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Radiocarbon dating

A method of obtaining age estimates on organic materials which has been used to date samples as old as 75,000 years. The method was developed immediately following World War II by Willard F. Libby and coworkers, and has provided age determinations in archeology, geology, geophysics, and other branches of science.

Radiocarbon (14C) determinations can be obtained on wood; charcoal; marine and fresh-water shell; bone and antler; peat and organic-bearing sediments; carbonate deposits such as tufa, caliche, and marl; and dissolved carbon dioxide (CO2) and carbonates in ocean, lake, and ground-water sources. Each sample type has specific problems associated with its use for dating purposes, including contamination and special environmental effects. While the impact of 14C dating has been most profound in archeological research and particularly in prehistoric studies, extremely significant contributions have also been made in hydrology and oceanography. In addition, beginning in the 1950s the testing of thermonuclear weapons injected large amounts of artificial 14C (“bomb 14C”) into the atmosphere, permitting it to be used as a geochemical tracer.

Basis of the Method

Carbon (C) has three naturally occurring isotopes. Both 12C and 13C are stable, but 14C decays by very weak beta decay (electron emission) to nitrogen-14 (14N) with a half-life of approximately 5700 years. Naturally occurring 14C is produced as a secondary effect of cosmic-ray bombardment of the upper atmosphere (Fig. 1). As 14CO2, it is distributed on a worldwide basis into various atmospheric, biospheric, and hydrospheric reservoirs on a time scale much shorter than its half-life. Metabolic processes in living organisms and relatively rapid turnover of carbonates in surface ocean waters maintain 14C levels at approximately constant levels in most of the biosphere. The natural 14C activity in the geologically recent contemporary “prebomb” biosphere was approximately 13.5 disintegrations per minute per gram of carbon.  See also: Cosmogenic nuclide; Isotope

Fig. 1  Generation, distribution, and decay of 14C.

To the degree that 14C production has proceeded long enough without significant variation to produce an equilibrium or steady-state condition, 14C levels observed in contemporary materials may be used to characterize the original 14C activity in the corresponding carbon reservoirs. Once a sample has been removed from exchange with its reservoir, as at the death of an organism, the amount of 14C begins to decrease as a function of its half-life. A 14C age determination is based on a measurement of the residual 14C activity in a sample compared to the activity of a sample of assumed zero age (a contemporary standard) from the same reservoir. The relationship between the 14C age and the 14C activity of a sample is given by the equation below, where t

is radiocarbon years B.P. (before the present), λ is the decay constant of 14C (related to the half-life t1/2 by the expression t1/2 = 0.693/λ), Ao is the activity of the contemporary standards, and As is the activity of the unknown age samples. Conventional radiocarbon dates are calculated by using this formula, an internationally agreed half-life value of 5568 ± 30 years, and a specific contemporary standard. Most laboratories define the contemporary standard value by using one of the standards prepared by the U.S. National Bureau of Standards [NBS; now known as the U.S. National Institute of Standards and Technology (NIST)], or a standard with a known relationship to the NBS/NIST oxalic acid preparations.

Measurement of Radiocarbon

The naturally occurring isotopes of carbon occur in the proportion of approximately 98.9% 12C, 1.1% 13C, and 10−10% 14C. The extremely small amount of radiocarbon in natural materials was one reason why 14C was one of the isotopes which had been produced artificially in the laboratory before being detected in natural concentrations. The routine development of the radiocarbon method was made possible by the development by Libby of a practical method of low-level counting. To detect the very weak beta-decay characteristic of 14C, a means had to be devised to introduce the sample directly into the sensitive volume of a detector. In all of Libby's early work, the sample was converted to solid carbon (amorphous elemental carbon) and deposited on a sleeve which fitted inside a screen-wall type of Geiger counter. The counting rate of an unshielded screen-wall counter was on the order of 500 counts per minute.

Since the activity from 14C decay of a modern sample was expected to be about six or seven counts per minute, the total background counting rate had to be radically reduced. This was accomplished initially by placing the instrument in an iron shield with 20-cm (8-in.) walls. This reduced the activity in the detector to 120 counts per minute, still unacceptably high. The final reduction was made possible by enclosing the sample counter in a ring of smaller Geiger counters. The sample counter and the outer guard ring were connected together electronically so that any pulse from any of the outer Geiger tubes would inactivate the sample counter for about 10−3 s. This anticoincidence system reduced the background in the center detector to about five counts per minute.

