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Radiocarbon Dating: A Practical Overview

Philip Barratt and Paula J. Reimer

Abstract

Today it would be difficult to imagine archaeology without the availability of radiocarbon dating. It has revolutionised our ability to provide absolute dates for objects and places, and allows us to compare their place in time with others from around the world. All of this has been made possible simply from measuring the properties of a simple and abundant element–carbon. This paper describes some of the stages in the development of the technique, why it works and how to use it. We especially highlight its role in Ireland, home to one of the world’s leading high-precision radiocarbon laboratories. We aim to provide the user of radiocarbon dating with the necessary information to obtain optimum results and how best to convey these to a wider audience.

Introduction

Time is inherently important to us all; we relate to our past and anticipate and plan our futures using concepts of time. The physical world we inhabit changes at scales of minutes to millennia. The environmental archaeologist attempts to describe both the human and environmental record through time in a way that is sensible to the nonspecialist. To do this, places and events of the human past need to be set in a chronological context along with the environments they inhabited. This is especially important when investigating the varying impact of people on a landscape that is changing on a range of temporal scales.

Since its discovery in the 1940s, radiocarbon dating has provided archaeologists with a tool that has revolutionised our understanding of the human past (Renfrew 1973). An increasing appreciation of the contribution of environmental and earth science disciplines to archaeology has, in part, been enabled through an improvement of chronological control provided by radiocarbon dating. Continuing advances in methods and technology allow the practitioner to begin to unravel the relationships between temporally complex landscapes and human activity over the Holocene. As people move and work within this environment the challenges for the environmental archaeologist will change and the understanding required to date the human occupation and use of the land may well pass through many paradigm shifts.

History of Radiocarbon Dating in Ireland

The Belfast Radiocarbon Laboratory, based in the Palaeoecology Centre at Queen’s University Belfast, has been providing dates since 1969 and has led the development of high precision liquid scintillation counting (Pearson 1979; 1980). Since the early days, researchers have been involved in dating archaeological and environmental materials. Contributions to the understanding of key archaeological sites in Ireland such as the Neolithic passage tombs at Newgrange and Knowth, Co. Meath, and Iron Age Navan Fort, Co. Armagh, have been taking place since the 1970s. The laboratory has also been involved with the dating of important sites in England such as the world renowned Stonehenge in Wiltshire (Cleal et al. 1995), and the so-called ‘Seahenge’ timber circle in East Anglia (Bayliss et al. 1999). The laboratory has worked closely with researchers from the Palaeoecology Centre at Queen’s, building a wealth of experience in archaeological and palaeoenvironmental applications. Perhaps one of the most important contributions to the latter is that of tephrochronology; the use of volcanic ash deposited after an eruption to date and correlate sedimentary horizons (see Pilcher, this volume). Assuming the tephra found in a deposit can be uniquely identified, a radiocarbon date on the sediments or plant macrofossils at the tephra horizon can be effectively transferred to other sites at the point where the same tephra has been identified. This is of course a simplified description of tephrochronology which has become an important part of the chronologist’s toolkit and the following references provide further explanation and uses of the technique–Pilcher et al. (1995), Haflidason et al. (2000), Plunkett et al. (2004) and Hall and Mauquoy (2005).

The Belfast Radiocarbon Laboratory, in conjunction with the Dendrochronology Laboratory in the Palaeoecology Centre, Queen’s University Belfast, began one of the earliest European radiocarbon calibration research programmes (Pearson et al. 1977) and it has been a key centre for the development of internationally accepted radiocarbon calibration curves. The work of the Belfast Radiocarbon Laboratory formed a fundamental part of the Holocene section of the 1986 calibration curve (Pearson et al. 1986), and is still actively contributing to on-going calibration efforts including IntCal04, the latest internationally ratified calibration curve (Reimer et al. 2004). Building upon this work the laboratory is now at the forefront of a Southern Hemisphere calibration programme in collaboration with the University of Waikato Radiocarbon Dating Laboratory in New Zealand (Hogg et al. 2002; McCormac et al. 2004). This work has dramatically improved dating resolution below the equator and has helped to resolve the processes behind the radiocarbon offsets measured between the Northern and Southern Hemispheres (McCormac et al. 1998a; 1998b). A new Accelerator Mass Spectrometry (AMS) facility, part of the 14CHRONO Centre, based in the School of Geography, Archaeology and Palaeoecology, Queen’s University Belfast, is the first of its kind in Ireland, and will certainly enhance the chronological aspect of environmental archaeology.

Methods

Where Does Radiocarbon Come From? Why and How does Radiocarbon Dating Work?

Carbon (C) exists in the environment as three distinct and naturally occurring isotopes (atoms of the same element with different atomic weights)–¹²C, ¹³C and ¹⁴C. Of the three, only ¹⁴C is radioactive–the other isotopes are stable and remain chemically intact in the environment. ¹⁴C is the least common isotope, and is present as only one part in a million, million of environmental carbon. Bombardment of nitrogen (¹⁴N) by cosmic radiation in the upper atmosphere creates a constantly renewed source of ¹⁴C; once created it quickly oxidises to form carbon dioxide (CO₂). Atmospheric circulation rapidly disperses this ¹⁴C ‘tagged’ CO₂ around the planet. Being radioactive the ¹⁴C undergoes radioactive decay emitting a beta (ß) particle in the process. This process is immutable and is independent (i.e. unaffected) of external environmental conditions and decreases at a constant rate. The rate of radioactive decay for each element is unique and unvarying and determines the half-life, which is the time it takes for half of the radioactive element to undergo the decay.

Once in the environment, exchange mechanisms, such as respiration in plants and ingestion by animals, incorporate the radioactive CO₂ into living organisms. Gaseous exchange pathways mix it into the oceans as dissolved carbonate, which is then taken up by organisms, and chemical processes combine it into the sedimentary record. All of the exchange mechanisms ideally take place in equilibrium with atmospheric concentrations of ¹⁴CO₂. However, when the exchange ceases due to biological death or sedimentary burial new ¹⁴CO₂ is no longer taken up, equilibrium with the environment is broken and decay becomes the dominant process. The difference between activity measured in the dead sample and the current atmospheric concentration can be used to determine the time elapsed since exchange ceased. Since the half-life of ¹⁴C has been measured (Libby et al. 1949; Godwin 1962) and a modern standard is available to determine an initial ¹⁴C concentration, a simple equation can be used to work out the age of a sample. However, from the earliest days of radiocarbon dating it was understood that it was necessary to adopt certain assumptions when applying the technique (Libby et al. 1949; Libby 1952):

— ¹⁴C would have to mix uniformly and travel through the global carbon reservoir much more quickly than the lifetime of an individual atom.

