Radiocarbon dating

Radiocarbon dating (or simply carbon dating) is a technique that uses the decay of carbon-14 (¹⁴C) to estimate the age of organic materials, such as wood and leather, up to about 58,000 to 62,000 years. Carbon dating was presented to the world by Willard Libby in 1949, for which he was awarded the Nobel Prize in Chemistry. Since its introduction it has been used to date many well-known items, including samples of the Dead Sea Scrolls, the Shroud of Turin, enough Egyptian artifacts to supply a chronology of Dynastic Egypt, and Ötzi the Iceman.

The dating method is based on the fact that carbon is found in various forms, including the main stable isotope (¹²C) and an unstable isotope (¹⁴C). Through photosynthesis, plants absorb both forms from carbon dioxide in the atmosphere. When an organism dies, it contains a ratio of ¹⁴C to ¹²C, but, as the ¹⁴C decays with no possibility of replenishment, the ratio decreases at a regular rate (the half-life of ¹⁴C). The measurement of ¹⁴C decay provides an indication of the age of any carbon-based material (a raw radiocarbon age). However, over time there are small fluctuations in the ratio of ¹⁴C to ¹²C in the atmosphere, fluctuations that have been noted in natural records of the past, such as sequences of tree rings and cave deposits. These records allow for the fine-tuning, or calibration, of the indications derived from measuring the carbon ratio. A raw radiocarbon age, once calibrated, yields a calendar date.

One of the most frequent uses of radiocarbon dating is to estimate the age of organic remains from archaeological sites.

Inventors of the method

The technique of radiocarbon dating was developed by Willard Libby and his colleagues at the University of Chicago in 1949. Emilio Segrè asserted in his autobiography that Enrico Fermi suggested the concept to Libby at a seminar in Chicago that year. Libby estimated that the steady state radioactivity concentration of exchangeable carbon-14 would be about 14 disintegrations per minute (dpm) per gram.

In 1960, Libby was awarded the Nobel Prize in chemistry for this work. He demonstrated the accuracy of radiocarbon dating by accurately estimating the age of wood from a series of samples for which the age was known, including an ancient Egyptian royal barge of 1850 BCE.

Physical and chemical background

1: Formation of carbon-14
2: Decay of carbon-14
3: The equation is for living organisms, and the inequality is for dead organisms, in which the ¹⁴C then decays (See 2).

Carbon has two stable, nonradioactive isotopes: carbon-12 (¹²C), and carbon-13 (¹³C). In addition, there are trace amounts of the unstable radioisotope carbon-14 (¹⁴C) on Earth. Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbon-14 in a sample is halved over the course of 5,730 years due to radioactive decay.

The Carbon-14 isotope would vanish from Earth's atmosphere in less than a million years were it not for the unremitting influx of cosmic rays interacting with molecules of nitrogen (N₂) or perhaps rather single nitrogen atoms (free nitrogen atoms, N), in the stratosphere, which constantly replenishes this isotope.

The high energy neutrons resulting from cosmic ray particle interactions with Earth's atmosphere participate in the following nuclear reaction on the atoms of nitrogen molecules (N₂) in the stratosphere, where p is a proton:

$n + \mathrm{^{14}_{7}N} \rightarrow \mathrm{^{14}_{6}C} + p$

The highest rate of carbon-14 production takes place at altitudes of 9 to 15 km (30,000 to 50,000 ft), and at high geomagnetic latitudes, where C-14 then reacts relatively rapidly with oxygen to form carbon dioxide (CO₂). The carbon dioxide containing the C-14 species spreads evenly throughout the atmosphere and the oceans, reacting with water to produce carbonic acid (CO₂ + H₂O → H₂CO₃).

Approximate dating

For approximate analysis it is assumed that the cosmic ray flux is constant over long periods of time; thus carbon-14 is produced at a constant rate and the proportion of radioactive to non-radioactive carbon is constant: ca. 1 part per trillion (600 billion atoms/mole).

Accurate dating

In 1958, Hessel de Vries showed that the concentration of carbon-14 in the atmosphere varies with both time and locality. In order to obtain the most accurate results in carbon dating, calibration curves must be employed.

