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Other carbon-14 sources Carbon-14 can also be produced by other neutron reactions, including in particular n,γ 14C and n,α 14C with , and n,d 14C and n, 3He 14C with. Carbon-14 may also be produced by lightning bolts but in the amounts negligible compared to cosmic rays. This led to estimates that the trees were between 24,000 and 19,000 years old, and hence this was taken to be the date of the last advance of the before its final retreat marked the end of the Pleistocene in North America.

Reporting dates Several formats for citing radiocarbon results have been used since the first samples were met. As radiocarbon dates began to prove these ideas wrong in many instances, it became apparent that these innovations must sometimes have arisen locally. Carbon dating laboratory older datasets an offset of about 50 years has been estimated. He is credited to be the first scientist to suggest that the unstable print isotope called radiocarbon or carbon 14 might exist in living matter. It was revised again in the early 1960s to 5,730 ± 40 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 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 14 C will be left. The initial 14C level for the calculation can either be servile, or else directly carbon dating laboratory with known year-by-year data from tree-ring data up to 10,000 years ago using overlapping data from live and dead trees in a given areaor else from cave depositsback to about 45,000 years before the present. It is rapidly met in air to form carbon dioxide and enters the global carbon cycle. There are several other possible sources of error that need to be considered. Metal grave goods, for example, cannot be radiocarbon dated, but they may be found in a grave with a coffin, charcoal, or other material which can be prime to have been deposited at the same time.

Calibrated 14 C dates are frequently reported as cal BP, cal BC, or cal AD, again with BP referring to the year 1950 as the zero date. Researchers have studied other radioactive isotopes created by cosmic rays to determine if they could also be used to assist in dating objects of archaeological interest; such isotopes include , , , , and. Calibrated 14 C dates are frequently reported as cal BP, cal BC, or cal AD, again with BP referring to the year 1950 as the zero date.

What is Carbon Dating? - Contamination Any addition of carbon to a sample of a different age will cause the measured date to be inaccurate. The new standard, Oxalic Acid II, was proven to have only a slight difference with Oxalic Acid I in terms of radiocarbon content.

Radiocarbon dating also referred to as carbon dating or carbon-14 dating is a method for of an object containing by using the properties of , a radioactive. The method was developed in the late 1940s by , who received the for his work in 1960. It is based on the fact that radiocarbon 14 C is constantly being created in the atmosphere by the interaction of with atmospheric. The resulting 14 C combines with atmospheric to form radioactive , which is incorporated into plants by ; 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 14 C undergoes. Measuring the amount of 14 C in a sample from a dead plant or animal such as a 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 14 C there is to be detected, and because the of 14 C 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 this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples. 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 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 is substantially longer than the time it takes for its 14 C to decay below detectable levels, fossil fuels 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 14 C in the atmosphere, which attained a maximum in about 1965 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 emitted by decaying 14 C atoms in a sample. More recently, has become the method of choice; it counts all the 14 C 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. In addition to permitting more accurate dating within archaeological sites than previous methods, it allows comparison of dates of events across great distances. Radiocarbon dating has allowed key transitions in prehistory to be dated, such as the end of the , and the beginning of the and in different regions. History In 1939, and of the 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. They synthesized 14 C using the laboratory's cyclotron accelerator and soon discovered that the atom's was far longer than had been previously thought. This was followed by a prediction by , then employed at the in , that the interaction of with 14 N in the upper atmosphere would create 14 C. It had previously been thought that 14 C would be more likely to be created by interacting with 13 C. At some time during World War II, , who was then at Berkeley, learned of Korff's research and conceived the idea that it might be possible to use radiocarbon for dating. In 1945, Libby moved to the where he began his work on radiocarbon dating. He published a paper in 1946 in which he proposed that the carbon in living matter might include 14 C as well as non-radioactive carbon. Libby and several collaborators proceeded to experiment with collected from sewage works in Baltimore, and after their samples they were able to demonstrate that they