A I Calculation of Radiocarbon Age and Standardization Procedure

Although it is not necessary for a user of radiocarbon dates to know, in detail, how the actual value is arrived at, some understanding of the procedure is enlightening, particularly when considering adjustments for 14C fractionation effects (see Section 3.2.1.4c). The whole subject is a complex sequence of calibrations, adjustments, and corrections. The following brief explanation is offered for the adventurous.

In order to make dates from different laboratories comparable, a standard material is used by all laboratories for the measurement of "modern" carbon isotope concentrations. This standard used to be "U.S. National Bureau of Standards oxalic acid I" (Ox I) prepared from West Indian sugar cane grown in 1955. Ninety-five percent of the 14C activity of this material is equivalent to the 14C activity of wood grown in 1890, so by this devious means, all laboratories standardized their results to a material that had not been contaminated by "atomic bomb" 14C. Because the original standard has now been exhausted, another oxalic acid standard (Ox II) is used with the old standard equivalent to (0.7459 Ox II). By convention, all dates are given in "years before 1950" (years B.P. or "before physics") so dates are adjusted to this temporal standard, rather than the possibly more logical time of 1890. A second adjustment is needed to correct for the fact that oxalic acid undergoes variable 13C and 14C

fractionation effects during analysis. To make interlaboratory comparisons of samples possible, standardization is necessary to take these fractionation effects into account. Fortunately, the fractionation effect of 14C is extremely close to twice that of 13C, which is far more abundant and can be measured easily in a mass spectrometer.39 The necessary standardization is thus achieved by measuring 13C rather than 14C. Following the detailed analysis of oxalic acid samples by Craig (1961a), it was agreed that all standard samples should be adjusted to a 13C value of-19.3%, where

Cox refers to the oxalic acid standard, and CPDB refers to another reference standard, a Cretaceous belemnite (Belemnitella americana) from the Peedee Formation of South Carolina (Craig, 1957). Updates to the reference standards are discussed by Coplen (1996).

Standardization of the 14C activity in the oxalic acid reference sample is achieved thus:

1000

where A'ox is the 14C activity of the reference oxalic acid and 13Cox is the 13C of the reference oxalic acid (Eq. A.l). The value of 0.95Aox then becomes the universal 14C standard activity from which all dates are calculated.

The procedure normally adopted for calculating the radiocarbon date of a sample can be summarized in three equations.

(a) The activity of the sample is expressed as a departure from the reference standard:

0.95AOX

where Asample is the 14C activity of the sample, corrected for background radiation, and Aox is the 1950 activity of NBS oxalic acid I (or equivalent), corrected for background and isotope fractionation.

(b) The activity of the sample is corrected for fractionation by normalizing to 813C = -25%o PDB, which is the average for wood (see the discussion that follows):

where

cl3r> _ (13C/12Qsample (13C/12C)pDB 3 8 C - (13C/12C)P x 10

/PDB

(c) Age (T) is then calculated using the "Libby" half-life of 5570 yr:

Tropical Deserts

Dominantly C3

Polar Desert Tundra

S^gg? Conifer Woodland/Forest Tropical/Temperate

Mixed C /C

Tropical/Temperate Desert Semi-Desert, Dry Steppe Tropical Scrub/Woodland

Dominantly C

Tropical/Temperate Grassland

Dominantly C3

Polar Desert Tundra

S^gg? Conifer Woodland/Forest Tropical/Temperate

Mixed C /C

Tropical/Temperate Desert Semi-Desert, Dry Steppe Tropical Scrub/Woodland

Dominantly C

Tropical/Temperate Grassland

Broad-leaved Forest

FIGURE AI. I Distribution of major ecosystems dominated by C3 or C4 vegetation.The northern limits of temperate grasslands in North America and Asia include a significant proportion of C3 plants due to the cool growing season (from Cerling and Quade, 1993).

A.2 Fractionation Effects

Because isotopic fractionation occurs to differing extents during plant photosynthesis and during shell carbonate deposition, it is necessary to know the magnitude of the effect so that dates on different materials can be compared. Lerman (1972) and Troughton (1972) have studied fractionation effects in modern plants and found a trimodal distribution; the magnitude of fractionation seems to be related to the particular biochemical pathway evolved by different plant species for photosynthesis. Thus, highest 13C depletion corresponds to so-called C3 plants, which utilize the Calvin photosynthetic cycle (CAL) and lowest depletion occurs in C4 plants utilizing the Hatch-Slack (HS) cycle. Succulents utilize a third metabolic pathway (crassu-lacean acid metabolism, CAM) and may fix carbon by either the HS or CAL pathways depending on temperature and photoperiod; they thus form a third group. Figure Al.l shows the large-scale distribution of ecosystems dominated by C3 or C4 plants. The implications for dating are that samples containing, say, a high proportion of HS plants would show 14C/12C ratios characteristic of these less depleted

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