With this system, the maximum age that could be measured was about 23,000 years and required the use of 10–12 g (0.35–0.42 oz) of carbon from sample materials. Because of self-absorption of the weak betas in the sample, the efficiency of the detector was only about 5%. Because of this and the susceptibility of the carbon black to contamination from airborne radioactive fallout, the solid carbon technique was replaced by either gas counters or liquid scintillation systems.  See also: Low-level counting; Radioactivity

Gas counters

In the early 1950s, both proportional (Fig. 2) and Geiger gas counters were employed in 14C work, using carbon dioxide, carbon disulfide, acetylene, methane, or ethane as counting gases. As in the case of the solid carbon system, the center counter containing the sample was surrounded by individual Geiger tubes or an annular or continuous ring guard, all housed within an iron or lead shield assembly. Efforts to reduce the background values in gas detectors have resulted in various types of experimental arrangements, including the location of counters in underground vaults. In such underground facilities, the contribution of the meson flux, the major contributor to the background rate, can be significantly reduced. Because of the 90–95% efficiency in most gas detector systems, the typical maximum age limits were extended to 40,000–60,000 years, depending on the experimental configuration, including the volume of the detectors and the level of the background count rates in specific detectors. Isotopic enrichment of sample gases permits the maximum age attainable to be extended several additional half-lives. In general, sample-size requirements with gas detectors were reduced from that required with the solid carbon method—special systems being designed to permit the measurement of a sample with as little as 0.1 g (3.5 × 10−3 oz) of carbon.  See also: Geiger-Müller counter; Ionization chamber; Meson

Fig. 2  Large-volume proportional counter, which is used for carbon-14 measurements. The outer shield is closed by rolling doors. The sample is introduced into the radiation counter in the form of carbon dioxide gas. (Geochemical Laboratory, Lamont-Doherty Geological Observatory, Columbia University)

Liquid scintillation systems

Current liquid scintillation systems involve the conversion of samples to benzene. The addition of a scintillator chemical allows beta-decay events to be monitored by photomultiplier tubes. Earlier liquid scintillation systems used for 14C measurements generally required larger samples. However, currently the amounts required are comparable to gas counting systems. Continuing developments in liquid scintillation technology for low-level measurement have provided the ability to monitor counter performance in much greater detail than typically is possible in gas counting, and have also resulted in reduced background values. In these systems, the maximum ages that can be measured can be extended beyond that possible with typical gas systems.

Direct detection

Both of the conventional decay counting methods share a common problem in that they employ an inherently inefficient means of monitoring 14C concentrations in samples. In 1 g of modern carbon, for every decay per minute there are about 4 × 109 atoms of 14C. Counting methods have been developed which employ particle accelerators as very sensitive mass spectrometers, thus counting the 14C atoms directly.

It has long been recognized that if the 14C atoms could be detected directly, rather than by waiting for their decay, smaller samples could be used for dating and older dates could be measured. A simple hypothetical example to illustrate this point is a sample containing only one atom of 14C. To measure the age (that is, the abundance of 14C), the sample can be placed into a mass spectrometer and that atom counted, or the sample can be placed into a Geiger counter and counted, requiring a wait on the average of 8000 years (the mean life of 14C) for the decay. In practice, neither the atoms nor the decays can be counted with 100% efficiency, but the huge advantage for atom counting remains.

Until 1977, attempts at direct atom counting for 14C and other natural radioisotopes failed, because of the extremely low concentration of 14C. Ordinary mass spectrometers could not see the tiny 14C signal in the background of other atoms and molecules in the sample. Even trace amounts of nitrogen would swamp the 14C signal, since 14N forms ions with nearly identical mass and identical charge to that of the 14C atoms.