— There would have to be equilibrium with the ¹⁴C available for exchange in the environment with that decaying and unavailable.

— Organisms would take up ¹⁴C, ¹³C, and ¹²C in atmospheric proportions.

— There are no post-mortem changes in the ¹⁴C other than from radioactive decay at a constant rate.

As with many assumptions, these are true only in a general sense and other processes such as fractionation (Burleigh et al. 1984), ocean-atmosphere interactions, and variations in production of ¹⁴C over time required corrections to be made.

 

How We Measure Radiocarbon: Gas, Liquid and AMS

Modified Geiger counters were used to determine the activity of samples in the early stages of radiocarbon dating (Libby et al. 1949). These simply detected the charged particles that were emitted from a radioactive sample. Improving methods and technology increased the sensitivity of the measurement equipment and reduced sample sizes, with two counting technologies becoming dominant in radiocarbon laboratories. The first development was Gas Proportional Counting (GPC), where the carbon sample is converted into CO₂ and expanded into the counter. A potential voltage is applied across a thin wire running down the centre of the counter. When the ¹⁴C decays, the ß particle, which is emitted from the nucleus, is accelerated across the potential difference. The ionisation pulse measured is proportional to its initial energy. Subsequently, Liquid Scintillation Counting (LSC) was developed. For this method the sample is converted to benzene and a scintillator is added, which fluoresces when a charged particle interacts with it. With both techniques sample preparation is a key part of the process and needs to be very carefully controlled to obtain precise counts (McCormac 1992).

During the 1970s a completely new way of determining the amount of ¹⁴C present in a sample was established: Accelerator Mass Spectrometry (AMS). This method directly measures the proportion of the carbon isotopes present in a sample which has been firstly converted to CO₂ and then to graphite and pressed into a target or cathode. The target is placed in the ion source where it is coated with caesium, thereby creating carbon ions. The ions are then accelerated through an electric field and magnets are used to refract the component isotopes into detectors (Bennett et al. 1977; Nelson et al. 1977). Early tests established the viability of the technique and its potential advantages over ß counting, such as the speed of measurement and the need for much smaller samples (Muller et al. 1978). However, AMS has only recently approached the precision attainable with the high-precision LSC and GPC methods (e.g. Stuiver and Pearson 1986; McCormac et al. 1998a; 1998b). Advancements in AMS technology and sample pre-treatment procedures have led to demonstrable improvements in the precision of AMS sample measurements (Guilderson et al. 2003; Bronk Ramsey et al. 2004). The small size of the AMS sample is an advantage, in that it may be possible to select specific fractions to date, perform more rigorous chemical pre-treatments, or run multiple sub-samples. It may also be a disadvantage, however, in that small amounts of contamination can be introduced at any stage in the process (Bronk Ramsey et al. 2004).

To convert the measured count rate or isotope ratio into a radiocarbon age, it is compared to that of a standard. Oxalic acid, produced by the U.S. National Institute of Standards and Technology, is the accepted standard for ¹⁴C. Radiocarbon, has by historical process, two half-life values in use. In order to ensure that results from radiocarbon laboratories are reproducible, frequent measurement of duplicates and/or secondary standards should be carried out. The on-going inter-laboratory comparison programme helps to ensure that results are accurate (Aitchison et al. 1990; Rozanski et al. 1992; Scott et al. 1998; 2004).

 

Fractionation Correction

Many biological processes, such as photosynthesis, more readily incorporate the lighter carbon isotopes into the reaction product so that the initial ¹⁴C/¹²C ratio and ¹³C/¹²C ratio in the plant is different than that of atmospheric CO₂. The two major photosynthetic pathways, C-3 and C-4, discriminate against the heavier isotope to differing degrees due to physiological differences in the way CO₂ is taken up in plants (O’Leary 1981). Most temperate region trees and shrubs are C-3 plants, so named because the first product in the photosynthetic reaction contains three carbons, while tropical grasses, such as maize and millet, are C-4 plants. Physical processes also discriminate against either heavier or lighter isotopes, so that CO₂ dissolved in water has a larger proportion of the heavier isotopes than the atmosphere. Thus algae and plankton, which use dissolved CO₂ for photosynthesis, will also have a larger proportion of the heavier isotopes. Because the heavier ¹⁴C atom is discriminated against approximately twice as much, relative to the ¹²C atom, compared to the ¹³ C atom, a correction for isotopic fractionation can be made using the ¹³C/¹²C ratio (Stuiver and Polach 1977). The isotope fractionation correction may be on the order of several hundred years for C-4 plant material or for samples formed in the marine or aquatic environment.

 

Calibration

Perhaps the most important correction made to radiocarbon measurements is to compensate for the variations in ¹⁴C concentrations over time. Research by Suess (1955) demonstrated that the amount of environmental ¹⁴C had not been constant since the nineteenth century due to emissions from industrial activity. In addition de Vries (1958) noted that appreciable variations occurred in the atmospheric ¹⁴C content. These variations were found to be the product of natural processes such as changes in the carbon cycle, solar activity and the Earth’s magnetic field (Stuiver 1961; Damon 1973; Stuiver et al. 1991; Bard 1998; Damon and Peristykh 2000; Beck et al. 2001). The effect of these processes became apparent during early practical applications of radiocarbon dating. Discrepancies of several hundred years were found when radiocarbon dates were compared with archaeological evidence and tree ring data (Libby 1963). In essence these variations or ‘wiggles’ were showing up as episodes of compressed and extended time on the radiocarbon scale compared to the calendrical scale.