contained 14 C. By contrast, methane created from petroleum showed no radiocarbon activity because of its age. The results were summarized in a paper in 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 proceeded to test the radiocarbon dating theory by analyzing samples with known ages. For example, two samples taken from the tombs of two Egyptian kings, and , 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. Within 11 years of their announcement, more than 20 radiocarbon dating laboratories had been set up worldwide. In 1960, Libby was awarded the for this work. The half-life of 14 C the time it takes for half of a given amount of 14 C to 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 and upper , primarily by galactic , and to a lesser degree by solar cosmic rays. These generate neutrons that in turn create 14 C when they strike 14 N atoms. Once produced, the 14 C quickly combines with the oxygen in the atmosphere to form first carbon monoxide CO , and ultimately carbon dioxide CO 2. Animals eat the plants, and ultimately the radiocarbon is distributed throughout the. The ratio of 14 C to 12 C is approximately 1. In addition, about 1% of the carbon atoms are of the stable isotope 13 C. Principles During its life, a plant or animal is in equilibrium with its surroundings by exchanging carbon either with the atmosphere, or through its diet. It will therefore have the same proportion of 14 C as the atmosphere, or in the case of marine animals or plants, with the ocean. Once it dies, it ceases to acquire 14 C, but the 14 C within its biological material at that time will continue to decay, and so the ratio of 14 C to 12 C in its remains will gradually decrease. Because 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 14 C will be left. Measurement of N, the number of 14 C atoms currently in the sample, allows the calculation of t, the age of the sample, using the equation above. The currently accepted value for the half-life of 14 C is 5,730 ± 40 years. This means that after 5,730 years, only half of the initial 14 C will remain; a quarter will remain 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 14 C in the atmosphere has remained constant over time. In fact, the level of 14 C 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 discussed below , which convert a measurement of 14 C in a sample into an estimated calendar age. Calculating radiocarbon ages also requires the value of the half-life for 14 C. In Libby's 1949 paper he used a value of 5720 ± 47 years, based on research by Engelkemeir et al. This was remarkably close to the modern value, but shortly afterwards the accepted value was revised to 5568 ± 30 years, and this value was in use for more than a decade. It was revised again in the early 1960s to 5,730 ± 40 years, which meant that many calculated dates in papers published prior to this were incorrect the error in the half-life is about 3%. Since the calibration curve IntCal also reports past atmospheric 14 C concentration using this conventional age, any conventional ages calibrated against the IntCal curve will produce a correct calibrated age. 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 14 C, and because no correction calibration has been applied for the historical variation of 14 C in the atmosphere over time. Carbon exchange reservoir Simplified version of the carbon exchange reservoir, showing proportions of carbon and relative activity of the 14 C 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 14 C generated by cosmic rays to fully mix with them. This affects the ratio of 14 C to 12 C in the different reservoirs, and hence the radiocarbon ages of samples that originated in each reservoir. The atmosphere, which is where 14 C is generated, contains about 1. The ratio of 14 C to 12 C in the atmosphere is taken as the baseline for the other reservoirs: if another reservoir has a lower ratio of 14 C to 12 C, it indicates that the carbon is older and hence that either some of the 14 C has decayed, or the reservoir is receiving carbon that is not at the atmospheric baseline. The ocean surface is an example: it contains 2. 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 14 C, and water recently at the surface, with 14 C in equilibrium with the atmosphere. These organisms contain about 1. There are several other possible sources of error that need to be considered. 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. The question was resolved by the : 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, was able to use the tree-ring sequence to show that the dates derived from radiocarbon were consistent with the dates assigned by Egyptologists. These curves are described in more detail. Coal and oil began to be burned in large quantities during the 19th century. Dating an object from the early 20th century hence gives an apparent date older than the true date. For the same reason, 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. A much larger effect comes from above-ground nuclear testing, which released large numbers of neutrons and created 14 C. From about 1950 until 1963, when atmospheric nuclear testing was banned, it is estimated that several tonnes of 14 C were created. Isotopic fractionation Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. In photosynthetic pathways 12 C is absorbed slightly more easily than 13 C, which in