Other mechanisms of producing C-14

¹⁴C can also be produced at ground level at a rate of 1 x 10⁻⁴ atoms per gram per second, which is not considered significant enough to impact on dating without a known other source of neutrons.

C-14 uptake in living organisms

Plants and all other photosynthesizing organisms (algae, some bacteria, some protists) use atmospheric carbon dioxide in the photosynthesis. The products of photosynthesis are ingested by animals. At the same time, all living organisms fueled by carbon molecules release carbon dioxide in the process of cellular respiration.

The decay of organic matter

This means that almost all living organisms are constantly exchanging carbon-14 atoms with their environment. This exchange stops when the organism dies. Nevertheless, release of CO₂ from the organism continues, by processes of molecular decay (disintegration). These processes, however, do not change the fraction of C-14 relative to the other two species of carbon (C-12 and C-13) in decaying organic matter.

Radioactive decay of C-14

It is a process of radioactive decay (i.e. beta decay) that gradually decreases the fraction of the C-14 isotope relative to the other two isotopes of carbon. The half-life of C-14 is 5,730 ± 40 years. This means that the fraction of C-14 relative to each of the two other species of carbon (C-12 and C-13) declines by half in approximately 5,730 years. The equation for the radioactive decay of C-14 involves the production of both a standard nitrogen atom species (N-14), an electron (e−, also called a beta-particle, β-particle ), and a subatomic particle called an electron antineutrino (ν
e):

$\mathrm{~^{14}_{6}C}\rightarrow\mathrm{~^{14}_{7}N}+ e^{-} + \bar{\nu}_e$

Computation of ages and dates

The number of decays per time period is proportional to the current number of radioactive atoms. This is expressed by the following differential equation, where N is the number of radioactive atoms and λ is a positive number called the decay constant:

$\frac{dN}{dt} = -\lambda N.$

As the solution to this equation, the number of radioactive atoms N can be written as a function of time:

$N(t) = N_0e^{-\lambda t}\,$,

which describes an exponential decay over a timespan t with an initial condition of N₀ radioactive atoms at t = 0. Canonically, t is 0 when the decay started. In this case, N₀ is the initial number of ¹⁴C atoms when the decay started.

For radiocarbon dating of a once living organism, the initial ratio of ¹⁴C atoms to the sum of all other carbon atoms at the point of the organism's death, and hence the point when the decay started, is approximately the same ratio as in the atmosphere at that time.

Two characteristic times can be defined:

• mean- or average-life: mean or average time each radiocarbon atom spends in a given sample until it decays
• half-life: time required for half the number of radiocarbon atoms in a given sample to decay

It can be shown that:

$t_{avg} \,$ = $\frac{1}{\lambda}$ = radiocarbon mean- or average-life = 8,033 years (Libby value)

$t_\frac{1}{2} \,$ = $t_{avg} \cdot \ln 2$ = radiocarbon half-life = 5,568 years (Libby value)

Notice that dates are customarily given in years BP, which implies t(BP) = –t because the time arrow for dates runs in reverse direction from the time arrow for the corresponding ages. From these considerations and the above equation, it results:

For a raw radiocarbon date:

$t(BP) = \frac{1}{\lambda} {\ln \frac{N}{N_0}}$

and for a raw radiocarbon age:

$t(BP) = -\frac{1}{\lambda} {\ln \frac{N}{N_0}}$

After replacing values, the raw radiocarbon age becomes any of the following equivalent formulae:

using logs base e and the average life:

$t(BP) = -t_{avg}\cdot \ln{\frac{N}{N_0}}$

and

using logs base 2 and the half-life:

$t(BP) = -t_\frac{1}{2}\cdot \log_2 \frac{N}{N_0}$

Wiggle matching uses the non-linear relationship between the ¹⁴C age and calendar age to match the shape of a series of closely sequentially spaced ¹⁴C dates with the ¹⁴C calibration curve.

Methods

Radiocarbon dating of soil organic matter (SOM) is problematic because SOM accumulates from heterogeneous sources. Fractionation of the heterogeneous organic carbon sources limits the application and interpretation of carbon dating of SOM. To remedy the inconsistencies in previous methods of carbon-14 dating of SOM, a high-temperature, pyrolysis-combustion technique was used. A combustion system used by the Illinois State Geological Survey (ISGS), under vacuum, fractions the SOM into a volatile and residual fraction. The volatile residue contains low-molecular-weight organic compounds, whereas, the residual residue contains high- molecular-weight organic compounds.

