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L'idea da cui deriva il metodo di datazione del radiocarbonio è semplice, ma sono occorsi anni per sviluppare la tecnica fino a raggiungere l'accuratezza delle date richiesta. A partire dagli anni sessanta, sono state condotte ricerche al fine di determinare quale fosse l'esatto rapporto tra ¹²C e ¹⁴C nell'atmosfera nel corso degli ultimi cinquantamila anni. I dati risultanti sono usati, sotto la forma di una curva di calibrazione, sono utilizzati per convertire una data misura del radiocarbonio di un campione nella corrispondente età del campione. Oltre a tale conversione, occorre applicare opportune correzioni per tener conto di altri fattori, quali la diversa proporzione di ¹⁴C in differenti organismi (frazionamento) e la variazione dei livelli di ¹⁴C all'interno della biosfera (effetto serbatoio). Ulteriori complicazioni si sono aggiunte più recentemente, prima a causa dell'utilizzo dei combustibili fossili, che ha introdotto in atmosfera notevoli quantità di carbonio antico riducendo il livello di ¹⁴C, poi dai test nucleari al suolo effettuati negli anni cinquanta e sessanta del ventesimo secolo, che hanno provocato un notevole incremento di produzione di ¹⁴C tramite irraggiamento.

Variazioni del rapporto tra ¹⁴C e ¹²C

Le variazioni del rapporto ¹⁴C/¹²C in differenti ambiti serbatoio fanno sì che un calcolo dell'età di un campione che venga effettuato direttamente dalla misura della quantità di ¹⁴C in esso contenuto dia spesso un risultato errato.

Vanno infatti considerate svariate cause che conducono a differenti livelli di ¹⁴C nei campioni, che si possono raggruppare in quattro sorgenti di errore principale:

• variazioni del rapporto ¹⁴C/¹²C nell'atmosfera, sia relative alla zona geografica sia nel tempo;
• frazionamento isotopico;
• variazioni del rapporto ¹⁴C/¹²C in diverse parti del serbatoio considerato;
• contaminazioni.

Variazioni in atmosfera

Fin dai primi anni di utilizzo della tecnica, si comprese che l'accuratezza del risultato dipendeva dall'assunto che il rapporto tra i vari isotopi del carbonio fosse rimasto costante nei millenni precedenti. Al fine di verificare l'accuratezza del metodo vennero quindi condotte varie misurazioni su artefatti databili anche con differenti metodi e il risultato di tali misurazioni fu che le età rilevate erano in accordo con l'età degli oggetti. Tuttavia, già nel 1958 Hessel de Vries dimostrò, misurando campioni di legno di età conosciuta, che il rapporto tra ¹⁴C e ¹²C era in realtà cambiato nel tempo e che vi erano significative deviazioni dai valori attesi. Questa discrepanza, a cui viene dato a volte il nome "effetto de Vries", venne misurata accuratamente tramite la dendrocronologia. Studiando gli anelli del legno di antichi tronchi, fu possibile infatti costruire una sequenza ininterrotta di misurazioni grazie al sovrapporsi di serie di anelli di diffferenti campioni, ottenendo una sequenza di anelli dei precedenti 8000 anni (ad oggi le serie sono state estese fino a 13900 anni).

La datazione del legno degli anelli stessi ha fornito le richieste conferme dei livelli di ¹⁴C nell'atmosfera: con un campione di data certa e una misurazione di N atomi di ¹⁴C rimasti nel campione, si può calcolare a ritroso N₀ - numero di atomi nel momento di formazione dell'anello - e da lì il rapporto ¹⁴C/¹²C nell'atmosfera.

Le principali ragioni di queste variazioni sono la fluttuazione del ritmo di creazione di ¹⁴C, i cambiamenti di temperatura cauasti dalle glaciazioni e le variazioni derivanti da attività antropiche.

= Variazioni nella produzione

Si osservano due differenti trend nelle serie di anelli degli alberi: una prima oscillazione a lungo termine con un periodo di circa 9000 anni, che causa l'"invecchiamento" delle date rilevate negli ultimi duemila anni e il "ringiovanimento" delle date rilevate precedenti, dovuto alle fluttuazioni della forza del campo magnetico terrestre che provocano una minore o maggiore deflessione dei raggi cosmici; e una seconda oscillazione a breve termine, composta da due cicli, uno di circa 200 anni e uno di 11 anni, causata da variazioni nelle emissioni solari, che cambiano il campo magnetico del Sole e provocano corrispondenti variazioni del flusso dei raggi cosmici.