turn is more easily absorbed than 14 C. This effect is known as isotopic fractionation. Because the PDB standard contains an unusually high proportion of 13 C, most measured δ 13C values are negative. At higher temperatures, CO 2 has poor solubility in water, which means there is less CO 2 available for the photosynthetic reactions. Under these conditions, fractionation is reduced, and at temperatures above 14 °C the δ 13C values are correspondingly higher, while at lower temperatures, CO 2 becomes more soluble and hence more available to marine organisms. The δ 13C value for animals depends on their diet. An animal that eats food with high δ 13C values will have a higher δ 13C than one that eats food with lower δ 13C 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 13 C relative to the diet. Typical values of δ 13C have been found by experiment for many plants, as well as for different parts of animals such as bone , but when dating a given sample it is better to determine the δ 13C value for that sample directly than to rely on the published values. The carbon exchange between atmospheric CO 2 and carbonate at the ocean surface is also subject to fractionation, with 14 C in the atmosphere more likely than 12 C to dissolve in the ocean. This increase in 14 C concentration almost exactly cancels out the decrease caused by the upwelling of water containing old, and hence 14 C depleted, carbon from the deep ocean, so that direct measurements of 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. The 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 CO 2. This exchange process brings 14 C from the atmosphere into the surface waters of the ocean, but the 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 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. This effect is not uniform — 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. 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. 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. Hemisphere effect The northern and southern hemispheres have systems that are sufficiently independent of each other that there is a noticeable time lag in mixing between the two. 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 14 C because of the marine effect, 14 C is removed from the southern atmosphere more quickly than in the north. The effect is strengthened by strong upwelling around Antarctica. For example, rivers that pass over , which is mostly composed of , will acquire carbonate ions. Similarly, groundwater can contain carbon derived from the rocks through which it has passed. This is known as the effect because it is often associated with calcium ions, which are characteristic of hard water; other sources of carbon such as can produce similar results, and can also reduce the apparent age if they are of more recent origin than the sample. 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. Dormant volcanoes can also emit aged carbon. 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 14 C, causes an error in the other direction independent of age — a sample contaminated with 1% old carbon will appear to be about 80 years older than it really is, regardless of the date of the sample. Main article: Samples for dating need to be converted into a form suitable for measuring the 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, the sample must be treated to remove any contamination and any unwanted constituents. This includes removing visible contaminants, such as rootlets that may have penetrated the sample since its burial. Alkali and acid washes can be used to remove humic acid and carbonate contamination, but care has to be taken to avoid removing the part of the sample that contains the carbon to be tested. Charcoal is often tested but is likely to need treatment to remove contaminants. If the bone was heated under , it and associated organic matter may have been carbonized. In this case the sample is often usable. 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. If testing recrystallized shell is unavoidable, it is sometimes possible to identify the original shell material from a sequence of tests. It is also possible to test , an organic protein found in shell, but it constitutes only 1—2% of shell material. 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. A particular difficulty with dried peat is the removal of rootlets, which are likely to be hard to distinguish from the sample material. 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. Preparation and size Particularly for older samples, it may be useful to enrich the amount of 14 C in the sample before testing. This can be done with a thermal diffusion column. Once contamination has been removed, samples must be converted to a form suitable for the measuring technology to be used. Where gas is required, CO 2 is widely used. For samples to be used in , the carbon must be in liquid form; the sample is typically converted to. For , solid graphite targets are the most common, although gaseous CO 2 can also be used. The quantity of material needed for testing depends on the sample type and the technology being used. There are two types of testing technology: detectors that record radioactivity, known as beta counters, and accelerator mass spectrometers. For beta counters, a sample weighing at least 10 grams 0. Accelerator mass spectrometry is much more