Radiocarbon Dating Principles
A summary by Richard Morlan.
What is radiocarbon?
About 75 years ago, Williard F. Libby, a Professor of Chemistry at the University of Chicago, predicted that a radioactive isotope of carbon, known as carbon-14, would be found to occur in nature. Since carbon is fundamental to life, occurring along with hydrogen in all organic compounds, the detection of such an isotope might form the basis for a method to establish the age of ancient materials. Working with several collaboraters, Libby established the natural occurrence of radiocarbon by detecting its radioactivity in methane from the Baltimore sewer. In contrast, methane made from petroleum products had no measurable radioactivity.
This discovery meant that there are three naturally occurring isotopes of carbon:
- carbon-12 (c12), comprising 99% of carbon atoms
- carbon-13 (c13), comprising about 1% of carbon atoms
- carbon-14 (c14), represented by one carbon atom per trillion
Whereas carbon-12 and carbon-13 are stable isotopes, carbon-14 is unstable or radioactive.
What is radiocarbon dating?
Carbon-14 is produced in the upper atmosphere when cosmic rays bombard nitrogen atoms. The ensuing atomic interactions create a steady supply of c14 that rapidly diffuses throughout the atmosphere. Plants take up c14 along with other carbon isotopes during photosynthesis in the proportions that occur in the atmosphere; animals acquire c14 by eating the plants (or other animals). During the lifetime of an organism, the amount of c14 in the tissues remains at an equilibrium since the loss (through radioactive decay) is balanced by the gain (through uptake via photosynthesis or consumption of organically fixed carbon). However, when the organism dies, the amount of c14 declines such that the longer the time since death the lower the levels of c14 in organic tissue. This is the clock that permits levels of c14 in organic archaeological, geological, and paleontological samples to be converted into an estimate of time.
The measurement of the rate of radioactive decay is known as its half-life, the time it takes for half of a sample to decay. Libby calculated the half-life of c14 as 5568 ± 30 years. This means that half of the c14 has decayed by the time an organism has been dead for 5568 years, and half of the remainder has decayed by 11,136 years after death, etc. The diminishing levels via decay means that the effective limit for using c14 to estimate time is about 50,000 years. After this time, there is little if any c14 left. Subsequent work has shown that the half-life of radiocarbon is actually 5730 ± 40 years, a difference of 3% compared to the Libby half-life. However, to avoid confusion all radiocarbon laboratories continue to use the half-life calculated by Libby, sometimes rounding it to 5570 years.
What can be dated?
Any organic material that is available in sufficient quantity can be prepared for radiocarbon dating. Modern AMS (accelerator mass spectroscopy) methods require tiny amounts, about 50 mg. AMS technology has allowed us to date very small samples (such as seeds) that were previously undatable. Since there are practical limits to the age range of the method, most samples must be younger than 50,000 years and older than 100 years. Most samples require chemical pre-treatment to ensure their purity or to recover particular components of the material. The objective of pre-treatment is to ensure that the carbon being analyzed is native to the sample submitted for dating. Pre-treatment seeks to remove from the sample any contaminating carbon that could yield an inaccurate date. Acids may be used to eliminate contaminating carbonates. Bases may be used to remove contaminating humic acids.
Some types of samples require more extensive pre-treatment than others, and these methods have evolved over the first 50 years of radiocarbon dating. For example, it was once standard practice to simply burn whole bones, but the results were eventually seen to be unreliable. Chemical methods for separating the organic (collagen) from the inorganic (apatite) components of bone created the opportunity to date both components and compare the results. The collagen fraction usually yields more reliable dates than the apatite fraction (see Dates on bones).
How is radiocarbon measured?
In addition to various pre-treatments, the sample must be burned and converted to a form suitable for the counter. The sample must be destroyed in order to measure its c14 content.
The first measurements of radiocarbon were made in screen-walled Geiger counters with the sample prepared for measurement in a solid form. These so-called "solid-carbon" dates were soon found to yield ages somewhat younger than expected, and there were many other technical problems associated with sample preparation and the operation of the counters. Gas proportional counters soon replaced the solid-carbon method in all laboratories, with the samples being converted to gases such as carbon dioxide, carbon disulfide, methane, or acetylene. Many laboratories now use liquid scintillation counters with the samples being converted to benzene. All of these counter types measure the C-14 content by monitering the rate of decay per unit time.