The technique for detecting 14C atoms [and other natural radioisotopes such as tritium, beryllium-10 (10Be), and chlorine-36 (36Cl)] is a combination of mass spectrometry and accelerator technology, called accelerator mass spectrometry (AMS). The approach was first demonstrated using a cyclotron. This accelerator, which sent particles along a spiral trajectory, was used as an ultrasensitive mass spectrometer to distinguish ionized carbon isotopes by their charge-to-mass ratio. Detecting 14C by this means was possible, but consistent results proved difficult to achieve despite years of effort.  See also: Mass spectrometry

Another type of AMS technology uses a tandem electrostatic accelerator (Fig. 3). The device employs two stages. First, a negative ion beam is accelerated and passed through a stripper, which removes the electrons, converting the beam to positive ions. Then the particles are further accelerated. The stripping process breaks up molecules of mass 14, which would otherwise interfere with the detection of 14C, and the negative ion beam eliminates 14N since there are no known stable negative nitrogen ions. Almost all AMS 14C applications currently use tandem accelerators to accomplish routine measurements.  See also: Particle accelerator

Fig. 3  Accelerator mass spectrometry system for the direct detection of 14C atoms. (Center for Mass Spectrometry, Lawrence Livermore National Laboratory)

The advent of AMS technology in the late 1970s brought about an enormous boost in detection efficiency that promised three important advantages for 14C dating. First the amount of carbon required was reduced from grams to milligrams. Second, counting times were reduced from days, weeks, or even months to minutes. Finally, it was initially thought that the detection sensitivity would increase so that the maximum age datable with 14C might be extended to 100,000 years. However, sensitivity is limited by very small amounts of contamination introduced during sample preparation. Much of this contamination stems from the requirement in most laboratories that samples be converted to graphitic carbon for measurement. In routine operation, current AMS technology can measure between 40,000 and 50,000 years, and rarely, 60,000 years.

The ability to use milligram (rather than gram) samples is very important for dating. Certain irreplaceable objects (for example, parchments, cloth, and chips of wood) would have had to be destroyed in order to extract the gram of carbon required for a date; for the accelerator method, only a small piece of the artifact is required. In addition, the ability to date by using only milligrams of carbon allows careful selection of the sample used. Any part of the object which may have been contaminated by modern carbon can be ignored; small seeds trapped in the object, or even specific amino acid compounds which are less likely to come from modern carbon contamination, can be selected.

Despite the sensitivity of the accelerator technique, decay dating will probably continue to be used for 14C dating when gram amounts of carbon are available. However, the technology of atomic mass spectrometry continues to be developed and will increasingly be used for routine 14C analysis. The accuracy of 14C values based on atomic mass spectrometry has become essentially comparable to that obtained with decay counting.

Accuracy of Radiocarbon Determinations

A measurement of the 14C content of an organic sample will provide an accurate determination of the sample's age if it is assumed that (1) the production of 14C by cosmic rays has remained essentially constant long enough to establish a steady state in the 14C/12C ratio in the atmosphere, (2) there has been a complete and rapid mixing of 14C throughout the various carbon reservoirs, (3) the carbon isotope ratio in the sample has not been altered except by 14C decay, and (4) the total amount of carbon in any reservoir has not been altered. In addition, the half-life of 14C must be known with sufficient accuracy, and it must be possible to measure natural levels of 14C to appropriate levels of accuracy and precision. Studies have shown that the primary assumptions on which the method rests have been violated both systematically and to varying degrees for particular sample types. Several approaches have been developed to provide calibration and corrections of conventional 14C values. The basis of the calibration and correction procedures will be discussed in the context of a brief review of the assumptions of the method.

Constancy in radiocarbon production rates

Carbon-14 determinations on known-age samples have revealed systematic discrepancies in the 14C time scale. The first hint of such anomalies came from early 14C measurements on Egyptian archeological materials. Samples which, on historical grounds, should have dated to the early part of the third millennium B.C. yielded 14C values some 700–800 years too young. Carbon-14 determinations carried out on dendrochronologically dated wood, periglacial varves, and lake sediments confirmed the fact that there have been systematic variations in 14C values over time. The data which first contributed most directly to the study of these anomalies was the dendrochronological time scale provided by the bristlecone pine (Pinus longaeva), from the White Mountains of east-central California, developed by C. W. Fergusson. His data provide an unbroken tree-ring series back to almost 6700 B.C. An independently developed bristlecone tree-ring chronology from a different locality in the southern portion of the White Mountains, developed by V. C. La Marche and T. P. Harlan, supports the accuracy of the Fergusson chronology at least as far back as about 3500 B.C. Carbon-14 determinations on bristlecone pine as well as tree-ring-dated samples from the sequoia (Sequoia gigantea) and European oaks (Quercus spp.) have been undertaken by a number of laboratories, and 14C determinations on these samples provide data over the last 10,000 years.  See also: Dendrochronology; Varve