There are two kinds of geophysical event which can affect ¹⁴C production: geomagnetic reversals and polarity excursions. In a geomagnetic reversal, the Earth's geomagnetic field weakens and stays weak for thousands of years during the transition to the opposite magnetic polarity and then regains strength as the reversal completes. A polarity excursion, which can be either global or local, is a shorter-lived version of a geomagnetic reversal. A local excursion would not significantly affect 14C production. During either a geomagnetic reversal or a global polarity excursion, ¹⁴C production increases during the period when the geomagnetic field is weak. It is fairly certain, though, that in the last 50,000 years there have been no geomagnetic reversals or global polarity excursions.^[1]

Since the earth's magnetic field varies with latitude, the rate of ¹⁴C production changes with latitude, too, but atmospheric mixing is rapid enough that these variations amount to less than 0.5% of the global concentration.^[2] This is close to the limit of detectability in most years,^[3] but the effect can be seen clearly in tree rings from years such as 1963, when ¹⁴C from nuclear testing rose sharply through the year.^[4] The latitudinal variation in ¹⁴C was much larger than normal that year, and tree rings from different latitudes show corresponding variations in their ¹⁴C content.^[4]

¹⁴C can also be produced at ground level, primarily by cosmic rays that penetrate the atmosphere as far as the earth's surface, but also by spontaneous fission of naturally occurring uranium. These sources of neutrons only produce ¹⁴C at a rate of 1 x 10⁻⁴ atoms per gram per second, which is not enough to have a significant impact on dating.^[4][5] At higher altitudes, the neutron flux can be substantially higher,^{[6][note 1]} 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 ¹⁴C content is minor, though for very old trees (such as some bristlecone pines) that grow at altitude some effect can be seen.^[6]

Impact of climatic cycles

Because the solubility of CO₂ in water increases with lower temperatures, glacial periods would have led to the faster absorption of atmospheric CO₂ by the oceans. In addition, any carbon stored in the glaciers would be depleted in ¹⁴C over the life of the glacier; when the glacier melted as the climate warmed, the depleted carbon would be released, reducing the global ¹⁴C/¹²C 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.^[2]

Effects of human activity

 

Atmospheric ¹⁴C, New Zealand^[7] and Austria.^[8] 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 ¹⁴C in the Northern Hemisphere.^[9] 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 ¹⁴C and, as a result, the CO₂ released substantially diluted the atmospheric ¹⁴C/¹²C ratio. Dating an object from the early 20th century hence gives an apparent date older than the true date. For the same reason, ¹⁴C 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 ¹⁴C 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.^[2][10]

A much larger effect comes from above-ground nuclear testing, which released large numbers of neutrons and created ¹⁴C. From about 1950 until 1963, when atmospheric nuclear testing was banned, it is estimated that several tonnes of ¹⁴C were created. If all this extra ¹⁴C had immediately been spread across the entire carbon exchange reservoir, it would have led to an increase in the ¹⁴C/¹²C ratio of only a few per cent, but the immediate effect was to almost double the amount of ¹⁴C in the atmosphere, with the peak level occurring in about 1965. The level has since dropped, as the "bomb carbon" (as it is sometimes called) percolates into the rest of the reservoir.^[2][10][11]

Isotopic fractionation

Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. Two different photosynthetic processes exist: the C3 pathway and the C4 pathway. About 90% of all plant life uses the C3 process; the remaining plants either use C4 or are 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 ¹²C being absorbed slightly more easily than ¹³C, which in turn is more easily absorbed than ¹⁴C. The differential uptake of the three carbon isotopes leads to ¹³C/¹²C and ¹⁴C/¹²C ratios in plants that differ from the ratios in the atmosphere. This effect is known as isotopic fractionation.^[6][12]

To determine the degree of fractionation that takes place in a given plant, the amounts of both ¹²C and ¹³C are measured, and the resulting ¹³C/¹²C ratio is then compared to a standard ratio known as PDB. (The ¹³C/¹²C ratio is used because it is much easier to measure than the ¹⁴C/¹²C ratio, and the ¹⁴C/¹²C ratio can be easily derived from it.) The resulting value, known as Template:Delta, is calculated as follows:^[6]

