14C is a cosmogenic radionuclide that is formed continuously but not quite at a constant rate by the reaction of thermal neutrons with atmospheric nitrogen:
It was the work of Willard Libby and his co-workers at the Institute for Nuclear Studies and Department of Chemistry at the University of Chicago that led to the development of the radiocarbon dating technique (e.g. Libby 1946; Anderson et al. 1947; Libby et al. 1949; Anderson and Libby, 1951).
The 14C that is produced in the upper atmosphere by the 14N(n, p)14C reaction is rapidly oxidised to 14CO2 and mixes with the stable isotope forms (13CO2 and 12CO2), giving a final atom ratio of approximately 1012 : 1010 : 1 of 12C : 13C : 14C. The CO2 is taken up by green plants in the terrestrial biosphere and converted to carbohydrates by the process of photosynthesis. Subsequent consumption of plants by animals (and animals by other animals) transfers the 14C throughout the entire terrestrial food chain and it is now well established that there is global uniformity in natural 14C/12C enrichment between the well mixed atmosphere and the terrestrial flora and fauna that atmospheric carbon supports, provided that due corrections are made for the degree of isotopic fractionation that takes place during the initial uptake and subsequent metabolic fixation of atmospheric carbon by the primary producers (plant life) and thereafter, any isotopic fractionation that occurs during subsequent transport through the food chain. In contrast, however, the oceans and the life that they support represent a rather heterogeneous reservoir that is not in equilibrium with the atmosphere.
The four fundamental assumptions in the conventional radiocarbon dating method are that:
- The rate of formation of 14C in the upper atmosphere has been constant over the entire applied 14C dating time-scale (approximately the last 50,000 years).
- The activity of the atmosphere and the biosphere with which it is in equilibrium has been constant over the applied time-scale.
- The rate of transfer of 14C between different reservoirs of the carbon cycle is rapid with respect to the average lifetime of 14C (approximately 8300 years).
- The half-life is accurately known
On the basis of the above assumptions, all living organisms, throughout the entire applied 14C dating time-scale, would have been labelled to the same extent with 14C during life, however, on death, 14C uptake ceases and only radioactive decay (which follows first order kinetics) then occurs.
The current internationally-accepted value for living, terrestrial carbonaceous matter was determined from tree rings formed in the year 1890 and is quoted as 0.226 Bq g-1 of carbon. The year 1890 was chosen as the last time that the 14C record was undisturbed. After this time, a significant dilution of the atmospheric 14CO2 was observed due to the burning of fossil fuels (Suess, 1953; 1955), often termed the Suess effect. Then, during the 1950s and early 1960s, the atmospheric testing of nuclear weapons increased the atmospheric 14C activity. In the northern hemisphere, the atmospheric activity almost doubled by the early 1960s, however, following the partial test ban treaty in 1963, the activity has declined exponentially as the excess 14C has entered the oceans and the terrestrial biosphere.
Age Ranges and Calculations
The entire applied radiocarbon dating time-scale extends from about 300 years BP to about 50,000 years BP. Samples more recent than 300 BP are indistinguishable from late 19th and early 20th samples because of the Suess effect while at 50,000 BP; measurements are approaching the limit of detection.
A radiocarbon age is calculated from a re-arranged form of the first order decay equation as follows:
where t = the time that has elapsed since removal of the carbonaceous material from the carbon cycle (ie. death of the organism), λ = decay constant (ln2/t½) = 1.2449 x 10-4 where t½ = Libby half-life = 5568 years, At = the activity of the carbonaceous material t years after death as measured in the radiocarbon laboratory and A0 = equilibrium living activity of 1890 wood (0.226 Bq g-1C), again as measured in the radiocarbon laboratory. Because 1890 wood, which can be considered to be the primary standard, is limited in supply, a secondary standard whose activity can be linked to that of the primary standard is typically measured. The current internationally-accepted standard is SRM-4990C, which is oxalic acid manufactured from the 1977 harvests of French sugar beet molasses. It is commonly known as Oxalic acid II and is distributed by the National Institute of Standards and Technology, Maryland, USA. SRM-4990, often termed Oxalic acid I, was the original standard but supplies of this material were largely exhausted some time ago.