A more recent innovation is the direct counting of c14 atoms by accelerator mass spectrometers (AMS). The sample is converted to graphite and mounted in an ion source from which it is sputtered and accelerated through a magnetic field. the field deflects atoms of different masses differently (heavier atoms deflect less). Targets tuned to different atomic weights count the number of c12, c13, and c 14 atoms in a sample.
What are the age limits of radiocarbon dating?
Many samples reported as "modern" have levels of radioactivity that are indistinguishable from modern standards such as oxalic acid. Due to contamination from bomb testing, some samples are even more radioactive than the modern standards. Other very young samples may be given maximum limits, such as <100 years. Very old samples may be given minimum limits, such as >40,000 years. The very old samples have such low radioactivity that they cannot be distinguished reliably from the background radiation. Very few laboratories are able to measure ages of more than 40,000 years.
Why do radiocarbon dates have plus-or-minus signs?
Several aspects of radiocarbon measurement have built-in uncertainties. Every laboratory must factor out background radiation that varies geographically and through time. The variation in background radiation is monitered by routinely measuring standards such as anthracite (coal), oxalic acid, and certain materials of well-known age. The standards offer a basis for interpreting the radioactivity of the unknown sample, but there is always a degree of uncertainty in any measurement. Since decay-counting records random events per unit time, uncertainty is an inherent aspect of the method.
Most laboratories express the uncertainty at one standard deviation (± 1 sigma), meaning that there is a probability of about 67% that the true age of the sample falls within the stated range, say ± 100 years. Most laboratories consider only the counting statistics, i.e., the activity of the sample, the standards, and the background, when establishing the 1-sigma limits. However, some laboratories factor in other variables such as the uncertainty in the measurement of the half-life. Two laboratories, the Geological Survey of Canada and the University of Waterloo, follow an unconventional practice by reporting 2-sigma errors, implying a probability of about 95% that the true age of the sample falls within the stated range. Some laboratories impose a minimum value on their error terms.
Most laboratories use a 2-sigma criterion to establish minimum and maximum ages. In keeping with its practice of quoting 2-sigma errors for so-called finite dates, the Geological Survey of Canada uses a 4-sigma criterion for non-finite dates.
What does BP mean?
The first radiocarbon dates reported had their ages calculated to the nearest year, expressed in years before present (BP). It was soon apparent that the meaning of BP would change every year and that one would need to know the date of the analysis in order to understand the age of the sample. To avoid confusion, an international convention established that the year A.D. 1950 would be adopted as the reference point for the expression BP. Thus, BP means years before A.D. 1950.
Some people continue to express radiocarbon dates in relation to the calendar by subtracting 1950 from the reported age. This practice is incorrect, because it is now known that radiocarbon years are not equivalent to calendar years. To express a radiocarbon date in calendar years it must be normalized, corrected as needed for reservoir effects, and calibrated.
What is the importance of association?
Radiocarbon dates can be obtained only from organic materials, and many archaeological sites offer little or no organic preservation. Even if organic preservation is excellent, the organic materials themselves are not always the items of greatest interest to the archaeologist. However, their association with cultural features such as house remains or fireplaces may make organic substances such as charcoal and bone suitable choices for radiocarbon dating. A crucial problem is that the resulting date measures only the time since the death of a plant or animal, and it is up to the archaeologist to record evidence that the death of the organism is directly related to or associated with the human activities represented by the artifacts and cultural features.
Many sites in Arctic Canada contain charcoal derived from driftwood that was collected by ancient people and used for fuel. A radiocarbon date on driftwood may be several centuries older than expected, because the tree may have died hundreds of years before it was used to light a fire. In forested areas it is not uncommon to find the charred roots of trees extending downward into archaeological materials buried at deeper levels in a site. Charcoal from such roots may be the result of a forest fire that occurred hundreds of years after the archaeological materials were buried, and a radiocarbon date on such charcoal will yield an age younger than expected.
Dates on Bones
Bone is second only to charcoal as a material chosen for radiocarbon dating. It offers some advantages over charcoal. For example, to demonstrate a secure association between bones and artifacts is often easier than to demonstrate a definite link between charcoal and artifacts. Indeed many studies seek to determine the time of death of an animal, and there is no question concerning association if the sample consists of the animal’s bone(s).
