radiocarbon for the Period 1950–2010|journal=Radiocarbon|volume=55|issue=4|pages=2059–2072|doi=10.2458/azu_js_rc.v55i2.16177|issn=0033-8222|doi-access=free|bibcode=2013Radcb..55.2059H }}</ref>

===Isotopic fractionation===
{{main|Fractionation of carbon isotopes in oxygenic photosynthesis}}
Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. In photosynthetic pathways {{chem|12|C}} is 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>Bowman (1995), pp.&nbsp;20–23.</ref><ref name=Leng_246>Maslin & Swann (2006), p.&nbsp;246.</ref>

To determine the degree of fractionation that takes place in a given plant, the amounts of both {{chem|12|C}} and {{chem|13|C}} isotopes are measured, and the resulting {{chem|13|C}}/{{chem|12|C}} ratio is then compared to a [[Reference materials for stable isotope analysis|standard ratio]] known as PDB.{{#tag:ref|"PDB" stands for "Pee Dee Belemnite", a fossil from the [[Pee Dee Formation|Pee Dee formation]] in South Carolina.<ref>Taylor & Bar-Yosef (2014), p. 125.</ref>|group = note}} The {{chem|13|C}}/{{chem|12|C}} ratio is used instead of {{chem|14|C}}/{{chem|12|C}} because the former is much easier to measure, and the latter can be easily derived: 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 the depletion for {{chem|14|C}} is twice the depletion of {{chem|13|C}}.<ref name=Aitken1990/> The fractionation of {{chem|13|C}}, known as {{delta|13|C|link}}, is calculated as follows:<ref name=Bowman_20/>

:<math chem>\delta \ce{^{13}C} = \left( \frac{\left( \frac{\ce{^{13}C}}{\ce{^{12}C}} \right)_{\text{sample}}}{\left( \frac{\ce{^{13}C}}{\ce{^{12}C}} \right)_{\text{standard}}} - 1 \right) \times 1000</math> ‰

where the ‰ sign indicates [[parts per thousand]].<ref name=Bowman_20/> Because the PDB standard contains an unusually high proportion of {{chem|13|C}},{{#tag:ref|The PDB value is 11.2372‰.<ref>Dass (2007), p. 276.</ref>|group = note}} most measured {{delta|13|C}} values are negative.

[[File:NR sheep.jpg|thumb|upright=1.35|left|[[North Ronaldsay sheep]] on the beach in [[North Ronaldsay]], Scotland. 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/>]]
{| class="wikitable" style="font-size: 10pt; margin-left: 2em; text-align: center; float: right"
! Material !! Typical {{delta|13|C}} range
|-
|PDB || 0‰

|-
| Marine plankton || −22‰ to −17‰<ref name=Leng_246/>
|-
| C3 plants || −30‰ to −22‰<ref name=Leng_246/>
|-
| C4 plants || −15‰ to −9‰<ref name=Leng_246/>
|-
| Atmospheric {{chem|CO|2}} || −8‰<ref name=Bowman_20/>
|-
| Marine {{chem|CO|2}} || −32‰ to −13‰<ref name=Leng_246/>
|}
For marine organisms, the details of the photosynthesis reactions are less well understood, and the {{delta|13|C}} values for marine photosynthetic organisms are dependent 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&nbsp;°C the {{delta|13|C}} values are correspondingly higher, while at lower temperatures, {{chem|CO|2}} becomes more soluble and hence more available to marine organisms.<ref name=Leng_246/> 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/> 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>Schoeninger (2010), p. 446.</ref>

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=Aitken1990/> 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/>

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=Aitken1990/><ref name=Cronin2010/>

===Reservoir effects===
Libby's original exchange reservoir hypothesis assumed that the {{chem|14|C}}/{{chem|12|C}} ratio in the exchange reservoir is constant all over the world,<ref name=Libby1965>Libby (1965), p. 6.</ref> but it has since been discovered that there are several causes of variation in the ratio across the reservoir.<ref name=Bowman1995/>