sensitive, and samples containing as little as 0. Measuring 14 C is now most commonly done with an accelerator mass spectrometer For decades after Libby performed the first radiocarbon dating experiments, the only way to measure the 14 C in a sample was to detect the radioactive decay of individual carbon atoms. In this approach, what is measured is the activity, in number of decay events per unit mass per time period, of the sample. In the late 1970s an alternative approach became available: directly counting the number of 14 C and 12 C atoms in a given sample, via accelerator mass spectrometry, usually referred to as AMS. For some time, beta counting methods were more accurate than AMS, but AMS is now more accurate and has become the method of choice for radiocarbon measurements. In addition to improved accuracy, AMS has two further significant advantages over beta counting: it can perform accurate testing on samples much too small for beta counting; and it is much faster — an accuracy of 1% can be achieved in minutes with AMS, which is far quicker than would be achievable with the older technology. Beta counting Libby's first detector was a of his own design. He converted the carbon in his sample to lamp black soot and coated the inner surface of a cylinder with it. This cylinder was inserted 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. Any interposing material would have interfered with the detection of radioactivity, since the beta particles emitted by decaying 14 C are so weak that half are stopped by a 0. Libby's method was soon superseded by gas , which were less affected by bomb carbon the additional 14 C created by nuclear weapons testing. These counters record bursts of ionization caused by the beta particles emitted by the decaying 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, 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. The other common technology used for measuring 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 14 C as they interact with a fluorescing agent added to the benzene. Like gas counters, liquid scintillation counters require shielding and anticoincidence counters. For both the gas proportional counter and liquid scintillation counter, what is measured is the number of beta particles detected in a given time period. Each measuring device is also 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 measured activity of the sample being dated to get the activity attributable solely to that sample's 14 C. In addition, a sample with a standard activity is measured, to provide a baseline for comparison. The ions are accelerated and passed through a stripper, which removes several electrons so that the ions emerge with a positive charge. The ions, which may have from 1 to 4 positive charges C + to C 4+ , depending on the accelerator design, 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 14 C stream, but since the volume of 12 C and 13 C, needed for calibration is too great for individual ion detection, counts are determined by measuring the electric current created in a. The large positive charge induced by the stripper forces molecules such as 13 CH, which has a weight close enough to 14 C to interfere with the measurements, to dissociate, so they are not detected. Most AMS machines also measure the sample's δ 13C , for use in calculating the sample's radiocarbon age. The use of AMS, as opposed to simpler forms of mass spectrometry, is necessary because of the need to distinguish the carbon isotopes from other atoms or molecules that are very close in mass, such as 14 N and 13 CH. As with beta counting, both blank samples and standard samples are used. Two different kinds of blank may be measured: a sample of dead carbon that has undergone no chemical processing, 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 which is being dated. Any 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 12 CH 2 or 13 CH. A 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. Calculations Main article: 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. 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. To determine this, a blank sample of old, or dead, carbon is measured, and a sample of known activity is measured. The additional samples allow errors such as background radiation and systematic errors in the laboratory setup to be detected and corrected for. The most common standard sample material is oxalic acid, such as the HOxII standard, 1,000 lb of which was prepared by the NIST in 1977 from French beet harvests. Both beta counting and AMS results have to be corrected for fractionation. Errors and reliability The reliability of the results can be improved by lengthening the testing time. For example, if counting beta decays for 250 minutes is enough to give an error of ± 80 years, with 68% confidence, then doubling the counting time to 500 minutes will allow a sample with only half as much 14 C to be measured with the same error term of 80 years. Radiocarbon dating is generally limited to dating samples no more than 50,000 years old, as samples older than that have insufficient 14 C to be measurable. Older dates have been obtained by using special sample preparation techniques, large samples, and very long measurement times. These techniques can allow measurement of dates up to 60,000 and in some cases up to 75,000 years before the