However, bone presents some special challenges, and methods of pre-treatment for bone, antler, horn and tusk samples have undergone profound changes during the past 50 years. Initially most laboratories merely burned whole bones or bone fragments, retaining in the sample both organic and inorganic carbon native to the bone, as well as any carbonaceous contaminants that may have been present. Indeed, it was believed, apparently by analogy with elemental charcoal, that bone was suitable for radiocarbon dating "when heavily charred" (Rainey and Ralph, 1959: 366). Dates on bone produced by such methods are highly suspect. They are most likely to err on the young side, but it is not possible to predict their reliability.
The development of chemical methods to isolate carbon from the organic and inorganic constituents of bone was a major step forward. Berger, Horney, and Libby (1964) published a method of extracting the organic carbon from bone. Many laboratories adopted this method which produced a gelatin presumed to consist mainly of collagen. This method is called "insoluble collagen extraction" in this database. Longin (1971) showed that collagen could be extracted in a soluble form that permitted a greater degree of decontamination of the sample. Many laboratories adopted Longin’s method, called "soluble collagen extraction" in this database.
C.V. Haynes (1968) presented a method of extracting the inorganic carbon from bone. This method was considered suitable for use in areas where collagen is rarely or poorly preserved in bones. Subsequent research cast doubt on the reliability of this method. Hassan and others (1977; Hassan and Ortner, 1977) showed that the inorganic carbon contained in bone apatite is highly susceptible to contamination by either younger or older carbon in the burial environment. It now appears that insoluble collagen extractions usually err on the young side, if at all (Rutherford and Wittenberg, 1979), whereas bone apatite can produce ages either older or younger than the true age, often by a considerable margin.
Ongoing research has continued to refine methods of extracting collagen, especially from small samples destined for AMS dating. For example, D.E. Nelson and his collaborators have experimented with modifications of Longin’s method, including the use of ultra-filtration to isolate components into "two fractions of nominal molecular weights >30 kD and <30 kD (kilo-Daltons)" (Morlan, et al. 1990: 77; Brown, et al. 1988; Nelson, et al. 1986). T.W. Stafford (1990; Stafford, et al. 1987) has extracted amino acids from bones and measured their ages separately. Hedges and Van Klinken (1992) review other recent advances in the pre-treatment of bone.
Why do radiocarbon dates require calibration?
One of the initial assumptions of the method was that the rate of production of radiocarbon is constant. This assumption is now known to be incorrect, meaning that radiocarbon years are not equivalent to calendar years. Long-term variations in the rate of production appear to correspond to fluctuations in the strength of the Earth’s magnetic field. Short-term variations, “wiggles,” are known as the de Vries effect (after Hessel de Vries) and may be related to variations in sunspot activity.
International collaboration by many laboratories has produced increasingly refined calibration curves. Minze Stuiver, one of de Vries’ students, has been a major leader in this effort. The latest calibration dataset, known as INTCAL98, links the dated tree-ring record to the uranium-thorium dating of corals and finally to terrestrial varve chronologies to achieve calibration over the interval 0-24,000 years. CALIB 4.0 is a computer program based on INTCAL98.
Whether radiocarbon dates must be calibrated depends on one’s purpose. Some studies can be conducted entirely in terms of radiocarbon years. Other studies, such as those focused on rates of change, may require more or less precise calibrations.
What are reservoir effects?
Examples of carbon reservoirs are found in the atmosphere, the lithosphere (the Earth’s crust), the oceans, and the biosphere (living organisms). Land plants and the food chains they support acquire most of their carbon from the atmosphere, whereas marine food chains acquire carbon mainly from the oceans. About 7.5 kg of C-14 is produced each year in the upper atmosphere, and its mixing with carbon in the oceans is less complete than its mixing with atmospheric carbon. Upward flow of deep ocean water also brings ancient, non-radioactive carbon to the surface waters. Therefore marine organisms are relatively depleted in C-14, and modern marine plants and animals can yield apparent ages of hundreds of years. This discrepancy is called the reservoir effect.
It was once thought that the reservoir effect was about 400 years in all the oceans, but it is now known that the size of the effect varies geographically and through time. Every regional study that employs radiocarbon dates on marine organisms must establish the appropriate correction factor for that region.
What is the Suess effect?