Unfortunately, there is no mathematical way of predicting these wiggles in the radiocarbon timeline so an empirical approach was needed. Such an approach required a material that could be independently and precisely dated, persisted for several thousand years and could be radiocarbon dated. Fortunately the discipline of dendrochronology had produced tree-ring chronologies in which the exact year of each tree-ring was known for a period stretching back over several thousand years (Pilcher et al. 1984). By radiocarbon dating the tree rings, an accurate ‘map’ of the location of the radiocarbon wiggles could be made. Joint efforts in America and Europe created a radiocarbon calibration curve. The curve graphically represented ¹⁴CO₂ variations on one axis and calendar (dendrochronology) dates on the other. To help standardise the results from calibrating dates the radiocarbon community set about creating and disseminating an international standardised radiocarbon calibration curve. In 1986 the journal Radiocarbon published data and graphs to be used as the de facto calibration standard for users of radiocarbon dates (Stuiver and Kra 1986). This provided publicly available datasets that could be used to find (calibrate) calendar dates from radiocarbon ages. Calibration was initially rudimentary, consisting of interpolating from a table of calibrated ages or drawing lines on graphs to read the dates at an intercept (Stuiver and Pearson 1986). The introduction of computer programs such as CALIB, Cal25, OxCal and BCal, available online, has since allowed a more sophisticated approach to be taken by incorporating statistical analyses (Stuiver and Reimer 1993; van der Plicht 1993; Bronk Ramsey 1995; 2001; Buck et al. 1999).

Figure 1.1: A section of the IntCal04 calibration curve (Reimer et al. 2004) to depict an example of the effect of the wiggles when calibrating dates. The position of two hypothetical, uncalibrated high-precision radiocarbon dates are marked as grey (Date One) and black (Date Two) triangles.

A simple example of the effect of the wiggles in calibrating dates is illustrated in Figure 1.1, which shows a section of the IntCal04 calibration curve (Reimer et al. 2004) and the position of two hypothetical, uncalibrated high-precision radiocarbon dates (grey and black triangles). The earliest date (Date One), indicated by the grey triangle, occurs on a relatively flat section or plateau of the curve whereas Date Two (black triangle) is located on a fairly steep section of the curve. When calibrated, Date One returns an age range of 100 years at one sigma (one sigma states the 68% probability that measurement will be within one standard deviation of the mean; two sigma within two standard deviations (95%)), whereas Date Two returns a calibrated range of only ten years. Although the samples are only 100 ¹⁴C years apart and have the same errors, the shape of the curve significantly affects their precision. The first radiocarbon date is effectively stretched across the length of the plateau, whereas the steepness of the slope has the opposite effect for Date Two. It is obvious from this example that a precise radiocarbon date does not necessarily provide a precise calibrated date, a point that will be discussed later in the text.

 

Age Limits and Accuracy

The theoretical age limit of radiocarbon dating is in excess of the ability of current technology and technique. Such limiting factors result from a number of causes– environmental emissions, errors in counting, sample preparation and laboratory efficiency. As the age of the sample increases, the radiocarbon activity decreases. This decrease in activity increases the affect of external errors on the age determination. To counter this there has been a continuing effort to control contributing errors in order to push back the dating limits. Initially ¹⁴C dating limits were around 20,000 years, whereas theoretical limits of 70,000 years have been discussed for over a decade, using current counting techniques (Long and Kalin 1993). An age limit of approximately 50–55,000 years is now generally accepted. For AMS, theoretical limits of 70,000–100,000 years have been suggested (Muller et al. 1978), although blanks of geological graphite prepared under argon have so far reached a machine limit of around 70,000 years (Schmidt et al. 1987).

 

What Can Be Measured?

The usefulness of radiocarbon lies in the broad range of materials that can be dated using this method. Increasing technological advances in radiocarbon dating technology and sample preparation continue to widen its applications for the environmental archaeologist. At a basic level there only needs to be enough measurable ¹⁴C in a sample to use the technique. In some cases there will be abundant material suitable for dating that can be gathered easily; in others careful extraction techniques will be required to provide sufficient material even from a relatively large sample, such as a bone. Dating of archaeological material such as clothing, bone and wood is widely known, however, other materials such as mortar and iron have also been investigated for their usefulness as dating materials (Sonninen and Jungner 2001; Scharf et al. 2004). Certain items do come with caveats, for example, only the dentine in teeth is considered reliable for radiocarbon dating in archaeological contexts because carbonate in the enamel exchanges with the environment (Hedges et al. 1995). The wide range of materials that may be encountered within environmental archaeology can require the use of methods that are at the cutting edge of technique and technology. Improving chemical extraction methods can be used to separate specific molecules such as amino acids, or even DNA, from samples of bone and hair (Stafford et al. 1991; Burky et al. 1998; Spaulding et al. 2005) and microbial biomarkers from sediments and soils (Eglinton et al. 1997) for AMS dating. Microscopic plant remains such as pollen grains, used widely in reconstructing past environments, can often be concentrated into sufficient quantities for dating purposes (Brown et al. 1989; Richardson and Hall 1994; Mensing and Southon 1999). Techniques for chemically separating suitable material for dating insects, specifically beetles, are also currently being developed and tested (Hodgins et al. 2001; Tripp et al. 2004). ¹⁴C is also incorporated into the hard carbonate shells produced by many terrestrial and marine organisms thereby allowing these creatures to be radiocarbon dated. Although the potential list of usable materials is extensive, the contexts from which they have been derived need to be considered. Corrections often need to be made for cases where the uptake of ¹⁴C may not have been at atmospheric levels. Such differences can occur in the oceans (the marine reservoir effect), karstic areas or near sources of volcanic or hydrothermal outgassing (Rubin et al. 1987; Cook et al. 2001; Proskurowski et al. 2004), where very old carbon with ¹⁴C at very low activity levels is present in the environment and has been taken up by an organism. The old ¹⁴C will ‘dilute’ the atmospheric ¹⁴C thereby reducing the radioactivity of a sample and causing the radiocarbon age to be older than is actually the case (Goodfriend 1987).

