Radiocarbon dating is a method used to determine the age of organic materials by measuring the decay of carbon-14 (), a radioactive isotope of carbon. Developed in the late 1940s, the technique has been widely used in archaeology, geology, and environmental science to date materials up to 50,000 years old.
The method relies on the carbon exchange reservoir, which includes the atmosphere, oceans, and biosphere. However, the / ratio in this reservoir is not constant over time or across different environments, which can introduce errors in radiocarbon dating calculations. Scientists have identified four main sources of error:
Variations in the / ratio in the atmosphere due to factors such as changes in Earth's magnetic field, solar activity, and human influences like fossil fuel burning. Isotope fractionation, where different carbon isotopes are absorbed at different rates by plants and animals. Reservoir effects, where certain environments (e.g., deep ocean water, freshwater sources) contain different concentrations, affecting the apparent age of samples. Contamination, where external sources of carbon (such as modern pollutants or ancient carbon from fossil fuels) alter a sample’s true radiocarbon signature.
Atmospheric variation
In the early years of using the technique, it was understood that it depended on the atmospheric / ratio having remained the same over the preceding few thousand years. To verify the accuracy of the method, several artifacts 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 was able to demonstrate that the / ratio had changed over time by testing wood samples of known ages and showing there was a significant deviation from the expected ratio. This discrepancy, often called the de Vries effect, was resolved by the study of tree rings.Bowman (1995), pp. 16–20.Suess (1970), p. 303. Comparison of overlapping series of tree rings allowed the construction of a continuous sequence of tree-ring data that spanned 8,000 years. (Since that time the tree-ring data series has been extended to 13,900 years.) Carbon-dating the wood from the tree rings themselves provided the check needed on the atmospheric / ratio: with a sample of known date, and a measurement of the value of N (the number of atoms of remaining in the sample), the carbon-dating equation allows the calculation of N0 – the number of atoms of in the sample at the time the tree ring was formed – and hence the / ratio in the atmosphere at that time. 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 / ratio.Bowman (1995), pp. 43–49. These curves are described in more detail below.
There are three main reasons for these variations in the historical / ratio: fluctuations in the rate at which is created, changes caused by glaciation, and changes caused by human activity.
Variations in production 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 strength of the Earth's magnetic field match up quite well with this oscillation: cosmic rays are deflected by magnetic fields, so when there is a weaker magnetic field, more is produced, leading to a younger apparent age for samples from those periods. Conversely, a stronger magnetic field leads to lower 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, and 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 .
There are two kinds of geophysical event which can affect 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 production. During either a geomagnetic reversal or a global polarity excursion, 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.Aitken (1990), pp. 68–69.
Since the Earth's magnetic field varies with latitude, the rate of production changes with latitude, too, but atmospheric mixing is rapid enough that these variations amount to less than 0.5% of the global concentration. This is close to the limit of detectability in most years,Rasskazov, Brandt & Brandt (2009), p. 40. but the effect can be clearly seen in tree rings from years such as 1963, when from nuclear testing rose sharply through the year. The latitudinal variation in was much larger than normal that year, and tree rings from different latitudes show corresponding variations in their content.
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 at a rate of 1 × 10−4 atoms per gram per second, which is not enough to have a significant effect on dating. At higher altitudes, the neutron flux can be substantially higher,Bowman (1995), pp. 20–23. 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 content is minor, though for very old trees (such as some bristlecone pines) that grow at altitude some effect can be seen.
Effect of climatic cycles Because the solubility of in water increases with lower temperatures, glacial periods would have led to the faster absorption of atmospheric by the oceans. In addition, any carbon stored in the glaciers would be depleted in over the life of the glacier; when the glacier melted as the climate warmed, the depleted carbon would be released, reducing the global / 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.
Effects of human activity
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 and, as a result, the released substantially diluted the atmospheric / ratio. Dating an object from the early 20th century hence gives an apparent date older than the true date. For the same reason, concentrations in the neighborhood 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 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.Aitken (1990), pp. 71–72.
A much larger effect comes from above-ground nuclear testing, which released large numbers of neutrons and created . From about 1950 until 1963, when atmospheric nuclear testing was banned, it is estimated that several tonnes of were created. If all this extra had immediately been spread across the entire carbon exchange reservoir, it would have led to an increase in the / ratio of only a few percent, but the immediate effect was to almost double the amount of 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.
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 being absorbed slightly more easily than , which in turn is more easily absorbed than . The differential uptake of the three carbon isotopes leads to / and / ratios in plants that differ from the ratios in the atmosphere. This effect is known as isotopic fractionation.Maslin & Swann (2006), p. 246.
To determine the degree of fractionation that takes place in a given plant, the amounts of both and are measured, and the resulting / ratio is then compared to a standard ratio known as PDB. (The / ratio is used because it is much easier to measure than the / ratio, and the / ratio can be easily derived from it.) The resulting value, known as , is calculated as follows: ‰ where the ‰ (permil) sign indicates parts per thousand. Because the PDB standard contains an unusually high proportion of , most measured 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‰. Atmospheric has a of −8‰.
For marine organisms, the details of the photosynthesis reactions are less well understood. Measured values for marine plankton range from −31‰ to −10‰; most lie between −22‰ and −17‰. The values for marine photosynthetic organisms also depend on temperature. At higher temperatures, has poor solubility in water, which means there is less available for the photosynthetic reactions. Under these conditions, fractionation is reduced, and at temperatures above 14 °C the values are correspondingly higher, reaching −13‰. At lower temperatures, becomes more soluble and hence more available to the marine organisms; fractionation increases and values can be as low as −32‰.
The value for animals depends on their diet. An animal that eats food with high values will have a higher than one that eats food with lower values. The animal's own biochemical processes can also affect the results: for example, both bone minerals and bone collagen typically have a higher concentration of than is found in the animal's diet, though for different biochemical reasons. The enrichment of bone also implies that excreted material is depleted in relative to the diet.Schoeninger (2010), p. 446.
Since makes up about 1% of the carbon in a sample, the / ratio can be accurately measured by mass spectrometry.Aitken (1990), pp. 61–66. Typical values of 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 value for that sample directly than to rely on the published values. The depletion of relative to is proportional to the difference in the atomic masses of the two isotopes, so once the value is known, the depletion for can be calculated: it will be twice the depletion of .