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| Rick
Healy, Systems Analyst at NOSAMS, programmed the
MatLab GUI which reduces AMS data to
final radiocarbon results. |
In AMS, the carbon or "graphite"
derived from a sample is compressed into a small cavity in an
aluminum "target" which acts as a cathode in the ion
source. The surface of the graphite is sputtered with heated
cesium and the ions produced are extracted and accelerated in
the AMS system. After acceleration
and removal of electrons, the emerging positive ions are magnetically
separated by mass and the 12C
and 13C ions are measured
in Faraday Cups where a ratio of their currents is recorded.
Simultaneously the 14C ions
are recorded in a gas ionization counter, so that instantaneous
ratios of 14C to 13C
and 12C are recorded. These
are the raw signals that are ultimately converted to a radiocarbon
age.
From a contemporary sample, about
150 14C counts per second
are collected. It is expected then, for a 5,570 year (1 half-life)
or 11,140 year old (2 half-lives) sample that 75 or 38 counts
per second would be obtained. Although one can simply measure
older samples for longer times, they are constantly being
consumed by the ion source, so there are practical limits
to the minimum sample activity that can be measured, depending
on how much material you have. At the present time, for a
1 milligram sample of graphite, this limiting age is about
ten half-lives, or 60,000 years, if set only by the sample
size. However, limiting ages or "backgrounds" are
also determined by process blanks which correspond to the
method used to extract the carbon from the sample.
Click here to access
a PDF version of the NOSAMS General Statement of 14C Procedures.
Process Blanks
The process blanks contain small but measurable amounts of
14C from contamination introduced
during chemical preparation, collection or handling. Organic
materials, which require the most processing, are limited
to younger ages by their corresponding process blank. Since
it is always necessary to subtract the counts due to blanks,
from the counts due to sample, it may become a statistical
limitation for very old samples (small number of 14C
atoms) where we are measuring the difference between very
small numbers. Thus, ages are limited by the age of the process
blanks (more on that below) and by the statistical uncertainty
of the 14C measurement.
Fraction Modern
The Fraction Modern (Fm) is basically computed from the expression:
Fm = (S - B) / (M - B)
In the equation, B, S and M represent the 14C/12C
ratios of the blank, the sample and the modern reference,
respectively. Fraction Modern is a measurement of the deviation
of the 14C/12C
ratio of a sample from "Modern." Modern is defined
as 95% of the radiocarbon concentration (in AD 1950) of NBS
Oxalic Acid I normalized to δ13CVPDB=-19
per mil (Olsson, 1970). AMS results are calculated using the
internationally accepted modern 14C/12C
ratio of 1.176 ± 0.010 x 10-12
(Karlen, et. al., 1968); all results are normalized to -25
per mil using the δ13CVPDB
of the sample (see below). The value used for this correction,
is specified in the report of final results.
δ13C
Correction
In addition to loss through decay of
radiocarbon, 14C is also affected
by natural isotopic fractionation. Fractionation is the term
used to describe the differential uptake of one isotope with
respect to another. While the three carbon isotopes are chemically
indistinguishable, lighter 12C
atoms are preferentially taken up before the 13C
atoms in biological pathways. Similarly, 13C
atoms are taken up before 14C.
The assumption is that the fractionation of 14C
relative to 12C is twice that
of 13C, reflecting the difference
in mass. Fractionation must be corrected for in order to make
use of radiocarbon measurements as a chronometric tool for all
parts of the biosphere. In order to remove the effects of isotopic
fractionation, the Fraction Modern is then corrected to the
value it would have if its original δ13C
were -25 per mil (the δ13C
value to which all radiocarbon measurements are normalized.)
The Fraction Modern corrected for δ13C,
Fmδ13C,
Errors
Atoms of 14C
contained in a sample are directly counted using the AMS method
of radiocarbon analysis. Accordingly, we calculate an internal
statistical error using the total number of
14C counts measured for each target ( ±
). An external error is calculated from the reproducibility
of multiple exposures for a given target. For example, we may
measure the 14C /12C
of a sample up to 9 separate times over the course of a 2-day
period. The reproducibility of these measurements gives us a
good estimate of the true experimental error. The final error
is the larger of the internal or external errors.
