Carbon has two stable isotopes, 12C (98.9%) and 13C (1.1%). The long-lived radioactive carbon isotope 14C, commonly called radiocarbon, has a half-life of 5730 + 40 a, and exists in minute concentration (~10-12) in natural carbon through cosmic ray interactions in the atmosphere.
14C is produced in the atmosphere by nuclear reactions of neutrons with 14N:
14N + n Þ 14C + p
The neutrons themselves are secondary products of spallation reactions of primary cosmic rays (high-energy protons). In these reactions, atmospheric nuclei (mainly 14N and 16O) are shattered releasing part of their constituents (protons and neutrons). Depending on the energy of the incident primary particles, these processes may continue over several generations producing a multiple of neutrons available for the production of 14C.
The freshly produced 14C quickly oxidises to 14CO through the reaction
14C + O2 Þ 14CO + O
and resides in the atmosphere for a period of about 2 to 6 months. It then gets further oxidised to 14CO2, mainly through reaction with the extremely rare but very reactive hydroxyl radical
14CO + OH Þ 14CO2 + H
14CO2 stays in the atmosphere for approximately ten years and gets well mixed with stable CO2. Through several pathways it eventually enters various terrestrial reservoirs such as the hydrosphere and the biosphere. The main entrance channel to the biosphere is the taking up of 14CO2 through the photosynthesis of plants.
Since 14C is radioactive and the cosmic ray production goes on for much longer periods than its half-life, an equilibrium between production rate and radioactive decay is established on a global scale. As a result, the average 14C/12C atomic ratio in carbon which is in exchange with the global 14C reservoir is about 10-12. Once the exchange ceases (e.g. through death of biomaterials), the radioactive clock starts running and the age of an object can be determined from the decreasing 14C/12C ratio. The 14C/12C ratio decreases to ½ of its starting value after one half-life (5730 a), to ¼ after two half-lives (11460 a), and so on. After ten half-lives (57300 a), the ratio has decreased to ~10-3 of its original value. (2-10 = 1/1024). This leads to 14C/12C ratios of 10-15, which are at the detection limit. Therefore, 14C dating beyond 50000 years is, in general, not feasible.
Ideal conditions for radiocarbon dating depend on the following simplified assumptions (Bowman, 1990):
The atmosphere has had the same 14C concentration in the past as now; this in turn assumes constant production, constant and rapid mixing, exchange and transfer rates, as well as constant size of reservoirs.
· As a corollary of this, the biosphere has the same overall concentration as the atmosphere and therefore it is assumed that there is rapid mixing between these two reservoirs.
· The same 14C concentration exists in all parts of the biosphere.
· The death of a plant or animal is the point at which it ceases to exchange with the environment.
· After ceasing exchange, the 14C concentration in a plant or animal is only affected by radioactive decay.
It is important to note that none of these assumptions is strictly correct, beyond a rough first approximation.
The geochemical and geophysical reasons for the breakdown of these assumptions can be summarised briefly as follows:
· processes affecting the global concentration of 14C in the atmosphere (e.g. cosmic-ray variations, change in exchange rate of CO2 between ocean and atmosphere)
· source or reservoir effects (e.g. marine life forms acquire lower 14C/12C ratios)
· alteration effects, i. e. changes of the genuine 14C/12C ratio after death due to processes other than radioactive decay (e.g. exchange of carbon with the environment through chemical and physical processes, and/or biological activity)
· contamination (e. g. addition of extraneous carbon during sample preparation) 'old wood' problem (e. g. wood from archaeological sites date the time of its growth rather than the date of its use; in addition, the wood may come from parts with older tree rings).
Radiocarbon dating is the art of dealing successfully with these problems.
There is no simple
way out of these problems. Willard
Libby, the inventor of the 14C dating method, expressed
the situation well when he noted in his Nobel Prize Lecture of 1960 that
"radiocarbon dating is something like the discipline of surgery -
cleanliness, care, seriousness, and practice." Thirty six years later,
his words are still true, even though in 1960 most of the break-down reasons
for the simplified assumptions listed above where not known. However, by
following Libby's general rules for radiocarbon dating, they were eventually
discovered.