Main trend

Upon examination of the data in Fig. 4 and other similar plots, it becomes apparent that radiocarbon years and calendar years are not necessarily equivalent. If such had been the case, all of the data points plotted on Fig. 4 would lie along the horizontal 0 line. In fact, some of the points lie above the line, indicating that 14C values in these periods are too old. Conversely, those below the 0 line are too young when compared to the tree-ring data. This plot indicates that there are two major components to the deviations. The first is a general main-trend secular variation phenomenon (the curved line) exhibiting during the Holocene, a sine-wave function with an apparent period of about 8500–9000 years, with a maximum deviation of about 800 years, approximately 8000 years ago.

Fig. 4  Secular variation/major trend; relationship between radiocarbon and dendrochronological age of wood samples. (After J. Klein et al., Calibration of radiocarbon dates, Radiocarbon, 24(2):103–150, 1982)

The characteristic of the secular variation anomalies in the period before about 10,000 years ago cannot, at present, be documented by tree-ring/14C data. It has been argued, however, that the major part of the effect may be estimated by examining the record of the Earth's dipole geomagnetic field over time. Variations in the intensity of the dipole field modulate the cosmic-ray flux in the vicinity of the Earth. An increase in the field strength, for example, diverts more of the cosmic-ray particles away from the Earth, resulting in a decrease in the production of 14C.

Geophysicists have collected data which document changes in the intensity of the Earth's dipole field for the last few hundred thousand years. Because of the apparent inverse relationship between the intensity of the field and the 14C production rate, it would, in theory, be possible to extrapolate the maximum and minimum secular variation deviations back to the limit of the 14C method. Unfortunately, such data are not yet as precise as might be wished. However, comparisons of 14C ages with uranium-thorium (U-Th) ages obtained on cores from coral deposits support conclusions based on the 14C/tree-ring data up to the limit of the current dendrochronological data. Uranium-thorium values can be used to continue to examine the 14C deviations over the last 30,000 years. Such data indicate that radiocarbon ages earlier than 10,000 years B.P. continue to be systematically younger than U-Th ages, with a maximum difference of about 3500 years approximately 20,000 years ago.  See also: Paleomagnetism; Rock magnetism

De Vries effect

In addition to the long-term secular variation phenomenon, the bristlecone pine data have revealed the presence of high-frequency components to the variation in 14C activity. These short-term oscillations or wiggles have sometimes been called the De Vries effect after the pioneering Dutch researcher, Hessel de Vries, who was one of the first to call attention to the existence of systematic anomalies in 14C values. Although almost all investigators concerned with the issue have agreed that the tree-ring/14C data definitely reveal the presence of a number of short-term perturbations, the frequency and magnitude of earlier episodes during the Pleistocene, (that is, > 10,000 years B.P.) have not been resolved. Likewise, there are uncertainties as to the causes of the De Vries effect, although variation in solar activity (heliomagnetic effects) has been seen as an important factor.

Calibration of radiocarbon dates

The existence of main trend and De Vries deviations has important implications in the interpretation of 14C determinations. The long-term variations result in the necessity to calibrate conventional 14C dates in terms of the known variation between radiocarbon time and real or calendar time as documented by the dendrochronological/14C values. The magnitude of the calibration varies depending on from what time period a sample is derived. For the period back to about 1000 B.C., corrections required by virtue of the secular-variation deviations do not exceed about 150 years. Prior to 1000 B.C., the magnitude of the correction steadily increases. By using data such as those presented in Fig. 4, various approaches have been developed to “calibrate” radiocarbon values. In this context, calibration involves taking a 14C age value expressed as a conventional radiocarbon date and adding or subtracting the number of years required to bring the conventional age into conformity with the 14C determinations on known-age tree-ring-dated samples.

