Methods and procedures applied


II. Radiocarbon dating - 14C

Radiocarbon is produced primarily by cosmic radiation from nitrogen with the nuclear reaction:

14N (n,p) 14C

and decays by b- emission (Emax =158 keV) with a half life of 5730 ± 40 years.The average specific activity of modern carbon is 13.56 + 0.07 dpm/g C; there is about 75t of radiocarbon on the Earth. The isotopic ratio of 14C to 12C is 1.2 x 10-12.

The radiocarbon formed in the upper atmosphere is oxidized to 14CO2. The rate is between 1.7 and 2.5 atoms/cm2/s. After mixing with atmospheric CO2 (0.03 vol %), it becomes part of the carbon cycle in the biosphere. Assimilated by plants, it enters the food chain and thus becomes part of all living organic matter. Except for slight isotopic fractionation, which can be corrected, the specific activity of 14C in terrestrial organic matter is the same as in atmospheric carbon dioxide.

The 14C/12C ratio decreased continuously since the beginning of industrialisation in the last century, when CO2 was released in growing amounts to the atmosphere from the combustion of fossil fuels, whose old carbon lacks 14C. This effect reduces the  14C concentration compared to the pre-industrial level (Suess-effect). The decrease amounts to about 3 % form 1850 to 1950.

Charcoal, wood, seeds, bone, ivory, horn, humus, peat, leaves, resin, lichen, tissue, hair, secondary carbonate (e.g., travertine and speleothem), mollusc shells, shells, egg, soil and sediment, as well as groundwater and ice can be dated, in the age range of 100 to 40,000 years.

Radiocarbon dating in LES implies sample pre-treatment, production of high purity CO2 gas, followed by GPC.

Different samples can be analysed:

  • Organic material
  • Bone
  • Shell, mollusc
  • DIC

Sample pre-treatment

Wood The samples are treated with AAA (acid-alkali-acid) and then fragmented into small pieces (<l0 mm) and ground. The sieved fraction (0.2mm < grain size < l mm) is treated with 4% HCl (80o C, 24 hr), then with 4% NaOH (80o C, 24 hr) and finally washed with highly diluted HCl until pH 3 is reached

Peat Samples are leached in 4% HCl at 80o C for 24 hr and dried.

Shell samples are ultrasonically washed several times; then 20-30% of the material is removed with 2% HCl. The remainder material is divided into one outer and one inner fraction.

Bone Samples are treated according to the Longin method to extract the collagen fraction of the bone. Bones are first mechanically cleaned (brushed with water), then ground to a grain size of about 0.2 mm. The bone-powder is treated with 8% HCl, finally the sample is washed to pH=3 and the collagen extracted by hot water at 90o C during 24 hours at pH=3 by the same procedure as suggested by Longin. The solution containing the collagen is separated by G5 glass filter and evaporated. The insoluble remains contain the inorganic parts and the humic acids as insoluble salts.

TDIC Sample collection is carried out in the field by precipitation of TDIC in the form of BaCO3. The volume of the sampling container is usually 60 l, which is sufficient for extracting about 2.5 g of carbon from water with a concentration of about 250 ppm of bicarbonates. BaCl2 solution is added to the water sample after adjusting the pH to convert all bicarbonates to carbonates (carbon-free concentrated NaOH is added until pH reaches about 8.5). Normally such a precipitate is fine grained and requires a day to settle completely. Carbon dioxide is evolved from the precipitate by adding concentrated H2SO4 or H3PO4. The chemically pre-treated sample is combusted or acid digested CO2 being obtained in a controlled oxygen stream. Gaseous impurities are removed by passing the produced CO2 through a hot copper furnace. The purified CO2 is trapped into stainless steel vessel and measured by gas proportional counting.

δ13C correction: Isotopic fractionation resulting from metabolic processes is responsible for slightly divergent initial 14C activities in different kinds of samples. Owing to small differences in the physical properties, biological and physical processes lead to characteristic shifts in the isotopic ratios of molecules or radicals (due to isotopic fractionation). These shifts can be easily determined for carbon from mass spectrometric measurements of the isotopic ratio of the two stable carbon isotopes. The shift in the 13C/12C is expressed as δ13C:

where Rsample is the 13C/12C ratio of the sample and Rstandard is provided by the PDB standard. Belemnite from the Peedee Formation in South Carolina was introduced as the PDB standard and by definition had a δ13C value of 0‰. Secondary standards calibrated to this primary standard have been used since the exhaustion of the Peedee Belemite.

The isotopic fractionation of 12C and 14C is proportional to that of 12C and 13C, the former being 2.3 times greater than the latter. Thus, theδ13C value is used to correct 14C activities so that all values are referred to the same initial 14C activity. According to international convention, a fractionation factor of 2 is used instead of 2.3. In addition, all conventional 14C ages have the same reference value for δ13C (-25‰) and must be corrected as follows (except NBS oxalic acid standard):

where A and ANS are the measured and corrected 14C activities, respectively.