present. Radiocarbon dates are generally presented with a range of one usually represented by the Greek letter sigma as 1σ on either side of the mean. However, a date range of 1σ represents only 68% confidence level, so the true age of the object being measured may lie outside the range of dates quoted. This was demonstrated in 1970 by an experiment run by the British Museum radiocarbon laboratory, in which weekly measurements were taken on the same sample for six months. The results varied widely though consistently with a of errors in the measurements , and included multiple date ranges of 1σ confidence that did not overlap with each other. The measurements included one with a range from about 4250 to about 4390 years ago, and another with a range from about 4520 to about 4690. Errors in procedure can also lead to errors in the results. If 1% of the benzene in a modern reference sample accidentally evaporates, scintillation counting will give a radiocarbon age that is too young by about 80 years. Calibration The stump of a very old bristlecone pine. Tree rings from these trees among others are used in building calibration curves. The calculations given above produce dates in radiocarbon years: i. 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. 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 led to the first such sequence: 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 by. Hans Suess used this data to publish the first calibration curve for radiocarbon dating in 1967. It was unclear for some time whether the wiggles were real or not, but they are now well-established. These short term fluctuations in the calibration curve are now known as de Vries effects, after. A calibration curve is used by taking the radiocarbon date reported by a laboratory, and reading across from that date on the vertical axis of the graph. The point where this horizontal line intersects the curve will give the calendar age of the sample on the horizontal axis. This is the reverse of the way the curve is constructed: a point on the graph is derived from a sample of known age, such as a tree ring; when it is tested, the resulting radiocarbon age gives a data point for the graph. The Northern hemisphere curve from INTCAL13. As of 2014 this is the most recent version of the standard calibration curve. The diagonal line shows where the curve would lie if radiocarbon ages and calendar ages were the same. Over the next thirty years many calibration curves were published using a variety of methods and statistical approaches. These were superseded by the INTCAL series of curves, beginning with INTCAL98, published in 1998, and updated in 2004, 2009, and 2013. The improvements to these curves are based on new data gathered from tree rings, , , plant , , and. The INTCAL13 data includes separate curves for the northern and southern hemispheres, as they differ systematically because of the hemisphere effect. The southern curve SHCAL13 is based on independent data where possible, and derived from the northern curve by adding the average offset for the southern hemisphere where no direct data was available. There is also a separate marine calibration curve, MARINE13. For a set of samples forming a sequence with a known separation in time, these samples form a subset of the calibration curve. The sequence can be compared to the calibration curve and the best match to the sequence established. Wiggle-matching can be used in places where there is a plateau on the calibration curve, and hence can provide a much more accurate date than the intercept or probability methods are able to produce. The technique is not restricted to tree rings; for example, a stratified sequence in New Zealand, known to predate human colonization of the islands, has been dated to 1314 AD ± 12 years by wiggle-matching. The wiggles also mean that reading a date from a calibration curve can give more than one answer: this occurs when the curve wiggles up and down enough that the radiocarbon age intercepts the curve in more than one place, which may lead to a radiocarbon result being reported as two separate age ranges, corresponding to the two parts of the curve that the radiocarbon age intercepted. For example, if a series of radiocarbon dates is taken from different levels in a stratigraphic sequence, Bayesian analysis can be used to evaluate dates which are outliers, and can calculate improved probability distributions, based on the prior information that the sequence should be ordered in time. When Bayesian analysis was introduced, its use was limited by the need to use mainframe computers to perform the calculations, but the technique has since been implemented on programs available for personal computers, such as OxCal. Reporting dates Several formats for citing radiocarbon results have been used since the first samples were dated. As of 2014, the standard format required by the journal is as follows. Calibrated 14 C dates are frequently reported as cal BP, cal BC, or cal AD, again with BP referring to the year 1950 as the zero date. Radiocarbon gives two options for reporting calibrated dates. 