Methodological Summary

Sampling

Ideally, strategies for sampling material for radiocarbon dating should be considered at the initial stages of planning an excavation or fieldwork. Radiocarbon dating is relatively expensive and limited understanding of the techniques, poor field practice, and a lack focus on the research/project questions can waste money and opportunities. However, the nature of archaeological excavation, especially on a commercial basis, can require decisions to be made quickly in the light of unexpected finds, external pressures from funders or developers, and limited time. This can often impact on the quality and the choice of samples taken. Poorly sampled material could very likely be contaminated, and give spurious results that have to be rejected or, more worryingly, form the basis for incorrect inferences. Sampled contexts should be secure; the contexts themselves should be such that they will provide useful information about the site or area, or the relationship between the material and the site. Again, the question should be asked of whether or not a date will necessarily provide useful information. To develop a detailed chronology for a site a sufficient number of samples are needed, ideally with clear stratigraphic relationships, so that Bayesian techniques, available in some calibration programs, can be applied to further constrain the calibrated ages (Buck et al. 1991). As such, the commissioning archaeologist may want to consider collaboration with a statistician or someone versed in these techniques (see Using the Dates below).

As mentioned previously, dateable material can be influenced by its context, through old carbon, reuse of material, reworking of sediments, or even the inherent age due to the longevity of an organism such as a tree. Wood charcoal provides an example of the potential problems involved. The carbon taken in by a tree during growth is fixed in the growth ring for that year; charcoal derived from the centre of a tree may well be several hundred years older than the fire in which it was burnt. Reuse of older timbers in a structure in a conflagration will produce similar results, providing interesting, but undesired, dating problems. Wood and charcoal samples should be identified to species level so that ideally only short-lived species would be selected for dating purposes. The quantity of a sample to take is also important and will often be dictated by how much there is and on the requirements of the technique that will be used to provide the date. The amount of carbon in a sample varies with the type of material and sample preservation, which can be problematic for bones in particular. Before planning a sampling scheme around bone, it might be worthwhile to send a typical sample in to the laboratory to test for protein preservation in the sample. Table 1.1 provides details of the amounts required for some of the materials the Belfast Radiocarbon Laboratory handles for high precision LSC dating and AMS dating. The estimated precision for a single sample c. 5000 years old is approximately ± 20 years and ± 35 years, for LSC and AMS dating respectively. The current AMS dating targets prepared at Belfast require 1.2 mg of carbon after pre-treatment although a new graphite line is currently under construction that will enable target preparation using sub-milligram quantities of carbon.

Material	High Precision	AMS
Wood	150 g	10 mg
Bone*	600 g	600 mg
Antler*	600 g	600 mg
Cremated bone	Not done	1.5 g
Charcoal	40 g	5-10 mg
Peat	250 g	10 mg
Cloth	120 g	10 mg
Humus Soil**	1200 g	100 mg
Shell	110 g	20 mg
Silt**	2000 g	200 mg

Table 1.1: Suggested minimum weights for high precision liquid scintillation radiometric and AMS radiocarbon dates. * = If collagen has been sufficiently preserved in the bone or antler. ** = Depending on % carbon.

Handling and Storage

The importance of the appropriate handling and storage of radiocarbon samples cannot be overstated. Potential for contamination is present at each stage and will affect the accuracy of any dates produced. The introduction of carbon to a sample needs to be avoided at all costs. Although treatment in the laboratory can remove many contaminants, the introduction of new ones will produce errors in addition to those that cannot be avoided. Contamination can occur at several stages as the samples progress through the dating process. Poor sampling in the field using dirty tools, the mixing of contexts or a lack of care whilst containing and storing the material will seriously affect results. Careful cleaning of tools between sample collection should always be carried out. The choice of a suitable container for the sample needs to be thought through before sampling takes place–even paper labels placed within sample bags can be a potential source of contaminating carbon. Extended storage of sediment samples can also be problematic, allowing fungal and bacterial growth to take place and potentially introduce contamination (Wohlfarth et al. 1998). For many samples, such as wood or bone, simply rinsing the material in distilled water and drying in a low temperature oven will prevent mould and fungal growth. These sources of error may be compounded by those that can be introduced during the laboratory cycle. Very high standards are required to reduce the risk of further contamination at this stage, especially when dealing with very small samples. Although seldom encountered in archaeological field sites, laboratory and storage facilities where ¹⁴C has been used in tracer experiments can seriously compromise the results (Buchholz et al. 2000). In high precision laboratories, such as that at Belfast, sources of error are accounted for in a constant effort to maintain and improve dating standards.

 

Submitting Samples

There is a choice of laboratories that can be used by the archaeologist when submitting a sample for radiocarbon dating offering different facilities, services, and accuracy, and the associated costs will vary accordingly. Most laboratories will offer perfectly adequate results for most archaeological situations. If one is interested in the general chronology of a site then extreme accuracy and precision will not be worth the extra cost. When the archaeologist needs to differentiate between or date contexts to within a few decades, however, only a few high precision laboratories will be able to carry out suitable measurements–Belfast being one. Laboratories may use an estimated ¹³C/¹²C ratio of the sample (reported as δ¹³C relative to the Vienna PeeDee Belemnite (VPDB) standard) for the fractionation correction, although many laboratories routinely include a δ¹³C measurement either as part of the price of the date or for a small additional charge. Measurement of the ¹³C/¹²C ratio of the sample will give a more precise result, especially if the natural variability of the material is large or must also be estimated.

The required measurement precision may also be determined by considering the effect of the calibration curve at the expected time period for the date. A radiocarbon age that falls on a plateau in the calibration curve will result in an imprecise calibrated age (see Figure 1.1), no matter how precisely the sample is radiocarbon dated (Guilderson et al. 2005). In addition to precision, sample size may dictate the technique required, i.e. radiometric or AMS dating, and so the choice of laboratory. The small sample size required and relatively short time involved should make AMS the favourite choice, although there are issues to be considered. Some GPC and high precision LSC systems offer greater precision for single samples than most AMS systems. Sampling can become more problematic when taking only very small samples or samples of very small things. Small samples may come from a non-representative section of the sampled item and some, such as pollen grains, may well be more mobile than the context they are in, thereby causing a higher probability of producing ‘unhelpful’ dates. On the other hand, the dating of identifiable plant remains, especially fragile macrofossils such as leaves, can provide assurance that the samples have not been transported a long distance before deposition. When only small samples, or samples with only very small amounts of datable material in them, are available AMS may well be the only method with which to achieve a date.