Because samples have to be corrected for fractionation, the equation is more correctly written as:
where AON is the activity of the Oxalic acid II standard normalised for fractionation and ASN is the normalised sample activity.
It is now well established that none of the four assumptions quoted above are strictly correct. For example:
- It is now well known that there are both long term and short-term variations in the 14C production rate (Elsasser et al. 1956; Stuiver 1961; Damon et al. 1989; Sternberg 1992).
- It follows that if the 14C production rate has not been constant, it is unlikely that the activity in the atmosphere and biosphere could have remained constant, in particular as reservoir sizes have also changed through time in response to climatic change.
- It is now well established that contemporaneous terrestrial and marine organisms will give different radiocarbon ages due to the long residence times of carbon in the deep oceans (approximately 2000-3000 years) and the fact that the surface oceans are a mix of ‘old’ carbon from the deep oceans and ‘new’ carbon from the atmosphere, resulting in organisms that are supported by surface ocean carbon having an age offset of about 400 years (marine reservoir effect). This is further complicated by the fact that thermohaline circulation and upwelling patterns mean that the oceanic environment and the plant and animal life that it supports represents a rather heterogeneous environment with respect to 14C activities, irrespective of corrections for fractionation. Therefore, a standard correction cannot be applied to ages derived from the marine environment to bring them into line with terrestrial 14C ages. However, calibration curves that are models based on the atmospheric 14C record are available for marine samples (Stuiver et al. 1998). The modelled marine calibration curve (Marine09) accounts for the global average surface water offset R(t); however, temporal and spatial deviations from this offset, known as R, are evident. In the absence of suitable terrestrial material, accurate and precise quantification of R is imperative for accurate calculation of calendar age ranges based on samples containing marine-derived carbon. This is a critical factor in Scottish archaeology where, owing to our island location, prehistoric communities typically exploited a large coastal resource base. Consequently, marine-derived material makes a considerable contribution to the national archaeological assemblages. Therefore, if 14C dating has to rely on marine-derived material from any of these sites, it is of paramount importance that variations in ῪR are well documented in order to ensure good chronological control. Previous SUERC studies within the British Isles to determine ῪR have been carried out by Ascough et al. (2004, 2005a, 2005b. 2006, 2007, 2009) and Russell et al. (2010, 2011a, 2011b), and further research is on-going
- The Libby half-life, which is significantly different from the true physical half-life, is still used in 14C age calculations.
In the case of samples derived from the terrestrial environment, assumption 3 does not really apply and the other three have been overcome by correlating the radiocarbon dating technique with dendrochronology. The latter has provided a continuous sequence of tree ring material of absolute known age, which covers the entire Holocene. Radiocarbon dating of decadal sequences of this material has provided a plot of true calendar age versus radiocarbon age, i.e. a calibration curve. This calibration curve has now been extended back to the upper limit of detection using paired 14C and U-series age measurements on coral sequences, 14C dated high-resolution marine varves, etc.
Available Radiocarbon Technology in Scotland
In terms of radiocarbon dating, Scotland is extremely fortunate to have 2 AMS instruments at the Scottish Universities Environmental Research Center (SUERC) and the combined AMS /14C expertise that exists within SUERC puts Scotland at the forefront of 14C research. The 5 MV tandem AMS (National Electrostatics Corporation) is a multi-purpose instrument used for 10Be, 26Al and 36Cl as well as 14C analysis. The second instrument is a 250 kV single stage AMS (SSAMS) (again National Electrostatics Corporation) which is dedicated to 14C analysis. The former satisfies the requirements of the Glasgow University, Edinburgh University and NERC cosmogenic isotope preparation facilities as well as the SUERC Radiocarbon Dating Laboratory and the Natural Environment Research Council (NERC) Radiocarbon Facility (Environment). The SSAMS is dedicated to making measurements for the two radiocarbon laboratories. For clarity, both radiocarbon laboratories are managed by SUERC. The NERC Radiocarbon Facility (Environment) was established to meet the need within the UK for radiocarbon analyses in NERC-supported areas of environmental and Earth sciences. The SUERC laboratory undertakes collaborative research within the university sector as well as its own in-house research and has received research funding from a variety of bodies including the UK Research Councils, the Leverhulme Trust, the UK Nuclear Industry, the Commission of European Communities, International Atomic Energy Agency, Historic Scotland and English Heritage. The commercial wing of the laboratory undertakes radiocarbon analyses in a number of fields but the main focus is archaeology. The laboratory currently has the capacity to produce around 5000 AMS targets per annum, of which approximately 3500 would be unknown age samples and 1500 would be standards. Currently a total of around 3500 targets are measured. The standard target size is 1.5 mg carbon for routine analyses but for research purposes samples of a few tens of micrograms have been measured. For standard-sized targets, routine precision for samples of Holocene age is ± 30-35 years at 1 sigma.
