Radiocarbon dating, principles

¹⁴C dating is a radiometric dating method that uses the naturally occurring isotope carbon-14 to determine the age of carbonaceous materials up to ca. 60,000 years. Within archaeology it is considered an absolute dating technique. The technique was discovered by Willard Frank Libby and his colleagues in 1949. In 1960, Libby was awarded the Nobel Prize in chemistry for carbon dating.

Basics
Carbon has two stable, nonradioactive isotopes: carbon-12 (12C), and carbon-13 (13C). In addition, there are tiny amounts of the unstable isotope carbon-14 (14C) on Earth. Carbon-14 has a half-life of just under 6000 years and would have long ago vanished from Earth were it not for the unremitting cosmic ray impacts on nitrogen in the Earth's atmosphere, which forms more of the isotope. When cosmic rays enter the atmosphere, they undergo various transformations, including the production of neutrons. The resulting neutrons participate in the following reaction:

n + 14N > 14C + 1H

This reaction is relatively common, as nitrogen constitutes nearly 80% of Earth's atmosphere. The highest rate of carbon-14 production takes place at altitudes of 30,000 to 50,000 feet, and at higher geomagnetic latitudes, but the carbon-14 spreads evenly throughout the atmosphere and reacts with oxygen to form carbon dioxide. Carbon dioxide also permeates the oceans, dissolving in the water. For approximate analysis it is assumed that the cosmic ray flux is constant over long periods of time; thus carbon-14 could be assumed to be continuously produced at a constant rate and therefore that the proportion of radioactive to non-radioactive carbon throughout the Earth's atmosphere and surface oceans is constant: ca. 1 ppt (600 billion atoms/mole). For more accurate work, the temporal variation of the cosmic ray flux can be compensated for with calibration curves. If these curves are used, their accuracy and shape will be the limiting factors in the determination of the radiocarbon age range of a given sample.

Measurements are traditionally made by counting the radioactive decay of individual carbon atoms by gas proportional counting or by Liquid scintillation counting, but this is relatively insensitive and subject to relatively large statistical uncertainties for small samples (below about 1g carbon). If there is little carbon-14 to begin with, a half-life that long means that very few of the atoms will decay while their detection is attempted (4 atoms/s/mole just after death, hence e.g. 1 atom/s/mole after 10 000 years). Sensitivity has since been greatly increased by the use of accelerator-based mass-spectrometric (AMS)techniques, where all the 14C atoms can be counted directly, rather than only those decaying during the counting interval allotted for each analysis. The AMS technique allows to date samples containing only a few mg of carbon.

Raw radiocarbon measurements are usually reported as 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.

Carbon dating labs generally report an uncertainty, e.g., 3000+-30BP indicates a standard deviation of 30 radiocarbon years. Traditionally this includes only the statistical counting uncertainty and some labs supply an "error multiplier" that can be multiplied by the uncertainty to account for other sources of error in the measuring process. Additional error is likely to arise from the nature and collection of the sample itself, e.g., a tree may accumulate carbon over a significant period of time. Such wood, turned into an artifact some time after the death of the tree, will reflect the date of the carbon in the wood.

The current maximum radiocarbon age limit lies in the range between 58,000 and 62,000 years. This limit is encountered when the radioactivity of the residual 14C in a sample is too low to be distinguished from the background radiation. The K-Ar and uranium decay series are used in dating older objects (see Radiometric dating).

Calibration
The raw BP date cannot be used directly as a calendar date, because the assumption that the level of 14C absorption remains constant does not hold true in practice. The level is maintained by high energy particles interacting with the earth's upper atmosphere, which may be affected by changes in the earth's magnetic field or in the cosmic ray background, e.g. variations caused by solar storms. In addition there are substantial reservoirs of carbon in organic matter, the ocean, ocean sediments (see methane hydrate), and sedimentary rocks; and changing climate can sometimes disrupt the carbon flow between these reservoirs and the atmosphere. The level has also been affected by human activities -- it was almost doubled for a short period due to atomic bomb tests in the 1950s and 1960s and has been reduced by the release of large amounts of CO2 from ancient organic sources where 14C is not present -- the fossil fuels used in industry and transportation.

The BP dates are therefore calibrated to give calendar dates. Standard calibration curves are available, based on comparison of radiocarbon dates with other methods such as examination of tree growth rings (dendrochronology), ice cores, deep ocean sediment cores, lake sediment varves, coral samples, and speleothems (cave deposits).

The difference between the Julian calendar and the Gregorian calendar can be ignored, because it's insignificant compared to the measurement uncertainty.

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 11000 to 10000 radiocarbon years BP, which is believed to be associated with changing ocean circulation during the Younger Dryas period. The accuracy of radiocarbon dating is lower for samples originating from such plateau periods.

It has been noted that the plateau itself can be used as a time marker when it appears in a time series.

Libby vs Cambridge half-life

Carbon dating was developed by a team led by Willard Libby. Originally a Carbon-14 half-life of 5568+-30 years was used, which is now known as the Libby half-life. Later a more accurate figure of 5730+-40 years was measured, which is known as the Cambridge half-life. However laboratories continue to use the Libby figure to avoid confusion. An uncalibrated dating using the Libby figure could be improved by multiplying by the ratio of these numbers (approximately 1.03), but this is usually unnecessary since the adjustment is included in modern calibration curves.

Impact on archaeology

Carbon dating had a large impact on archaeology, particularly on many of archaeology's theoretical assumptions until this tool was introduced after World War II. In effect, radiocarbon dating established that many artifacts are now known to be far older than previously thought, and thus going back to earlier ages than otherwise could have been if they had been only the inspired and diffused products of the Near Eastern civilization. Therefore, the notion that the ancient Near East was the fount of global human civilization can no longer hold true. Clearly, various centers of civilization arose independently of one another even if the Near Eastern one remains the oldest on record.

Radiocarbon dating principles

How is C14 used for dating the past?

¹⁴C (or Radiocarbon) is the radioactive isotope of the common element carbon. It is generally formed in the upper atmosphere by the interaction of cosmic rays with nitrogen gas (N₂). The radiocarbon is oxidised to carbon dioxide (or CO₂) and is instantantly mixed throughout the atmosphere. As carbon dioxide is used as the basis for photosynthesis, the radiocarbon is integrated into all living things. As far as plant or animal dies, the radiocarbon decays.

It is known that half-life of radiocarbon is 5730 years. At radiocarbon dating laboratory could be measured the amount of remaining radiocarbon relative to the stable one which don’t change in concentration. Back-calculation to the time of death could be done using the known radiocarbon half-life (T_1/2).

Radiocarbon content in the earth atmosphere is varying in time due to past changes in the strength of the earth’s magnetic field, the strength of the sun and changes in the carbon cycle. It cause that the one radiocarbon year does not equal one calendar year. Therefore radiocarbon age should be converted to calendar age using one of several available software packages CALIB 4, http://www.arch.ox.ac.uk/rlaha/ : OxCal, CalPal.

Aspects of studying of radiocarbon and radiocarbon dating are well described in paper of Wally Levchenko (in Russian) presented at: http://hbar.phys.msu.ru/