 

Using the Dates

Even before the date has been produced by the laboratory the archaeologist should think about how it is to be used and published. The raw radiocarbon age is not equivalent to a calendar date because the ¹⁴C in the major carbon reservoirs has not been constant as is assumed in the calculation of the raw radiocarbon age (see Calibration above). These radiocarbon years can meaningfully be compared against each other, but if one wants to compare the results against an historic event or against dates produced using another dating method such as dendrochronology or uranium-thorium dating then the date will need to be calibrated. Presentation of the dates is also important and as much information about the date should be provided as possible. Simply publishing a calibrated date will not show how the date was produced, which calibration data was used, which laboratory produced the date and what error margins are associated with the laboratory measurement. Raw dates and the uncertainty at one sigma along with the unique laboratory identification code given to each submission should always be made available so that others can reproduce the calibrated date or update it if new calibration data becomes available e.g. 1234 ± 56 (UB789). The laboratory identification code is unique and allows the measurement to be traced back to the original submission. If an author wishes to use the calibrated rather than raw date in a text this should be made clear and the raw date made available elsewhere in the publication, linked by the laboratory code. Measured or estimated δ¹³C (see Fractionation Correction above) should also be reported if available together with any reservoir corrections used, these can be placed in an appendix and linked to the date through the laboratory code. Standardisation for presenting radiocarbon dates has been discussed for over 20 years but there remains inertia about wider implementation by the archaeological community (Stuiver and Polach 1977). Calibrated age ranges (one and/or two sigma) should also be given, in most cases, with a reference to the calibration curve used. The two sigma calibrated age ranges are generally preferred because these include 95% of the calibrated probability distribution. The calibrated age ranges can be presented as the minimum and maximum calibrated ages–e.g. 2340–1890 cal. BC–or multiple ranges may be given–e.g. 2340–2280 cal. BC and 2010–1890 cal. BC) accompanied by the probability associated with each range as shown in Table 1.2.

Table 1.2: Suggested reporting of two sigma (2 σ) calibrated radiocarbon ages and relative probabilities.

There is a temptation to present the midpoint of the calibrated age ranges with a symmetric uncertainty but this oversimplification is a misrepresentation of the calibrated probability distribution (Telford et al. 2004). However, simple calibrated age-depth plots using the midpoint of the calibrated age range or other single estimator have often been used successfully in palaeoenvironmental studies due to a lack of more sophisticated tools at the time. For example, Weir (1995) used simple calibrated age-depth plots of radiocarbon ages and tephra dates to suggest an ‘Iron Age hiatus’ in agricultural activity between 200 BC and AD 200 based on pollen sequences from two former lake sites (Essexford Lough and Whiterath Bog) and a raised bog (Redbog) in County Louth.

Because stratigraphic information or other dating evidence is often available in palaeoenvironmental sequences, including this information in a statistical framework using Bayes Theorem (Bayes 1763) can help refine the chronology. The Bayesian Theory has been adapted for use with radiocarbon data (Buck et al. 1991; Christen 1994) and made available in the computer programs BCal and OxCal (Bronk Ramsey 1995; 2001; Buck et al. 1999). These programs have been widely used by archaeologists to construct and test chronological models, such as for the re-evaluation of the chronology of Stonehenge (Bayliss et al. 1997), the sequence of construction and destruction of Navan Fort, Co. Armagh (Gault 2002) and the timing of the volcanic destruction of the Minoan Civilization (Manning et al. 2006). Although not as widely used in environmental sequences, there has been a great deal of interest in the adaptation of Bayesian techniques to sedimentary processes in order to construct calibrated age-depth models (Bennett 2005; Blaauw and Christen 2005; Bronk Ramsey in press; Millard and Brooks in prep.).

When a sequence of samples with known calendar spacing can be radiocarbon dated, such as tree-rings in a timber or log, then the shape of the calibration curve can be used to improve the resolution of the calibrated age range. This process, known as ‘wiggle-matching’, can be applied using classical statistical methods (Pearson 1986) or with Bayesian statistical methods where it is known as a defined sequence. Examples of the use of ‘wiggle-matching’ in archaeology are the refinement of the construction dates for the royal tombs of Pazyryk, south Siberia (Mallory et al. 2002), and in the confirmation of the dendrochronological result for the Seahenge timber circle (Bayliss et al. 1999). ‘Wiggle-matching’ can also be applied to peat sequences if an assumption about the growth rate of the peat is made. Pilcher et al. (1995) used this technique to provide a calendar age estimate of the Hekla 3 Icelandic tephra and Plunkett (1999) established a date for the Hekla 3 event based on the position of the tephra between other well-dated events in a profile from Claraghmore Bog, Co. Tyrone. Both of these tephras are widely used as time-stratigraphic markers in Ireland.

Conclusion

Radiocarbon dating continues to be of major importance to the archaeological community. Although other dating techniques, such as dendrochronology, thermoluminescence (TL), optically stimulated luminescence (OSL), and uranium-thorium, are available for some types of samples only radiocarbon has the breadth of application required to answer many archaeological problems. The well-tested calibration curve for the Holocene period provides radiocarbon dating with an accuracy that only dendrochronology can surpass when suitable material is available. For the environmental archaeologist, radiocarbon dating is an essential tool by which the interactions between human activity and the environment can be interrogated. Closer working relationships between the environmental archaeologist and radiocarbon laboratory personnel in exchanging ideas and advice at the outset of a project will aid in sample selection and interpretation of results.

Improvements in AMS technology and sample preparation techniques look certain to increase the precision and application of this technique as a dating tool, while inter-laboratory comparisons and analysis of known age material improve accuracy. The efforts by the laboratory in Belfast and many other laboratories continue to increase the accuracy of the calibration curve during and before the Holocene and to extend the calibration curve back to 50–55 ka. Work in the Southern Hemisphere is providing opportunities for archaeologists to calibrate dates to an accuracy and robustness that has previously only been available in the Northern Hemisphere. Online resources are providing access to sophisticated dating tools and archives (see below) of existing archaeological dates from Britain and Ireland and beyond. Although radiocarbon has had a short history in relation to many other aspects of archaeology and environmental studies its impact has been dramatic and continues to be vital for the progress of ideas and practice.

