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Carbon dating

                                                     
Carbon dating :
 (also referred to as carbon radiocarbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon (14C), a radioactive isotope of carbon.
The method was developed by Willard Libby in the late 1940s and soon became a standard tool for archaeologists. Libby received the Nobel Prize for his work in 1960.
The radiocarbon dating method is based on the fact that radiocarbon is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen. The resulting radiocarbon combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; animals then acquire 14 C by eating the plants. When the animal or plant dies, it stops exchanging carbon with its environment, and from that point onwards the amount of 14 C it contains begins to decrease as the 14C undergoes radioactive decay. Measuring the amount of 14C in a sample from a dead plant or animal such as piece of wood or a fragment of bone provides information that can be used to calculate when the animal or plant died. The older a sample is, the less 14C there is to be detected, and because the half-life of 14C (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by radiocarbon dating are around 50,000 years ago, although special preparation methods occasionally permit dating of older samples.
The idea behind radiocarbon dating is straightforward, but years of work were required to develop the technique to the point where accurate dates could be obtained. Research has been ongoing since the 1960s to determine what the proportion of 14
C in the atmosphere has been over the past fifty thousand years. The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age. Other corrections must be made to account for the proportion of 14
C in different types of organisms (fractionation), and the varying levels of 14
C throughout the biosphere (reservoir effects). Additional complications come from the burning of fossil fuels such as coal and oil, and from the above-ground nuclear tests done in the 1950s and 1960s. Because the time it takes to convert biological materials to fossil fuels is substantially longer than the time it takes for its 14
C to decay below detectable levels, they contain almost no 14
C, and as a result there was a noticeable drop in the proportion of 14
C in the atmosphere beginning in the late 19th century. Conversely, nuclear testing increased the amount of 14C in the atmosphere, which attained a maximum in 1963 of almost twice what it had been before the testing began.
Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of beta radiation emitted by decaying 14C atoms in a sample. More recently, accelerator mass spectrometry has become the method of choice; it counts all the 14C atoms in the sample and not just the few that happen to decay during the measurements; it can therefore be used with much smaller samples (as small as individual plant seeds), and gives results much more quickly. The development of radiocarbon dating has had a profound impact on archaeology. In addition to permitting more accurate dating within archaeological sites than previous methods, it allows comparison of dates of events across great distances. Histories of archaeology often refer to its impact as the "radiocarbon revolution". Radiocarbon dating has allowed key transitions in prehistory to be dated, such as the end of the last ice age, and the beginning of the Neolithic and Bronze Age in different regions.

History:

In the early 1930s Willard Libby was a chemistry student at the University of California, Berkeley, receiving his Ph.D. in 1933. He remained there as an instructor until the end of the decade. In 1939 the Radiation Laboratory at Berkeley began experiments to determine if any of the elements common in organic matter had isotopes with half-lives long enough to be of value in biomedical research. It was soon discovered that 14
C's half-life was far longer than had been previously thought, and in 1940 this was followed by proof that the interaction of slow neutrons with 14N was the main pathway by which 14C was created. It had previously been thought that 14C would be more likely to be created by deuterons interacting with 13C.At some time during World War II Libby read a paper by W. E. Danforth and S. A. Korff, published in 1939, which predicted the creation of 14C in the atmosphere by neutrons from cosmic rays that had been slowed down by collisions with molecules of atmospheric gas. It was this paper that gave Libby the idea that radiocarbon dating might be possible.
In 1945, Libby moved to the University of Chicago. He published a paper in 1946 in which he proposed that the carbon in living matter might include 14C as well as non-radioactive carbon. Libby and several collaborators proceeded to experiment with methane collected from sewage works in Baltimore, and after isotopically enriching their samples they were able to demonstrate that they contained radioactive 14C. By contrast, methane created from petroleum showed no radiocarbon activity. The results were summarized in a paper in Science in 1947, in which the authors commented that their results implied it would be possible to date materials containing carbon of organic origin.
Libby and James Arnold proceeded to experiment with samples of wood of known age. For example, two 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. These results were published in Science in 1949. In 1960, Libby was awarded the Nobel Prize in Chemistry for this work.

