View source: R/fissiontracks.R
set.zeta  R Documentation 
Determines the zeta calibration constant of a fission track dataset (EDM or LAICPMS) given its true age and analytical uncertainty.
set.zeta(x, tst, exterr = FALSE, oerr = 1, sigdig = NA, update = TRUE)
x 
an object of class 
tst 
a twoelement vector with the true age and its standard error 
exterr 
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. 
oerr 
indicates whether the analytical uncertainties of the output are reported as:
(only used when 
sigdig 
the number of significant digits (only used when

update 
logical flag indicating whether the function should return an updated version of the input data, or simply return a twoelement 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}
Uconcentration 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}
Uconcentration indirectly, using the induced fission
of neutronirradiated ^{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 coirradiated glass of known
Uconcentration. \rho_d
allows the \zeta
factor to be
‘recycled’ between irradiations.
LAICPMS is an alternative means of determining the
^{238}
Ucontent of fission track samples without the need for
neutron irradiation. The resulting Uconcentrations can be plugged
directly into the fundamental age equation (eq.1). but this is
limited by the accuracy of the Uconcentration 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}
Uconcentration (in ppm) or for the U/Ca (for
apatite) or U/Si (for zircon) ratio measurement (Vermeesch, 2017).
an object of class fissiontracks
with an updated
x$zeta
value or (if update
is FALSE
), a
2element matrix with the zeta estimate and its uncertainty.
Fleischer, R. and Hart, H. Fission track dating: techniques and problems. In Bishop, W., Miller, J., and Cole, S., editors, Calibration of Hominoid Evolution, pages 135170. Scottish Academic Press Edinburgh, 1972.
Hurford, A. J. and Green, P. F. The zeta age calibration of fissiontrack dating. Chemical Geology, 41:285317, 1983.
Vermeesch, P., 2017. Statistics for LAICPMS based fission track dating. Chemical Geology, 456, pp.1927.
age
attach(examples)
print(FT1$zeta)
FT < set.zeta(FT1,tst=c(250,5))
print(FT$zeta)
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