Online Archive Sources

http://ads.ahds.ac.uk/catalogue/specColl/c14_cba/
http://www.historic-scotland.gov.uk/wwd_carbondatingsearch
http://www.canadianarchaeology.ca/
http://bcal.shef.ac.uk/
http://calib.qub.ac.uk/calib/
http://c14.arch.ox.ac.uk/oxcal.OxCalPlot.html

References

Aitchison, T. C., Scott, E. M., Harkness, D. D., Baxter, M. S. and Cook, G. T. 1990. Report on Stage-3 of the International Collaborative Program. Radiocarbon 32, 271–8.

Bard, E. 1998. Geochemical and geophysical implications of the radiocarbon calibration. Geochimica et Cosmochimica Acta 62, 2025–38.

Bayes, T. 1763. An essay toward solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London 53, 370–418.

Bayliss, A., Bronk Ramsey, C. and McCormac, F. G. 1997. Dating Stonehenge, pp. 39–59 in Cunliffe, B. and Renfrew, C. (eds.), Science and Stonehenge (Proceedings of the British Academy 92). Oxford: British Academy.

Bayliss, A, McCormac, F. G., Groves, C., Baillie, M. G.L. and Brown, D. 1999. The Norfolk Bronze Age timber circle. Nature 402, 479.

Beck, J. W., Richards, D. A., Edwards, R. L., Silverman, B. W., Smart, P. L., Donahue, D. J., Hererra-Osterheld, S., Burr, G. S., Calsoyas, L., Jull, A. J. T. and Biddulph, D. 2001. Extremely large variations of atmospheric ¹⁴C concentration during the last glacial period. Science 292, 2453–8.

Bennett, C. L., Beukens, R. P., Clover, M. R., Gove, H. E., Liebert, R. B., Litherland, A. E., Purser, K. H. and Sondheim, W. E. 1977. Radiocarbon dating using electrostatic accelerators–negative-ions provide key. Science 198, 508–10.

Bennett, K. D. 2005. Psimpoll manual. http://www.kv.geo.uu.se/psimpoll.html.

Blaauw, M. and Christen, J. A. 2005. Radiocarbon peat chronologies and environmental change. Applied Statistics 54, 805–16.

Bowman, S. 1990. Radiocarbon Dating. London: British Museum Press.

Bronk Ramsey, C. 1995. Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37, 425–30.

Bronk Ramsey, C. 2001. Development of the radiocarbon calibration program. Radiocarbon 43, 355–63.

Bronk Ramsey, C. in press. Age depth modeling in OxCal4. Proceedings of the 19th International Radiocarbon Conference. Oxford. April 2006. Radiocarbon 48.

Bronk Ramsey, C., Higham, T. and Leach, P. 2004. Towards high-precision AMS: progress and limitations. Radiocarbon 46, 17–24.

Brown, T. A., Nelson, D. E., Mathewes, R. W., Vogel, J.S. and Southon, J. R. 1989. Radiocarbon dating of pollen by accelerator mass-spectrometry. Quaternary Research 32, 205–12.

Buchholz, B. A., Freeman, S. P. H. T., Haack, K. W. and Vogel, J. S. 2000. Tips and traps in the ¹⁴C bio-AMS preparation laboratory. Nuclear Instruments and Methods in Physics Research B 172, 404–8.

Buck, C. E. and Andrés, C. J. 1998. A novel approach to selecting samples for radiocarbon dating. Journal of Archaeological Science 25, 303–10.

Buck, C. E., Christen, J. A. and James, G. N. 1999. BCal: An on-line Bayesian radiocarbon calibration tool. Internet Archaeology 7.

Buck, C. E., Kenworthy, J. B., Litton, C. D. and Smith, A. F.M. 1991. Combining archaeological and radiocarbon information: a Bayesian approach to calibration. Antiquity 65, 808–21.

Burky, R. R., Kirner, D. L., Taylor, R. E., Hare, P. E. and Southon, J. R. 1998. C-14 dating of bone using gamma-carboxyglutamic acid and alpha-carboxyglycine (aminomalonate). Radiocarbon 40, 11–20.

Burleigh, R., Matthews, K. and Leese, M. 1984. Consensus δ¹³C values. Radiocarbon 26, 46–53.

Christen, J. A. 1994. Bayesian Interpretation of Radiocarbon Results. Unpublished Ph.D. thesis, University of Nottingham.

Cleal, R. M. J., Walker, K. E. and Montague, R. (eds.) 1995. Stonehenge in its Landscape: The Twentieth-century Excavations (English Heritage Archaeological Report 10). London: English Heritage.

Cook, A. C., Hainsworth, L. J., Sorey, M. L., Evans, W. C. and Southon, J. R. 2001. Radiocarbon studies of plant leaves and tree rings from Mammoth Mountain, CA: a long-term record of magmatic CO₂ release. Chemical Geology 177, 117–31.

Damon, P. E. 1973. Heliomagnetic-geomagnetic modulation of radiocarbon production in earth’s atmosphere. Proceedings of the National Academy of Sciences of the United States of America 70, 2178.

Damon, P.E. and Peristykh, A. N. 2000. Radiocarbon calibration and application to geophysics, solar physics, and astrophysics. Radiocarbon 42, 137–50.

de Vries, H. 1958. Variation in concentration of radiocarbon with time and location on earth. Proceedings of the Koninklijke Nederlandse Akademie Van Wetenschappen Series B–Palaeontology, Geology, Physics, Chemistry, Anthropology B61, 94–102.

Eglinton, T. I., Benitez-Nelson, B. C., Pearson, A., McNichol, A. P., Bauer, J. E. and Druffel, E. R. M. 1997. Variability in radiocarbon ages of individual organic compounds from marine sediments. Science 277, 796–9.

Gault, A., 2002. Applying Bayesian mathematics to the Navan Fort radiocarbon chronology. Emania 19, 25–34.

Godwin, H. 1962. Half-life of radiocarbon. Nature 195, 984.

Goodfriend, G. A. 1987. Radiocarbon age anomalies in shell carbonate of land snails from semi arid areas. Radiocarbon 29, 159–67.