The documentation of the presence of the De Vries or short-term anomalies has introduced a second problem in the calibration of 14C values. Periods of rapid change in the 14C content of the atmosphere result in situations where a single 14C value may reflect two or more points in real time. The characteristics of the short-term anomalies are illustrated in Fig. 5. During periods of particularly rapid change in 14C activity, it is usually not possible to use 14C data to document temporal intervals in units of less than a few hundred years. Thus the dendrochronologically based calibration data can be used to identify the general degree of deviation of 14C values from real time and also the degree of maximum precision which is possible for specific temporal intervals.

Fig. 5  Secular variation/De Vries effect. Example of short-term variations in 14C activity; detail of De Vries effects using high-precision measurements for period of approximately 4500–5100 14C years B.P. (After A. F. M. de Jong and W. G. Mook, Medium-term atmospheric 14C variations, Radiocarbon, 22(2):267–272, 1980)

The impact of the De Vries effects on the precision of 14C values, as applied to archeological and historical problems, must be considered. The need to take into account these shorter-term variations have, for example, been demonstrated in the evaluation of 14C values on twelfth- and fourteenth-century European medieval archeological materials.  See also: Archeological chronology

Lack of geographical and altitude variations

Concern has been expressed as to whether variation in the 14C content of wood samples taken from a small number of localities in the Northern Hemisphere can be used to document worldwide secular variation effects. This question has been specifically answered as a result of studies of 14C concentrations in tree rings from Patagonia, Canada, and Europe. The maximum deviations noted in contemporaneous woods were between those grown in the Southern and Northern hemispheres. However, even in this case, the variation did not exceed 0.5% or about the equivalent of 40 years.

Studies have also shown the lack of any significant altitude effect on 14C concentrations in wood. A concern had been expressed that solar protons of appropriate energies would interact with nitrogen to form 14C directly in wood samples growing at high elevations. The projected effect would be to inflate the 14C content of a sample so that the 14C age would appear to be significantly younger than its true age. However, calculations indicate that the maximum effect that could be obtained, assuming the most advantageous parameters, would not exceed 40 years. Other evidence suggests the actual effect is much less. The bristlecone pine wood of the White Mountains grows at about the 3350-m (11,000-ft) level. That there is no measurable 14C produced as a function of altitude is indicated by the essential agreement in age between the high-altitude bristlecone and low-altitude European and American sequoia samples of the same dendrochronological age.

Variability in radiocarbon distribution

An important feature of the 14C method is its potential to provide directly comparable age determinations on a worldwide basis for a wide variety of organic samples. For this potential to be realized, 14C, following its production, has to be mixed rapidly and completely throughout all of the carbon-containing reservoirs on a time scale not exceeding a few tens of years. To the degree that such conditions prevail, the contemporary 14C content of all organic samples will be essentially identical. It was quickly determined that such is not the case. The initial 14C content of samples could be significantly affected as a result of environmental conditions. A classic illustration of the problem was the discovery of living organisms from a fresh-water lake exhibiting 14C ages of approximately 2000 years. In this case a large percentage of the carbon used by the organisms was derived from dissolved CO2 from the limestone bed of the lake. The fictional age of the modern samples had been produced as a result of the dilution of contemporary 14C activity by “dead” carbon (that is, containing no 14C) from the limestone. Another example is provided from trees growing in active volcanic areas. The CO2 emitted during volcanic discharges is characteristically depleted of its 14C. Living trees exhibiting apparent ages as much as 1000 years from such environments have been reported.

One effect of the recognition that the geochemical environment of a sample can affect its initial 14C concentration has been to cast doubt on the reliability of particular types of samples. The use of shells in 14C studies has been affected, since a tradition arose that their use should be discouraged. Terrestrial shells (gastropods) from most fresh-water environments generally merit this negative evaluation, since they typically take up carbonate which is not in equilibrium with atmospheric 14C. The reputation of marine shells was adversely affected primarily as a result of early experiences with shells taken from several archeological sites along the Peruvian coast. Marine shell samples were found to have 14C values that exhibited an apparent age as much as 900 years greater than that of charcoal samples assumed to have been deposited contemporaneously. It was therefore assumed that marine shells would consistently yield anomalous values.