Radiocarbon age calculation

The age of a sample is calculated by assuming the constancy of atmospheric 14C level in all past times. The specific activity of this hypothetical atmospheric carbon level, after normalising to - 25 per mil for 13C is by definition equal to the specific activity of the absolute international standard Aabs. For a Libby half-life of 5568 yrs. and when measured in 1950 the age (t) of a sample before 1950 AD is therefore given by:

t = - 8033 ln(ASN(in1950)/AON(in1950)),

where AON is the 95% of the activity of the NBS oxalic acid standard normalised for δ13C = -19‰:

The actual measurements of sample and oxalic acid activities were, of course not made in 1950. The measured ratio ASN/AON, however does not change with time. It stays equal to the 1950 ratio because both sample and oxalic acid lose their 14C at the same rate. Thus, the calculated age (t) is given by t = - 8033 ln ASN/AON. It always implies an age prior to AD 1950 (i.e. AD 1950 equals 0 yrs BP).

Ages calculated in the above manner are called conventional radiocarbon ages (years BP). This term implies:

  • the use of the 5568 yr. half-life (mean life 8033 y) —
  • the assumption of constancy of 14C atmospheric level during the past —
  • the use of oxalic acid as a standard —
  • isotopic fractionation normalisation of all sample activities to the base of δ13C = -25 per mill (relative to the 13C/12C ratio of PDB) —
  • the year 1950 is automatically the base year, with ages given in years BP (i.e., present is AD 1950)

Calibrated radiocarbon ages:

Conventional 14C ages differ from actual ages given in solar years. This is because Libby's assumption that the initial 14C concentration has not changed over geological periods of time is not fulfilled. Deviations of the 14C time-scale from the solar time-scale have been determined for the last 10,000 years. For the correction of raw 14C data internationally accepted calibration curves and tables are available. These were prepared on the basis of precise radiocarbon measurements on dendrochronologically dated wood made by an international team of radiocarbon researchers and dendrochronologists.

Different calibration curves and tables are available for different time spans represented by the samples. Samples formed within one year, for example, almost always yield larger dendrochronologically corrected age intervals than samples formed over a longer time span. Often a sample contains different amounts of material for the different parts of the time span represented by the sample. For example, the inner, older rings or a branch contain significantly less mass than the outer, younger ones. In such cases, weighted averages must be used.

Dendrochronological corrections cannot be applied to samples that have components of different ages in unknown proportions (e.g., soils) or whose reservoir effect cannot be given exactly (e.g., TDIC in groundwater and travertine).

Within the last 2000 years the differences between conventional 14C and actual ages vary within 200 years. For the period from 7300 to 2000 years ago, this difference increases to about 800 years. This difference increases to about 1100 years between 8000 and 11,000 BP. The difference for the pre-Holocene to about 35,000 BP could be larger (up to 5000 years). One reason for this may be that the atmospheric CO2 concentration was about 30% less during the last pleniglacial than that of the Holocene, whereas the production rate of cosmogenic radionuclides.

Variations in the atmospheric 14C content complicate the conversion of conventional ages BP into real calendar ages (AD/BC). These variations are indirectly observed in tree rings from European and North American wood. During the last decades, hundreds of measurements have been made on dendrochronologically dated wood resulting in the generally accepted calibration curves from Stuiver and Pearson (1986) (AD 1940 - 500 BC), Pearson and Stuiver (1986) (500-2490 BC) and Pearson et al (1986) (AD 1840 - 5210 BC).

The 14C age results from a radioactive decay measurement; closely approaches statistically a Gaussian probability distribution with a defined standard deviation. The real calendar age probability distribution, however, is no longer Gaussian, since the calibration curve has a highly irregular shape. The calibration age, then, cannot generally be stated as the most probable result, with an associated error bar. The following procedure was adopted. First, the calibration curve uncertainty is taken into account according to:

Next, an age range is given, generally obtained by determining the points on the real calendar that are connected to the points (BP ± σ) via the calibration curve. Within the range(s) selected, all dates are equally valid. Computer programs exist to perform such calibrations (Stuiver and Reimer, 1986).

Computer programs calculate the probability distribution of the calibrated age. They provide a graphic representation of the calibration procedure.

Averaging more than one calibration date

To average several calibrated dates, the Gaussians can be taken together to yield a final average, which is again a Gaussian distribution with a new smaller standard deviation:

and

To determine the probability distribution of more than one BP date, we first calibrate each BP date as described above which yields a real calendar age distribution y(x). Results are then normalised so that the area . Only then the individual real age distributions y(x) may be added. Of the total summed function ytot(x), the probability distribution P(x) can again be obtained, again normalised to a total probability of 1 (or l00%).

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