Guilderson, T. P., Reimer, P. J. and Brown, T. A. 2005. The boon and bane of radiocarbon dating. Science 307, 362–4.

Guilderson, T. P., Southon, J. R. and Brown, T. A. 2003. High-precision AMS C-14 results on TIRI/FIRI turbidite. Radiocarbon 45, 75–80.

Haflidason, H., Eiriksson, J. and Van Kreveld, S. 2000. The tephrochronology of Iceland and the North Atlantic region during the Middle and Late Quaternary: a review. Journal of Quaternary Science 15, 3–22.

Hall, V. A. and Mauquoy, D. 2005. Tephra-dated climate- and human-impact studies during the last 1500 years from a raised bog in central Ireland. The Holocene 15, 1086–93.

Hall, V. A., Pilcher, J. R. and McCormac, F. G. 1994. Icelandic volcanic ash and the mid-Holocene Scots pine decline (Pinus sylvestris) in the north of Ireland: no correlation. The Holocene 4, 79–83.

Hedges, R. E. M., LeeThorp, J. A. and Tuross, N. C. 1995. Is tooth enamel carbonate a suitable material for radiocarbon dating? Radiocarbon 37, 285–90.

Hodgins, G. W. L., Thorpe, J. L., Coope, G. R. and Hedges, R. E. M. 2001. Protocol development for purification and characterization of sub-fossil insect chitin for stable isotopic analysis and radiocarbon dating. Radiocarbon 43, 199–208.

Hogg, A. G., McCormac, F. G., Higham, T. F. G., Reimer, P. J., Baillie, M. G. L. and Palmer, J. G. 2002. High-precision radiocarbon measurements of contemporaneous tree-ring dated wood from the British Isles and New Zealand: AD 1850–1950. Radiocarbon 44, 633–40.

Libby, W. F. 1952. Radiocarbon Dating. Chicago: University of Chicago Press.

Libby, W. F. 1963. Accuracy of radiocarbon dates. Science 140, 279–80.

Libby, W. F., Anderson, E. C. and Arnold, J. R. 1949. Age determination by radiocarbon content: world-wide assay of natural radiocarbon. Science 109, 227–8.

Long, A. and Kalin, R. M. 1993. High-sensitivity radiocarbon dating in the 50,000 to 70,000 BP range without isotopic enrichment. Radiocarbon 34, 351–9.

Mallory, J. P., McCormac, F. G., Reimer, P. J. and Marsadolov, L. S. 2002. The date of Pazyryk, pp. 199–211 in Boyle, K., Renfrew, C. and Levine, M. A. (eds.), Ancient Interactions: East and West in Eurasia (McDonald Institute Monograph Series). Cambridge: The McDonald Institute for Archaeological Research.

Manning, S. W., Ramsey, C. B., Kutschera, W., Higham, T., Kromer, B., Steier, P. and Wild, E. M. 2006. Chronology for the Aegean Late Bronze Age 1700–1400 BC. Science 312, 565–9.

McCormac, F.G. 1992. Liquid scintillation-counter characterization, optimization and benzene purity correction. Radiocarbon 34, 37–45.

McCormac, F. G., Hogg, A. G., Blackwell, P. G., Buck, C. E., Higham, T. F. G. and Reimer, P. J. 2004. SHCal04 Southern Hemisphere calibration, 0–11.0 cal kyr BP. Radiocarbon 46, 1087–92.

McCormac, F. G., Hogg, A. G., Higham, T. F. G., Baillie, M. G. L., Palmer, J. G., Xiong, L. M., Pilcher, J. R., Brown, D. and Hoper, S. T. 1998a. Variations of radiocarbon in tree rings: Southern Hemisphere offset, preliminary results. Radiocarbon 40, 1153–9.

McCormac, F. G., Hogg, A. G., Higham, T. F. G., Lynch-Stieglitz, J., Broecker, W. S., Baillie, M. G. L., Palmer, J., Xiong, L., Pilcher, J. R., Brown, D. and Hoper, S. T. 1998b. Temporal variation in the interhemispheric C-14 offset. Geophysical Research Letters 25, 1321–4.

Mensing, S. A. and Southon, J. R. 1999. A simple method to separate pollen for AMS radiocarbon dating and its application to lacustrine and marine sediments. Radiocarbon 41, 1–8.

Millard, A. R. and Brooks, S. P. in prep. Age-depth models for sediment cores with changes in accumulation rate.

Muller, R. A, Stephenson, E. J. and Mast, T. S. 1978. Radio-isotope dating with an accelerator: a blind measurement. Science 201, 347–8.

Nelson, D. E., Korteling, R. G. and Stott, W. R. 1977. C–14–direct detection at natural concentrations. Science 198, 507–8.

O’Leary, M. 1981. Carbon isotope fractionation in plants. Phytochemistry 20, 553–67.

Pearson, G. W. 1979. Precise C-14 measurement by liquid scintillation-counting. Radiocarbon 21, 1–21.

Pearson, G. W. 1980. High-precision radiocarbon dating by liquid scintillation-counting applied to radiocarbon time-scale calibration. Radiocarbon 22, 337–45.

Pearson, G. W. 1986. Precise calendrical dating of known growth-period samples using a curve fitting technique. Radiocarbon 28, 292–9.

Pearson, G. W., Pilcher, J. R., Baillie, M. G. L. and Hillam, J. 1977. Absolute radiocarbon dating using a low altitude European tree-ring calibration. Nature 270, 25–8.

Pearson, G. W., Pilcher, J. R., Baillie, M. G. L., Corbett, D. M. and Qua, F. 1986. High-precision ¹⁴C measurement of Irish oaks to show the natural ¹⁴C variations from AD 1840–5210 BC. Radiocarbon 28, 911–34.

Pilcher, J. R., Hall, V. A. and McCormac, F. G. 1995. Dates of Holocene Icelandic volcanic-eruptions from tephra layers in Irish peats. The Holocene 5, 103–10.

Pilcher, J. R., Baillie, M. G. L., Schmidt, B. and Becker, B. 1984. A 7,272-year tree-ring chronology for Western Europe. Nature 312, 150–2.

Plunkett, G. M. 1999. Environmental Change in the Late Bronze Age in Ireland (1200–600 Cal. BC). Unpublished Ph.D. thesis, Queen’s University Belfast.