Preceding extraction of carbon dioxide from SOM samples, pretreatment is necessary. Each sample must be pretreated with heated 2 N HCl followed by rinsing with deionized water and vacuum filtration. Drying of the sample in a furnace will reduce the accumulation of water within the system.

The combustion system utilized by the ISGS consists of an inner and an outer quartz tube. To ensure pure CO₂ production, a vacuum of -25 psi must be established. During volatile pyrolysis, the inner tube is purged with argon while the outer tube is purged with oxygen. As the oxygen is purged through the outer tube, the volatile compounds released from the sample are carried by the argon into the outer tube where they are oxidized at 800 degree Celsius to form carbon dioxide. The CO₂ and other gases produced from the volatile fraction are then passed through a cupric oxide furnace and wash traps including 0.5 N AgNO₃ solution and a solution of 7.3 g Na₂Cr₂O₇ in 50% H₂SO₄ for purification purposes. After the filtration, the CO₂ is then passed through a dry ice-isopropanol trap to trap the water and the CO₂ is finally collected in liquid nitrogen traps. The end of the volatile fraction is marked by the disappearance of the flame in the ignition furnace. Once the purified CO₂ is transferred, the residual pyrolysis begins with the purging of the inner tube with oxygen and outer tube with argon. In pyrolysis of large samples, a stainless steel chamber and a crucible furnace connected to the inner tube of the combustion system must be used.

The purified CO₂ is then converted to benzene for liquid scintillation spectrometry.

Measurements and scales

The use of accelerator mass spectrometers can improve the sensitivity of radiocarbon dating.

Measurements are traditionally made by counting the radioactive decay of individual carbon atoms by gas proportional counting or by liquid scintillation counting. For samples of sufficient size (several grams of carbon), this method is still widely used in the 2000s. Among others, all the tree ring samples used for the calibration curves (see below) were determined by these counting techniques. Such decay counting, however, is relatively insensitive and subject to large statistical uncertainties for small samples. When there is little carbon-14 to begin with, the long radiocarbon half-life means that very few of the carbon-14 atoms will decay during the time allotted for their detection, resulting in few disintegrations per minute.

The sensitivity of radiocarbon dating has been greatly increased by the use of accelerator mass spectrometry (AMS). With this technique ¹⁴C atoms can be detected and counted directly, as opposed to detecting radioactive decay. Radiocarbon AMS samples are prepared by completely burning the sample, collecting the resulting carbon dioxide, and reducing it to a solid carbon target for sputtering atomic carbon ions into the mass spectrometer. This method allows dating samples containing only a few milligrams of carbon.

Raw radiocarbon ages (i.e., those not calibrated) are usually reported in "years Before Present" (BP). This is the number of radiocarbon years before 1950, based on a nominal (and assumed constant – see "calibration" below) level of carbon-14 in the atmosphere equal to the 1950 level. These raw dates are also based on a slightly incorrect historic value for the radiocarbon half-life. Such value is used for consistency with earlier published dates (see "Radiocarbon half-life" below). See the section on computation for the basis of the calculations.

Radiocarbon dating laboratories generally report an uncertainty for each date. For example, 3000 ± 30 BP indicates a standard deviation of 30 radiocarbon years. Traditionally, this included only the statistical counting uncertainty. However, some laboratories supplied an "error multiplier" that could be multiplied by the uncertainty to account for other sources of error in the measuring process. More recently, laboratories try to quote the overall uncertainty, which is determined from control samples of known age and verified by international intercomparison exercises. In 2008, a typical uncertainty better than ±40 radiocarbon years can be expected for samples younger than 10,000 years. This, however, is only a small part of the uncertainty of the final age determination (see section Calibration below).

Samples older than the upper age-limit cannot be dated because the small number of remaining intrinsic ¹⁴C atoms will be obscured by the ¹⁴C background atoms introduced into the samples while they still resided in the environment, during sample preparation, or in the detection instrument. As of 2007, the limiting age for a 1 milligram sample of graphite is about ten half-lives, approximately 60,000 years. This age is derived from that of the calibration blanks used in an analysis, whose ¹⁴C content is assumed to be the result of contamination during processing (as a result of this, some facilities will not report an age greater than 60,000 years for any sample).