${\displaystyle \mathrm {\delta ^{13}C} ={\Biggl (}\mathrm {\frac {{\bigl (}{\frac {^{13}C}{^{12}C}}{\bigr )}_{sample}}{{\bigl (}{\frac {^{13}C}{^{12}C}}{\bigr )}_{PDB}}} -1{\Biggr )}\times 1000\ ^{o}\!/\!_{oo}}$ 

where the ‰ (permil) sign indicates parts per thousand.^[6] Because the PDB standard contains an unusually high proportion of ¹³C,^{[note 2]} most measured Template:Delta 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‰.^[12] Atmospheric CO₂ has a Template:Delta of −8‰.^[6]

 

Sheep on the beach in North Ronaldsay. In the winter, these sheep eat seaweed, which has a higher Template:Delta content than grass; samples from these sheep have a Template:Delta value of about −13‰, which is much higher than for sheep that feed on grasses.^[6]

For marine organisms, the details of the photosynthesis reactions are less well understood. Measured Template:Delta values for marine plankton range from −31‰ to −10‰; most lie between −22‰ and −17‰. The Template:Delta values for marine photosynthetic organisms also depend on temperature. At higher temperatures, CO₂ has poor solubility in water, which means there is less CO₂ available for the photosynthetic reactions. Under these conditions, fractionation is reduced, and at temperatures above 14 °C the Template:Delta values are correspondingly higher, reaching −13‰. At lower temperatures, CO₂ becomes more soluble and hence more available to the marine organisms; fractionation increases and Template:Delta values can be as low as −32‰.^[12]

The Template:Delta value for animals depends on their diet. An animal that eats food with high Template:Delta values will have a higher Template:Delta than one that eats food with lower Template:Delta values.^[6] 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 ¹³C than is found in the animal's diet, though for different biochemical reasons. The enrichment of bone ¹³C also implies that excreted material is depleted in ¹³C relative to the diet.^[14]

Since ¹³C makes up about 1% of the carbon in a sample, the ¹³C/¹²C ratio can be accurately measured by mass spectrometry.^[15] Typical values of Template:Delta 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 Template:Delta value for that sample directly than to rely on the published values.^[6] The depletion of ¹³C relative to ¹²C is proportional to the difference in the atomic masses of the two isotopes, so once the Template:Delta value is known, the depletion for ¹⁴C can be calculated: it will be twice the depletion of ¹³C.^[15]

The carbon exchange between atmospheric CO₂ and carbonate at the ocean surface is also subject to fractionation, with ¹⁴C in the atmosphere more likely than ¹²C to dissolve in the ocean. The result is an overall increase in the ¹⁴C/¹²C ratio in the ocean of 1.5%, relative to the ¹⁴C/¹²C ratio in the atmosphere. This increase in ¹⁴C concentration almost exactly cancels out the decrease caused by the upwelling of water (containing old, and hence ¹⁴C depleted, carbon) from the deep ocean, so that direct measurements of ¹⁴C 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.^[15]

Reservoir effects

Libby's original exchange reservoir hypothesis assumed that the ¹⁴C/¹²C ratio in the exchange reservoir is constant all over the world,^[16] but it has since been discovered that there are several causes of variation in the ratio across the reservoir.^[17]

Marine effect

The CO₂ 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 CO₂.^[16] This exchange process brings¹⁴C from the atmosphere into the surface waters of the ocean, but the ¹⁴C 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 CO₂ 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).^[17] 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.^[17][18] 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.^[17] 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.^[18]

Hard water effect

If the carbon in freshwater is partly acquired from aged carbon, such as rocks, then the result will be a reduction in the ¹⁴C/¹²C 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 ¹⁴C, so this carbon lowers the ¹⁴C/¹²C 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.^[15] 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.^[17]

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.^[17]

Volcanoes

Volcanic eruptions eject large amounts of carbon into the air. The carbon is of geological origin and has no detectable ¹⁴C, so the ¹⁴C/¹²C 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 ¹⁴C/¹²C 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, 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.^[17]

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 ¹⁴C/¹²C 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 ¹⁴C because of the marine effect, ¹⁴C is removed from the southern atmosphere more quickly than in the north.^[17]

Island effect

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 ¹⁴C/¹²C 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.^[17]