Subsequent studies showed that marine shells can yield generally acceptable values if the conventional 14C values can be corrected for upwelling effects. By examining 14C concentrations in shells collected alive in the period before nuclear testing contributed bomb 14C, it was determined that many marine shells exhibited apparent ages ranging as high as 1200 years. Part of the reason has to do with the fact that ocean water depleted of 14C by long residence times in the deeper parts of the ocean is periodically upwelled or brought to the surface and mixed with surface ocean water. The effect is to dilute the contemporary 14C activity of the surface ocean near the westward-facing continental margins, resulting in a spurious apparent age for the organisms utilizing surface-ocean-water carbonates. Shells growing in locations adjacent to the outlets of major river systems whose water is depleted of 14C as a result of exchange with limestone or other carbonate-bearing rocks can also give spurious apparent ages. This is probably the explanation for the false ages exhibited by shells growing in the Gulf of California (Colorado River discharge) and the northern part of the Gulf of Mexico (Mississippi River discharge).  See also: Continental margin; Upwelling

Upwelling and other reservoir effects are highly variable depending on location and specific environmental conditions. For the western coasts of North and South America, for example, the magnitude of the upwelling effects can range from about 80 to 1000 years. It is most severe along the Peruvian coast, contributing to an explanation for the problematical 14C values on marine shells from that region. Unfortunately, it is possible for shells from highly localized regions to exhibit a sizable range in apparent ages. Samples from the Galápagos Islands show a variation of about 350 years. Such a fluctuation in such a relatively small area emphasizes the fact that the magnitude of upwelling effects for any region must be carefully established by multiple sampling of closely spaced areas.

Problems similar to those associated with marine shells arise for a number of sample types and geochemical environments where contemporary samples may not be in equilibrium with the atmosphere. In each case, empirically derived values for the contemporary standard must be obtained for each sample type or locality, or both. In practice, this is accomplished by determining the degree of deviation from whatever contemporary standard is used to define modern or “zero 14C age” samples. For example, specific values are required for marine shells from different oceanic regions, for fresh-water shells in specific terrestrial environments, and for Arctic and Antarctic specimens.

Variability in carbon isotope ratios

For the 14C method, the basic physical measurement used to index time is the 14C/12C ratio. However, carbon has three naturally occurring isotopes. Variation in this ratio can be effected by influences other than the decay of 14C. The most common problem occurs when carbon-containing compounds not indigenous to the original samples are physically or chemically introduced into the sample matrix resulting in the contamination of the sample. Usually less difficult to deal with are fractionation effects in which a variation in the stable carbon ratio translates into a change in the 14C/12C ratio.

Contamination

The sources and effects of the introduction of foreign organics into samples are complex; they depend on the nature and condition of the sample materials, the characteristics of the environment to which the samples were exposed, and the period of time over which the exposure occurred. Precautions exercised to avoid contamination effects are unique to each sample type and source locality. A series of procedures to remove potential contaminants in samples has been established by research laboratories. Most sample preparation techniques are concerned with completely removing what is assumed to have not been present when the original sample died or was removed from exchange with its carbon reservoir. Samples such as wood and charcoal, which can be subjected to treatment with strong acids and bases to facilitate the removal of absorbed carbonates and soil humic and fulvic acids and other soluble soil organic matter, are preferred. Less desirable are cases where it is difficult to distinguish between contamination and the original sample as with various types of carbonate samples, such as tufa and caliche.

It is usually possible to infer the effect of known contamination effects on a given sample in terms of the direction that the age change will take for a given type of contamination, but the magnitude of the errors can be calculated only if the true age of the original sample, the age of the contaminant, and the percentage contribution of the contaminant are all known. Usually this is difficult to determine. However, with few exceptions, problems of contamination for samples with ages of less than about 10,000 years can be solved, usually by applying standard pretreatment approaches developed by 14C laboratories. For materials with expected ages in excess of 10,000 years, sample contamination problems typically become more serious, and laboratories must exercise even more rigorous care in the pretreatment processes.

Fractionation effects

While all the isotopes of carbon follow the same chemical or physical pathway, the rate at which this occurs varies as a function of their difference in mass. The pioneering studies of Harmon Craig pointed to the need to consider variations in the stable isotope ratio (13C/12C) of samples to obtain precise 14C values. Variations equivalent to up to several hundred years can result if 14C values are not standardized in light of 13C/12C ratios. Fortunately, no significant fractionation effects are usually observed in standard sample materials such as charcoal or wood. Problems arise, however, when it is necessary to compare 14C values from a variety of sample types such as grasses, grains, seeds, succulents, and marine carbonates, as well as standard terrestrial organics. In such cases, it is necessary to use the stable isotope ratios to correct the 14C values onto a common scale.