A variety of sample processing and instrument-based constraints have been postulated to explain the upper age-limit. To examine instrument-based background activities in the AMS instrument of the W. M. Keck Carbon Cycle Accelerator Mass Spectrometry Laboratory of the University of California, a set of natural diamonds were dated. Natural diamond samples from different sources within rock formations with standard geological ages in excess of 100 Ma yielded¹⁴C apparent ages 64,920 ± 430 BP to 80,000 ± 1100 BP as reported in 2007.

Calibration

The need for calibration

Calibration curve for the radiocarbon dating scale. Data sources: Reimer, P.J., et al. (1998). Samples with a real date more recent than AD 1950 are dated and/or tracked using the N- & S-Hemisphere graphs. See following figure.

Atmospheric ¹⁴C, New Zealand and Austria. The New Zealand curve is representative for the Southern Hemisphere, the Austrian curve is representative for the Northern Hemisphere. Atmospheric nuclear weapon tests almost doubled the concentration of ¹⁴C in the Northern Hemisphere.

Dates may be expressed as either uncalibrated or calibrated years (the latter abbreviated as cal or cal.). A raw BP date cannot be used directly as a calendar date, because the level of atmospheric ¹⁴C has not been strictly constant during the span of time that can be radiocarbon dated, producing radiocarbon plateaus. The level is affected by variations in the cosmic ray intensity, which is, in turn, affected by variations in the Earth's magnetosphere. In addition, there are substantial reservoirs of carbon in organic matter, the ocean, ocean sediments (see methane hydrate), and sedimentary rocks. Changes in the Earth's climate can affect the carbon flows between these reservoirs and the atmosphere, leading to changes in the atmosphere's ¹⁴C fraction.

As the graph to the right shows, the uncalibrated, raw BP date underestimates the actual age by 3,000 years at 15000 BP. The underestimation generally runs about 10% to 20%, with 3% of that underestimation attributable to the use of 5,568 years as the half-life of ¹⁴C instead of the more accurate 5,730 years. To maintain consistency with a large body of published research, the out-of-date half-life figure is still used in all radiocarbon measurements.

An uncalibrated radiocarbon date is abbreviated as ¹⁴C yr BP or C14 yr BP or simply BP, although the last is ambiguously also sometimes used with dating methods other than radiocarbon, such as stratigraphy. A calibrated, or calendar date, is abbreviated as cal yr BP or cal BP, interpretable as "calibrated years before present" or "calendar years before present". In academic practice calibrated dates are generally presented along with their source uncalibrated dates, as the accuracy of the presently established calibration curve varies by time period.

The standard radiocarbon calibration curve is continuously being refined on the basis of new data gathered from tree rings, coral, and other studies. In addition to the natural variation of the curve throughout time, the carbon-14 level has also been affected by human activities in recent centuries. From the beginning of the industrial revolution in the 18th century to the 1950s, the fractional level of ¹⁴C decreased because of the admixture of CO₂ into the atmosphere from the combustion of fossil fuels. This decline, which is known as the Suess effect, also affects the ¹³C isotope. However, atmospheric ¹⁴C was almost doubled during the 1950s and 1960s, due to atmospheric atomic bomb tests.

Calibration methods

The raw radiocarbon dates, in BP years, are calibrated to give calendar dates. Standard calibration curves are available, based on comparison of radiocarbon dates of samples that can be dated independently by other methods such as examination of tree growth rings (dendrochronology), deep ocean sediment cores, lake sediment varves, coral samples, and speleothems (cave deposits).

The calibration curves can vary significantly from a straight line, so comparison of uncalibrated radiocarbon dates (e.g., plotting them on a graph or subtracting dates to give elapsed time) is likely to give misleading results. There are also significant plateaus in the curves, such as the one from 11,000 to 10,000 radiocarbon years BP, which is believed to be associated with changing ocean circulation during the Younger Dryas period. Over the historical period (from 0 to 10,000 years BP), the average width of the uncertainty of calibrated dates was found to be 335 years - in well-behaved regions of the calibration curve the width decreased to about 113 years, while in ill-behaved regions it increased to a maximum of 801 years. Significantly, in the ill-behaved regions of the calibration curve, increasing the precision of the measurements does not have a significant effect on increasing the accuracy of the dates.