Aside from the normal statistical errors intrinsic to the
counting of 14C events, there are additional statistical
errors associated with the corrections applied to the Fraction
Modern that we account for. For example, the δ13C
correction, from a stable mass spectrometer has an uncertainty
of approximately 0.1%. The error associated with δ13C
is calculated by:
This component of the Fm error is then added in quadrature
as follows:
Radiocarbon Age
Radiocarbon age is calculated from the
δ13C-corrected Fraction Modern according
to the following formula:
Age = -8033 ln (Fm)
Reporting of ages and/or activities
follows the convention outlined by Stuiver and Polach (1977)
and Stuiver (1980). Ages are calculated using 5568 years as
the half-life of radiocarbon and are reported without reservoir
corrections or calibration to calendar years. For freeware
programs, we suggest that you look at the following web site
for a list of programs that will calibrate radiocarbon results
to calendar years (including making reservoir corrections).[
Radiocarbon-Related Information Sources]
The error in the age is given by 8033 times the relative error
in the Fm . Therefore a 1% error in fraction-modern leads
to an 80 year error in the age. Ages are rounded according
to the convention of Stuiver & Polach, shown below.
Rounding Convention
| Age |
Nearest |
Error |
Nearest |
| <1000 |
5 |
<100 |
5 |
| 1000-9999 |
10 |
100-1000 |
10 |
| 10000-20000 |
50 |
>1000 |
100 |
| >20000 |
100 |
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Limiting Ages
There are two situations that limit an age; the first is that
the measured Fm is smaller than that of the corresponding
process blank measured in the same suite of samples on the
AMS. If this is the case, then the reported age will be quoted
as an age greater than the age of the process blank. No age
is reported greater than 60,000 years. The typical background
age for organic combustions is 48,000 years and for inorganic
carbon samples, 52,000 years.
One other situation that limits the age (if not already limited
by the background age) is the error of the AMS result. If
twice the reported error of the Fraction Modern (let's call
this 2sigma) is larger than the sample Fraction Modern, then
a limiting age is reported. The limiting age is then calculated
as -8033 * ln(2sigma) and rounded according to conventions
outlined above.
Age > Modern
Since Modern is defined as 95% of the 14C activity
for AD 1950, as defined by the oxalic acid standard, sample
activities can be substantially greater than Modern, and so
the ages are reported as > Modern.
Δ14C
We also report the Δ14C
value as defined in Stuiver and Pollach (1977) as the relative
difference between the absolute international standard
(base year 1950) and sample activity corrected for age and
δ13C. The Δ14C is age corrected
to account for decay that took place between collection (or
death) and the time of measurement so that two measurements
of the same sample made years apart will produce the same
calculated Δ14C result. Collection year must
be specified in question 8 of the submittal form in order
for Δ14C results to
be calculated.
Δ14C = [ Fm * exp(lambda*[ 1950 - Yc] ) -
1 ]* 1000
lambda is 1/(true mean-life) of radiocarbon = 1/8267 = 0.00012097
Yc is year of collection.
References
Karlen, I., Olsson, I.U., Kallburg,
P. and Kilici, S., 1968. Absolute determination of the activity
of two 14C dating standards. Arkiv Geofysik,
4:465-471.
Olsson, I.U., 1970. The use of Oxalic acid as a Standard.
In I.U. Olsson, ed., Radiocarbon Variations and Absolute Chronology,
Nobel Symposium, 12th Proc., John Wiley & Sons,
New York, p. 17.
Stuiver, M. and Polach, H.A., 1977. Discussion: Reporting
of 14C data. Radiocarbon, 19:355-363.
Stuiver, M., 1980. Workshop on 14C data reporting.
Radiocarbon, 22:964-966.
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