Determines the zeta calibration constant of a fission track dataset (EDM or LA-ICP-MS) given its true age and analytical uncertainty.
set.zeta(x, tst, exterr = FALSE, oerr = 1, sigdig = NA, update = TRUE)an object of class fissiontracks with an updated
x$zeta value or (if update is FALSE), a
2-element matrix with the zeta estimate and its uncertainty.
an object of class fissiontracks
a two-element vector with the true age and its standard error
logical flag indicating whether the external uncertainties associated with the age standard or the dosimeter glass (for the EDM) should be accounted for when propagating the uncertainty of the zeta calibration constant.
indicates whether the analytical uncertainties of the output are reported as:
1: 1\(\sigma\) absolute uncertainties.
2: 2\(\sigma\) absolute uncertainties.
3: absolute (1-\(\alpha\))% confidence intervals, where
\(\alpha\) equales the value that is stored in
settings('alpha').
4: 1\(\sigma\) relative uncertainties (\(\%\)).
5: 2\(\sigma\) relative uncertainties (\(\%\)).
6: relative (1-\(\alpha\))% confidence intervals, where
\(\alpha\) equales the value that is stored in
settings('alpha').
(only used when update is FALSE)
the number of significant digits (only used when
update is FALSE).
logical flag indicating whether the function should return an updated version of the input data, or simply return a two-element vector with the calibration constant and its standard error.
The fundamental fission track age is given by:
\(t = \frac{1}{\lambda_{238}} \ln\left(1 + \frac{\lambda_{238}}{\lambda_f} \frac{2 N_s}{[^{238}U]A_sL}\right) \) (eq.1)
where \(N_s\) is the number of spontaneous fission tracks measured over an area \(A_s\), \([^{238}U]\) is the \(^{238}\)U-concentration in atoms per unit volume, \(\lambda_f\) is the fission decay constant, \(L\) is the etchable fission track length, and the factor 2 is a geometric factor accounting for the fact that etching reveals tracks from both above and below the internal crystal surface. Two analytical approaches are used to measure \([^{238}U]\): neutron activation and LAICPMS. The first approach estimates the \(^{238}\)U-concentration indirectly, using the induced fission of neutron-irradiated \(^{235}\)U as a proxy for the \(^{238}\)U. In the most common implementation of this approach, the induced fission tracks are recorded by an external detector made of mica or plastic that is attached to the polished grain surface (Fleischer and Hart, 1972; Hurford and Green, 1983). The fission track age equation then becomes:
\(t = \frac{1}{\lambda_{238}} \ln\left(1 + \frac{\lambda_{238}\zeta\rho_d}{2}\frac{N_s}{N_i}\right) \) (eq.2)
where \(N_i\) is the number of induced fission tracks counted in the external detector over the same area as the spontaneous tracks, \(\zeta\) is a `zeta'-calibration factor that incorporates both the fission decay constant and the etchable fission track length, and \(\rho_d\) is the number of induced fission tracks per unit area counted in a co-irradiated glass of known U-concentration. \(\rho_d\) allows the \(\zeta\)-factor to be `recycled' between irradiations.
LAICPMS is an alternative means of determining the \(^{238}\)U-content of fission track samples without the need for neutron irradiation. The resulting U-concentrations can be plugged directly into the fundamental age equation (eq.1). but this is limited by the accuracy of the U-concentration measurements, the fission track decay constant and the etching and counting efficiencies. Alternatively, these sources of bias may be removed by normalising to a standard of known fission track age and defining a new `zeta' calibration constant \(\zeta_{icp}\):
\( t = \frac{1}{\lambda_{238}} \ln\left( 1 + \frac{\lambda_{238}\zeta_{icp}}{2} \frac{N_s}{[{}^{238}U] A_s} \right) \)(eq.3)
where \([{}^{238}U]\) may either stand for the \(^{238}\)U-concentration (in ppm) or for the U/Ca (for apatite) or U/Si (for zircon) ratio measurement (Vermeesch, 2017).
Fleischer, R. and Hart, H. Fission track dating: techniques and problems. In Bishop, W., Miller, J., and Cole, S., editors, Calibration of Hominoid Evolution, pages 135-170. Scottish Academic Press Edinburgh, 1972.
Hurford, A. J. and Green, P. F. The zeta age calibration of fission-track dating. Chemical Geology, 41:285-317, 1983.
Vermeesch, P., 2017. Statistics for LA-ICP-MS based fission track dating. Chemical Geology, 456, pp.19-27.
age
attach(examples)
print(FT1$zeta)
FT <- set.zeta(FT1,tst=c(250,5))
print(FT$zeta)
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