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. In addition, an article in Radiocarbon in 2014 about radiocarbon date reporting conventions recommends that information should be provided about sample treatment, including the sample material, pretreatment methods, and quality control measurements; that the citation to the software used for calibration should specify the version number and any options or models used; and that the calibrated date should be given with the associated probabilities for each range. Interpretation A key concept in interpreting radiocarbon dates is : what is the true relationship between two or more objects at an archaeological site? It frequently happens that a sample for radiocarbon dating can be taken directly from the object of interest, but there are also many cases where this is not possible. Metal grave goods, for example, cannot be radiocarbon dated, but they may be found in a grave with a coffin, charcoal, or other material which can be assumed to have been deposited at the same time. In these cases a date for the coffin or charcoal is indicative of the date of deposition of the grave goods, because of the direct functional relationship between the two. There are also cases where there is no functional relationship, but the association is reasonably strong: for example, a layer of charcoal in a rubbish pit provides a date which has a relationship to the rubbish pit. Contamination is of particular concern when dating very old material obtained from archaeological excavations and great care is needed in the specimen selection and preparation. As a tree grows, only the outermost tree ring exchanges carbon with its environment, so the age measured for a wood sample depends on where the sample is taken from. This means that radiocarbon dates on wood samples can be older than the date at which the tree was felled. In addition, if a piece of wood is used for multiple purposes, there may be a significant delay between the felling of the tree and the final use in the context in which it is found. One example is the Bronze Age at Withy Bed Copse, in England; the trackway was built from wood that had clearly been worked for other purposes before being re-used in the trackway. Another example is driftwood, which may be used as construction material. It is not always possible to recognize re-use. Other materials can present the same problem: for example, is known to have been used by some communities to waterproof baskets; the bitumen's radiocarbon age will be greater than is measurable by the laboratory, regardless of the actual age of the context, so testing the basket material will give a misleading age if care is not taken. A separate issue, related to re-use, is that of lengthy use, or delayed deposition. For example, a wooden object that remains in use for a lengthy period will have an apparent age greater than the actual age of the context in which it is deposited. Use outside archaeology Archaeology is not the only field to make use of radiocarbon dating. The ability to date minute samples using AMS has meant that palaeobotanists and palaeoclimatologists can use radiocarbon dating on pollen samples. Radiocarbon dates can also be used in geology, sedimentology, and lake studies, for example. Dates on organic material recovered from strata of interest can be used to correlate strata in different locations that appear to be similar on geological grounds. Dating material from one location gives date information about the other location, and the dates are also used to place strata in the overall geological timeline. The , the current geological epoch, begins about 11,700 years ago, when the Pleistocene ends. At , in Wisconsin, a fossil forest was discovered , and subsequent research determined that the destruction of the forest was caused by the Valders ice readvance, the last southward movement of ice before the end of the Pleistocene in that area. Before the advent of radiocarbon dating, the fossilized trees had been dated by correlating sequences of annually deposited layers of sediment at Two Creeks with sequences in Scandinavia. This led to estimates that the trees were between 24,000 and 19,000 years old, and hence this was taken to be the date of the last advance of the before its final retreat marked the end of the Pleistocene in North America. In 1952 Libby published radiocarbon dates for several samples from the Two Creeks site and two similar sites nearby; the dates were averaged to 11,404 BP with a standard error of 350 years. This result was uncalibrated, as the need for calibration of radiocarbon ages was not yet understood. Further results over the next decade supported an average date of 11,350 BP, with the results thought to be most accurate averaging 11,600 BP. There was initial resistance to these results on the part of , the who had worked on the Scandinavian varve series, but his objections were eventually discounted by other geologists. In the 1990s samples were tested with AMS, yielding uncalibrated dates ranging from 11,640 BP to 11,800 BP, both with a standard error of 160 years. Subsequently, a sample from the fossil forest was used in an interlaboratory test, with results provided by over 70 laboratories. These tests produced a median age of 11,788 ± 8 BP 2σ confidence which when calibrated gives a date range of 13,730 to 13,550 cal BP. The Two Creeks radiocarbon dates are now regarded as a key result in developing the modern understanding of North American glaciation at the end of the Pleistocene. Dead Sea Scrolls Part of the Great Isaiah Scroll, one of the Dead Sea Scrolls In 1947, were discovered in caves