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 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 ¹⁴C, 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.^[19]

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.^[20] 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.^[21] Samples should be packed in glass vials or aluminium foil if possible;^[20][22] polyethylene bags are also acceptable but some plastics, such as PVC, can contaminate the sample.^[21] Contamination can also occur before the sample is collected: humic acids 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 ¹⁴C content.^[20]

Notes

1. ^ Aitken (1990), pp. 68–69.
2. Errore nelle note: Errore nell'uso del marcatore <ref>: non è stato indicato alcun testo per il marcatore Bowman_16-20
3. ^ Rasskazov, Brandt & Brandt (2009), p. 40.
4. Pieter M. Grootes, Subtle ¹⁴C Signals: The Influence of Atmospheric Mixing, Growing Season and In-Situ Production, in Radiocarbon, vol. 34, n. 2, 1992, pp. 219–225.
5. ^ C.B. Ramsey, Radiocarbon dating: revolutions in understanding, in Archaeometry, vol. 50, n. 2, 2008, pp. 249–275, DOI:10.1111/j.1475-4754.2008.00394.x.
6. Bowman (1995), pp. 20–23.
7. ^ Atmospheric δ¹⁴C record from Wellington, in Carbon Dioxide Information Analysis Center. URL consultato il 1º May 2008 (archiviato dall'url originale il 1º February 2014 Il valore del parametro dataarchivio non combacia con la data decodificata dall'URL: 1º febbraio 2014 (aiuto)).
8. ^ δ¹⁴CO₂ record from Vermunt, in Carbon Dioxide Information Analysis Center. URL consultato il 1º May 2008.
9. ^ Lloyd A. Currie, The remarkable metrological history of radiocarbon dating II, in Journal of Research of the National Institute of Standards and Technology, vol. 109, 2004, pp. 185–217, DOI:10.6028/jres.109.013.
10. Aitken (1990), pp. 71–72.
11. ^ Limited Test Ban Treaty, in Science Magazine. URL consultato il July 26, 2013.
12. Maslin & Swann (2006), p. 246.
13. ^ Miller & Wheeler (2012), p. 186.
14. ^ Schoeninger (2010), p. 446.
15. Aitken (1990), pp. 61–66.
16. Libby (1965), p. 6.
17. Bowman (1995), pp. 24–27.
18. Cronin (2010), p. 35.
19. ^ Aitken (1990), pp. 85–86.
20. Bowman (1995), pp. 27–30.
21. Aitken (1990), p. 89.
22. ^ Burke, Smith & Zimmerman (2009), p. 175.

Footnotes

References

• M.J. Aitken, Science-based Dating in Archaeology, London, Longman, 1990, ISBN 0-582-49309-9.
• Sheridan Bowman, Radiocarbon Dating, London, British Museum Press, 1995, ISBN 0-7141-2047-2.
• Heather Burke, The Archaeologist's Field Handbook, North American, Lanham, MD, AltaMira Press, 2009, ISBN 978-0-7591-0882-0.
• Thomas M. Cronin, Paleoclimates: Understanding Climate Change Past and Present, New York, Columbia University Press, 2010, ISBN 978-0-231-14494-0.
• Application of environmental radionuclides in radiochronology: Radiocarbon, in Man-made and Natural Radioactivity in Environmental Pollution and Radiochronology, Dordrecht, Kluwer Academic Publishers, 2004, pp. 150–179, ISBN 1-4020-1860-6.
• Willard F. Libby, Radiocarbon Dating, 2nd (1955), Chicago, Phoenix, 1965.
• Isotopes in marine sediments, in Isotopes in Palaeoenvironmental Research, Springer, 2006, pp. 227–290, ISBN 978-1-4020-2503-7.
• Sergei V. Rasskazov, Radiogenic Isotopes in Geologic Processes, Dordrecht, Springer, 2009, ISBN 978-90-481-2998-0.
• Margaret J. Schoeninger, Diet reconstruction and ecology using stable isotope ratios, in A Companion to Biological Anthropology, Oxford, Blackwell, 2010, pp. 445–464, ISBN 978-1-4051-8900-2.
• H.E. Suess, Bristlecone-pine calibration of the radiocarbon time-scale 5200 B.C. to the present, in Radiocarbon Variations and Absolute Chronology, New York, John Wiley & Sons, 1970, pp. 303–311.

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