The 2004 version of the calibration curve extends back quite accurately to 26,000 years BP. Any errors in the calibration curve do not contribute more than ±16 years to the measurement error during the historic and late prehistoric periods (0–6,000 yrs BP) and no more than ±163 years over the entire 26,000 years of the curve, although its shape can reduce the accuracy as mentioned above.

In late 2009, the journal Radiocarbon announced agreement on the INTCAL09 standard, which extends a more accurate calibration curve to 50,000 years. The results of research on varves in Lake Suigetsu, Japan, which was announced in 2012, realised this aim. "In most cases, the radiocarbon levels deduced from marine and other records have not been too far wrong. However, having a truly terrestrial record gives us better resolution and confidence in radiocarbon dating," said Bronk Ramsey. "It also allows us to look at the differences between the atmosphere and oceans and study the implications for our understanding of the marine environment as part of the global carbon cycle."

History

Carbon dating was developed by American scientist Willard Libby and his team at the University of Chicago. Libby calculated the half-life of carbon-14 as 5,568 ± 30 years, a figure now known as the Libby half-life. Following a conference at the University of Cambridge in 1962, a more accurate figure of 5,730 ± 40 years was agreed upon, which was based on more recent experimental data (this figure is now known as the Cambridge half-life).

The chairman of the Cambridge conference, Harry Godwin, wrote to the scientific journal Nature, recommending that the Libby half-life continue to be used for the time being, as the Cambridge figure might itself be improved by future experiments. Laboratories today continue to use the Libby figure to avoid inconsistencies with earlier publications, although the Cambridge half-life is still the most accurate figure that is widely known and accepted. However, the inaccuracy of the Libby half-life is not relevant if calibration is applied: the mathematical term representing the half-life is canceled out as long as the same value is used throughout a calculation.

Carbon exchange reservoir

Libby's original exchange reservoir hypothesis assumed that the exchange reservoir is constant all over the world. The calibration method also assumes that the temporal variation in ¹⁴C level is global, such that a small number of samples from a specific year are sufficient for calibration. However, since Libby's early work was published (1950 to 1958), latitudinal and continental variations in the carbon exchange reservoir have been observed by Hessel de Vries (1958; as reviewed by Lerman et al.). Subsequently, methods have been developed that allow the correction of these so-called reservoir effects, including:

• When CO₂ is transferred from the atmosphere to the oceans, it initially shares the ¹⁴C concentration of the atmosphere. However, turnaround times of CO₂ in the ocean are similar to the half-life of ¹⁴C (making ¹⁴C also a dating tool for ocean water). Marine organisms feed on this "old" carbon, and thus their radiocarbon age reflects the time of CO₂ uptake by the ocean rather than the time of death of the organism. This marine reservoir effect is partly handled by a special marine calibration curve, but local deviations of several hundred years exist.

• Erosion and immersion of carbonate rocks (which are generally older than 80,000 years and so shouldn't contain measurable ¹⁴C) causes an increase in ¹²C and ¹³C in the exchange reservoir, which depends on local weather conditions and can vary the ratio of carbon that living organisms incorporate. This is believed to be negligible for the atmosphere and atmosphere-derived carbon, since most erosion will flow into the sea. The atmospheric ¹⁴C concentration may differ substantially from the concentration in local water reservoirs. Eroded from CaCO₃ or organic deposits, old carbon may be assimilated easily and provide diluted ¹⁴C carbon into trophic chains. So the method is less reliable for such materials, as well as for samples derived from animals with such plants in their food chain.

• Volcanic eruptions eject large amounts of carbon into the air, causing an increase in ¹²C and ¹³C in the exchange reservoir and can vary the exchange ratio locally. This explains the often irregular dating achieved in volcanic areas.

• The earth is not affected evenly by cosmic radiation, the magnitude of the radiation at a particular place depends on both its altitude and the local strength of the earth's magnetic field strength, thus causing minor variation in the local ¹⁴C production. This is accounted for by having calibration curves for different locations of the globe. However, this could not always be performed, as tree rings for calibration were only recoverable from certain locations in 1958. The rebuttals by Münnich et al. and by Barker both maintain that, while variations of carbon-14 exist, they are about an order of magnitude smaller than those implied by Crowe's calculations.