Physical and chemical details

In nature, carbon exists as two stable, nonradioactive isotopes: carbon-12 (12C), and carbon-13 (13C), and a radioactive isotope, carbon-14 (14C), also known as "radiocarbon". The half-life of 14C (the time it takes for half of a given amount of 14C to decay) is about 5,730 years, so its concentration in the atmosphere might be expected to reduce over thousands of years, but 14 C is constantly being produced in the lower stratosphere and upper troposphere by cosmic rays, which generate neutrons that in turn create 14C when they strike nitrogen-14 (14N) atoms. The following nuclear reaction creates 14C:

where n represents a neutron and p represents a proton.
Once produced, the 14C quickly combines with the oxygen in the atmosphere to form carbon dioxide (CO2). 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 ratio of 14C to 12C is approximately 1.5 parts of 14C to 10¹² parts of 12C . In addition, about 1% of the carbon atoms are of the stable isotope 13C.
The equation for the radioactive decay of 14C is:

By emitting a beta particle (an electron, e⁻) and an electron antineutrino (νe), one of the neutrons in the 14C nucleus changes to a proton and the 14C nucleus reverts to the stable (non-radioactive) isotope 14N.

Principles:

During its life, a plant or animal is exchanging carbon with its surroundings, so the carbon it contains will have the same proportion of 14C as the atmosphere. Once it dies, it ceases to acquire 14
C, but the 14C within its biological material at that time will continue to decay, and so the ratio of 14C to 12C in its remains will gradually decrease. Because 14C 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 14C will be left.
The equation governing the decay of a radioactive isotope is:

where N₀ is the number of atoms of the isotope in the original sample (at time t = 0, when the organism from which the sample was taken died), and N is the number of atoms left after time t. λ is a constant that depends on the particular isotope; for a given isotope it is equal to the reciprocal of the mean-life – i.e. the average or expected time a given atom will survive before undergoing radioactive decay. The mean-life, denoted by τ, of 14C is 8,267 years, so the equation above can be rewritten as:

The sample is assumed to have originally had the same 14C/12C ratio as the ratio in the atmosphere, and since the size of the sample is known, the total number of atoms in the sample can be calculated, yielding N₀, the number of 14C atoms in the original sample. Measurement of N, the number of 14C atoms currently in the sample, allows the calculation of t, the age of the sample, using the equation above.
The half-life of a radioactive isotope (usually denoted by t_1/2) 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 14C's half-life than its mean-life. The currently accepted value for the half-life of 14C is 5,730 years. This means that after 5,730 years, only half of the initial 14C will have remained; a quarter will have remained after 11,460 years; an eighth after 17,190 years; and so on.
The above calculations make several assumptions, such as that the level of 14C in the atmosphere has remained constant over time. In fact, the level of 14C in the atmosphere has varied significantly and as a result the values provided by the equation above have to be corrected by using data from other sources. This is done by calibration curves, which convert a measurement of 14C in a sample into an estimated calendar age. The calculations involve several steps and include an intermediate value called the "radiocarbon age", which is the age in "radiocarbon years" of the sample: an age quoted in radiocarbon years means that no calibration curve has been used − the calculations for radiocarbon years assume that the 14C/12C ratio has not changed over time. Calculating radiocarbon ages also requires the value of the half-life for 14C, which for more than a decade after Libby's initial work was thought to be 5,568 years. This was revised in the early 1960s to 5,730 years, which meant that many calculated dates in papers published prior to this were incorrect (the error in the half-life is about 3%). For consistency with these early papers, and to avoid the risk of a double correction for the incorrect half-life, radiocarbon ages are still calculated using the incorrect half-life value. A correction for the half-life is incorporated into calibration curves, so even though radiocarbon ages are calculated using a half-life value that is known to be incorrect, the final reported calibrated date, in calendar years, is accurate. When a date is quoted, the reader should be aware that if it is an uncalibrated date (a term used for dates given in radiocarbon years) it may differ substantially from the best estimate of the actual calendar date, both because it uses the wrong value for the half-life of 14C, and because no correction (calibration) has been applied for the historical variation of 14C in the atmosphere over time.