There are a number of opportunities arising from the on-going research at SUERC. These include the following:
High precision AMS analysis: the capability to measure unknown 14C samples to a precision of between 1 and 2‰ (i.e. 8-16 years) has been demonstrated (Cook et al. 2010). These results were backed up by quality assesment data that confirmed both the accuracy and precision of the measurements on the unknowns. This capability will be used in an application currently being prepared that will include the dating of Early Iron Age crannogs whose construction phase falls on the so-called ‘Hallstat Plateau’. There are many other potential applications that would benefit from high precision data, particularly if used in combination with Bayesian statistics (see section 6).
Maximisation of Impact of dating formation: There is a need for people in Scotland with a good background in Bayesian statistics (and archaeology) who can help archaeologists to design their 14C dating programs to achieve the maximum amount of information. In particular, someone with a good grasp of calibration programs such as OxCal that use Bayesian techniques. Dr Derek Hamilton is a recent appointment to SUERC staff and has that expertise.
Compound Specific 14C dating: Dr Gillian MacKinnon is a SAGES appointment whose remit is partly to develop compound specific 14C dating. This presents an opportunity for research grant applications on such topics as food residues in pottery, etc.
Enhanced understanding of marine and freshwater reservoir effects: There is a definite requirement for archaeologists to understand the effects of non terrestrial food resources in the human diet on calibration of 14C ages of human remains. There are potential opportunities for research in this area. The SUERC lab. has been researching both marine and freshwater reservoir effects for around a decade (Cook et al. 2001, 2002; Ascough et al. 2004, 2005, 2006; Russell et al. 2010).
More generally, there is an opportunity for archaeologists in Scotland (in the professional, academic and private sectors) to formulate and submit research grant applications with SUERC staff and to achieve meaningful collaborations on a range of archaeological problems requiring 14C and/or stable isotope measurements. Historic Scotland (HS) has funded the development of an on-line system to handle archaeologists’ applications for HS funded radiocarbon dating. The system is based on a database, linked to the Online AccesS to the Index of archaeological investigationS (OASIS), which will provide the applicant with an on-screen application form and will permit the submission of the form electronically to the HS programme supervisor for consideration. The programme supervisor’s decision will be transmitted directly back to the applicant and forward to the 14C laboratory. If approved, the applicant will then be instructed to dispatch the samples and the lab will be forewarned of their imminent arrival. The system will allow applicant and supervisor to communicate to resolve problems. Once the analysis is complete, the system will then transmit the radiocarbon result certificate to both the supervisor and applicant. At the time of writing (April 2012), the system is undergoing further bench-testing. Some minor faults remains to be ironed out but HS hope to see the system running by late summer 2011.
HS also hope that once the system is up and running well they will be able to upload all the existing 14C results funded through HS or its predecessor bodies. These data will be available through the same on-line database system and will be supplemented as each new batch of result certificates is issued. The system has the facility of not moving results into the public domain if some compelling reason exists for confidentiality
Graphical representation of the calibration of radiocarbon results for carbonised residues from Perth, Scotland. The chronological model for Shelly Ware in Perth is as previously described in Hall et al. (2007). It is composed of the 14C measurements on 15 carbonized residues from 11 different archaeological contexts. The measurements are in agreement with the model assumption that they belong to a single phase of activity . This activity dates the introduction of Shelly Ware in Perth to cal AD 930-1020 (95% probability; start Shellyware: Perth, Scotland) [cal AD 960-1000 (68% probability)]. Shelly Ware fell out of use in Perth in cal AD 1020-1120 (95% probability; end Shellyware: Perth, Scotland) [cal AD 1030-1070 (68% probability)]. (N.B. These results vary very slightly from those analysed using OxCal 3.10 and reported in Hall et al. (2007).