====Marine effect====
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=Libby1965/> 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 uneven. The main mechanism that brings deep water to the surface is upwelling, which is more common in regions closer to the equator. Upwelling is also influenced by 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=Bowman1995/> This effect is not uniform&nbsp;– the average effect is about 400 years, but there are local deviations of several hundred years for areas that are geographically close to each other.<ref name=Bowman1995/><ref name=Cronin2010/> These deviations can be accounted for in calibration, and users of software such as CALIB can provide as an input the appropriate correction for the location of their samples.<ref name=Alves2018>{{cite journal|last1=Queiroz-Alves|first1=Eduardo|last2=Macario|first2=Kita |last3=Ascough|first3=Philippa |last4=Bronk Ramsey|first4=Christopher |year=2018|title=The worldwide marine radiocarbon reservoir effect: Definitions, mechanisms and prospects|journal=Reviews of Geophysics |volume=56|issue=1|pages=278–305|doi=10.1002/2017RG000588|bibcode=2018RvGeo..56..278A| s2cid=59153548 |url=http://eprints.gla.ac.uk/160036/7/160036.pdf}}</ref> 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=Bowman1995/>

====Hemisphere effect====
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 about 40 years for radiocarbon results from the south as compared to the north.{{#tag:ref|Two recent estimates included 8–80 radiocarbon years over the last 1000 years, with an average of 41 ± 14 years; and −2 to 83 radiocarbon years over the last 2000 years, with an average of 44 ± 17 years. For older datasets an offset of about 50 years has been estimated.<ref name=Hoggetal/>|group=note}} This is 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=Bowman1995/><ref name=Hoggetal>{{Cite journal | last1=Hogg | first1=A.G. | last2=Hua | first2=Q. | last3=Blackwell | first3=P.G. | last4=Niu | first4=M. | last5=Buck | first5=C.E. | last6=Guilderson | first6=T.P. | last7=Heaton | first7=T.J. | last8=Palmer | first8=J.G. | last9=Reimer | first9=P.J. | last10=Reimer | first10=R.W. | last11=Turney | first11=C.S.M. | last12=Zimmerman | first12=S.R.H. | date=2013 | title=SHCal13 Southern Hemisphere Calibration, 0–50,000 Years cal BP | journal=Radiocarbon | volume=55 | issue=4 | pages=1889–1903 | doi=10.2458/azu_js_rc.55.16783| s2cid=59269731 | doi-access=free | bibcode=2013Radcb..55.1889H | hdl=10289/7799 | hdl-access=free }}</ref> The effect is strengthened by strong upwelling around Antarctica.<ref name="Russel" />

====Other effects====
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=Aitken1990/> This is known as the [[hard water]] effect because it is often associated with calcium ions, which are characteristic of hard water; other sources of carbon such as [[humus]] can produce similar results, and can also reduce the apparent age if they are of more recent origin than the sample.<ref name=Bowman1995/> The effect varies greatly and there is no general offset that can be applied; additional research is usually needed to determine the size of the offset, for example by comparing the radiocarbon age of deposited freshwater shells with associated organic material.<ref>Taylor & Bar-Yosef (2014), pp. 74–75.</ref>

[[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 near 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 in the neighbourhood of the [[Furnas]] caldera in the [[Azores]] were found to have apparent ages that ranged from 250 years to 3320 years.<ref>{{Cite journal |last1=Pasquier-Cardin |first1=Aline |last2=Allard |first2=Patrick |last3=Ferreira |first3=Teresa |last4=Hatte |first4=Christine |last5=Coutinho |first5=Rui |last6=Fontugne |first6=Michel |last7=Jaudon |first7=Michel |date=1999 |title=Magma-derived {{chem|14|C|O|2}} emissions recorded in {{chem|14|C}} and {{chem|13|C}} content of plants growing in Furnas caldera, Azores |journal=Journal of Volcanology and Geothermal Research |volume=92 |issue=1–2 |pages=200–201|doi=10.1016/S0377-0273(99)00076-1 }}</ref>

===Contamination===
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 17,000 years old is contaminated so that 1% of the sample is 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 independent of age&nbsp;– a sample contaminated with 1% old carbon will appear to be about 80 years older than it truly is, regardless of the date of the sample.<ref>Aitken (1990), pp. 85–86.</ref>