Plunkett, G. M., Pilcher, J. R., McCormac, F. G. and Hall, V. A. 2004. New dates for first millennium BC tephra isochrones in Ireland. The Holocene 14, 780–6.

Proskurowski, G., Lilley, M. D. and Brown, T. A. 2004. Isotopic evidence of magmatism and seawater bicarbonate removal at the Endeavour hydrothermal system. Earth and Planetary Science Letters 225, 53–61.

Reimer, P. J., Baillie, M. G. L., Bard, E., Bayliss, A., Beck, J. W., Bertrand, C. J. H., Blackwell, P. G., Buck, C. E., Burr, G. S., Cutler, K. B., Damon, P. E., Edwards, R. L., Fairbanks, R. G., Friedrich, M ., Guilderson, T. P., Hogg, A. G., Hughen, K. A., Kromer, B., McCormac, F. G., Manning, S., Ramsey, C. B., Reimer, R. W., Remmele, S., Southon, J. R., Stuiver, M., Talamo, S., Taylor, F. W., van der Plicht, J. and Weyhenmeyer, C. E. 2004. IntCal04 Terrestrial Radiocarbon Age Calibration, 0–26 Cal kyr Bp. Radiocarbon 46, 1029–58.

Renfrew, C. 1973. Before Civilization: The Radiocarbon Revolution and Prehistoric Europe. London: Jonathon Cape.

Richardson, F. and Hall, V. A. 1994. Pollen concentrate preparation from highly organic Holocene peat and lake deposits for AMS dating. Radiocarbon 36, 407–12.

Roberts, M. L. and Southon, J. R. in press. A determination of the absolute ¹⁴C/¹²C ratio of Ox-I. Proceedings of the 19th International Radiocarbon Conference. Oxford. April 2006. Radiocarbon 48.

Rozanski, K., Stichler, W., Gonfiantini, R., Scott, E. M., Beukens, R. P., Kromer, B. and van der Plicht, J. 1992. The IAEA C-14 intercomparison exercise 1990. Radiocarbon 34, 506–19.

Rubin, M., Lockwood, J. P. and Friedamn, I. 1987. Effects of volcanic emanations on carbon-isotope content of modern plants near Kilauea Volcano, pp. 209–11 in Decker, R. W., Wright, T. L. and Stauffer, P. H. (eds.), Volcanism in Hawaii (USGS Professional Paper 1350). Washington: US Government Printing office.

Scharf, A., Kretschmer, W., Morgenroth, G., Uhl, T., Kritzler, K., Hunger, K. and Pernicka, E. 2004. Radiocarbon dating of iron artefacts at the Erlangen AMS Facility. Radiocarbon 46, 175–80.

Schmidt, F. H., Balsley, D. R. and Leach, D. D. 1987. Early expectations of AMS: greater ages and tiny fractions. One failure?–One success. Nuclear Instruments and Methods in Physics Research B 29, 97–9.

Scott, E. M., Harkness, D. D. and Cook, G. T. 1998. Interlaboratory comparisons: lessons learned. Radiocarbon 40, 331–40.

Scott, E. M., Bryant, C., Carmi, I., Cook, G., Gulliksen, S., Harkness, D., Heinemeier, J., McGee, E., Naysmith, P., Possnert, G., van der Plicht, H. and van Strydonck, M. 2004. Precision and accuracy in applied C-14 dating: some findings from the Fourth International Radiocarbon Inter-comparison. Journal of Archaeological Science 31, 1209–13.

Spaulding, K. L., Bhardwaj, R. D., Buchholz, B. A., Druid, H. and Frisen, J. 2005. Retrospective birth dating of cells in humans. Cell 122, 133–43.

Sonninen, E. and Jungner, H. 2001. An improvement in preparation of mortar for radiocarbon dating. Radiocarbon 43, 271–3.

Stafford, T. W., Hare, P. E., Currie, L., Jull, A. J. T. and Donahue, D. J. 1991. Accelerator radiocarbon dating at the molecular-level. Journal of Archaeological Science 18, 35–72.

Stuiver, M., 1961. Variations in radiocarbon concentration and sunspot activity. Journal of Geophysical Research 66, 273–6.

Stuiver, M. and Kra, R. S. (eds.) 1986. Calibration Issue. Radiocarbon 28.

Stuiver, M. and Pearson, G. W. 1986. High precision calibration of the C14 time scale, AD 1950–500 BC. Radiocarbon 28, 805–38.

Stuiver, M. and Polach, H. A. 1977. Reporting of ¹⁴C data. Radiocarbon 19, 355–63.

Stuiver, M. and Reimer, P. J. 1993. Extended C-14 data-base and revised CALIB 3.0 C-14 age calibration program. Radiocarbon 35, 215–30.

Stuiver, M., Braziunas, T. F., Becker, B. and Kromer, B. 1991. Climatic, solar, oceanic, and geomagnetic influences on Late-Glacial and Holocene atmospheric C-14/C-12 change. Quaternary Research 35, 1–24.

Suess, H. E. 1955. Radiocarbon concentration in modern wood. Science 122, 415–17.

Telford, R. J., Heegaard, E. and Birks, H. J. B. 2004. The intercept is a poor estimate of a calibrated radiocarbon age. The Holocene 14, 296–8.

Tripp, J. A., Higham, T. F. G. and Hedges, R. E. M. 2004. A pretreatment procedure for the AMS radiocarbon dating of sub-fossil insect remains. Radiocarbon 46, 147–54.

van der Plicht, J. 1993. The Groningen Radiocarbon Calibration Program. Radiocarbon 35, 231–7.

Vogel, J. S., Ognibene, T., Palmblad, M. and Reimer, P. 2004. Counting statistics and ion interval density in AMS. Radiocarbon 46, 1103–9.

Weir, D. A. 1995. A palynological study of landscape and agricultural development in County Louth from the second millennium BC to the first millennium AD. Final report. Discovery Programme Reports 2, 77–126.

Wohlfarth, B., Skog, G., Possnert, G. and Holmquist, B. 1998. Pitfalls in the AMS radiocarbon-dating of terrestrial macrofossils. Journal of Quaternary Science 13, 137–45.