A reliable absolute age determination with 14C depends on the knowledge of the variations of the atmospheric 14C/12C ratio with time. Fortunately, these variations are now well established for the past ten thousand years through detailed measurements of 14C/12C ratios in tree rings of known age (Fig. 1).
Dendrochronology, the art of assigning an exact date to a tree ring through pattern recognition, provided the absolute time calibration. To relate a measured 14C/12C ratio in tree rings to an atmospheric 14C/12C ratio for a particular calendar year, two important conditions must be fulfilled: The carbon in a tree ring must be representative for the ambient atmospheric 14C/12C ratio and the tree ring must be a closed system after the end of one year. Both conditions seem to be well born out in a number of long-lived trees used for the dendro calibration (e.g. bristlecone pine, North Pacific sequoia, Douglas fir, German and Irish oaks). In addition, the long residence time of 14CO2 in the atmosphere leads to a well mixed global distribution, even though the 14C production rate is latitude dependent due to the geomagnetic shielding effect for cosmic rays.
The result of the tree ring measurements are calibration curves which allow one to convert an uncalibrated "radiocarbon age" into a calendar year. Basically, the radiocarbon age, t, is calculated from the measured ratio (14C/12C)t, by applying the radioactive decay law:
(14C/12C)t = (14C/12C)t = 0 e-lambda t
Here, (14C/12C)t=0 is a well defined (but arbitrarily chosen) ratio for the year 1950 AD, assumed to be the same at all times. The decay constant is related to the half-life through = ln2/t½, with t½=5568 a. It is irrelevant - yet sometimes confusing - that this half-life (the so-called Libby half-life) is about 3% shorter than the currently accepted half-life value of 5730 + 40 a (Goodwin, 1962).
The radiocarbon age is given in years BP (Before Present, which is set at 1950 AD). It is important to note that this age does only depend on the measured ratio and otherwise fixed quantities (the 14C/12C ratio at 1950 AD and the Libby half-life), but it does not give the true age. The latter can only be determined through the calibration curve and can deviate substantially from the radiocarbon age due to the large changes of the 14C content in the atmosphere (Fig. 1). On the other hand, the radiocarbon age, once determined, does not change with time, whereas the calibrated age might change depending on possible refinements of the calibration curve. Therefore, the radiocarbon age is the more relevant quantity to be reported if comparisons with earlier measurements are to be performed.
Two examples of the calibration curve are shown in Fig. 2, relevant for the Early Bronze Age period of the Cemetery in Franzhausen I (Fig. 2a), and for the Avar Period (Fig. 2b), proposed to be investigated in detail. It is possible that the calibration curves will improve as time goes on. Therefore, precisely measured 14C/12C ratios for the samples to be investigated may lead to better absolute ages as time goes on. In addition, if several radiocarbon ages are measured for a particular time period, "wiggle matching" to the corresponding section of the calibration curve may also lead to an absolute age assignment.
(together with Christopher Bronk Ramsey)
We studied and tested four available 14C-calibration programs. Calib 3.03 from Seattle (Stuiver, Reimer, 1993), Cal 2.0 from Groningen (Van der Plicht, 1993), CalibETH 1.5 from ETH-Zürich (Niklaus, 1991) and OxCal 2.18 from Oxford (Bronk Ramsey,1995). We came to the conclusion that OxCal is the most advanced and sophisticated program at the moment. Therefore we asked the author of the program, Christopher Bronk Ramsey, if he would like to co-operate with us for the further development of OxCal. He agreed and we developed together the following proposal for the future of OxCal.
This grant proposal relates to the statistical analysis of dating evidence in the study of archaeological and environmental sites. The use of Bayesian statistics (Bayes, 1763) in this area is becoming more widespread with the development of the computer program OxCal which is currently used by groups from all over the world. With a substantial amount of feedback from these users and from our own experience of analysing archaeological sites we see some important areas where development is needed.