 

3Carbon exchange reservoir:

Simplified version of the carbon exchange reservoir, showing proportions of carbon and relative activity of the 14C in each reservoir

Carbon is distributed throughout the atmosphere, the biosphere, and the oceans; these are referred to collectively as the carbon exchange reservoir, and each component is also referred to individually as a carbon exchange reservoir. The different elements of the carbon exchange reservoir vary in how much carbon they store, and in how long it takes for the 14C generated by cosmic rays to fully mix with them. This affects the ratio of 14C to 12C in the different reservoirs, and hence the radiocarbon ages of samples that originated in each reservoir. The atmosphere, which is where 14C is generated, contains about 1.9% of the total carbon in the reservoirs, and the 14C it contains mixes in less than seven years. The ratio of 14C to 12C in the atmosphere is taken as the baseline for the other reservoirs: if another reservoir has a lower ratio of 14C to 12C, it indicates that the carbon is older and hence that some of the 14C has decayed. The ocean surface is an example: it contains 2.4% of the carbon in the exchange reservoir, but there is only about 95% as much 14C as would be expected if the ratio were the same as in the atmosphere. The time it takes for carbon from the atmosphere to mix with the surface ocean is only a few years, but the surface waters also receive water from the deep ocean, which has more than 90% of the carbon in the reservoir. 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 14C, and water recently at the surface, with 14C in equilibrium with the atmosphere.
Creatures living at the ocean surface have the same 14C ratios as the water they live in, and as a result of the reduced 14C/12C ratio, the radiocarbon age of marine life is typically about 440 years. Organisms on land are in closer equilibrium with the atmosphere and have the same 14C/12C ratio as the atmosphere. 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. 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 14C/12C ratio lower than that of the biosphere.

Dating considerations

The variation in the 14C/12C 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 14C 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 14C/12C ratio in the atmosphere, both geographically and over time;
• isotopic fractionation;
• variations in the 14
  C/12
  C ratio in different parts of the reservoir;
• contamination.

Atmospheric variation

In the early years of using the technique, it was understood that it depended on the atmospheric 14C/12C 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. 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 14C/12C ratio had changed over time. The question was resolved by the study of tree rings: 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.) 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 14C/12C 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 14C replenished and instead start losing 14C through decay. Hence each ring preserves a record of the atmospheric 14C/12C ratio of the year it grew in. Carbon-dating the wood from the tree rings themselves provides the check needed on the atmospheric 14C/12C ratio: with a sample of known date, and a measurement of the value of N (the number of atoms of 14C remaining in the sample), the carbon-dating equation allows the calculation of N₀ – the number of atoms of 14C in the sample at the time the tree ring was formed – and hence the 14C/12C 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 14C/12C ratio. These curves are described in more detail below.

Atmospheric 14C, New Zealandand Austria. 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.^] 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 19th century. Both 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.
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.

Isotopic fractionation:

Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. In photosynthetic pathways 12C is 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.
To determine the degree of fractionation that takes place in a given plant, the amounts of both 12C and 13C isotopes are measured, and the resulting 13C/12C ratio is then compared to a standard ratio known as PDB.  The 13C/12C ratio is used instead of 14C/12C because the former is much easier to measure, and the latter can be easily derived: the depletion of 13C relative to 12C is proportional to the difference in the atomic masses of the two isotopes, so the depletion for 14C is twice the depletion of 13C. The fractionation of 13C, known as δ¹³C, is calculated as follows:

where the ‰ sign indicates parts per thousand. Because the PDB standard contains an unusually high proportion of 13C, most measured δ¹³C values are negative.

Sheep on the beach in North Ronaldsay. In the winter, these sheep eat seaweed, which has a higher δ¹³C content than grass; samples from these sheep have a δ¹³C value of about −13‰, which is much higher than for sheep that feed on grasses.

Material	Typical δ13C range
PDB	0‰
Marine plankton	−22‰ to −17‰
C3 plants	−30‰ to −22‰
C4 plants	−15‰ to −9‰
Atmospheric CO2	−8‰
Marine CO2	−32‰ to −13‰

For marine organisms, the details of the photosynthesis reactions are less well understood, and the δ¹³C values for marine photosynthetic organisms are dependent 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 above14 °C the δ¹³C values are correspondingly higher, while at lower temperatures, CO2 becomes more soluble and hence more available to marine organisms. The δ¹³C value for animals depends on their diet. An animal that eats food with high δ¹³C values will have a higher δ¹³C than one that eats food with lower δ¹³C values. 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 13
C than is found in the animal's diet, though for different biochemical reasons. The enrichment of bone 13
C also implies that excreted material is depleted in 13C relative to the diet.
Since 13C makes up about 1% of the carbon in a sample, the 13C/12C ratio can be accurately measured by mass spectrometry. Typical values of δ¹³C 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 δ¹³C value for that sample directly than to rely on the published values.

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 440 years for ocean surface water.