near the that proved to contain writing in and , most of which are thought to have been produced by the , a small Jewish sect. These scrolls are of great significance in the study of Biblical texts because many of them contain the earliest known version of books of the Hebrew bible. A sample of the linen wrapping from one of these scrolls, the , was included in a 1955 analysis by Libby, with an estimated age of 1,917 ± 200 years. Based on an analysis of the writing style, estimates were made of the age of 21 of the scrolls, and samples from most of these, along with other scrolls which had not been palaeographically dated, were tested by two AMS laboratories in the 1990s. The results ranged in age from the early 4th century BC to the mid 4th century AD. In all but two cases the scrolls were determined to be within 100 years of the palaeographically determined age. The Isaiah scroll was included in the testing and was found to have two possible date ranges at a 2σ confidence level, because of the shape of the calibration curve at that point: there is a 15% chance that it dates from 355—295 BC, and an 84% chance that it dates from 210—45 BC. Subsequently, these dates were criticized on the grounds that before the scrolls were tested, they had been treated with modern castor oil in order to make the writing easier to read; it was argued that failure to remove the castor oil sufficiently would have caused the dates to be too young. Multiple papers have been published both supporting and opposing the criticism. Impact Soon after the publication of Libby's 1949 paper in Science, universities around the world began establishing radiocarbon-dating laboratories, and by the end of the 1950s there were more than 20 active 14 C research laboratories. It quickly became apparent that the principles of radiocarbon dating were valid, despite certain discrepancies, the causes of which then remained unknown. In the words of anthropologist R. It provides more accurate dating within sites than previous methods, which usually derived either from stratigraphy or from typologies e. The advent of radiocarbon dating may even have led to better field methods in archaeology, since better data recording leads to firmer association of objects with the samples to be tested. These improved field methods were sometimes motivated by attempts to prove that a 14 C date was incorrect. Taylor also suggests that the availability of definite date information freed archaeologists from the need to focus so much of their energy on determining the dates of their finds, and led to an expansion of the questions archaeologists were willing to research. For example, from the 1970s questions about the evolution of human behaviour were much more frequently seen in archaeology. The dating framework provided by radiocarbon led to a change in the prevailing view of how innovations spread through prehistoric Europe. Researchers had previously thought that many ideas spread by diffusion through the continent, or by invasions of peoples bringing new cultural ideas with them. As radiocarbon dates began to prove these ideas wrong in many instances, it became apparent that these innovations must sometimes have arisen locally. More broadly, the success of radiocarbon dating stimulated interest in analytical and statistical approaches to archaeological data. Taylor has also described the impact of AMS, and the ability to obtain accurate measurements from very small samples, as ushering in a third radiocarbon revolution. Occasionally, radiocarbon dating techniques date an object of popular interest, for example the , a piece of linen cloth thought by some to bear an image of Jesus Christ after his crucifixion. Three separate laboratories ; the results pointed to 14th-century origins, raising doubts about the shroud's authenticity as an alleged 1st-century relic. Researchers have studied other radioactive isotopes created by cosmic rays to determine if they could also be used to assist in dating objects of archaeological interest; such isotopes include , , , , and. With the development of AMS in the 1980s it became possible to measure these isotopes precisely enough for them to be the basis of useful dating techniques, which have been primarily applied to dating rocks. Naturally occurring radioactive isotopes can also form the basis of dating methods, as with , , and. Other dating techniques of interest to archaeologists include , , , and , as well as techniques that depend on annual bands or layers, such as , , and chronology. However, this pathway is estimated to be responsible for less than 0. This effect is accounted for during calibration by using a different marine calibration curve; without this curve, modern marine life would appear to be 400 years old when radiocarbon dated. Similarly, the statement about land organisms is only true once fractionation is taken into account. For older datasets an offset of about 50 years has been estimated. Journal of the Franklin Institute. Glasgow, Scotland UK: University of Glasgow. Retrieved 11 December 2017. Journal of Research of the National Institute of Standards and Technology. Memoirs of the Society for American Archaeology 8 : 1—19. Retrieved 9 December 2017. Retrieved 9 December 2017. Warren; Blackwell, Paul G. US Department of State. Retrieved 2 February 2015. 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