These effects were first confirmed when samples of wood from around the world, which all had the same age (based on tree ring analysis), showed deviations from the dendrochronological age. Calibration techniques based on tree-ring samples have contributed to increased accuracy since 1962, when they were accurate to 700 years at worst.

Speleothem studies extend ¹⁴C calibration

Speleothems (such as stalagmites) are calcium carbonate deposits that form from drips in limestone caves. Individual speleothems can be tens of thousands of years old. Scientists are attempting to extend the record of atmospheric carbon-14 by measuring radiocarbon in speleothems which have been independently dated using uranium-thorium dating. These results are improving the calibration for the radiocarbon technique and extending its usefulness to 45,000 years into the past. Initial results from a cave in the Bahamas suggested a peak in the amount of carbon-14 that was twice as high as modern levels. A recent study does not reproduce this extreme shift and suggests that analytical problems may have produced the anomalous result.

Examples

• Ancient footprints of Acahualinca
• Chauvet Cave
• The Dead Sea Scrolls
• Dolaucothi
• Eve of Naharon
• Haraldskær Woman
• Kennewick Man
• Shroud of Turin
• Skeleton Lake
• Thera eruption
• Vinland map

See also

• Arizona Accelerator Mass Spectrometry Laboratory
• Carbon sequestration
• Cosmogenic isotopes
• Discussion of half-life and average-life or mean-lifetime
• Environmental isotopes
• Old wood

Further reading

• Bowman, Sheridan (1990). Interpreting the Past: Radiocarbon Dating. Berkeley: University of California Press. ISBN 0-520-07037-2. 
• Currie, L. (2004). "The Remarkable Metrological History of Radiocarbon Dating II". J. Res. Natl. Inst. Stand. Technol. 109: 185–217. 
• Friedrich, M.; et al. (2004). "The 12,460-Year Hohenheim Oak and Pine Tree-Ring Chronology from Central Europe—a Unique Annual Record for Radiocarbon Calibration and Paleoenvironment Reconstructions". Radiocarbon 46: 1111–1122. 
• Gove, H. E. (1999) From Hiroshima to the Iceman. The Development and Applications of Accelerator Mass Spectrometry. Bristol: Institute of Physics Publishing.
• Kovar, Anton J. (1966). "Problems in Radiocarbon Dating at Teotihuacan". American Antiquity (Society for American Archaeology) 31 (3): 427–430. doi:10.2307/2694748. JSTOR 2694748. 
• Lorenz, R. D.; Jull, A. J. T.; Lunine, J. I.; Swindle, T. (2002). "Radiocarbon on Titan". Meteoritics and Planetary Science 37 (6): 867–874. Bibcode:2002M&PS...37..867L. doi:10.1111/j.1945-5100.2002.tb00861.x. 
• Mook, W. G.; van der Plicht, J. (1999). "Reporting ¹⁴C activities and concentrations". Radiocarbon 41: 227–239. 
• Weart, S. (2004) The Discovery of Global Warming - Uses of Radiocarbon Dating.
• Willis, E.H. (1996) Radiocarbon dating in Cambridge: some personal recollections. A Worm's Eye View of the Early Days.

External links

• Radiocarbon - The main international journal of record for research articles and date lists relevant to 14C
• C14dating.com - General information on Radiocarbon dating
• calib.org - Calibration program, Marine Reservoir database, and bomb calibration
• NOSAMS: National Ocean Sciences Accelerator Mass Spectrometry Facility at the Woods Hole Oceanographic Institution
• Discussion of calibration (from U Oxford)
• Several calibration programs can be found at www.radiocarbon.org
• CalPal Online (Cologne Radiocarbon Calibration & Paleoclimate Research Package)
• OxCal program (Oxford Calibration)
• Fairbanks' Radiocarbon Calibration program (for prior to 12400 BP)
• Notes on radiocarbon dating, including movies illustrating the atomic physics (from UC Santa Barbara)
• Carbon Dating-How it works?
• How is physics used in archaeology? (from physics.org)