Variability in amount of carbon

In addition to the variation in production and distribution of 14C over time and within portions of various carbon reservoirs, variations may result from situations where carbon not in equilibrium with the contemporary standard values is added or removed from any reservoir. Two instances are well documented since they occurred within the last century as a result of human intervention in the carbon cycle. The first, beginning in the middle of the nineteenth century, is known as the industrial or Suess effect. The combustion of fossil fuels added enough “dead” 14C to the atmosphere to result in the reduction by about 3% in biospheric 14C activity. In the more recent atomic bomb or Libby effect, relating to the detonation of thermonuclear devices in the atmosphere in the early 1950s, large amounts of artificial 14C were produced, almost doubling the amount of 14C in the terrestrial biosphere. When combined with the late-eighteenth-century De Vries excurses, the Suess effect makes it difficult to distinguish 14C concentrations within the last two centuries. This is one of the reasons why laboratories generally use 100 or 150 years as the minimum age which can be cited. It also explains why laboratories cannot use modern wood as a contemporary reference.

Half-life of radiocarbon

The fundamental constant which permits the conversion of a 14C/12C ratio into an age value is the half-life or decay constant of 14C. Initially in the development of the method, Libby and collaborators used the value 5720 ± 47 as the half-life figure, but soon adopted the weighted average of three independently obtained measurements. The average value was 5568 ± 30 and this became identified as the Libby half-life. In 1962, at the 5th Radiocarbon Dating Conference at Cambridge, it was decided that 5730 ± 40 probably represented a more accurate approximation of the actual half-life. It was agreed, however, that the Libby half-life would be used in the calculation of conventional 14C determinations. The stated reason was that any changes in the value would introduce unneeded confusion in the radiocarbon literature.

The issue of the correct half-life for 14C has lost a considerable amount of its significance because of the discovery and documentation of similiar variation and De Vries effects. The existence of dendrochronologically documented relationships between 14C age and calendar age, for samples up to about 10,000 years old, enables researchers to circumvent the problem of the actual 14C half-life and proceed to calibrate these 14C age values directly.

Statistical and contextual uncertainties

Most 14C determinations are expressed in the form: age value (in 14C years B.P.) ± statistical uncertainty. The age value is calculated by using the equation previously presented. The measurement uncertainty results from statistical considerations inherent in the random decay process characteristic of all radioactive isotopes. A date, for example, of 5600 ± 80 14C years B.P. reflects the fact that the count rate of the sample is about 50% of the modern reference standard (that is, it has decayed for a period of about one Libby half-life) and the age value is known to about 1% or 80 years. Statistical uncertainties in 14C work are usually cited in terms of one standard deviation errors. The expression 5600 ± 80 is a shorthand manner of stating that there are two chances out of three that the age equivalent of the counting rate for this sample will be contained within the range 5520 to 5680. An accurate statement of the results of a 14C determination must include a listing of the measurement uncertainty. In addition, some laboratories increase this value to take into consideration changes that affect counting conditions, such as drift of electronic equipment and changes in barometric pressure. Statistical errors are not cited only when the counting rate of a sample is statistically indistinguishable from the background counting rate for the counter being used. The result is expressed as a minimum or infinite value by stating that the age is “greater than” a limit imposed by the characteristics of the counting system being employed (for example, >40,000).

The processing and counting of a sample to determine its 14C age is a challenging analytical procedure. However, a technically correct value which has been carelessly collected may be scientifically worthless. Often the significance and importance of a 14C determination are only as good as the attention to detail which went into documenting the geological, historical, or archeological context of the sample. It is important to be aware of what a 14C date does and does not indicate. A 14C value provides a temporal index of when the sample was removed from its reservoir. For example, a 14C determination on a piece of charcoal or wood provides an age value for the tree rings which make up the sample. A 14C date taken on a piece of wood taken from a beam excavated from a ruined structure may indicate the time when the building was constructed if the sample was taken from the outside rings of the tree used as the source of the timber and if the timber itself did not happen to be reused from an earlier structure. Problems such as these often confront geologists and archeologists as they attempt to critically interpret the dating evidence provided by the 14C method.

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