Hans Suess was the first to point out that the burning of fossil fuels has a profound influence on carbon reservoirs. These fuels, obtained from the Earth’s crust, are so ancient that they contain no C-14 at all. Indeed some of these materials are used as standards to enable the laboratories to monitor the background radiation. When the fuels are burned, their carbon is released into the atmosphere as carbon dioxide and certain other compounds. The annual release of this “dead” carbon amounts to approximately 5,000,000,000,000,000 kg as compared to the 7.5 kg of C-14 produced annually by cosmic radiation in the upper atmosphere.
What is isotopic fractionation?
During photosynthesis, plants discriminate against the heavier isotopes of carbon, taking up proportionally less C-13 and C-14 than is available in their carbon reservoir. The result is isotopic fractionation, and it is passed along to the consumers of the plants (the herbivores) and to their consumers (the carnivores). In fact, additional fractionation occurs when herbivores eat the plants and when carnivores eat the herbivores. It is believed that all organisms discriminate against C-14 about twice as much as against C-13, and the ratio between the stable C-12 and C-13 atoms can be used to correct for the initial depletion of C-14. Radiocarbon dates can be corrected for isotopic fractionation, a correction called normalization. The amount of isotopic fractionation depends on the photosynthetic pathway used by the plant. Most flowering plants, trees, shrubs and temperate zone grasses are known as C3 plants, because they create a molecule with three carbon atoms using the Calvin-Benson photosynthetic cycle. Grasses that are adapted to arid regions, such as buffalo grass (Bouteloua) and maize (Zea), are known as C4 plants, because they create a molecule with four carbon atoms using the Hatch-Slack cycle. C3 plants discriminate against the heavier carbon isotopes more strongly than do C4 plants.
How are radiocarbon dates normalized?
Normalization is a correction for isotopic fractionation. It is based on the ratio between C-12 and C-13, called δ13C, which is expressed in parts per mil (parts per thousand) with respect to a standard known as Pee Dee Belemnite (PDB). Belemnite is a calcareous Cretaceous fossil found in Pee Dee, South Carolina. Most organic materials contain less C-13 than PDB, yielding negative values for δ13C. For example, most C3 plants have C-13 ratios near -25 parts per mil, whereas C-13 ratios in C4 plants are in the range of -10 to -12.5 parts per mil. Herbivores are less selective against the heavier isotopes, and their bone collagen is enriched by 5 parts per mil in relation to their diet. Yet another change occurs in carnivores whose bone collagen is enriched by an additional 1 part per mil. Marine plants are similar to C3 plants, but they obtain their carbon from dissolved oceanic bicarbonates that differ from the atmosphere in their isotope ratios, and this difference is passed up the marine food chain.
Radiocarbon dates can be normalized to any chosen value, and the value chosen by international convention is -25 parts per mil based on an internationally accepted oak standard. Every part per mil difference from -25 is equivalent to 16 years. For example, bone collagen from marine mammals commonly has a C-13 ratio of -15 parts per mil. That difference of 10 parts per mil from the oak standard means that the age of the marine mammal bone can be normalized by adding 160 years to its measured age.
What if the C-13 ratio is unknown?
If δ13C has not been measured for a given sample, it can be estimated on the basis of thousands of such measurements that have already been reported. However, the estimate contributes an additional degree of uncertainty that is reflected by an error term in the correction formulae. Corrections for isotopic fractionation in commonly dated materials are summarized below:
|peat, humus||-27||35 ± 95|
|marine mammal fat||-23||20 ± 35|
|terrestrial collagen||-20||80 ± 20|
|bison collagen||-20||80 ± 20|
|human collagen||-19||100 ± 20|
|marine collagen||-15||160 ± 20|
|maize||-10||245 ± 20|
|bone apatite||-10||245 ± 35|
|freshwater shells||-8||275 ± 50|
|marine shells||0||410 ± 70|
It is important to note that the formulae for bison collagen and human collagen yield only minimum corrections. In the case of bison, one cannot know, unless δ13C has been measured, the proportion of C4 plants that comprised the animal’s diet. The estimated value, -20 parts per mil, yields an adequate correction only if the animal never consumed C4 plants. Likewise, the estimated value for human collagen, -19 parts per mil, yields an adequate correction for humans that consumed no marine resources, no C4 plant-eating bison, and no corn. Increases in any of these dietary resources would enrich the C-13 ratio above -19 and render the age correction too small by 16 years for every part per mil change in the ratio.