Some updating of the program is needed to keep pace with current developments in information technology. In particular a new 32-bit version of the program with a more standardised installation procedure for Windows 95 or Windows NT is required. As well as simplifying certain aspects of the display capabilities of the program (such as defining axes for comparisons of cultural groups) new methods are also required for the display of cultural sequences both on their own and in conjunction with radiocarbon dates. Also relevant to this is the ability to plot other information such as oxygen isotope records on the same diagrams.
The other main area of development we see is in the interface between OxCal and radiocarbon databases. Here the program needs to be able to calibrate large numbers of samples in batch mode and generate plot files in Postscript format for publication.
Another interesting possibility is the automatic generation of time tables, how they are normally used in archaeology to show the sequence of culture groups in one area and the contemporaneity of groups in different areas.
Also very interesting is the usage of GIS (Geographic Information Systems) or alike programs to show chronological information on distribution maps. Here a link could be made to SERION , a program package developed by Stadler (Stadler, 1992).
The OxCal WWW site already provides information on radiocarbon calibration to the research community. We would like to expand this further by providing (either directly or via links to other institutions) information such as isotope records, cultural chronologies and pollen sequences in a format which can be displayed using OxCal, thereby allowing users of the program to look at their own data in the wider archaeological and environmental context. Here the collaboration between Oxford an Vienna will also include the Vienna archaeological 14C dates database.
In cases where radiocarbon dating is being used to date events by association, the problems of residual and intrusive material are widespread. As a result careful investigators perform groups of radiocarbon dates for each horizon where this is possible. It is then possible to identify obvious outliers, but in the absence of any other technique the remaining radiocarbon dates are often combined directly. This practice is both statistically invalid and can give misleading results. There are three widely applicable models which could be used for analysis of this kind of information:
all material is residual (for example a destruction layer where all of the material should predate the event of interest) - sometimes referred to as the "old wood effect" or "old wood problem".
all material post-dates the event (for example where short-lived material within a ditch is used to date its construction).
both residual and intrusive material are present because of general mixing.
In all cases the dates will cluster towards the event of interest but simple combination will give an incorrect date (too early in case 1 and too late in case 2). By modelling the distributions of dates using Bayesian statistics it is possible to give a better estimate of the true date (along with realistic error terms) and for the timescale over which the material accumulated.
Particularly in environmental studies, material is dated from sequences in order to supply both the absolute age of the sequence and the deposition rate. Given that the resolution of radiocarbon dates is frequently similar to the sampling intervals it is not easy to estimate the deposition rate directly. By modelling the deposition rate as uniform, or by putting some constraints on its variability, it is possible to obtain an estimate for the deposition rate and to assign to this realistic error limits. The ability to perform such analysis routinely would be very valuable and would be much less susceptible to misinterpretation than a simple "best fit" approximation for which the precision is unspecified.
When radiocarbon dates are close to the limits of the techniques the errors become very asymmetric and interpretation becomes difficult. For example a radiocarbon date of 45,000 ± 5000BP has a significant chance of being 70,000BP. Even the quoting of asymmetric errors does not overcome this problem. In addition some dates are quoted as "greater than dates". In such cases a new Bayesian approach is needed in order to give reliable answers to chronological questions and so that groups of such dates with stratigraphic relationships can be dealt with satisfactorily.
In sites where dateable material is difficult to come by or where the period of interest extends beyond the range of some techniques, the chronological information on a site is frequently of more than one type. The program OxCal does allow information of this sort to be entered but with the exception of calibrated radiocarbon dates the probability distributions must be essentially gaussian in form. In practice for many dating techniques (such as Uranium series, TL and OSL) the distributions are not gaussian. While this does not matter if the dates are merely being compared to one another, if the probability distributions are to be combined using Bayesian statistics it becomes essential that the forms of these distributions are better characterised. In most of these cases the mathematical information is available but algorithms need to be developed to use this information to generate probability distributions.
Within this project we hope to resolve part of the above list of possible improvements of OxCal.